Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP222^2 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:07:16 AM UTC 2026

% Result   : Theorem 71.94s 24.75s
% Output   : Refutation 74.76s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : ITP222^2 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.11  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.21/0.31  % Computer : n013.cluster.edu
% 0.21/0.31  % Model    : x86_64 x86_64
% 0.21/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.31  % Memory   : 8046.5625MB
% 0.21/0.31  % OS       : Linux 6.8.0-71-generic
% 0.21/0.31  % CPULimit : 300
% 0.21/0.31  % WCLimit  : 300
% 0.21/0.31  % DateTime : Tue Sep 29 20:19:21 UTC 2026
% 0.21/0.32  % CPUTime  : 
% 0.21/0.32  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.95/0.77  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 8.71/2.92  % [INFO] 	 Parsing done (2148ms). 
% 8.71/2.94  % [INFO] 	 Running in sequential loop mode. 
% 9.28/3.29  % [INFO] 	 eprover registered as external prover. 
% 9.28/3.30  % [INFO] 	 Scanning for conjecture ... 
% 10.99/3.87  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8982 axioms. Running axiom selection ... 
% 13.15/4.99  % [INFO] 	 Axiom selection finished. Selected 814 axioms (removed 8168 axioms). 
% 14.83/5.44  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 14.83/5.48  % [INFO] 	 Type checking passed. 
% 14.83/5.49  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 71.94/24.74  % External prover 'e' found a proof!
% 71.94/24.74  % [INFO] 	 Killing All external provers ... 
% 71.94/24.74  % Time passed: 24297ms (effective reasoning time: 21799ms)
% 71.94/24.74  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 71.94/24.75  % Axioms used in derivation (814): fact_793_less__eq__Suc__le, fact_263_add__strict__mono, fact_75_enat__add__left__cancel__less, tcon_Real_Oreal___Rings_Odvd_349, fact_723_Suc__leD, fact_64_plus__enat__simps_I3_J, fact_823_mult__le__0__iff, fact_448_mult__0__right, fact_1023_nat__mult__le__cancel1, fact_1726_diff__mult__distrib2, fact_932_mult__left__less__imp__less, fact_235_add__mono__thms__linordered__semiring_I4_J, fact_1677_idiff__0, fact_847_not__square__less__zero, fact_205_add__le__mono, tcon_Extended__Nat_Oenat___Complete__Lattices_OSup_472, tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__sup__bot_454, fact_4546_one__natural_Orsp, tcon_fun___Complete__Lattices_OInf, fact_1549_zle__diff1__eq, fact_1696_diff__Suc__1, tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring_477, fact_846_mult__neg__neg, fact_2742_abs__zmult__eq__1, fact_106_add__lessD1, tcon_Nat_Onat___Lattices_Olattice_93, fact_1462_nat__mult__dvd__cancel1, fact_9_enat_Odistinct_I2_J, fact_1676_idiff__infinity, fact_93_less__not__refl3, fact_1683_diff__diff__cancel, fact_776_i0__lb, tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_474, fact_1558_dvd__antisym, fact_913_nat__mult__less__cancel1, fact_800_Suc__leI, fact_1719_Nat_Odiff__diff__eq, fact_836_linordered__nonzero__semiring__class_Ozero__le__one, fact_1762_nat__le__add__iff2, fact_1691_diff__is__0__eq_H, fact_1722_Nat_Odiff__cancel, tcon_Int_Oint___Groups_Oplus, fact_92_less__not__refl2, fact_753_not__gr0, tcon_Int_Oint___Rings_Olinordered__semiring__strict, fact_2796_nat__ivt__aux, tcon_Real_Oreal___Rings_Oordered__comm__semiring_279, tcon_Real_Oreal___Rings_Ocomm__semiring__0_300, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, fact_4828_max__nat_Oright__neutral, tcon_Real_Oreal___Groups_Omonoid__add_323, fact_90_nat__neq__iff, fact_827_mult__nonpos__nonpos, fact_1044_mult__less__cancel__right2, fact_1177_times__int__code_I1_J, fact_1191_mult__le__cancel__iff1, fact_1120_verit__la__generic, fact_674_add__is__1, tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__linorder, fact_779_imult__is__0, fact_151_VEBT_Oinject_I2_J, fact_933_mult__strict__mono, tcon_Int_Oint___Groups_Ozero, fact_4830_max__nat_Oleft__neutral, tcon_Int_Oint___Groups_Ostrict__ordered__ab__semigroup__add, fact_658_zero__induct, fact_1678_idiff__0__right, fact_1041_mult__less__cancel__left1, fact_1689_add__diff__cancel__enat, fact_4836_nat__mult__max__right, tcon_Int_Oint___Rings_Omult__zero, fact_253_less__eqE, fact_729_zero__le, fact_78_numeral__ne__infinity, fact_1693_Nat_Odiff__diff__right, fact_2642_abs__mult__pos, fact_1681_diff__0__eq__0, fact_1630_ordered__ring__class_Ole__add__iff2, fact_1740_Nat_Odiff__add__assoc2, fact_1728_dvd__diff__nat, tcon_Real_Oreal___Rings_Oordered__ring_316, fact_198_add__mult__distrib2, fact_759_le__0__eq, fact_672_Ex__less__Suc2, tcon_Nat_Onat___Groups_Oone_103, fact_652_zero__reorient, fact_797_inc__induct, fact_159_enat__ord__simps_I1_J, fact_1174_conj__le__cong, fact_16_enat_Osimps_I4_J, fact_1736_diff__add__0, fact_1326_dvd__1__iff__1, fact_813_Suc__eq__plus1, fact_177_mult_Oleft__commute, fact_857_mult__less__cancel__left__pos, tcon_Int_Oint___Rings_Oordered__semiring, tcon_Real_Oreal___Groups_Osemigroup__mult_302, fact_295_nat__1__eq__mult__iff, fact_409_combine__common__factor, tcon_Extended__Nat_Oenat___Rings_Oordered__comm__semiring_461, fact_449_mult__is__0, fact_443_bot__nat__0_Oextremum, fact_954_mult__left__le__one__le, tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors_265, fact_872_add__less__zeroD, fact_858_mult__strict__left__mono__neg, fact_802_less__add__Suc1, fact_936_mult__strict__mono_H, fact_2801_nat0__intermed__int__val, fact_763_plus__nat_Oadd__0, tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__distrib__lattice_450, tcon_Nat_Onat___Divides_Ounique__euclidean__semiring__numeral_24, fact_459_mult__eq__0__iff, fact_2693_zdvd1__eq, fact_468_add__eq__0__iff__both__eq__0, fact_2__C2_Ohyps_C_I5_J, tcon_Extended__Nat_Oenat___Rings_Osemiring_492, fact_863_mult__less__cancel__right__disj, fact_353_not__numeral__less__one, fact_804_less__iff__Suc__add, fact_1179_int__distrib_I1_J, fact_11_enat_Oexhaust, tcon_Real_Oreal___Num_Onumeral_343, fact_1695_Nat_Oadd__diff__assoc, fact_837_not__one__le__zero, fact_556_nat__mult__le__cancel__disj, fact_339_less__numeral__extra_I4_J, fact_444_add__is__0, fact_108_not__add__less1, tcon_Int_Oint___Rings_Oring__1, fact_1478_dvd__mult__cancel1, fact_1181_zmult__zless__mono2, tcon_Nat_Onat___Rings_Osemiring__0_91, fact_718_Suc__n__not__le__n, tcon_Nat_Onat___Rings_Oordered__comm__semiring_56, tcon_Real_Oreal___Complete__Lattices_OInf_304, fact_4825_max__Suc__Suc, fact_751_bot__nat__0_Oextremum__strict, fact_754_not__less0, fact_843_add__nonpos__nonpos, fact_408_linorder__neqE__linordered__idom, tcon_Real_Oreal___Rings_Olinordered__semiring__strict_264, fact_199_add__mult__distrib, fact_19_enat__ex__split, fact_326_one__reorient, fact_1744_diff__Suc__eq__diff__pred, fact_911_ex__least__nat__le, fact_1442_zdvd__period, fact_1463_bezout__add__strong__nat, fact_321_nat__le__linear, fact_1627_int__le__induct, tcon_Extended__Nat_Oenat___Countable__Complete__Lattices_Ocountable__complete__lattice_449, fact_4776_max__0__1_I5_J, fact_1444_unity__coeff__ex, fact_555_mult__le__cancel2, fact_8116_mono__Suc, fact_859_mult__strict__left__mono, fact_654_not0__implies__Suc, fact_98_infinite__descent__measure, fact_794_less__Suc__eq__le, fact_854_zero__less__mult__pos, tcon_Real_Oreal___Rings_Olinordered__idom_298, fact_410_distrib__right, fact_670_All__less__Suc2, fact_915_mult__less__mono2, fact_868_add__neg__neg, fact_10_enat_Odistinct_I1_J, fact_96_infinite__descent, fact_4774_max__0__1_I2_J, fact_1684_diff__diff__left, tcon_Nat_Onat___Rings_Olinordered__semiring_58, fact_948_add__pos__nonneg, fact_937_mult__less__cancel__right, fact_1764_nat__diff__add__eq2, fact_861_mult__strict__right__mono__neg, tcon_Extended__Nat_Oenat___Power_Opower_494, tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__0_470, tcon_Real_Oreal___Fields_Olinordered__field_293, fact_835_zero__less__one__class_Ozero__le__one, fact_2708_zabs__less__one__iff, fact_1186_int__one__le__iff__zero__less, fact_678_enat__0__iff_I2_J, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_266, fact_4821_max__enat__simps_I3_J, tcon_Real_Oreal___Groups_Oab__semigroup__add_292, tcon_Int_Oint___Lattices_Olattice_12, fact_192_le__neq__implies__less, fact_322_le__antisym, fact_256_add__mono__thms__linordered__semiring_I1_J, tcon_Extended__Nat_Oenat___Orderings_Oorder__bot_480, fact_254_add__left__mono, tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add_252, fact_1515_zero__diff, fact_1757_nat__diff__split__asm, fact_6249_top__enat__def, fact_342_nat__mult__1__right, tcon_Int_Oint___Groups_Oordered__comm__monoid__add, tcon_Extended__Nat_Oenat___Rings_Olinordered__nonzero__semiring_457, fact_252_add__right__mono, fact_1479_dvd__mult__cancel2, fact_407_enat__1__iff_I2_J, fact_807_Suc__mult__le__cancel1, fact_703_less__Suc__eq, fact_1628_int__less__induct, fact_89_measure__induct__rule, fact_801_less__natE, fact_229_add_Ocommute, fact_237_ab__semigroup__add__class_Oadd__ac_I1_J, fact_712_not__less__less__Suc__eq, fact_495_nat__0__less__mult__iff, fact_711_strict__inc__induct, fact_338_le__numeral__extra_I4_J, fact_6_enat_Osimps_I5_J, tcon_Extended__Nat_Oenat___Rings_Osemiring__0_488, fact_4819_max__enat__simps_I5_J, tcon_Int_Oint___Groups_Oab__semigroup__mult, fact_611_unique__quotient__lemma__neg, fact_232_add_Oassoc, fact_719_le__Suc__eq, fact_1039_mult__le__cancel__right1, fact_796_Suc__le__lessD, fact_619_unique__quotient__lemma, fact_220_mono__nat__linear__lb, tcon_fun___Lattices_Obounded__semilattice__sup__bot, fact_651_zero__one__enat__neq_I1_J, fact_1537_diff__add__zero, tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__comm__monoid__add_452, fact_1746_dvd__diffD, fact_700_less__SucE, fact_1749_bezout1__nat, fact_204_add__le__mono1, fact_1731_Suc__diff__Suc, fact_499_less__one, fact_669_gr0__implies__Suc, fact_71_enat__ord__number_I2_J, fact_1078_convex__bound__lt, fact_721_le__SucI, fact_84_infinity__ilessE, fact_1638_square__diff__one__factored, fact_494_nat__mult__less__cancel__disj, fact_735_zero__less__iff__neq__zero, fact_833_zero__less__numeral, fact_840_add__decreasing2, fact_206_le__Suc__ex, tcon_Int_Oint___Groups_Omonoid__add, fact_697_Suc__lessD, fact_496_mult__less__cancel2, fact_1742_Nat_Ole__diff__conv2, fact_939_mult__le__cancel__left__pos, tcon_Nat_Onat___Groups_Omonoid__add_89, fact_41_enat__ord__simps_I3_J, fact_756_gr__implies__not0, fact_400_less__eq__real__def, tcon_Real_Oreal___Groups_Osemigroup__add_307, tcon_Int_Oint___Rings_Olinordered__ring, fact_6212_top_Oextremum__unique, fact_1755_diff__Suc__less, fact_2657_sin__bound__lemma, tcon_Int_Oint___Groups_Oab__semigroup__add, fact_294_nat__mult__eq__1__iff, fact_85_less__infinityE, fact_643_q__pos__lemma, fact_941_mult__right__le__imp__le, fact_470_add__0, fact_742_zero__neq__one, fact_1790_Suc__if__eq, fact_799_Suc__le__eq, fact_1713_diff__less__mono2, fact_83_less__enatE, fact_1435_dvd__pos__nat, tcon_Extended__Nat_Oenat___Rings_Ozero__less__one_476, fact_1725_diff__add__inverse2, fact_2653_abs__diff__le__iff, tcon_Int_Oint___Groups_Osemigroup__add, fact_704_not__less__eq, fact_1734_diff__less__mono, fact_4829_max__nat_Oneutr__eq__iff, tcon_Nat_Onat___Groups_Osemigroup__add_80, fact_803_less__add__Suc2, tcon_Int_Oint___Rings_Osemiring, tcon_Nat_Onat___Rings_Odvd_104, fact_912_less__imp__add__positive, fact_492_one__eq__mult__iff, tcon_Real_Oreal___Lattices_Olattice_328, fact_811_Suc__eq__plus1__left, tcon_Int_Oint___Complete__Lattices_OSup_9, fact_403_infinity__ne__i1, fact_211_add__leE, tcon_Int_Oint___Rings_Ocomm__semiring, tcon_Extended__Nat_Oenat___Rings_Oordered__semiring_467, fact_446_mult__cancel2, tcon_Extended__Nat_Oenat___Groups_Oplus_497, fact_798_dec__induct, fact_730_field__lbound__gt__zero, fact_1038_mult__le__cancel__left2, fact_970_zero__less__two, fact_1745_dvd__minus__self, fact_440_neq0__conv, fact_717_not__less__eq__eq, tcon_Real_Oreal___Groups_Ozero_344, tcon_Nat_Onat___Rings_Omult__zero_95, fact_686_one__less__mult, fact_2654_abs__diff__less__iff, fact_1682_diff__self__eq__0, fact_91_less__not__refl, fact_1763_nat__diff__add__eq1, fact_934_mult__less__cancel__left, fact_1697_idiff__infinity__right, fact_1437_zdvd__mono, tcon_Int_Oint___Num_Onumeral, fact_1679_Suc__diff__diff, fact_4832_max__enat__simps_I1_J, fact_170_numeral__le__enat__iff, fact_696_Nat_OlessE, tcon_Real_Oreal___Rings_Olinordered__ring_297, fact_943_mult__less__le__imp__less, fact_1685_idiff__enat__0, fact_554_mult__Suc__right, fact_1033_imult__infinity, fact_856_mult__less__cancel__left__neg, fact_427_ex__has__greatest__nat__lemma, fact_203_trans__le__add1, fact_1256_less__induct, fact_707_less__antisym, fact_714_transitive__stepwise__le, tcon_Real_Oreal___Rings_Osemiring__0_325, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_26, fact_13_enat3__cases, fact_708_Suc__less__SucD, fact_680_zero__enat__def, fact_8114_mono__times__nat, fact_489_Suc__le__mono, fact_739_no__zero__divisors, tcon_Nat_Onat___Rings_Ozero__less__one_81, tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__inf__top_455, fact_1434_nat__dvd__not__less, fact_1440_bezout__lemma__nat, tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_269, tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_466, fact_687_n__less__m__mult__n, tcon_Nat_Onat___Num_Onumeral_100, fact_4545_one__integer_Orsp, fact_113_less__add__eq__less, fact_1141_zle__add1__eq__le, fact_666_old_Onat_Odistinct_I2_J, tcon_Int_Oint___Groups_Osemigroup__mult, tcon_Int_Oint___Rings_Olinordered__idom, fact_830_zero__le__square, fact_191_less__mono__imp__le__mono, fact_685_ex__least__nat__less, tcon_Nat_Onat___Groups_Oplus_102, fact_4826_max__0R, fact_297_times__enat__simps_I1_J, fact_87_enat__add__left__cancel__le, fact_1733_Suc__diff__le, tcon_Int_Oint___Divides_Ounique__euclidean__semiring__numeral, fact_1176_less__eq__int__code_I1_J, fact_1251_exists__least__iff, fact_320_Nat_Oex__has__greatest__nat, fact_715_nat__induct__at__least, fact_65_enat__ord__simps_I4_J, fact_354_one__plus__numeral__commute, fact_455_le__zero__eq, fact_679_enat__0__iff_I1_J, fact_180_ab__semigroup__mult__class_Omult__ac_I1_J, fact_4777_max__0__1_I6_J, fact_944_field__le__epsilon, fact_758_infinite__descent0__measure, fact_412_comm__semiring__class_Odistrib, fact_947_add__nonpos__neg, fact_1441_zdvd__reduce, tcon_Nat_Onat___Orderings_Owellorder, tcon_Real_Oreal___Rings_Olinordered__semiring__1_280, fact_1761_nat__le__add__iff1, tcon_Int_Oint___Rings_Ozero__less__one, fact_1593_int__distrib_I4_J, tcon_Real_Oreal___Groups_Oplus_345, fact_1372_dvdI, fact_4_not__enat__eq, fact_1631_ordered__ring__class_Ole__add__iff1, tcon_Real_Oreal___Groups_Oone_348, fact_324_le__trans, fact_728_le__numeral__extra_I3_J, fact_55_nat__add__left__cancel__less, tcon_Extended__Nat_Oenat___Orderings_Oorder__top_479, tcon_Real_Oreal___Rings_Omult__zero_330, fact_454_i0__less, fact_4837_nat__add__max__left, fact_435_even__odd__cases, fact_817_zero__le__mult__iff, fact_1776_dvd__minus__add, fact_210_le__add1, fact_775_ile0__eq, fact_17_enat_Osimps_I6_J, fact_2662_lemma__interval, fact_1037_mult__le__cancel__left1, fact_77_enat__add__left__cancel, fact_178_mult_Ocommute, fact_1436_zdvd__antisym__nonneg, fact_31_enat__ord__code_I5_J, tcon_Int_Oint___Rings_Olinordered__semiring__1, fact_111_trans__less__add1, fact_1327_dvd__1__left, fact_1178_times__int__code_I2_J, fact_814_zero__le__numeral, fact_2086_mult__commute__abs, fact_439_bot__nat__0_Onot__eq__extremum, fact_42_case__enat__def, fact_931_mult__le__cancel__right, fact_1646_minusinfinity, fact_160_distrib__right__numeral, tcon_Nat_Onat___Num_Osemiring__numeral_79, fact_3849_fun__cong__unused__0, fact_12_enat2__cases, fact_447_mult__cancel1, fact_437_old_Onat_Oinject, tcon_Extended__Nat_Oenat___Num_Onumeral_495, tcon_Real_Oreal___Rings_Olinordered__ring__strict_275, tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_31, tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add_253, tcon_Nat_Onat___Complete__Lattices_OSup_75, fact_826_mult__left__mono, tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_475, fact_1706_diff__commute, tcon_Nat_Onat___Rings_Ocomm__semiring__0_73, fact_286_times__enat__simps_I2_J, fact_82_numeral__eq__enat, fact_562_times__enat__simps_I3_J, fact_1768_Suc__diff__eq__diff__pred, fact_838_add__decreasing, fact_1183_int__ge__induct, fact_94_less__irrefl__nat, fact_1040_mult__le__cancel__right2, fact_1371_dvdE, tcon_Extended__Nat_Oenat___Groups_Oordered__comm__monoid__add_460, fact_1774_nat__less__add__iff2, fact_865_less__numeral__extra_I1_J, fact_174_mult__le__mono, fact_1460_dvd__imp__le, tcon_Real_Oreal___Power_Opower_342, fact_88_measure__induct, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_41, fact_665_old_Onat_Odistinct_I1_J, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add, fact_851_mult__pos__pos, fact_768_infinity__ne__i0, fact_79_chain__incr, tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_451, fact_1__C2_OIH_C_I2_J, fact_725_add__Suc, fact_352_one__le__numeral, fact_66_enat__ord__simps_I6_J, tcon_Int_Oint___Power_Opower, fact_940_mult__left__le__imp__le, fact_1143_incr__mult__lemma, fact_659_n__not__Suc__n, fact_766_mult__0, fact_251_le__iff__add, fact_1034_imult__infinity__right, fact_456_not__gr__zero, tcon_Int_Oint___Rings_Olinordered__semiring__1__strict, fact_193_less__or__eq__imp__le, fact_805_less__imp__Suc__add, fact_852_mult__pos__neg2, fact_201_nat__le__iff__add, fact_150_nat__add__left__cancel__le, tcon_Int_Oint___Rings_Oordered__ring, fact_1043_mult__less__cancel__right1, tcon_Int_Oint___Rings_Ozero__neq__one, fact_1148_add1__zle__eq, fact_734_gr__implies__not__zero, fact_258_add__mono__thms__linordered__semiring_I3_J, tcon_fun___Complete__Lattices_OSup, fact_946_add__nonneg__pos, fact_1147_zless__imp__add1__zle, fact_8115_mono__add, fact_561_times__enat__simps_I4_J, fact_161_distrib__left__numeral, tcon_Int_Oint___Complete__Lattices_OInf_10, fact_486_lessI, tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_262, fact_4773_max__0__1_I4_J, fact_842_add__nonneg__nonneg, fact_109_not__add__less2, tcon_Nat_Onat___Complete__Lattices_OInf_76, fact_411_distrib__left, fact_1769_Suc__pred_H, tcon_Nat_Onat___Rings_Olinordered__semiring__strict_43, fact_1652_decr__mult__lemma, fact_1772_add__eq__if, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors_44, fact_208_add__leD1, fact_1185_zless__add1__eq, tcon_Real_Oreal___Rings_Ozero__neq__one_315, fact_405_one__enat__def, fact_828_mult__left__mono__neg, fact_815_not__numeral__le__zero, fact_4818_max__enat__simps_I4_J, tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_453, fact_938_mult__le__cancel__left__neg, fact_4775_max__0__1_I1_J, tcon_Real_Oreal___Rings_Oring__1_339, fact_916_mult__less__mono1, fact_406_enat__1__iff_I1_J, fact_752_gr0I, fact_914_nat__mult__eq__cancel1, fact_36_enat__ord__simps_I5_J, tcon_fun___Orderings_Oorder__bot, fact_738_divisors__zero, fact_1020_ex__has__least__nat, fact_668_less__Suc__eq__0__disj, fact_720_Suc__le__D, fact_175_le__square, fact_1694_Nat_Oadd__diff__assoc2, fact_1724_diff__add__inverse, fact_197_left__add__mult__distrib, tcon_Nat_Onat___Rings_Osemiring_97, fact_1439_bezout__add__nat, fact_772_not__iless0, fact_660_diff__induct, fact_8_enat_Osimps_I7_J, fact_850_mult__pos__neg, fact_701_less__SucI, fact_469_zero__eq__add__iff__both__eq__0, tcon_Extended__Nat_Oenat___Groups_Oone_498, fact_255_add__mono, fact_1699_Suc__pred, fact_956_sum__squares__ge__zero, fact_952_mult__le__one, fact_73_plus__enat__simps_I1_J, fact_1739_Nat_Ole__imp__diff__is__add, fact_1723_diff__cancel2, fact_95_nat__less__induct, fact_942_mult__le__less__imp__less, fact_40_enat__ile, tcon_Extended__Nat_Oenat___Rings_Odvd_499, fact_490_add__Suc__right, fact_1758_less__diff__conv2, fact_968_not__sum__squares__lt__zero, fact_845_add__nonpos__eq__0__iff, fact_1759_nat__eq__add__iff1, fact_925_imult__is__infinity, fact_172_mult__le__mono2, fact_762_less__eq__nat_Osimps_I1_J, fact_848_mult__less__0__iff, fact_1042_mult__less__cancel__left2, fact_1743_le__diff__conv, fact_1323_nat__dvd__1__iff__1, tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_48, fact_1144_le__imp__0__less, fact_2754_dvd__imp__le__int, fact_30_infinity__ileE, fact_1647_int__induct, fact_760_bot__nat__0_Oextremum__uniqueI, fact_163_enat__ord__number_I1_J, tcon_fun___Complete__Lattices_Ocomplete__distrib__lattice, fact_497_not__real__square__gt__zero, fact_726_add__Suc__shift, fact_1036_field__le__mult__one__interval, fact_179_mult_Oassoc, fact_462_add_Oright__neutral, fact_764_add__eq__self__zero, tcon_Real_Oreal___Complete__Lattices_OSup_303, fact_74_numeral__less__enat__iff, fact_240_iadd__le__enat__iff, fact_765_nat__mult__eq__cancel__disj, fact_844_add__nonneg__eq__0__iff, tcon_Real_Oreal___Rings_Olinordered__semiring__1__strict_257, tcon_Int_Oint___Rings_Osemiring__no__zero__divisors, fact_1711_minus__nat_Odiff__0, fact_1747_dvd__diffD1, fact_5382_nat__descend__induct, fact_662_Suc__inject, fact_1721_eq__diff__iff, fact_926_enat__0__less__mult__iff, fact_825_mult__right__mono__neg, fact_809_mult__Suc, fact_1735_less__diff__iff, fact_671_gr0__conv__Suc, fact_664_nat_OdiscI, tcon_Extended__Nat_Oenat___Complete__Lattices_OInf_473, fact_824_mult__right__mono, fact_1700_diff__Suc__diff__eq1, fact_112_trans__less__add2, fact_620_zdiv__mono2__neg__lemma, fact_663_old_Onat_Oexhaust, tcon_Nat_Onat___Rings_Oordered__semiring_68, fact_657_Suc__neq__Zero, fact_667_nat_Odistinct_I1_J, fact_457_mult__zero__left, fact_950_add__strict__increasing2, fact_1645_plusinfinity, fact_698_Suc__lessE, fact_2658_abs__add__one__gt__zero, fact_5_not__infinity__eq, fact_438_nat_Oinject, fact_870_canonically__ordered__monoid__add__class_OlessE, fact_196_nat__less__le, fact_484_zero__less__Suc, fact_780_lambda__zero, fact_690_nat__induct__non__zero, tcon_Extended__Nat_Oenat___Orderings_Owellorder_478, fact_732_gr__zeroI, fact_1717_diff__le__self, tcon_Int_Oint___Rings_Ocomm__semiring__0, fact_737_mult__not__zero, tcon_fun___Lattices_Obounded__lattice_5, fact_841_add__increasing2, fact_6216_top_Oextremum__strict, tcon_fun___Orderings_Oorder__top, fact_63_plus__enat__simps_I2_J, fact_2585_abs__mult__self__eq, fact_792_le__imp__less__Suc, fact_949_add__strict__increasing, fact_4835_nat__mult__max__left, fact_867_zero__less__one, fact_1313_mult__less__iff1, fact_458_mult__zero__right, fact_8097_mono__mult, fact_4839_nat__minus__add__max, fact_1189_pos__zmult__eq__1__iff, fact_699_Suc__lessI, fact_706_Suc__less__eq2, fact_1720_le__diff__iff, fact_257_add__mono__thms__linordered__semiring_I2_J, fact_655_Zero__not__Suc, tcon_Nat_Onat___Groups_Osemigroup__mult_74, fact_369_linordered__field__no__ub, tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_248, fact_627_zdiv__mono2__lemma, fact_15_enat_Oinject, fact_80_enat__iless, fact_343_nat__mult__1, fact_417_add__mono1, fact_1594_int__distrib_I3_J, fact_1149_odd__less__0__iff, fact_1754_add__diff__assoc__enat, fact_1175_imp__le__cong, tcon_Real_Oreal___Rings_Osemiring_335, tcon_Nat_Onat___Groups_Ozero_101, fact_1714_less__imp__diff__less, fact_6217_top_Onot__eq__extremum, fact_871_pos__add__strict, fact_195_less__imp__le__nat, tcon_Nat_Onat___Orderings_Oorder__bot_83, fact_722_le__SucE, fact_945_add__neg__nonpos, fact_202_trans__le__add2, tcon_Nat_Onat___Groups_Oab__semigroup__add_67, fact_673_one__is__add, tcon_Int_Oint___Rings_Olinordered__semiring, fact_716_full__nat__induct, fact_1702_Suc__diff__1, fact_1716_le__diff__iff_H, fact_1373_dvd__def, fact_727_Suc__mult__cancel1, fact_757_infinite__descent0, fact_1692_diff__is__0__eq, fact_4772_max__0__1_I3_J, fact_493_mult__eq__1__iff, tcon_Extended__Nat_Oenat___Rings_Ozero__neq__one_482, tcon_Nat_Onat___Rings_Ozero__neq__one_85, tcon_Real_Oreal___Rings_Ocomm__semiring_311, tcon_Real_Oreal___Rings_Olinordered__semiring_283, fact_173_mult__le__mono1, fact_2786_decr__lemma, fact_1753_diff__enat__def, tcon_Nat_Onat___Power_Opower_99, fact_755_less__zeroE, fact_1727_diff__mult__distrib, fact_2623_abs__one, fact_862_mult__strict__right__mono, tcon_Int_Oint___Rings_Odvd, tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_32, fact_4831_max__nat_Oeq__neutr__iff, fact_207_add__leD2, fact_2785_incr__lemma, fact_774_iadd__is__0, fact_702_Ex__less__Suc, tcon_Int_Oint___Rings_Olinordered__ring__strict, tcon_Real_Oreal___Num_Osemiring__numeral_306, fact_6211_top__greatest, fact_1307_Euclid__induct, fact_832_mult__mono, fact_955_sum__squares__le__zero__iff, tcon_Int_Oint___Rings_Oordered__comm__semiring, fact_710_less__Suc__induct, fact_1100_Lattices__Big_Oex__has__greatest__nat, tcon_Real_Oreal___Rings_Ozero__less__one_310, fact_110_add__less__mono1, tcon_Int_Oint___Rings_Osemiring__0, fact_445_Nat_Oadd__0__right, tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_471, fact_1718_diff__le__mono, fact_1632_less__add__iff2, tcon_Extended__Nat_Oenat___Groups_Ozero_496, fact_1748_less__eq__dvd__minus, fact_709_less__trans__Suc, fact_194_le__eq__less__or__eq, fact_839_add__increasing, fact_217_VEBT__internal_Oelim__dead_Osimps_I1_J, fact_967_sum__squares__gt__zero__iff, tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_464, fact_2764_zdvd__mult__cancel1, fact_661_nat__induct, fact_171_enat__less__induct, fact_485_less__Suc0, fact_1180_int__distrib_I2_J, fact_2584_abs__numeral, fact_491_add__gr__0, fact_1701_diff__Suc__diff__eq2, fact_849_mult__neg__pos, tcon_Real_Oreal___Groups_Oab__semigroup__mult_289, fact_422_discrete, fact_731_less__numeral__extra_I3_J, fact_761_bot__nat__0_Oextremum__unique, tcon_Nat_Onat___Groups_Oab__semigroup__mult_63, fact_1707_zero__induct__lemma, fact_1737_less__diff__conv, fact_795_le__less__Suc__eq, fact_442_le0, fact_323_eq__imp__le, fact_1055_convex__bound__le, fact_6213_top_Oextremum__uniqueI, fact_1792_Bolzano, fact_869_add__pos__pos, fact_1760_nat__eq__add__iff2, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_724_nat__arith_Osuc1, fact_1773_nat__less__add__iff1, fact_1461_dvd__mult__cancel, fact_653_vebt__buildup_Ocases, fact_1688_idiff__self, fact_4820_max__enat__simps_I2_J, fact_812_plus__1__eq__Suc, fact_2630_abs__mult__less, fact_228_add_Oleft__commute, fact_1686_idiff__enat__0__right, fact_688_n__less__n__mult__m, fact_1687_idiff__enat__enat, fact_1690_zero__less__diff, fact_860_mult__less__cancel__left__disj, fact_1680_diff__Suc__Suc, fact_831_mult__mono_H, fact_853_zero__less__mult__iff, fact_487_Suc__mono, fact_1182_odd__nonzero, fact_656_Zero__neq__Suc, tcon_fun___Lattices_Obounded__semilattice__inf__top, fact_35_enat__ord__code_I3_J, fact_1741_Nat_Odiff__add__assoc, tcon_Extended__Nat_Oenat___Groups_Omonoid__add_486, fact_1019_bounded__Max__nat, tcon_Int_Oint___Groups_Oordered__cancel__comm__monoid__add, fact_705_All__less__Suc, fact_209_le__add2, fact_107_add__less__mono, fact_1438_zdvd__mult__cancel, fact_1184_int__gr__induct, tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_459, fact_1738_add__diff__inverse__nat, fact_866_not__one__less__zero, fact_1192_mult__le__cancel__iff2, fact_919_mult__eq__self__implies__10, fact_553_one__le__mult__iff, fact_2784_nat__intermed__int__val, fact_1712_diffs0__imp__equal, tcon_Real_Oreal___Rings_Oordered__semiring_294, fact_103_plus__enat__def, tcon_Extended__Nat_Oenat___Rings_Osemiring__no__zero__divisors_458, tcon_fun___Countable__Complete__Lattices_Ocountable__complete__lattice, fact_1756_nat__diff__split, tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, fact_1329_nat__mult__dvd__cancel__disj, tcon_Int_Oint___Num_Osemiring__numeral, fact_953_mult__right__le__one__le, fact_806_Suc__mult__less__cancel1, fact_1775_mult__eq__if, fact_86_enat__ord__code_I4_J, tcon_Int_Oint___Groups_Oone, fact_1732_diff__less, fact_76_plus__eq__infty__iff__enat, fact_4827_max__0L, fact_441_less__nat__zero__code, fact_1032_Suc__ile__eq, fact_855_zero__less__mult__pos2, fact_733_not__less__zero, fact_951_mult__left__le, fact_1730_diff__less__Suc, tcon_Extended__Nat_Oenat___Lattices_Obounded__lattice_1, fact_1464_zdvd__imp__le, fact_1022_times__enat__def, fact_488_Suc__less__eq, fact_930_mult__le__cancel__left, fact_368_linordered__field__no__lb, fact_1633_less__add__iff1, fact_325_le__refl, fact_676_One__nat__def, fact_97_linorder__neqE__nat, fact_834_not__numeral__less__zero, fact_72_enat__ord__simps_I2_J, fact_829_split__mult__pos__le, fact_524_sum__squares__eq__zero__iff, fact_176_le__cube, fact_4838_nat__add__max__right, fact_935_mult__right__less__imp__less, tcon_Extended__Nat_Oenat___Rings_Omult__zero_490, tcon_Nat_Onat___Rings_Ocomm__semiring_82, tcon_fun___Lattices_Olattice, tcon_Int_Oint___Groups_Ostrict__ordered__comm__monoid__add, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_45, fact_816_ordered__comm__semiring__class_Ocomm__mult__left__mono, tcon_Extended__Nat_Oenat___Lattices_Olattice_489, fact_1715_diff__le__mono2
% 71.94/24.75  % No. of inferences in proof: 1719
% 71.94/24.75  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24297 ms resp. 21799 ms w/o parsing
% 74.26/25.29  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 74.26/25.29  thf(vEBT_VEBT_type, type, vEBT_VEBT: $tType).
% 74.26/25.29  thf(code_integer_type, type, code_integer: $tType).
% 74.26/25.29  thf(product_unit_type, type, product_unit: $tType).
% 74.26/25.29  thf(extended_enat_type, type, extended_enat: $tType).
% 74.26/25.29  thf(complex_type, type, complex: $tType).
% 74.26/25.29  thf(char_type, type, char: $tType).
% 74.26/25.29  thf(real_type, type, real: $tType).
% 74.26/25.29  thf(rat_type, type, rat: $tType).
% 74.26/25.29  thf(num_type, type, num: $tType).
% 74.26/25.29  thf(nat_type, type, nat: $tType).
% 74.26/25.29  thf(int_type, type, int: $tType).
% 74.26/25.29  thf(bounded_lattice_decl, type, bounded_lattice: !> [TA: $tType]: $o).
% 74.26/25.29  thf(dvd_decl, type, dvd: !> [TA: $tType]: $o).
% 74.26/25.29  thf(one_decl, type, one: !> [TA: $tType]: $o).
% 74.26/25.29  thf(plus_decl, type, plus: !> [TA: $tType]: $o).
% 74.26/25.29  thf(zero_decl, type, zero: !> [TA: $tType]: $o).
% 74.26/25.29  thf(numeral_decl, type, numeral: !> [TA: $tType]: $o).
% 74.26/25.29  thf(power_decl, type, power: !> [TA: $tType]: $o).
% 74.26/25.29  thf(ring_1_decl, type, ring_1: !> [TA: $tType]: $o).
% 74.26/25.29  thf(semiring_decl, type, semiring: !> [TA: $tType]: $o).
% 74.26/25.29  thf(mult_zero_decl, type, mult_zero: !> [TA: $tType]: $o).
% 74.26/25.29  thf(lattice_decl, type, lattice: !> [TA: $tType]: $o).
% 74.26/25.29  thf(semiring_0_decl, type, semiring_0: !> [TA: $tType]: $o).
% 74.26/25.29  thf(monoid_add_decl, type, monoid_add: !> [TA: $tType]: $o).
% 74.26/25.29  thf(ordered_ring_decl, type, ordered_ring: !> [TA: $tType]: $o).
% 74.26/25.29  thf(zero_neq_one_decl, type, zero_neq_one: !> [TA: $tType]: $o).
% 74.26/25.29  thf(order_bot_decl, type, order_bot: !> [TA: $tType]: $o).
% 74.26/25.29  thf(order_top_decl, type, order_top: !> [TA: $tType]: $o).
% 74.26/25.29  thf(wellorder_decl, type, wellorder: !> [TA: $tType]: $o).
% 74.26/25.29  thf(comm_semiring_decl, type, comm_semiring: !> [TA: $tType]: $o).
% 74.26/25.29  thf(zero_less_one_decl, type, zero_less_one: !> [TA: $tType]: $o).
% 74.26/25.29  thf(semigroup_add_decl, type, semigroup_add: !> [TA: $tType]: $o).
% 74.26/25.29  thf(semiring_numeral_decl, type, semiring_numeral: !> [TA: $tType]: $o).
% 74.26/25.29  thf(complete_Inf_decl, type, complete_Inf: !> [TA: $tType]: $o).
% 74.26/25.29  thf(complete_Sup_decl, type, complete_Sup: !> [TA: $tType]: $o).
% 74.26/25.29  thf(semigroup_mult_decl, type, semigroup_mult: !> [TA: $tType]: $o).
% 74.26/25.29  thf(comm_semiring_0_decl, type, comm_semiring_0: !> [TA: $tType]: $o).
% 74.26/25.29  thf(linordered_idom_decl, type, linordered_idom: !> [TA: $tType]: $o).
% 74.26/25.29  thf(linordered_ring_decl, type, linordered_ring: !> [TA: $tType]: $o).
% 74.26/25.29  thf(ordered_semiring_decl, type, ordered_semiring: !> [TA: $tType]: $o).
% 74.26/25.29  thf(linordered_field_decl, type, linordered_field: !> [TA: $tType]: $o).
% 74.26/25.29  thf(ab_semigroup_add_decl, type, ab_semigroup_add: !> [TA: $tType]: $o).
% 74.26/25.29  thf(comm_monoid_diff_decl, type, comm_monoid_diff: !> [TA: $tType]: $o).
% 74.26/25.29  thf(ab_semigroup_mult_decl, type, ab_semigroup_mult: !> [TA: $tType]: $o).
% 74.26/25.29  thf(linordered_semiring_decl, type, linordered_semiring: !> [TA: $tType]: $o).
% 74.26/25.29  thf(linord6961819062388156250ring_1_decl, type, linord6961819062388156250ring_1: !> [TA: $tType]: $o).
% 74.26/25.29  thf(ordere2520102378445227354miring_decl, type, ordere2520102378445227354miring: !> [TA: $tType]: $o).
% 74.26/25.29  thf(linord4710134922213307826strict_decl, type, linord4710134922213307826strict: !> [TA: $tType]: $o).
% 74.26/25.29  thf(ordere6911136660526730532id_add_decl, type, ordere6911136660526730532id_add: !> [TA: $tType]: $o).
% 74.26/25.29  thf(ordere6658533253407199908up_add_decl, type, ordere6658533253407199908up_add: !> [TA: $tType]: $o).
% 74.26/25.29  thf(semiri3467727345109120633visors_decl, type, semiri3467727345109120633visors: !> [TA: $tType]: $o).
% 74.26/25.29  thf(linord8928482502909563296strict_decl, type, linord8928482502909563296strict: !> [TA: $tType]: $o).
% 74.26/25.29  thf(linord181362715937106298miring_decl, type, linord181362715937106298miring: !> [TA: $tType]: $o).
% 74.26/25.29  thf(linord715952674999750819strict_decl, type, linord715952674999750819strict: !> [TA: $tType]: $o).
% 74.26/25.29  thf(comple5582772986160207858norder_decl, type, comple5582772986160207858norder: !> [TA: $tType]: $o).
% 74.26/25.29  thf(bounde4346867609351753570nf_top_decl, type, bounde4346867609351753570nf_top: !> [TA: $tType]: $o).
% 74.26/25.29  thf(bounde4967611905675639751up_bot_decl, type, bounde4967611905675639751up_bot: !> [TA: $tType]: $o).
% 74.26/25.29  thf(canoni5634975068530333245id_add_decl, type, canoni5634975068530333245id_add: !> [TA: $tType]: $o).
% 74.26/25.29  thf(ordere8940638589300402666id_add_decl, type, ordere8940638589300402666id_add: !> [TA: $tType]: $o).
% 74.26/25.29  thf(strict7427464778891057005id_add_decl, type, strict7427464778891057005id_add: !> [TA: $tType]: $o).
% 74.26/25.29  thf(strict9044650504122735259up_add_decl, type, strict9044650504122735259up_add: !> [TA: $tType]: $o).
% 74.26/25.29  thf(unique1627219031080169319umeral_decl, type, unique1627219031080169319umeral: !> [TA: $tType]: $o).
% 74.26/25.29  thf(comple592849572758109894attice_decl, type, comple592849572758109894attice: !> [TA: $tType]: $o).
% 74.26/25.29  thf(counta3822494911875563373attice_decl, type, counta3822494911875563373attice: !> [TA: $tType]: $o).
% 74.26/25.29  thf(extended_enat2_decl, type, extended_enat2: (nat > extended_enat)).
% 74.26/25.29  thf(extended_case_enat_decl, type, extended_case_enat: !> [TA: $tType]: ((nat > TA) > (TA > (extended_enat > TA)))).
% 74.26/25.29  thf(extended_rec_enat_decl, type, extended_rec_enat: !> [TA: $tType]: ((nat > TA) > (TA > (extended_enat > TA)))).
% 74.26/25.29  thf(extend4730790105801354508finity_decl, type, extend4730790105801354508finity: !> [TA: $tType]: TA).
% 74.26/25.29  thf(abs_abs_decl, type, abs_abs: !> [TA: $tType]: (TA > TA)).
% 74.26/25.29  thf(minus_minus_decl, type, minus_minus: !> [TA: $tType]: (TA > (TA > TA))).
% 74.26/25.29  thf(one_one_decl, type, one_one: !> [TA: $tType]: TA).
% 74.26/25.29  thf(plus_plus_decl, type, plus_plus: !> [TA: $tType]: (TA > (TA > TA))).
% 74.26/25.29  thf(times_times_decl, type, times_times: !> [TA: $tType]: (TA > (TA > TA))).
% 74.26/25.29  thf(zero_zero_decl, type, zero_zero: !> [TA: $tType]: TA).
% 74.26/25.29  thf(if_decl, type, if: !> [TA: $tType]: ($o > (TA > (TA > TA)))).
% 74.26/25.29  thf(suc_decl, type, suc: (nat > nat)).
% 74.26/25.29  thf(numeral_numeral_decl, type, numeral_numeral: !> [TA: $tType]: (num > TA)).
% 74.26/25.29  thf(ord_less_decl, type, ord_less: !> [TA: $tType]: (TA > (TA > $o))).
% 74.26/25.29  thf(ord_less_eq_decl, type, ord_less_eq: !> [TA: $tType]: (TA > (TA > $o))).
% 74.26/25.29  thf(ord_max_decl, type, ord_max: !> [TA: $tType]: (TA > (TA > TA))).
% 74.26/25.29  thf(order_mono_decl, type, order_mono: !> [TA: $tType,TB: $tType]: ((TB > TA) > $o)).
% 74.26/25.29  thf(top_top_decl, type, top_top: !> [TA: $tType]: TA).
% 74.26/25.29  thf(dvd_dvd_decl, type, dvd_dvd: !> [TA: $tType]: (TA > (TA > $o))).
% 74.26/25.29  thf(vEBT_Leaf_decl, type, vEBT_Leaf: ($o > ($o > vEBT_VEBT))).
% 74.26/25.29  thf(vEBT_V8194947554948674370ptions_decl, type, vEBT_V8194947554948674370ptions: (vEBT_VEBT > (nat > $o))).
% 74.26/25.29  thf(vEBT_VEBT_elim_dead_decl, type, vEBT_VEBT_elim_dead: (vEBT_VEBT > (extended_enat > vEBT_VEBT))).
% 74.26/25.29  thf(summarya_decl, type, summarya: vEBT_VEBT).
% 74.26/25.29  thf(sk1_decl, type, sk1: (nat > (nat > ((nat > int) > $o)))).
% 74.26/25.29  thf(sk2_decl, type, sk2: ((nat > int) > (nat > (nat > nat)))).
% 74.26/25.29  thf(sk3_decl, type, sk3: (int > ((nat > int) > (nat > (nat > nat))))).
% 74.26/25.29  thf(sk2_def, definition, sk2 = (^ [A:(nat > int),B:nat,C:nat]: (@+ [D:nat]: ~ (((ord_less_eq @ nat @ C @ D) & (ord_less @ nat @ D @ B)) => (ord_less_eq @ int @ (abs_abs @ int @ (minus_minus @ int @ (A @ (suc @ D)) @ (A @ D))) @ (one_one @ int))))) ).
% 74.26/25.29  thf(sk3_def, definition, sk3 = (^ [A:int,B:(nat > int),C:nat,D:nat]: (@+ [E:nat]: ((ord_less_eq @ nat @ D @ E) & (ord_less_eq @ nat @ E @ C) & ((B @ E) = A)))) ).
% 74.26/25.29  thf(678,axiom,((! [TA: $tType]: ((linordered_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_mult__left__less__imp__less)).
% 74.26/25.29  thf(3021,plain,((! [TA: $tType]: ((linordered_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[678])).
% 74.26/25.29  thf(622,axiom,((! [TA: $tType]: ((semiri3467727345109120633visors @ TA) => (! [A:TA,B:TA]: (((times_times @ TA @ A @ B) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) | (B = (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_mult__eq__0__iff)).
% 74.26/25.29  thf(2822,plain,((! [TA: $tType]: ((semiri3467727345109120633visors @ TA) => (! [A:TA,B:TA]: (((times_times @ TA @ A @ B) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) | (B = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[622])).
% 74.26/25.29  thf(189,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ B @ C) => (ord_less_eq @ TA @ B @ (plus_plus @ TA @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839_add__increasing)).
% 74.26/25.29  thf(1411,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ B @ C) => (ord_less_eq @ TA @ B @ (plus_plus @ TA @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
% 74.26/25.29  thf(71,axiom,((! [A:nat,B:nat]: (((ord_max @ nat @ A @ B) = (zero_zero @ nat)) = ((A = (zero_zero @ nat)) & (B = (zero_zero @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4831_max__nat_Oeq__neutr__iff)).
% 74.26/25.29  thf(1024,plain,((! [A:nat,B:nat]: (((ord_max @ nat @ A @ B) = (zero_zero @ nat)) = ((A = (zero_zero @ nat)) & (B = (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
% 74.26/25.29  thf(690,axiom,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ C @ A) @ (times_times @ TA @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_826_mult__left__mono)).
% 74.26/25.29  thf(3053,plain,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ C @ A) @ (times_times @ TA @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[690])).
% 74.26/25.29  thf(606,axiom,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ B) @ C) @ (plus_plus @ TA @ (times_times @ TA @ D @ B) @ E)) = (ord_less @ TA @ C @ (plus_plus @ TA @ (times_times @ TA @ (minus_minus @ TA @ D @ A) @ B) @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1632_less__add__iff2)).
% 74.26/25.29  thf(2778,plain,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ B) @ C) @ (plus_plus @ TA @ (times_times @ TA @ D @ B) @ E)) = (ord_less @ TA @ C @ (plus_plus @ TA @ (times_times @ TA @ (minus_minus @ TA @ D @ A) @ B) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[606])).
% 74.26/25.29  thf(385,axiom,((semiring_numeral @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Osemiring__numeral)).
% 74.26/25.29  thf(2072,plain,((semiring_numeral @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])).
% 74.26/25.29  thf(278,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (minus_minus @ nat @ C @ B) @ (minus_minus @ nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1715_diff__le__mono2)).
% 74.26/25.29  thf(1729,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (minus_minus @ nat @ C @ B) @ (minus_minus @ nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])).
% 74.26/25.29  thf(805,axiom,((semiring @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring_492)).
% 74.26/25.29  thf(3434,plain,((semiring @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[805])).
% 74.26/25.29  thf(521,axiom,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (A = (suc @ (minus_minus @ nat @ A @ (one_one @ nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1769_Suc__pred_H)).
% 74.26/25.29  thf(2463,plain,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (A = (suc @ (minus_minus @ nat @ A @ (one_one @ nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[521])).
% 74.26/25.29  thf(312,axiom,((! [A:nat,B:nat]: (((minus_minus @ nat @ A @ B) = (zero_zero @ nat)) = (ord_less_eq @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1692_diff__is__0__eq)).
% 74.26/25.29  thf(1840,plain,((! [A:nat,B:nat]: (((minus_minus @ nat @ A @ B) = (zero_zero @ nat)) = (ord_less_eq @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])).
% 74.26/25.29  thf(355,axiom,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA]: ((((ord_less_eq @ TA @ (zero_zero @ TA) @ A) & (ord_less_eq @ TA @ (zero_zero @ TA) @ B)) | ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) & (ord_less_eq @ TA @ B @ (zero_zero @ TA)))) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_split__mult__pos__le)).
% 74.26/25.29  thf(1982,plain,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA]: ((((ord_less_eq @ TA @ (zero_zero @ TA) @ A) & (ord_less_eq @ TA @ (zero_zero @ TA) @ B)) | ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) & (ord_less_eq @ TA @ B @ (zero_zero @ TA)))) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[355])).
% 74.26/25.29  thf(814,axiom,(((extend4730790105801354508finity @ extended_enat) != (zero_zero @ extended_enat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_infinity__ne__i0)).
% 74.26/25.29  thf(3449,plain,((~ ((extend4730790105801354508finity @ extended_enat) = (zero_zero @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[814])).
% 74.26/25.29  thf(552,axiom,((! [TA: $tType]: (! [A:(TA > extended_enat),B:nat]: ((! [C:TA]: ? [D:TA]: (ord_less @ extended_enat @ (A @ C) @ (A @ D))) => (? [C:TA]: (ord_less @ extended_enat @ (extended_enat2 @ B) @ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_chain__incr)).
% 74.26/25.29  thf(2544,plain,((! [TA: $tType]: (! [A:(TA > extended_enat),B:nat]: ((! [C:TA]: ? [D:TA]: (ord_less @ extended_enat @ (A @ C) @ (A @ D))) => (? [C:TA]: (ord_less @ extended_enat @ (extended_enat2 @ B) @ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[552])).
% 74.26/25.29  thf(233,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((dvd_dvd @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = (dvd_dvd @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1462_nat__mult__dvd__cancel1)).
% 74.26/25.29  thf(1549,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((dvd_dvd @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = (dvd_dvd @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
% 74.26/25.29  thf(264,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ (suc @ B)) = ((ord_less @ nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_less__Suc__eq)).
% 74.26/25.29  thf(1686,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)],[264])).
% 74.26/25.29  thf(320,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_le__antisym)).
% 74.26/25.29  thf(1879,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])).
% 74.26/25.29  thf(274,axiom,((! [A:nat,B:nat]: ((times_times @ nat @ (suc @ A) @ B) = (plus_plus @ nat @ B @ (times_times @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_mult__Suc)).
% 74.26/25.29  thf(1718,plain,((! [A:nat,B:nat]: ((times_times @ nat @ (suc @ A) @ B) = (plus_plus @ nat @ B @ (times_times @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])).
% 74.26/25.29  thf(594,axiom,((! [TA: $tType]: ((linord715952674999750819strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ E) => (((plus_plus @ TA @ D @ E) = (one_one @ TA)) => (ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ D @ A) @ (times_times @ TA @ E @ C)) @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_convex__bound__lt)).
% 74.26/25.29  thf(2744,plain,((! [TA: $tType]: ((linord715952674999750819strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ E) => (((plus_plus @ TA @ D @ E) = (one_one @ TA)) => (ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ D @ A) @ (times_times @ TA @ E @ C)) @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[594])).
% 74.26/25.29  thf(308,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/sandbox2/benchmark/theBenchmark.p',fact_673_one__is__add)).
% 74.26/25.29  thf(1823,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)],[308])).
% 74.26/25.29  thf(123,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less @ nat @ C @ (suc @ A)) & (B @ C))) = ((B @ A) | ? [C:nat]: ((ord_less @ nat @ C @ A) & (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_Ex__less__Suc)).
% 74.26/25.29  thf(1190,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less @ nat @ C @ (suc @ A)) & (B @ C))) = ((B @ A) | ? [C:nat]: ((ord_less @ nat @ C @ A) & (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
% 74.26/25.29  thf(397,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (zero_zero @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_le__numeral__extra_I3_J)).
% 74.26/25.29  thf(2109,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (zero_zero @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[397])).
% 74.26/25.29  thf(204,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less @ nat @ D @ E) => (ord_less @ nat @ (A @ D) @ (A @ E)))) => ((ord_less_eq @ nat @ B @ C) => (ord_less_eq @ nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_less__mono__imp__le__mono)).
% 74.26/25.29  thf(1454,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less @ nat @ D @ E) => (ord_less @ nat @ (A @ D) @ (A @ E)))) => ((ord_less_eq @ nat @ B @ C) => (ord_less_eq @ nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
% 74.26/25.29  thf(373,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_old_Onat_Oinject)).
% 74.26/25.29  thf(2031,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[373])).
% 74.26/25.29  thf(360,axiom,((ordere6911136660526730532id_add @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__comm__monoid__add)).
% 74.26/25.29  thf(1995,plain,((ordere6911136660526730532id_add @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])).
% 74.26/25.29  thf(444,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_linordered__nonzero__semiring__class_Ozero__le__one)).
% 74.26/25.29  thf(2263,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[444])).
% 74.26/25.29  thf(236,axiom,((! [A:int,B:int,C:$o,D:$o]: ((A = B) => (((ord_less_eq @ int @ (zero_zero @ int) @ B) => (C = D)) => (((ord_less_eq @ int @ (zero_zero @ int) @ A) & (C)) = ((ord_less_eq @ int @ (zero_zero @ int) @ B) & (D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_conj__le__cong)).
% 74.26/25.29  thf(1559,plain,((! [A:int,B:int,C:$o,D:$o]: ((A = B) => (((ord_less_eq @ int @ (zero_zero @ int) @ B) => (C = D)) => (((ord_less_eq @ int @ (zero_zero @ int) @ A) & (C)) = ((ord_less_eq @ int @ (zero_zero @ int) @ B) & (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
% 74.26/25.29  thf(101,axiom,((linordered_idom @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom)).
% 74.26/25.29  thf(1105,plain,((linordered_idom @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
% 74.26/25.29  thf(635,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less_eq @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = (ord_less_eq @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1023_nat__mult__le__cancel1)).
% 74.26/25.29  thf(2876,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less_eq @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = (ord_less_eq @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[635])).
% 74.26/25.29  thf(141,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((dvd_dvd @ nat @ (times_times @ nat @ A @ B) @ A) = (B = (one_one @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1478_dvd__mult__cancel1)).
% 74.26/25.29  thf(1237,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((dvd_dvd @ nat @ (times_times @ nat @ A @ B) @ A) = (B = (one_one @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
% 74.26/25.29  thf(11,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((times_times @ TA @ (abs_abs @ TA @ B) @ A) = (abs_abs @ TA @ (times_times @ TA @ B @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2642_abs__mult__pos)).
% 74.26/25.29  thf(846,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((times_times @ TA @ (abs_abs @ TA @ B) @ A) = (abs_abs @ TA @ (times_times @ TA @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 74.26/25.29  thf(647,axiom,((! [TA: $tType]: (((numeral @ TA) & (semiring @ TA)) => (! [A:TA,B:TA,C:num]: ((times_times @ TA @ (plus_plus @ TA @ A @ B) @ (numeral_numeral @ TA @ C)) = (plus_plus @ TA @ (times_times @ TA @ A @ (numeral_numeral @ TA @ C)) @ (times_times @ TA @ B @ (numeral_numeral @ TA @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_distrib__right__numeral)).
% 74.26/25.29  thf(2921,plain,((! [TA: $tType]: (((numeral @ TA) & (semiring @ TA)) => (! [A:TA,B:TA,C:num]: ((times_times @ TA @ (plus_plus @ TA @ A @ B) @ (numeral_numeral @ TA @ C)) = (plus_plus @ TA @ (times_times @ TA @ A @ (numeral_numeral @ TA @ C)) @ (times_times @ TA @ B @ (numeral_numeral @ TA @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[647])).
% 74.26/25.29  thf(73,axiom,((linord715952674999750819strict @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__semiring__1__strict_257)).
% 74.26/25.29  thf(1031,plain,((linord715952674999750819strict @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
% 74.26/25.29  thf(144,axiom,((linord181362715937106298miring @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Olinordered__nonzero__semiring_457)).
% 74.26/25.29  thf(1256,plain,((linord181362715937106298miring @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
% 74.26/25.29  thf(406,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (~ (ord_less @ TA @ (one_one @ TA) @ (one_one @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_less__numeral__extra_I4_J)).
% 74.26/25.29  thf(2145,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (~ (ord_less @ TA @ (one_one @ TA) @ (one_one @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])).
% 74.26/25.29  thf(2146,plain,(! [TA:$tType] : ((~ (linord181362715937106298miring @ TA)) | (~ (ord_less @ TA @ (one_one @ TA) @ (one_one @ TA))))),inference(cnf,[status(esa)],[2145])).
% 74.26/25.29  thf(3532,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less @ TA @ (one_one @ TA) @ (one_one @ TA))) | ((linord181362715937106298miring @ extended_enat) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1256,2146])).
% 74.26/25.29  thf(3533,plain,(! [TA:$tType] : ((~ (ord_less @ TA @ (one_one @ TA) @ (one_one @ TA))) | ((linord181362715937106298miring @ extended_enat) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3532])).
% 74.26/25.29  thf(3534,plain,((~ (ord_less @ extended_enat @ (one_one @ extended_enat) @ (one_one @ extended_enat)))),inference(pattern_uni,[status(thm)],[3533:[bind_type(TA,$thf(extended_enat))]])).
% 74.26/25.29  thf(52,axiom,((! [A:nat,B:nat]: ((~ (ord_less @ nat @ A @ B)) => ((plus_plus @ nat @ B @ (minus_minus @ nat @ A @ B)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1738_add__diff__inverse__nat)).
% 74.26/25.29  thf(977,plain,((! [A:nat,B:nat]: ((~ (ord_less @ nat @ A @ B)) => ((plus_plus @ nat @ B @ (minus_minus @ nat @ A @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
% 74.26/25.29  thf(664,axiom,((! [TA: $tType]: ((linordered_ring @ TA) => (! [A:TA,B:TA]: (ord_less_eq @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_956_sum__squares__ge__zero)).
% 74.26/25.29  thf(2976,plain,((! [TA: $tType]: ((linordered_ring @ TA) => (! [A:TA,B:TA]: (ord_less_eq @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[664])).
% 74.26/25.29  thf(787,axiom,((! [TA: $tType]: (! [A:(nat > TA),B:TA]: ((extended_rec_enat @ TA @ A @ B @ (extend4730790105801354508finity @ extended_enat)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_enat_Osimps_I7_J)).
% 74.26/25.29  thf(3317,plain,((! [TA: $tType]: (! [A:(nat > TA),B:TA]: ((extended_rec_enat @ TA @ (A) @ B @ (extend4730790105801354508finity @ extended_enat)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[787])).
% 74.26/25.29  thf(617,axiom,((! [TA: $tType]: ((unique1627219031080169319umeral @ TA) => ((ord_less @ TA) = (^ [A:TA]: (ord_less_eq @ TA @ (plus_plus @ TA @ A @ (one_one @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_discrete)).
% 74.26/25.29  thf(2808,plain,((! [TA: $tType]: ((unique1627219031080169319umeral @ TA) => ((ord_less @ TA) = (^ [A:TA]: (ord_less_eq @ TA @ (plus_plus @ TA @ A @ (one_one @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[617])).
% 74.26/25.29  thf(534,axiom,((zero_less_one @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__less__one_81)).
% 74.26/25.29  thf(2495,plain,((zero_less_one @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[534])).
% 74.26/25.29  thf(605,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq @ int @ (plus_plus @ int @ (times_times @ int @ A @ B) @ C) @ (plus_plus @ int @ (times_times @ int @ A @ D) @ E)) => ((ord_less_eq @ int @ E @ (zero_zero @ int)) => ((ord_less @ int @ A @ E) => ((ord_less @ int @ A @ C) => (ord_less_eq @ int @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_unique__quotient__lemma__neg)).
% 74.26/25.29  thf(2776,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq @ int @ (plus_plus @ int @ (times_times @ int @ A @ B) @ C) @ (plus_plus @ int @ (times_times @ int @ A @ D) @ E)) => ((ord_less_eq @ int @ E @ (zero_zero @ int)) => ((ord_less @ int @ A @ E) => ((ord_less @ int @ A @ C) => (ord_less_eq @ int @ D @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[605])).
% 74.26/25.29  thf(685,axiom,((! [TA: $tType]: ((zero @ TA) => (! [A:TA]: (((zero_zero @ TA) = A) = (A = (zero_zero @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_zero__reorient)).
% 74.26/25.29  thf(3040,plain,((! [TA: $tType]: ((zero @ TA) => (! [A:TA]: (((zero_zero @ TA) = A) = (A = (zero_zero @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[685])).
% 74.26/25.29  thf(655,axiom,((! [A:extended_enat]: ((minus_minus @ extended_enat @ A @ (extended_enat2 @ (zero_zero @ nat))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1686_idiff__enat__0__right)).
% 74.26/25.29  thf(2947,plain,((! [A:extended_enat]: ((minus_minus @ extended_enat @ A @ (extended_enat2 @ (zero_zero @ nat))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[655])).
% 74.26/25.29  thf(90,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (~ (! [C:nat]: (B != (suc @ (plus_plus @ nat @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_less__natE)).
% 74.26/25.29  thf(1073,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)],[90])).
% 74.26/25.29  thf(230,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd @ int @ A @ (plus_plus @ int @ B @ (times_times @ int @ A @ C))) = (dvd_dvd @ int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1441_zdvd__reduce)).
% 74.26/25.29  thf(1544,plain,((! [A:int,B:int,C:int]: ((dvd_dvd @ int @ A @ (plus_plus @ int @ B @ (times_times @ int @ A @ C))) = (dvd_dvd @ int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
% 74.26/25.29  thf(484,axiom,((! [A:nat]: ~ (ord_less @ nat @ A @ (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_less__zeroE)).
% 74.26/25.29  thf(2380,plain,((! [A:nat]: ~ (ord_less @ nat @ A @ (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])).
% 74.26/25.29  thf(795,axiom,((! [A:extended_enat]: (ord_less_eq @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_enat__ord__simps_I3_J)).
% 74.26/25.29  thf(3402,plain,((! [A:extended_enat]: (ord_less_eq @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[795])).
% 74.26/25.29  thf(157,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_less__numeral__extra_I1_J)).
% 74.26/25.29  thf(1305,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])).
% 74.26/25.29  thf(63,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (minus_minus @ nat @ A @ B) @ C) = (minus_minus @ nat @ (minus_minus @ nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1706_diff__commute)).
% 74.26/25.29  thf(1005,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (minus_minus @ nat @ A @ B) @ C) = (minus_minus @ nat @ (minus_minus @ nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
% 74.26/25.29  thf(427,axiom,((linord181362715937106298miring @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_262)).
% 74.26/25.29  thf(2210,plain,((linord181362715937106298miring @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])).
% 74.26/25.29  thf(400,axiom,((mult_zero @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Omult__zero_330)).
% 74.26/25.29  thf(2117,plain,((mult_zero @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[400])).
% 74.26/25.29  thf(244,axiom,((one @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oone_348)).
% 74.26/25.29  thf(1596,plain,((one @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
% 74.26/25.29  thf(152,axiom,((suc = (^ [A:nat]: (plus_plus @ nat @ A @ (one_one @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_813_Suc__eq__plus1)).
% 74.26/25.29  thf(1290,plain,(((suc) = (^ [A:nat]: (plus_plus @ nat @ A @ (one_one @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
% 74.26/25.29  thf(321,axiom,((! [A:nat]: ((A != (zero_zero @ nat)) => (ord_less @ nat @ (zero_zero @ nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_752_gr0I)).
% 74.26/25.29  thf(1882,plain,((! [A:nat]: ((~ (A = (zero_zero @ nat))) => (ord_less @ nat @ (zero_zero @ nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])).
% 74.26/25.29  thf(490,axiom,((! [A:nat]: ((times_times @ nat @ (zero_zero @ nat) @ A) = (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_mult__0)).
% 74.26/25.29  thf(2395,plain,((! [A:nat]: ((times_times @ nat @ (zero_zero @ nat) @ A) = (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[490])).
% 74.26/25.29  thf(643,axiom,((! [TA: $tType]: ((semiring @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((plus_plus @ TA @ (times_times @ TA @ A @ B) @ (plus_plus @ TA @ (times_times @ TA @ C @ B) @ D)) = (plus_plus @ TA @ (times_times @ TA @ (plus_plus @ TA @ A @ C) @ B) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_combine__common__factor)).
% 74.26/25.29  thf(2908,plain,((! [TA: $tType]: ((semiring @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((plus_plus @ TA @ (times_times @ TA @ A @ B) @ (plus_plus @ TA @ (times_times @ TA @ C @ B) @ D)) = (plus_plus @ TA @ (times_times @ TA @ (plus_plus @ TA @ A @ C) @ B) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[643])).
% 74.26/25.29  thf(396,axiom,((! [TA: $tType]: (! [A:(TA > nat),B:(TA > $o),C:TA]: ((! [D:TA]: (((A @ D) = (zero_zero @ nat)) => (B @ D))) => ((! [D:TA]: ((ord_less @ nat @ (zero_zero @ nat) @ (A @ D)) => ((~ (B @ D)) => (? [E:TA]: ((ord_less @ nat @ (A @ E) @ (A @ D)) & ~ (B @ E)))))) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_758_infinite__descent0__measure)).
% 74.26/25.29  thf(2099,plain,((! [TA: $tType]: (! [A:(TA > nat),B:(TA > $o),C:TA]: ((! [D:TA]: (((A @ D) = (zero_zero @ nat)) => (B @ D))) => ((! [D:TA]: ((ord_less @ nat @ (zero_zero @ nat) @ (A @ D)) => ((~ (B @ D)) => (? [E:TA]: ((ord_less @ nat @ (A @ E) @ (A @ D)) & ~ (B @ E)))))) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])).
% 74.26/25.29  thf(453,axiom,((linordered_field @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field_293)).
% 74.26/25.29  thf(2282,plain,((linordered_field @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[453])).
% 74.26/25.29  thf(195,axiom,((monoid_add @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__add)).
% 74.26/25.29  thf(1426,plain,((monoid_add @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
% 74.26/25.29  thf(807,axiom,((ab_semigroup_add @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_466)).
% 74.26/25.29  thf(3439,plain,((ab_semigroup_add @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[807])).
% 74.26/25.29  thf(107,axiom,((! [A:nat,B:nat]: ((times_times @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (extended_enat2 @ (times_times @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_times__enat__simps_I1_J)).
% 74.26/25.29  thf(1137,plain,((! [A:nat,B:nat]: ((times_times @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (extended_enat2 @ (times_times @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
% 74.26/25.29  thf(573,axiom,((! [TA: $tType]: ((comm_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ (plus_plus @ TA @ A @ B) @ C) = (plus_plus @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_comm__semiring__class_Odistrib)).
% 74.26/25.29  thf(2686,plain,((! [TA: $tType]: ((comm_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ (plus_plus @ TA @ A @ B) @ C) = (plus_plus @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[573])).
% 74.26/25.29  thf(159,axiom,((plus @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oplus_345)).
% 74.26/25.29  thf(1310,plain,((plus @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
% 74.26/25.29  thf(375,axiom,((! [A:nat,B:nat]: (((minus_minus @ nat @ A @ B) = (zero_zero @ nat)) => (((minus_minus @ nat @ B @ A) = (zero_zero @ nat)) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1712_diffs0__imp__equal)).
% 74.26/25.29  thf(2035,plain,((! [A:nat,B:nat]: (((minus_minus @ nat @ A @ B) = (zero_zero @ nat)) => (((minus_minus @ nat @ B @ A) = (zero_zero @ nat)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])).
% 74.26/25.29  thf(404,axiom,((! [A:int,B:int]: ((ord_less_eq @ int @ A @ B) | (A = B) | (ord_less_eq @ int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_verit__la__generic)).
% 74.26/25.29  thf(2141,plain,((! [A:int,B:int]: ((ord_less_eq @ int @ A @ B) | (A = B) | (ord_less_eq @ int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])).
% 74.26/25.29  thf(582,axiom,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: ~ (ord_less @ TA @ (top_top @ TA) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6216_top_Oextremum__strict)).
% 74.26/25.29  thf(2712,plain,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: ~ (ord_less @ TA @ (top_top @ TA) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[582])).
% 74.26/25.29  thf(137,axiom,((mult_zero @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Omult__zero)).
% 74.26/25.29  thf(1233,plain,((mult_zero @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
% 74.26/25.29  thf(563,axiom,((! [A:extended_enat]: ((A != (extend4730790105801354508finity @ extended_enat)) => ((minus_minus @ extended_enat @ A @ A) = (zero_zero @ extended_enat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1688_idiff__self)).
% 74.26/25.29  thf(2580,plain,((! [A:extended_enat]: ((~ (A = (extend4730790105801354508finity @ extended_enat))) => ((minus_minus @ extended_enat @ A @ A) = (zero_zero @ extended_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[563])).
% 74.26/25.29  thf(786,axiom,((! [A:nat]: ((extend4730790105801354508finity @ extended_enat) != (extended_enat2 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_enat_Odistinct_I2_J)).
% 74.26/25.29  thf(3313,plain,((! [A:nat]: ~ ((extend4730790105801354508finity @ extended_enat) = (extended_enat2 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[786])).
% 74.26/25.29  thf(378,axiom,((! [A:int,B:int,C:(int > $o)]: ((ord_less @ int @ A @ B) => ((C @ (minus_minus @ int @ B @ (one_one @ int))) => ((! [D:int]: ((ord_less @ int @ D @ B) => ((C @ D) => (C @ (minus_minus @ int @ D @ (one_one @ int)))))) => (C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1628_int__less__induct)).
% 74.26/25.29  thf(2042,plain,((! [A:int,B:int,C:(int > $o)]: ((ord_less @ int @ A @ B) => ((C @ (minus_minus @ int @ B @ (one_one @ int))) => ((! [D:int]: ((ord_less @ int @ D @ B) => ((C @ D) => (C @ (minus_minus @ int @ D @ (one_one @ int)))))) => (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])).
% 74.26/25.29  thf(116,axiom,((semiring_0 @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__0_91)).
% 74.26/25.29  thf(1164,plain,((semiring_0 @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
% 74.26/25.29  thf(464,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ B @ C) => (ord_less_eq @ TA @ B @ (plus_plus @ TA @ C @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_841_add__increasing2)).
% 74.26/25.29  thf(2316,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ B @ C) => (ord_less_eq @ TA @ B @ (plus_plus @ TA @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[464])).
% 74.26/25.29  thf(812,axiom,((((?) @ extended_enat) = (^ [A:(extended_enat > $o)]: ((A @ (extend4730790105801354508finity @ extended_enat)) | ? [B:nat]: (A @ (extended_enat2 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_enat__ex__split)).
% 74.26/25.29  thf(3446,plain,((((?) @ extended_enat) = (^ [A:(extended_enat > $o)]: ((A @ (extend4730790105801354508finity @ extended_enat)) | ? [B:nat]: (A @ (extended_enat2 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[812])).
% 74.26/25.29  thf(513,axiom,((ordere6658533253407199908up_add @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_266)).
% 74.26/25.29  thf(2448,plain,((ordere6658533253407199908up_add @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[513])).
% 74.26/25.29  thf(651,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B))) = ((A != (zero_zero @ TA)) | (B != (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_sum__squares__gt__zero__iff)).
% 74.26/25.29  thf(2933,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B))) = (~ (A = (zero_zero @ TA)) | ~ (B = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[651])).
% 74.26/25.29  thf(335,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq @ nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq @ nat @ A @ D) => ((C @ D) => (C @ (suc @ D))))) => (C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_nat__induct__at__least)).
% 74.26/25.29  thf(1919,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq @ nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq @ nat @ A @ D) => ((C @ D) => (C @ (suc @ D))))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])).
% 74.26/25.29  thf(752,axiom,((counta3822494911875563373attice @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Countable__Complete__Lattices_Ocountable__complete__lattice_449)).
% 74.26/25.29  thf(3253,plain,((counta3822494911875563373attice @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[752])).
% 74.26/25.29  thf(519,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (times_times @ TA @ B @ A) @ (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_852_mult__pos__neg2)).
% 74.26/25.29  thf(2459,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (times_times @ TA @ B @ A) @ (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])).
% 74.26/25.29  thf(804,axiom,((! [A:extended_enat,B:extended_enat]: (((? [C:nat]: (A = (extended_enat2 @ C))) => (! [C:nat]: (B != (extended_enat2 @ C)))) => (((? [C:nat]: (A = (extended_enat2 @ C))) => (B != (extend4730790105801354508finity @ extended_enat))) => (((A = (extend4730790105801354508finity @ extended_enat)) => (! [C:nat]: (B != (extended_enat2 @ C)))) => (~ ((A = (extend4730790105801354508finity @ extended_enat)) => (B != (extend4730790105801354508finity @ extended_enat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_enat2__cases)).
% 74.26/25.29  thf(3414,plain,((! [A:extended_enat,B:extended_enat]: (((? [C:nat]: (A = (extended_enat2 @ C))) => (! [C:nat]: ~ (B = (extended_enat2 @ C)))) => (((? [C:nat]: (A = (extended_enat2 @ C))) => (~ (B = (extend4730790105801354508finity @ extended_enat)))) => (((A = (extend4730790105801354508finity @ extended_enat)) => (! [C:nat]: ~ (B = (extended_enat2 @ C)))) => (~ ((A = (extend4730790105801354508finity @ extended_enat)) => (~ (B = (extend4730790105801354508finity @ extended_enat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[804])).
% 74.26/25.29  thf(173,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_nat_Oinject)).
% 74.26/25.29  thf(1342,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])).
% 74.26/25.29  thf(343,axiom,((strict7427464778891057005id_add @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_31)).
% 74.26/25.29  thf(1954,plain,((strict7427464778891057005id_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])).
% 74.26/25.29  thf(626,axiom,((! [TA: $tType]: ((ring_1 @ TA) => (! [A:TA]: ((minus_minus @ TA @ (times_times @ TA @ A @ A) @ (one_one @ TA)) = (times_times @ TA @ (plus_plus @ TA @ A @ (one_one @ TA)) @ (minus_minus @ TA @ A @ (one_one @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1638_square__diff__one__factored)).
% 74.26/25.29  thf(2844,plain,((! [TA: $tType]: ((ring_1 @ TA) => (! [A:TA]: ((minus_minus @ TA @ (times_times @ TA @ A @ A) @ (one_one @ TA)) = (times_times @ TA @ (plus_plus @ TA @ A @ (one_one @ TA)) @ (minus_minus @ TA @ A @ (one_one @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[626])).
% 74.26/25.29  thf(131,axiom,((! [TA: $tType]: ((numeral @ TA) => (! [A:num]: ((plus_plus @ TA @ (one_one @ TA) @ (numeral_numeral @ TA @ A)) = (plus_plus @ TA @ (numeral_numeral @ TA @ A) @ (one_one @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_one__plus__numeral__commute)).
% 74.26/25.29  thf(1222,plain,((! [TA: $tType]: ((numeral @ TA) => (! [A:num]: ((plus_plus @ TA @ (one_one @ TA) @ (numeral_numeral @ TA @ A)) = (plus_plus @ TA @ (numeral_numeral @ TA @ A) @ (one_one @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])).
% 74.26/25.29  thf(40,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ (zero_zero @ nat) @ C) => (ord_less @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_916_mult__less__mono1)).
% 74.26/25.29  thf(930,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ (zero_zero @ nat) @ C) => (ord_less @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
% 74.26/25.29  thf(477,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:(TA > nat),C:TA]: ((! [D:TA]: ((~ (A @ D)) => (? [E:TA]: ((ord_less @ nat @ (B @ E) @ (B @ D)) & ~ (A @ E))))) => (A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_infinite__descent__measure)).
% 74.26/25.29  thf(2360,plain,((! [TA: $tType]: (! [A:(TA > $o),B:(TA > nat),C:TA]: ((! [D:TA]: ((~ (A @ D)) => (? [E:TA]: ((ord_less @ nat @ (B @ E) @ (B @ D)) & ~ (A @ E))))) => (A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])).
% 74.26/25.29  thf(6,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA]: ((times_times @ TA @ (abs_abs @ TA @ A) @ (abs_abs @ TA @ A)) = (times_times @ TA @ A @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2585_abs__mult__self__eq)).
% 74.26/25.29  thf(829,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA]: ((times_times @ TA @ (abs_abs @ TA @ A) @ (abs_abs @ TA @ A)) = (times_times @ TA @ A @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 74.26/25.29  thf(125,axiom,(((times_times @ extended_enat) = (^ [A:extended_enat,B:extended_enat]: (extended_case_enat @ extended_enat @ (^ [C:nat]: (extended_case_enat @ extended_enat @ (^ [D:nat]: (extended_enat2 @ (times_times @ nat @ C @ D))) @ (if @ extended_enat @ (C = (zero_zero @ nat)) @ (zero_zero @ extended_enat) @ (extend4730790105801354508finity @ extended_enat)) @ B)) @ (if @ extended_enat @ (B = (zero_zero @ extended_enat)) @ (zero_zero @ extended_enat) @ (extend4730790105801354508finity @ extended_enat)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1022_times__enat__def)).
% 74.26/25.29  thf(1196,plain,(((times_times @ extended_enat) = (^ [A:extended_enat,B:extended_enat]: (extended_case_enat @ extended_enat @ (^ [C:nat]: (extended_case_enat @ extended_enat @ (^ [D:nat]: (extended_enat2 @ (times_times @ nat @ C @ D))) @ (if @ extended_enat @ (C = (zero_zero @ nat)) @ (zero_zero @ extended_enat) @ (extend4730790105801354508finity @ extended_enat)) @ B)) @ (if @ extended_enat @ (B = (zero_zero @ extended_enat)) @ (zero_zero @ extended_enat) @ (extend4730790105801354508finity @ extended_enat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
% 74.26/25.29  thf(704,axiom,((! [A:(extended_enat > $o),B:extended_enat]: ((! [C:extended_enat]: ((! [D:extended_enat]: ((ord_less @ extended_enat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_enat__less__induct)).
% 74.26/25.29  thf(3103,plain,((! [A:(extended_enat > $o),B:extended_enat]: ((! [C:extended_enat]: ((! [D:extended_enat]: ((ord_less @ extended_enat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[704])).
% 74.26/25.29  thf(533,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__not__refl2)).
% 74.26/25.29  thf(2491,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[533])).
% 74.26/25.29  thf(367,axiom,((comm_semiring_0 @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__semiring__0)).
% 74.26/25.29  thf(2020,plain,((comm_semiring_0 @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])).
% 74.26/25.29  thf(80,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_857_mult__less__cancel__left__pos)).
% 74.26/25.29  thf(1046,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
% 74.26/25.29  thf(248,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => ((B != (suc @ A)) => (~ (! [C:nat]: ((ord_less @ nat @ A @ C) => (B != (suc @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_Nat_OlessE)).
% 74.26/25.29  thf(1613,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => ((~ (B = (suc @ A))) => (~ (! [C:nat]: ((ord_less @ nat @ A @ C) => (~ (B = (suc @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])).
% 74.26/25.29  thf(183,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(TA > nat),D:nat]: ((A @ B) => ((! [E:TA]: ((A @ E) => (? [F:TA]: ((A @ F) & ~ (ord_less_eq @ nat @ (C @ F) @ (C @ E)))))) => (? [E:TA]: ((A @ E) & ~ (ord_less @ nat @ (C @ E) @ (plus_plus @ nat @ (C @ B) @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_ex__has__greatest__nat__lemma)).
% 74.26/25.29  thf(1386,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(TA > nat),D:nat]: ((A @ B) => ((! [E:TA]: ((A @ E) => (? [F:TA]: ((A @ F) & ~ (ord_less_eq @ nat @ (C @ F) @ (C @ E)))))) => (? [E:TA]: ((A @ E) & ~ (ord_less @ nat @ (C @ E) @ (plus_plus @ nat @ (C @ B) @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
% 74.26/25.29  thf(276,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ A @ C) => (ord_less @ nat @ (minus_minus @ nat @ C @ B) @ (minus_minus @ nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1713_diff__less__mono2)).
% 74.26/25.29  thf(1724,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ A @ C) => (ord_less @ nat @ (minus_minus @ nat @ C @ B) @ (minus_minus @ nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])).
% 74.26/25.29  thf(543,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ D) => (ord_less_eq @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_mult__le__mono)).
% 74.26/25.29  thf(2516,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ D) => (ord_less_eq @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[543])).
% 74.26/25.29  thf(329,axiom,((ordered_semiring @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oordered__semiring_294)).
% 74.26/25.29  thf(1904,plain,((ordered_semiring @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])).
% 74.26/25.29  thf(134,axiom,((ordered_ring @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oordered__ring)).
% 74.26/25.29  thf(1228,plain,((ordered_ring @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
% 74.26/25.29  thf(633,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ A @ C)) & ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ C @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_937_mult__less__cancel__right)).
% 74.26/25.29  thf(2869,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ A @ C)) & ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[633])).
% 74.26/25.29  thf(668,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: (ord_less_eq @ TA @ (zero_zero @ TA) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_zero__le)).
% 74.26/25.29  thf(2985,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: (ord_less_eq @ TA @ (zero_zero @ TA) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[668])).
% 74.26/25.29  thf(240,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ (suc @ B)) = ((ord_less_eq @ nat @ A @ B) | (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_le__Suc__eq)).
% 74.26/25.29  thf(1576,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ (suc @ B)) = ((ord_less_eq @ nat @ A @ B) | (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
% 74.26/25.29  thf(413,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ (suc @ B)) => ((~ (ord_less_eq @ nat @ A @ B)) => (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_le__SucE)).
% 74.26/25.29  thf(2173,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ (suc @ B)) => ((~ (ord_less_eq @ nat @ A @ B)) => (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])).
% 74.26/25.29  thf(177,axiom,((linordered_ring @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__ring_297)).
% 74.26/25.29  thf(1366,plain,((linordered_ring @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])).
% 74.26/25.29  thf(492,axiom,((! [A:nat,B:nat]: ((plus_plus @ nat @ A @ (suc @ B)) = (suc @ (plus_plus @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_add__Suc__right)).
% 74.26/25.29  thf(2400,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)],[492])).
% 74.26/25.29  thf(623,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((~ (ord_less @ TA @ (zero_zero @ TA) @ A)) = (A = (zero_zero @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_not__gr__zero)).
% 74.26/25.29  thf(2825,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((~ (ord_less @ TA @ (zero_zero @ TA) @ A)) = (A = (zero_zero @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[623])).
% 74.26/25.29  thf(223,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)) => ((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ (zero_zero @ TA) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_zero__less__mult__pos)).
% 74.26/25.29  thf(1529,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)) => ((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ (zero_zero @ TA) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
% 74.26/25.29  thf(758,axiom,((plus @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oplus_497)).
% 74.26/25.29  thf(3263,plain,((plus @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[758])).
% 74.26/25.29  thf(470,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ C @ (suc @ (minus_minus @ nat @ B @ A))) = (minus_minus @ nat @ (plus_plus @ nat @ C @ A) @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1700_diff__Suc__diff__eq1)).
% 74.26/25.29  thf(2328,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ C @ (suc @ (minus_minus @ nat @ B @ A))) = (minus_minus @ nat @ (plus_plus @ nat @ C @ A) @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[470])).
% 74.26/25.29  thf(197,axiom,((zero @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_344)).
% 74.26/25.29  thf(1430,plain,((zero @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
% 74.26/25.29  thf(619,axiom,((! [A:extended_enat]: ((ord_max @ extended_enat @ A @ (zero_zero @ extended_enat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4820_max__enat__simps_I2_J)).
% 74.26/25.29  thf(2814,plain,((! [A:extended_enat]: ((ord_max @ extended_enat @ A @ (zero_zero @ extended_enat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[619])).
% 74.26/25.29  thf(331,axiom,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ A @ (plus_plus @ nat @ B @ C)) = (plus_plus @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_add__mult__distrib2)).
% 74.26/25.29  thf(1907,plain,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ A @ (plus_plus @ nat @ B @ C)) = (plus_plus @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])).
% 74.26/25.29  thf(164,axiom,((ordere8940638589300402666id_add @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_32)).
% 74.26/25.29  thf(1323,plain,((ordere8940638589300402666id_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
% 74.26/25.29  thf(34,axiom,((one @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oone)).
% 74.26/25.29  thf(917,plain,((one @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
% 74.26/25.29  thf(358,axiom,((semiri3467727345109120633visors @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors_265)).
% 74.26/25.29  thf(1992,plain,((semiri3467727345109120633visors @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])).
% 74.26/25.29  thf(522,axiom,((numeral @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral_100)).
% 74.26/25.29  thf(2466,plain,((numeral @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[522])).
% 74.26/25.29  thf(750,axiom,(((times_times @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_times__enat__simps_I2_J)).
% 74.26/25.29  thf(3248,plain,(((times_times @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[750])).
% 74.26/25.29  thf(84,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (((plus_plus @ TA @ A @ B) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_add__nonpos__eq__0__iff)).
% 74.26/25.29  thf(1055,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (((plus_plus @ TA @ A @ B) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
% 74.26/25.29  thf(810,axiom,(((top_top @ extended_enat) = (extend4730790105801354508finity @ extended_enat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6249_top__enat__def)).
% 74.26/25.29  thf(3442,plain,(((top_top @ extended_enat) = (extend4730790105801354508finity @ extended_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[810])).
% 74.26/25.29  thf(377,axiom,((! [A:nat,B:nat]: (((times_times @ nat @ A @ B) = (zero_zero @ nat)) = ((A = (zero_zero @ nat)) | (B = (zero_zero @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_mult__is__0)).
% 74.26/25.29  thf(2039,plain,((! [A:nat,B:nat]: (((times_times @ nat @ A @ B) = (zero_zero @ nat)) = ((A = (zero_zero @ nat)) | (B = (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])).
% 74.26/25.29  thf(766,axiom,((! [A:extended_enat]: ((ord_less @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) = (A != (extend4730790105801354508finity @ extended_enat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_enat__ord__simps_I4_J)).
% 74.26/25.29  thf(3275,plain,((! [A:extended_enat]: ((ord_less @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) = (~ (A = (extend4730790105801354508finity @ extended_enat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[766])).
% 74.26/25.29  thf(288,axiom,(((plus_plus @ nat @ (one_one @ nat)) = suc)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_812_plus__1__eq__Suc)).
% 74.26/25.29  thf(1760,plain,(((plus_plus @ nat @ (one_one @ nat)) = (suc))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])).
% 74.26/25.29  thf(256,axiom,((! [A:nat]: ((suc @ A) != (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_Suc__neq__Zero)).
% 74.26/25.29  thf(1660,plain,((! [A:nat]: ~ ((suc @ A) = (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])).
% 74.26/25.29  thf(510,axiom,((unique1627219031080169319umeral @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Divides_Ounique__euclidean__semiring__numeral)).
% 74.26/25.29  thf(2444,plain,((unique1627219031080169319umeral @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[510])).
% 74.26/25.29  thf(148,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((dvd_dvd @ nat @ A @ B) = (dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1748_less__eq__dvd__minus)).
% 74.26/25.29  thf(1264,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((dvd_dvd @ nat @ A @ B) = (dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
% 74.26/25.29  thf(431,axiom,((zero_neq_one @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ozero__neq__one_315)).
% 74.26/25.29  thf(2217,plain,((zero_neq_one @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])).
% 74.26/25.29  thf(708,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => (((plus_plus @ nat @ (times_times @ nat @ A @ C) @ D) = (plus_plus @ nat @ (times_times @ nat @ B @ C) @ E)) = (D = (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1760_nat__eq__add__iff2)).
% 74.26/25.29  thf(3125,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => (((plus_plus @ nat @ (times_times @ nat @ A @ C) @ D) = (plus_plus @ nat @ (times_times @ nat @ B @ C) @ E)) = (D = (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[708])).
% 74.26/25.29  thf(309,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_add__neg__neg)).
% 74.26/25.29  thf(1826,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])).
% 74.26/25.29  thf(802,axiom,((semigroup_mult @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_471)).
% 74.26/25.29  thf(3410,plain,((semigroup_mult @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[802])).
% 74.26/25.29  thf(417,axiom,((comm_monoid_diff @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff)).
% 74.26/25.29  thf(2185,plain,((comm_monoid_diff @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[417])).
% 74.26/25.29  thf(769,axiom,((! [A:extended_enat]: ((plus_plus @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_plus__enat__simps_I3_J)).
% 74.26/25.29  thf(3280,plain,((! [A:extended_enat]: ((plus_plus @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[769])).
% 74.26/25.29  thf(206,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (ord_less_eq @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_enat__ord__simps_I1_J)).
% 74.26/25.29  thf(1462,plain,((! [A:nat,B:nat]: ((ord_less_eq @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (ord_less_eq @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])).
% 74.26/25.29  thf(686,axiom,((! [TA: $tType]: ((linordered_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_935_mult__right__less__imp__less)).
% 74.26/25.29  thf(3043,plain,((! [TA: $tType]: ((linordered_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[686])).
% 74.26/25.29  thf(48,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ~ (ord_less_eq @ TA @ (numeral_numeral @ TA @ A) @ (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_not__numeral__le__zero)).
% 74.26/25.29  thf(949,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ~ (ord_less_eq @ TA @ (numeral_numeral @ TA @ A) @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
% 74.26/25.29  thf(560,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ (times_times @ extended_enat @ A @ B)) = ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ A) & (ord_less @ extended_enat @ (zero_zero @ extended_enat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_enat__0__less__mult__iff)).
% 74.26/25.29  thf(2571,plain,((! [A:extended_enat,B:extended_enat]: ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ (times_times @ extended_enat @ A @ B)) = ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ A) & (ord_less @ extended_enat @ (zero_zero @ extended_enat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[560])).
% 74.26/25.29  thf(501,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_846_mult__neg__neg)).
% 74.26/25.29  thf(2420,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])).
% 74.26/25.29  thf(298,axiom,((linordered_semiring @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__semiring_283)).
% 74.26/25.29  thf(1800,plain,((linordered_semiring @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])).
% 74.26/25.29  thf(12,axiom,((! [A:nat,B:nat,C:(nat > int),D:int]: ((! [E:nat]: (((ord_less_eq @ nat @ A @ E) & (ord_less @ nat @ E @ B)) => (ord_less_eq @ int @ (abs_abs @ int @ (minus_minus @ int @ (C @ (suc @ E)) @ (C @ E))) @ (one_one @ int)))) => ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ int @ (C @ A) @ D) => ((ord_less_eq @ int @ D @ (C @ B)) => (? [E:nat]: ((ord_less_eq @ nat @ A @ E) & (ord_less_eq @ nat @ E @ B) & ((C @ E) = D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2784_nat__intermed__int__val)).
% 74.26/25.29  thf(849,plain,((! [A:nat,B:nat,C:(nat > int),D:int]: ((! [E:nat]: (((ord_less_eq @ nat @ A @ E) & (ord_less @ nat @ E @ B)) => (ord_less_eq @ int @ (abs_abs @ int @ (minus_minus @ int @ (C @ (suc @ E)) @ (C @ E))) @ (one_one @ int)))) => ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ int @ (C @ A) @ D) => ((ord_less_eq @ int @ D @ (C @ B)) => (? [E:nat]: ((ord_less_eq @ nat @ A @ E) & (ord_less_eq @ nat @ E @ B) & ((C @ E) = D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 74.26/25.29  thf(850,plain,((! [A:nat,B:nat,C:(nat > int)]: ((! [D:nat]: (((ord_less_eq @ nat @ A @ D) & (ord_less @ nat @ D @ B)) => (ord_less_eq @ int @ (abs_abs @ int @ (minus_minus @ int @ (C @ (suc @ D)) @ (C @ D))) @ (one_one @ int)))) => ((ord_less_eq @ nat @ A @ B) => (! [D:int]: ((ord_less_eq @ int @ (C @ A) @ D) => ((ord_less_eq @ int @ D @ (C @ B)) => (? [E:nat]: ((ord_less_eq @ nat @ A @ E) & (ord_less_eq @ nat @ E @ B) & ((C @ E) = D)))))))))),inference(miniscope,[status(thm)],[849])).
% 74.26/25.29  thf(851,plain,(! [D:int,C:(nat > int),B:nat,A:nat] : ((((ord_less_eq @ nat @ A @ (sk2 @ (C) @ B @ A)) | (sk1 @ A @ B @ C)) & ((ord_less @ nat @ (sk2 @ (C) @ B @ A) @ B) | (sk1 @ A @ B @ C)) & (~ (ord_less_eq @ int @ (abs_abs @ int @ (minus_minus @ int @ (C @ (suc @ (sk2 @ (C) @ B @ A))) @ (C @ (sk2 @ (C) @ B @ A)))) @ (one_one @ int)) | (sk1 @ A @ B @ C)) & (~ (sk1 @ A @ B @ C) | ~ (ord_less_eq @ nat @ A @ B) | ~ (ord_less_eq @ int @ (C @ A) @ D) | ~ (ord_less_eq @ int @ D @ (C @ B)) | (ord_less_eq @ nat @ A @ (sk3 @ D @ (C) @ B @ A))) & (~ (sk1 @ A @ B @ C) | ~ (ord_less_eq @ nat @ A @ B) | ~ (ord_less_eq @ int @ (C @ A) @ D) | ~ (ord_less_eq @ int @ D @ (C @ B)) | (ord_less_eq @ nat @ (sk3 @ D @ (C) @ B @ A) @ B)) & (~ (sk1 @ A @ B @ C) | ~ (ord_less_eq @ nat @ A @ B) | ~ (ord_less_eq @ int @ (C @ A) @ D) | ~ (ord_less_eq @ int @ D @ (C @ B)) | ((C @ (sk3 @ D @ (C) @ B @ A)) = D))))),inference(cnf,[status(esa)],[850])).
% 74.26/25.29  thf(853,plain,(! [C:(nat > int),B:nat,A:nat] : ((ord_less_eq @ nat @ A @ (sk2 @ (C) @ B @ A)) | (sk1 @ A @ B @ C))),inference(cnfConj,[status(thm)],[851])).
% 74.26/25.29  thf(181,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (suc @ B) @ A) = (suc @ (minus_minus @ nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1733_Suc__diff__le)).
% 74.26/25.29  thf(1379,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (suc @ B) @ A) = (suc @ (minus_minus @ nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])).
% 74.26/25.29  thf(493,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ A @ (plus_plus @ nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_trans__le__add2)).
% 74.26/25.29  thf(2403,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ A @ (plus_plus @ nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])).
% 74.26/25.29  thf(17,axiom,(((plus_plus @ nat) = (^ [A:nat,B:nat]: (if @ nat @ (A = (zero_zero @ nat)) @ B @ (suc @ (plus_plus @ nat @ (minus_minus @ nat @ A @ (one_one @ nat)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1772_add__eq__if)).
% 74.26/25.29  thf(870,plain,(((plus_plus @ nat) = (^ [A:nat,B:nat]: (if @ nat @ (A = (zero_zero @ nat)) @ B @ (suc @ (plus_plus @ nat @ (minus_minus @ nat @ A @ (one_one @ nat)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 74.26/25.29  thf(210,axiom,((ordere2520102378445227354miring @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oordered__comm__semiring)).
% 74.26/25.29  thf(1479,plain,((ordere2520102378445227354miring @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])).
% 74.26/25.29  thf(239,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (plus_plus @ nat @ B @ C) @ A) = (plus_plus @ nat @ (minus_minus @ nat @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1740_Nat_Odiff__add__assoc2)).
% 74.26/25.29  thf(1572,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (plus_plus @ nat @ B @ C) @ A) = (plus_plus @ nat @ (minus_minus @ nat @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
% 74.26/25.29  thf(66,axiom,((! [A:nat]: ((ord_max @ nat @ (zero_zero @ nat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4830_max__nat_Oleft__neutral)).
% 74.26/25.29  thf(1013,plain,((! [A:nat]: ((ord_max @ nat @ (zero_zero @ nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
% 74.26/25.29  thf(184,axiom,((ring_1 @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oring__1_339)).
% 74.26/25.29  thf(1398,plain,((ring_1 @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
% 74.26/25.29  thf(571,axiom,((! [A:$o,B:$o,C:$o,D:$o]: (((vEBT_Leaf @ A @ B) = (vEBT_Leaf @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_VEBT_Oinject_I2_J)).
% 74.26/25.29  thf(2602,plain,((! [A:$o,B:$o,C:$o,D:$o]: (((vEBT_Leaf @ A @ B) = (vEBT_Leaf @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[571])).
% 74.26/25.29  thf(2621,plain,((((vEBT_Leaf @ ($false) @ ($false)) = (vEBT_Leaf @ ($true) @ ($false))) = ((($false) = ($true)) & (($false) = ($false))))),inference(instance,[status(thm)],[2602])).
% 74.26/25.29  thf(2622,plain,((~ ((vEBT_Leaf @ ($false) @ ($false)) = (vEBT_Leaf @ ($true) @ ($false))))),inference(simp,[status(thm)],[2621])).
% 74.26/25.29  thf(2635,plain,(((vEBT_Leaf @ ($false) @ ($false)) != (vEBT_Leaf @ ($true) @ ($false)))),inference(lifteq,[status(thm)],[2622])).
% 74.26/25.29  thf(237,axiom,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((suc @ (minus_minus @ nat @ A @ (suc @ (zero_zero @ nat)))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1699_Suc__pred)).
% 74.26/25.29  thf(1568,plain,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((suc @ (minus_minus @ nat @ A @ (suc @ (zero_zero @ nat)))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
% 74.26/25.29  thf(347,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => ((suc @ (minus_minus @ nat @ B @ (suc @ A))) = (minus_minus @ nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1731_Suc__diff__Suc)).
% 74.26/25.29  thf(1963,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => ((suc @ (minus_minus @ nat @ B @ (suc @ A))) = (minus_minus @ nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])).
% 74.26/25.29  thf(725,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (times_times @ TA @ A @ B)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ (one_one @ TA) @ B)) & ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => (ord_less @ TA @ B @ (one_one @ TA))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1041_mult__less__cancel__left1)).
% 74.26/25.29  thf(3180,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (times_times @ TA @ A @ B)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ (one_one @ TA) @ B)) & ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => (ord_less @ TA @ B @ (one_one @ TA))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[725])).
% 74.26/25.29  thf(743,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_943_mult__less__le__imp__less)).
% 74.26/25.29  thf(3231,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[743])).
% 74.26/25.29  thf(99,axiom,((! [A:nat]: ((minus_minus @ nat @ (suc @ A) @ (one_one @ nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1696_diff__Suc__1)).
% 74.26/25.29  thf(1100,plain,((! [A:nat]: ((minus_minus @ nat @ (suc @ A) @ (one_one @ nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])).
% 74.26/25.29  thf(1,conjecture,(((vEBT_VEBT_elim_dead @ summarya @ (extend4730790105801354508finity @ extended_enat)) = summarya)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 74.26/25.29  thf(2,negated_conjecture,((~ ((vEBT_VEBT_elim_dead @ summarya @ (extend4730790105801354508finity @ extended_enat)) = summarya))),inference(neg_conjecture,[status(cth)],[1])).
% 74.26/25.29  thf(817,plain,((~ ((vEBT_VEBT_elim_dead @ summarya @ (extend4730790105801354508finity @ extended_enat)) = summarya))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 74.26/25.29  thf(575,axiom,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounde4967611905675639751up_bot @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__sup__bot)).
% 74.26/25.29  thf(2691,plain,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounde4967611905675639751up_bot @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[575])).
% 74.26/25.29  thf(545,axiom,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ B) @ C) @ (plus_plus @ TA @ (times_times @ TA @ D @ B) @ E)) = (ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ (minus_minus @ TA @ A @ D) @ B) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1631_ordered__ring__class_Ole__add__iff1)).
% 74.26/25.29  thf(2520,plain,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ B) @ C) @ (plus_plus @ TA @ (times_times @ TA @ D @ B) @ E)) = (ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ (minus_minus @ TA @ A @ D) @ B) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[545])).
% 74.26/25.29  thf(589,axiom,((! [TA: $tType]: ((ab_semigroup_mult @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ (times_times @ TA @ A @ B) @ C) = (times_times @ TA @ A @ (times_times @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_ab__semigroup__mult__class_Omult__ac_I1_J)).
% 74.26/25.29  thf(2730,plain,((! [TA: $tType]: ((ab_semigroup_mult @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ (times_times @ TA @ A @ B) @ C) = (times_times @ TA @ A @ (times_times @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[589])).
% 74.26/25.29  thf(370,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/sandbox2/benchmark/theBenchmark.p',fact_491_add__gr__0)).
% 74.26/25.29  thf(2024,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)],[370])).
% 74.26/25.29  thf(253,axiom,((! [A:nat,B:nat]: (((one_one @ nat) = (times_times @ nat @ A @ B)) = ((A = (one_one @ nat)) & (B = (one_one @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_nat__1__eq__mult__iff)).
% 74.26/25.29  thf(1641,plain,((! [A:nat,B:nat]: (((one_one @ nat) = (times_times @ nat @ A @ B)) = ((A = (one_one @ nat)) & (B = (one_one @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])).
% 74.26/25.29  thf(761,axiom,((lattice @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Olattice_489)).
% 74.26/25.29  thf(3268,plain,((lattice @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[761])).
% 74.26/25.29  thf(755,axiom,((! [A:extended_enat]: ((ord_less_eq @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (A = (extend4730790105801354508finity @ extended_enat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_enat__ord__simps_I5_J)).
% 74.26/25.29  thf(3258,plain,((! [A:extended_enat]: ((ord_less_eq @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (A = (extend4730790105801354508finity @ extended_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[755])).
% 74.26/25.29  thf(416,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => ((! [D:nat]: (A @ D @ (zero_zero @ nat))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ D @ (plus_plus @ nat @ D @ E)))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1307_Euclid__induct)).
% 74.26/25.29  thf(2178,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => ((! [D:nat]: (A @ D @ (zero_zero @ nat))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ D @ (plus_plus @ nat @ D @ E)))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])).
% 74.26/25.29  thf(732,axiom,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA,B:TA]: ((! [C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ A @ (plus_plus @ TA @ B @ C)))) => (ord_less_eq @ TA @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_944_field__le__epsilon)).
% 74.26/25.29  thf(3199,plain,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA,B:TA]: ((! [C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ A @ (plus_plus @ TA @ B @ C)))) => (ord_less_eq @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[732])).
% 74.26/25.29  thf(392,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => (? [C:nat]: (B = (plus_plus @ nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_le__Suc__ex)).
% 74.26/25.29  thf(2090,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)],[392])).
% 74.26/25.29  thf(719,axiom,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_832_mult__mono)).
% 74.26/25.29  thf(3163,plain,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[719])).
% 74.26/25.29  thf(816,axiom,((power @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Power_Opower_494)).
% 74.26/25.29  thf(3453,plain,((power @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[816])).
% 74.26/25.29  thf(636,axiom,((! [A:int]: ((ord_less_eq @ int @ (zero_zero @ int) @ A) => (ord_less @ int @ (zero_zero @ int) @ (plus_plus @ int @ (one_one @ int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_le__imp__0__less)).
% 74.26/25.29  thf(2880,plain,((! [A:int]: ((ord_less_eq @ int @ (zero_zero @ int) @ A) => (ord_less @ int @ (zero_zero @ int) @ (plus_plus @ int @ (one_one @ int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[636])).
% 74.26/25.29  thf(310,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less @ nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_nat__less__induct)).
% 74.26/25.29  thf(1828,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less @ nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])).
% 74.26/25.29  thf(374,axiom,((linord6961819062388156250ring_1 @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semiring__1)).
% 74.26/25.29  thf(2034,plain,((linord6961819062388156250ring_1 @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])).
% 74.26/25.29  thf(4,axiom,((! [A:real,B:real,C:real,D:real]: ((A = B) => ((ord_less_eq @ real @ (abs_abs @ real @ C) @ D) => (ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (plus_plus @ real @ A @ C) @ B)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2657_sin__bound__lemma)).
% 74.26/25.29  thf(821,plain,((! [A:real,B:real,C:real,D:real]: ((A = B) => ((ord_less_eq @ real @ (abs_abs @ real @ C) @ D) => (ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (plus_plus @ real @ A @ C) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 74.26/25.29  thf(214,axiom,((! [TA: $tType]: ((linordered_ring @ TA) => (! [A:TA]: ~ (ord_less @ TA @ (times_times @ TA @ A @ A) @ (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_not__square__less__zero)).
% 74.26/25.29  thf(1489,plain,((! [TA: $tType]: ((linordered_ring @ TA) => (! [A:TA]: ~ (ord_less @ TA @ (times_times @ TA @ A @ A) @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
% 74.26/25.29  thf(656,axiom,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less_eq @ TA @ A @ B) & (ord_less_eq @ TA @ C @ D)) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_add__mono__thms__linordered__semiring_I1_J)).
% 74.26/25.29  thf(2950,plain,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less_eq @ TA @ A @ B) & (ord_less_eq @ TA @ C @ D)) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[656])).
% 74.26/25.29  thf(340,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ C) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ B) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_838_add__decreasing)).
% 74.26/25.29  thf(1946,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ C) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])).
% 74.26/25.29  thf(207,axiom,((semigroup_add @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_80)).
% 74.26/25.29  thf(1465,plain,((semigroup_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
% 74.26/25.29  thf(156,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ A @ C)) = (minus_minus @ nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1722_Nat_Odiff__cancel)).
% 74.26/25.29  thf(1302,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ A @ C)) = (minus_minus @ nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
% 74.26/25.29  thf(257,axiom,((! [A:int]: ((times_times @ int @ A @ (zero_zero @ int)) = (zero_zero @ int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_times__int__code_I1_J)).
% 74.26/25.29  thf(1664,plain,((! [A:int]: ((times_times @ int @ A @ (zero_zero @ int)) = (zero_zero @ int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])).
% 74.26/25.29  thf(468,axiom,((one @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone_103)).
% 74.26/25.29  thf(2324,plain,((one @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])).
% 74.26/25.29  thf(371,axiom,((dvd @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Odvd_349)).
% 74.26/25.29  thf(2027,plain,((dvd @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[371])).
% 74.26/25.29  thf(458,axiom,((! [A:nat]: (ord_less_eq @ nat @ (zero_zero @ nat) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_less__eq__nat_Osimps_I1_J)).
% 74.26/25.29  thf(2291,plain,((! [A:nat]: (ord_less_eq @ nat @ (zero_zero @ nat) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[458])).
% 74.26/25.29  thf(69,axiom,((semiring_numeral @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Osemiring__numeral_79)).
% 74.26/25.29  thf(1020,plain,((semiring_numeral @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
% 74.26/25.29  thf(346,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ (minus_minus @ nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1714_less__imp__diff__less)).
% 74.26/25.29  thf(1960,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ (minus_minus @ nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])).
% 74.26/25.29  thf(701,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => ((ord_less_eq @ TA) = (^ [A:TA,B:TA]: ? [C:TA]: (B = (plus_plus @ TA @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_le__iff__add)).
% 74.26/25.29  thf(3093,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => ((ord_less_eq @ TA) = (^ [A:TA,B:TA]: ? [C:TA]: (B = (plus_plus @ TA @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[701])).
% 74.26/25.29  thf(557,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = ((ord_less @ nat @ (zero_zero @ nat) @ A) => (ord_less_eq @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_nat__mult__le__cancel__disj)).
% 74.26/25.29  thf(2555,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = ((ord_less @ nat @ (zero_zero @ nat) @ A) => (ord_less_eq @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[557])).
% 74.26/25.29  thf(774,axiom,((strict7427464778891057005id_add @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__comm__monoid__add_452)).
% 74.26/25.29  thf(3290,plain,((strict7427464778891057005id_add @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[774])).
% 74.26/25.29  thf(472,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ((ord_max @ TA @ (numeral_numeral @ TA @ A) @ (zero_zero @ TA)) = (numeral_numeral @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4773_max__0__1_I4_J)).
% 74.26/25.29  thf(2335,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ((ord_max @ TA @ (numeral_numeral @ TA @ A) @ (zero_zero @ TA)) = (numeral_numeral @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])).
% 74.26/25.29  thf(50,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_less__SucI)).
% 74.26/25.29  thf(966,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
% 74.26/25.29  thf(120,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (ord_less @ nat @ (minus_minus @ nat @ A @ (suc @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1755_diff__Suc__less)).
% 74.26/25.29  thf(1183,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (ord_less @ nat @ (minus_minus @ nat @ A @ (suc @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
% 74.26/25.29  thf(386,axiom,((! [A:nat]: ~ (ord_less @ nat @ A @ (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_less__nat__zero__code)).
% 74.26/25.29  thf(2073,plain,((! [A:nat]: ~ (ord_less @ nat @ A @ (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])).
% 74.26/25.29  thf(313,axiom,((semiring_0 @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__0)).
% 74.26/25.29  thf(1843,plain,((semiring_0 @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])).
% 74.26/25.29  thf(440,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (~ (ord_less @ TA @ (zero_zero @ TA) @ (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_less__numeral__extra_I3_J)).
% 74.26/25.30  thf(2245,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (~ (ord_less @ TA @ (zero_zero @ TA) @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[440])).
% 74.26/25.30  thf(2246,plain,(! [TA:$tType] : ((~ (linord181362715937106298miring @ TA)) | (~ (ord_less @ TA @ (zero_zero @ TA) @ (zero_zero @ TA))))),inference(cnf,[status(esa)],[2245])).
% 74.26/25.30  thf(3535,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less @ TA @ (zero_zero @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ extended_enat) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1256,2246])).
% 74.26/25.30  thf(3536,plain,(! [TA:$tType] : ((~ (ord_less @ TA @ (zero_zero @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ extended_enat) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3535])).
% 74.26/25.30  thf(3537,plain,((~ (ord_less @ extended_enat @ (zero_zero @ extended_enat) @ (zero_zero @ extended_enat)))),inference(pattern_uni,[status(thm)],[3536:[bind_type(TA,$thf(extended_enat))]])).
% 74.26/25.30  thf(180,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ~ (ord_less @ TA @ (numeral_numeral @ TA @ A) @ (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_not__numeral__less__zero)).
% 74.26/25.30  thf(1377,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ~ (ord_less @ TA @ (numeral_numeral @ TA @ A) @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])).
% 74.26/25.30  thf(326,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ (suc @ A) @ B) => (ord_less_eq @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_723_Suc__leD)).
% 74.26/25.30  thf(1896,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)],[326])).
% 74.26/25.30  thf(530,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (~ (ord_less_eq @ TA @ (one_one @ TA) @ (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_not__one__le__zero)).
% 74.26/25.30  thf(2482,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (~ (ord_less_eq @ TA @ (one_one @ TA) @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[530])).
% 74.26/25.30  thf(2483,plain,(! [TA:$tType] : ((~ (linord181362715937106298miring @ TA)) | (~ (ord_less_eq @ TA @ (one_one @ TA) @ (zero_zero @ TA))))),inference(cnf,[status(esa)],[2482])).
% 74.26/25.30  thf(480,axiom,((! [A:nat,B:nat]: ((~ (ord_less @ nat @ A @ B)) = (ord_less @ nat @ B @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_not__less__eq)).
% 74.26/25.30  thf(2371,plain,((! [A:nat,B:nat]: ((~ (ord_less @ nat @ A @ B)) = (ord_less @ nat @ B @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[480])).
% 74.26/25.30  thf(222,axiom,((! [A:nat]: ~ (ord_less @ nat @ A @ (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_751_bot__nat__0_Oextremum__strict)).
% 74.26/25.30  thf(1526,plain,((! [A:nat]: ~ (ord_less @ nat @ A @ (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
% 74.26/25.30  thf(748,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ A) = (((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ B @ (one_one @ TA))) & ((ord_less @ TA @ A @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (one_one @ TA) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1038_mult__le__cancel__left2)).
% 74.26/25.30  thf(3243,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ A) = (((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ B @ (one_one @ TA))) & ((ord_less @ TA @ A @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (one_one @ TA) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[748])).
% 74.26/25.30  thf(790,axiom,((monoid_add @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Omonoid__add_486)).
% 74.26/25.30  thf(3327,plain,((monoid_add @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[790])).
% 74.26/25.30  thf(246,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((dvd_dvd @ nat @ A @ B) => ((dvd_dvd @ nat @ A @ C) => ((((times_times @ nat @ B @ D) = (plus_plus @ nat @ (times_times @ nat @ C @ E) @ A)) | ((times_times @ nat @ C @ D) = (plus_plus @ nat @ (times_times @ nat @ B @ E) @ A))) => (? [F:nat,G:nat]: ((dvd_dvd @ nat @ A @ B) & (dvd_dvd @ nat @ A @ (plus_plus @ nat @ B @ C)) & (((times_times @ nat @ B @ F) = (plus_plus @ nat @ (times_times @ nat @ (plus_plus @ nat @ B @ C) @ G) @ A)) | ((times_times @ nat @ (plus_plus @ nat @ B @ C) @ F) = (plus_plus @ nat @ (times_times @ nat @ B @ G) @ A)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1440_bezout__lemma__nat)).
% 74.26/25.30  thf(1600,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((dvd_dvd @ nat @ A @ B) => ((dvd_dvd @ nat @ A @ C) => ((((times_times @ nat @ B @ D) = (plus_plus @ nat @ (times_times @ nat @ C @ E) @ A)) | ((times_times @ nat @ C @ D) = (plus_plus @ nat @ (times_times @ nat @ B @ E) @ A))) => (? [F:nat,G:nat]: ((dvd_dvd @ nat @ A @ B) & (dvd_dvd @ nat @ A @ (plus_plus @ nat @ B @ C)) & (((times_times @ nat @ B @ F) = (plus_plus @ nat @ (times_times @ nat @ (plus_plus @ nat @ B @ C) @ G) @ A)) | ((times_times @ nat @ (plus_plus @ nat @ B @ C) @ F) = (plus_plus @ nat @ (times_times @ nat @ B @ G) @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])).
% 74.26/25.30  thf(736,axiom,((! [TA: $tType,TB: $tType]: ((comple592849572758109894attice @ TA) => (comple592849572758109894attice @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_Ocomplete__distrib__lattice)).
% 74.26/25.30  thf(3211,plain,((! [TA: $tType,TB: $tType]: ((comple592849572758109894attice @ TA) => (comple592849572758109894attice @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[736])).
% 74.26/25.30  thf(565,axiom,((! [TA: $tType]: ((linordered_ring @ TA) => (! [A:TA,B:TA]: ~ (ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B)) @ (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_not__sum__squares__lt__zero)).
% 74.26/25.30  thf(2586,plain,((! [TA: $tType]: ((linordered_ring @ TA) => (! [A:TA,B:TA]: ~ (ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B)) @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[565])).
% 74.26/25.30  thf(351,axiom,((ab_semigroup_add @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_67)).
% 74.26/25.30  thf(1975,plain,((ab_semigroup_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])).
% 74.26/25.30  thf(600,axiom,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (order_mono @ TA @ TA @ (times_times @ TA @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8097_mono__mult)).
% 74.26/25.30  thf(2762,plain,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (order_mono @ TA @ TA @ (times_times @ TA @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[600])).
% 74.26/25.30  thf(540,axiom,((! [TA: $tType]: ((comm_monoid_diff @ TA) => (! [A:TA]: ((minus_minus @ TA @ (zero_zero @ TA) @ A) = (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1515_zero__diff)).
% 74.26/25.30  thf(2508,plain,((! [TA: $tType]: ((comm_monoid_diff @ TA) => (! [A:TA]: ((minus_minus @ TA @ (zero_zero @ TA) @ A) = (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[540])).
% 74.26/25.30  thf(661,axiom,((! [A:int,B:(int > $o),C:(int > $o)]: ((ord_less @ int @ (zero_zero @ int) @ A) => ((! [D:int,E:int]: ((B @ D) = (B @ (minus_minus @ int @ D @ (times_times @ int @ E @ A))))) => ((? [D:int]: ! [E:int]: ((ord_less @ int @ D @ E) => ((C @ E) = (B @ E)))) => ((? [D:int]: (B @ D)) => (? [D:int]: (C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1645_plusinfinity)).
% 74.26/25.30  thf(2964,plain,((! [A:int,B:(int > $o),C:(int > $o)]: ((ord_less @ int @ (zero_zero @ int) @ A) => ((! [D:int,E:int]: ((B @ D) = (B @ (minus_minus @ int @ D @ (times_times @ int @ E @ A))))) => ((? [D:int]: ! [E:int]: ((ord_less @ int @ D @ E) => ((C @ E) = (B @ E)))) => ((? [D:int]: (B @ D)) => (? [D:int]: (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[661])).
% 74.26/25.30  thf(546,axiom,((! [TA: $tType]: ((monoid_add @ TA) => (! [A:TA]: ((plus_plus @ TA @ A @ (zero_zero @ TA)) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_add_Oright__neutral)).
% 74.26/25.30  thf(2523,plain,((! [TA: $tType]: ((monoid_add @ TA) => (! [A:TA]: ((plus_plus @ TA @ A @ (zero_zero @ TA)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[546])).
% 74.26/25.30  thf(548,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ B) => (~ (! [C:TA]: ((B = (plus_plus @ TA @ A @ C)) => (C = (zero_zero @ TA)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_canonically__ordered__monoid__add__class_OlessE)).
% 74.26/25.30  thf(2530,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ B) => (~ (! [C:TA]: ((B = (plus_plus @ TA @ A @ C)) => (C = (zero_zero @ TA)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[548])).
% 74.26/25.30  thf(174,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq @ nat @ A @ B) => ((C @ B) => ((! [D:nat]: ((ord_less_eq @ nat @ A @ D) => ((ord_less @ nat @ D @ B) => ((C @ (suc @ D)) => (C @ D))))) => (C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_797_inc__induct)).
% 74.26/25.30  thf(1345,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq @ nat @ A @ B) => ((C @ B) => ((! [D:nat]: ((ord_less_eq @ nat @ A @ D) => ((ord_less @ nat @ D @ B) => ((C @ (suc @ D)) => (C @ D))))) => (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
% 74.26/25.30  thf(614,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus @ nat @ B @ C)) = (((ord_less @ nat @ B @ C) => (A @ (zero_zero @ nat))) & ! [D:nat]: ((B = (plus_plus @ nat @ C @ D)) => (A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1756_nat__diff__split)).
% 74.26/25.30  thf(2799,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus @ nat @ B @ C)) = (((ord_less @ nat @ B @ C) => (A @ (zero_zero @ nat))) & ! [D:nat]: ((B = (plus_plus @ nat @ C @ D)) => (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[614])).
% 74.26/25.30  thf(455,axiom,((ordere8940638589300402666id_add @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__cancel__comm__monoid__add)).
% 74.26/25.30  thf(2286,plain,((ordere8940638589300402666id_add @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])).
% 74.26/25.30  thf(596,axiom,((! [A:extended_enat,B:extended_enat]: (((times_times @ extended_enat @ A @ B) = (extend4730790105801354508finity @ extended_enat)) = (((A = (extend4730790105801354508finity @ extended_enat)) & (B != (zero_zero @ extended_enat))) | ((B = (extend4730790105801354508finity @ extended_enat)) & (A != (zero_zero @ extended_enat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_imult__is__infinity)).
% 74.26/25.30  thf(2750,plain,((! [A:extended_enat,B:extended_enat]: (((times_times @ extended_enat @ A @ B) = (extend4730790105801354508finity @ extended_enat)) = (((A = (extend4730790105801354508finity @ extended_enat)) & ~ (B = (zero_zero @ extended_enat))) | ((B = (extend4730790105801354508finity @ extended_enat)) & ~ (A = (zero_zero @ extended_enat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[596])).
% 74.26/25.30  thf(187,axiom,((! [A:nat]: ((plus_plus @ nat @ A @ (zero_zero @ nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_Nat_Oadd__0__right)).
% 74.26/25.30  thf(1405,plain,((! [A:nat]: ((plus_plus @ nat @ A @ (zero_zero @ nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])).
% 74.26/25.30  thf(143,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq @ nat @ D @ C))) => (~ (! [D:nat]: ((A @ D) => (~ (! [E:nat]: ((A @ E) => (ord_less_eq @ nat @ E @ D))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_bounded__Max__nat)).
% 74.26/25.30  thf(1242,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq @ nat @ D @ C))) => (~ (! [D:nat]: ((A @ D) => (~ (! [E:nat]: ((A @ E) => (ord_less_eq @ nat @ E @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
% 74.26/25.30  thf(798,axiom,((wellorder @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Owellorder_478)).
% 74.26/25.30  thf(3406,plain,((wellorder @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[798])).
% 74.26/25.30  thf(425,axiom,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ (minus_minus @ nat @ A @ B) @ C) = (minus_minus @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1727_diff__mult__distrib)).
% 74.26/25.30  thf(2205,plain,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ (minus_minus @ nat @ A @ B) @ C) = (minus_minus @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])).
% 74.26/25.30  thf(657,axiom,((! [TA: $tType]: ((zero_neq_one @ TA) => ((zero_zero @ TA) != (one_one @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_zero__neq__one)).
% 74.26/25.30  thf(2952,plain,((! [TA: $tType]: ((zero_neq_one @ TA) => (~ ((zero_zero @ TA) = (one_one @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[657])).
% 74.26/25.30  thf(2953,plain,(! [TA:$tType] : ((~ (zero_neq_one @ TA)) | (~ ((zero_zero @ TA) = (one_one @ TA))))),inference(cnf,[status(esa)],[2952])).
% 74.26/25.30  thf(2954,plain,(! [TA:$tType] : (((zero_zero @ TA) != (one_one @ TA)) | (~ (zero_neq_one @ TA)))),inference(lifteq,[status(thm)],[2953])).
% 74.26/25.30  thf(715,axiom,((! [TA: $tType]: ((mult_zero @ TA) => (! [A:TA]: ((times_times @ TA @ A @ (zero_zero @ TA)) = (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_mult__zero__right)).
% 74.26/25.30  thf(3151,plain,((! [TA: $tType]: ((mult_zero @ TA) => (! [A:TA]: ((times_times @ TA @ A @ (zero_zero @ TA)) = (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[715])).
% 74.26/25.30  thf(676,axiom,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((A = B) & (C = D)) => ((plus_plus @ TA @ A @ C) = (plus_plus @ TA @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__mono__thms__linordered__semiring_I4_J)).
% 74.26/25.30  thf(3011,plain,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((A = B) & (C = D)) => ((plus_plus @ TA @ A @ C) = (plus_plus @ TA @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[676])).
% 74.26/25.30  thf(45,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ (suc @ B)) => (ord_less @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_Suc__less__SucD)).
% 74.26/25.30  thf(942,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ (suc @ B)) => (ord_less @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
% 74.26/25.30  thf(266,axiom,((! [A:nat,B:nat]: ((minus_minus @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (extended_enat2 @ (minus_minus @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1687_idiff__enat__enat)).
% 74.26/25.30  thf(1691,plain,((! [A:nat,B:nat]: ((minus_minus @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (extended_enat2 @ (minus_minus @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])).
% 74.26/25.30  thf(561,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ B @ C)) & ((ord_less @ TA @ A @ (zero_zero @ TA)) => (ord_less_eq @ TA @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_930_mult__le__cancel__left)).
% 74.26/25.30  thf(2574,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ B @ C)) & ((ord_less @ TA @ A @ (zero_zero @ TA)) => (ord_less_eq @ TA @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[561])).
% 74.26/25.30  thf(727,axiom,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__right__mono)).
% 74.26/25.30  thf(3186,plain,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[727])).
% 74.26/25.30  thf(401,axiom,((! [A:(nat > $o),B:nat]: ((A @ (zero_zero @ nat)) => ((! [C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ C) => ((~ (A @ C)) => (? [D:nat]: ((ord_less @ nat @ D @ C) & ~ (A @ D)))))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_757_infinite__descent0)).
% 74.26/25.30  thf(2118,plain,((! [A:(nat > $o),B:nat]: ((A @ (zero_zero @ nat)) => ((! [C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ C) => ((~ (A @ C)) => (? [D:nat]: ((ord_less @ nat @ D @ C) & ~ (A @ D)))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])).
% 74.26/25.30  thf(172,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ (minus_minus @ nat @ B @ A)) = (ord_less_eq @ nat @ (plus_plus @ nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1742_Nat_Ole__diff__conv2)).
% 74.26/25.30  thf(1338,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ (minus_minus @ nat @ B @ A)) = (ord_less_eq @ nat @ (plus_plus @ nat @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
% 74.26/25.30  thf(363,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ C) => ((minus_minus @ nat @ (minus_minus @ nat @ B @ A) @ (minus_minus @ nat @ C @ A)) = (minus_minus @ nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1719_Nat_Odiff__diff__eq)).
% 74.26/25.30  thf(2000,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ C) => ((minus_minus @ nat @ (minus_minus @ nat @ B @ A) @ (minus_minus @ nat @ C @ A)) = (minus_minus @ nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[363])).
% 74.26/25.30  thf(684,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((A != (zero_zero @ TA)) => (ord_less @ TA @ (zero_zero @ TA) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_gr__zeroI)).
% 74.26/25.30  thf(3037,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((~ (A = (zero_zero @ TA))) => (ord_less @ TA @ (zero_zero @ TA) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[684])).
% 74.26/25.30  thf(315,axiom,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) = (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_gr0__conv__Suc)).
% 74.26/25.30  thf(1863,plain,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) = (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])).
% 74.26/25.30  thf(806,axiom,((! [A:num]: ((numeral_numeral @ extended_enat @ A) != (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_numeral__ne__infinity)).
% 74.26/25.30  thf(3435,plain,((! [A:num]: ~ ((numeral_numeral @ extended_enat @ A) = (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[806])).
% 74.26/25.30  thf(780,axiom,((strict9044650504122735259up_add @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_451)).
% 74.26/25.30  thf(3301,plain,((strict9044650504122735259up_add @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[780])).
% 74.26/25.30  thf(424,axiom,((linordered_semiring @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semiring_58)).
% 74.26/25.30  thf(2204,plain,((linordered_semiring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])).
% 74.26/25.30  thf(279,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (~ (ord_less @ TA @ (one_one @ TA) @ (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_866_not__one__less__zero)).
% 74.26/25.30  thf(1732,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (~ (ord_less @ TA @ (one_one @ TA) @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])).
% 74.26/25.30  thf(1733,plain,(! [TA:$tType] : ((~ (linord181362715937106298miring @ TA)) | (~ (ord_less @ TA @ (one_one @ TA) @ (zero_zero @ TA))))),inference(cnf,[status(esa)],[1732])).
% 74.26/25.30  thf(3529,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ extended_enat) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1256,1733])).
% 74.26/25.30  thf(3530,plain,(! [TA:$tType] : ((~ (ord_less @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ extended_enat) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3529])).
% 74.26/25.30  thf(3531,plain,((~ (ord_less @ extended_enat @ (one_one @ extended_enat) @ (zero_zero @ extended_enat)))),inference(pattern_uni,[status(thm)],[3530:[bind_type(TA,$thf(extended_enat))]])).
% 74.26/25.30  thf(127,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ (zero_zero @ nat))) => (? [C:nat]: ((ord_less_eq @ nat @ C @ B) & ! [D:nat]: ((ord_less @ nat @ D @ C) => (~ (A @ D))) & (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_911_ex__least__nat__le)).
% 74.26/25.30  thf(1199,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ (zero_zero @ nat))) => (? [C:nat]: ((ord_less_eq @ nat @ C @ B) & ! [D:nat]: ((ord_less @ nat @ D @ C) => (~ (A @ D))) & (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
% 74.26/25.30  thf(209,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less @ nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_infinite__descent)).
% 74.26/25.30  thf(1470,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less @ nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
% 74.26/25.30  thf(393,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ B) => (ord_less @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_Suc__lessD)).
% 74.26/25.30  thf(2093,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ B) => (ord_less @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[393])).
% 74.26/25.30  thf(160,axiom,((! [A:nat]: (((extended_enat2 @ A) = (zero_zero @ extended_enat)) = (A = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_enat__0__iff_I1_J)).
% 74.26/25.30  thf(1311,plain,((! [A:nat]: (((extended_enat2 @ A) = (zero_zero @ extended_enat)) = (A = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
% 74.26/25.30  thf(460,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: (ord_less @ TA @ (zero_zero @ TA) @ (numeral_numeral @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_zero__less__numeral)).
% 74.26/25.30  thf(2296,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: (ord_less @ TA @ (zero_zero @ TA) @ (numeral_numeral @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[460])).
% 74.26/25.30  thf(88,axiom,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ A @ (minus_minus @ nat @ B @ C)) = (minus_minus @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1726_diff__mult__distrib2)).
% 74.26/25.30  thf(1067,plain,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ A @ (minus_minus @ nat @ B @ C)) = (minus_minus @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
% 74.26/25.30  thf(535,axiom,((zero @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_101)).
% 74.26/25.30  thf(2496,plain,((zero @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[535])).
% 74.26/25.30  thf(610,axiom,((! [A:int,B:int]: ((ord_less_eq @ int @ (plus_plus @ int @ A @ (one_one @ int)) @ B) = (ord_less @ int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_add1__zle__eq)).
% 74.26/25.30  thf(2790,plain,((! [A:int,B:int]: ((ord_less_eq @ int @ (plus_plus @ int @ A @ (one_one @ int)) @ B) = (ord_less @ int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[610])).
% 74.26/25.30  thf(291,axiom,((! [A:int,B:int]: ((ord_less_eq @ int @ (zero_zero @ int) @ A) => ((ord_less_eq @ int @ (zero_zero @ int) @ B) => ((dvd_dvd @ int @ A @ B) => ((dvd_dvd @ int @ B @ A) => (A = B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1436_zdvd__antisym__nonneg)).
% 74.26/25.30  thf(1768,plain,((! [A:int,B:int]: ((ord_less_eq @ int @ (zero_zero @ int) @ A) => ((ord_less_eq @ int @ (zero_zero @ int) @ B) => ((dvd_dvd @ int @ A @ B) => ((dvd_dvd @ int @ B @ A) => (A = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])).
% 74.26/25.30  thf(642,axiom,((! [A:nat]: ~ (ord_less_eq @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_infinity__ileE)).
% 74.26/25.30  thf(2905,plain,((! [A:nat]: ~ (ord_less_eq @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[642])).
% 74.26/25.30  thf(70,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (minus_minus @ nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus @ nat @ (minus_minus @ nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1679_Suc__diff__diff)).
% 74.26/25.30  thf(1021,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (minus_minus @ nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus @ nat @ (minus_minus @ nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
% 74.26/25.30  thf(14,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => ((abs_abs @ TA @ (one_one @ TA)) = (one_one @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2623_abs__one)).
% 74.26/25.30  thf(862,plain,((! [TA: $tType]: ((linordered_idom @ TA) => ((abs_abs @ TA @ (one_one @ TA)) = (one_one @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 74.26/25.30  thf(407,axiom,((! [A:nat,B:(nat > $o)]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((B @ (one_one @ nat)) => ((! [C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ C) => ((B @ C) => (B @ (suc @ C))))) => (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_nat__induct__non__zero)).
% 74.26/25.30  thf(2147,plain,((! [A:nat,B:(nat > $o)]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((B @ (one_one @ nat)) => ((! [C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ C) => ((B @ C) => (B @ (suc @ C))))) => (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])).
% 74.26/25.30  thf(744,axiom,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: (ord_less_eq @ TA @ A @ (top_top @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6211_top__greatest)).
% 74.26/25.30  thf(3233,plain,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: (ord_less_eq @ TA @ A @ (top_top @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[744])).
% 74.26/25.30  thf(249,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq @ nat @ A @ B) => ((! [D:nat]: (C @ D @ D)) => ((! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_transitive__stepwise__le)).
% 74.26/25.30  thf(1619,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq @ nat @ A @ B) => ((! [D:nat]: (C @ D @ D)) => ((! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])).
% 74.26/25.30  thf(751,axiom,((! [A:extended_enat]: ((ord_max @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4818_max__enat__simps_I4_J)).
% 74.26/25.30  thf(3250,plain,((! [A:extended_enat]: ((ord_max @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[751])).
% 74.26/25.30  thf(756,axiom,((order_top @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder__top_479)).
% 74.26/25.30  thf(3261,plain,((order_top @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[756])).
% 74.26/25.30  thf(25,axiom,((! [A:nat,B:nat,C:nat]: (((times_times @ nat @ A @ B) = (times_times @ nat @ C @ B)) = ((A = C) | (B = (zero_zero @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_mult__cancel2)).
% 74.26/25.30  thf(894,plain,((! [A:nat,B:nat,C:nat]: (((times_times @ nat @ A @ B) = (times_times @ nat @ C @ B)) = ((A = C) | (B = (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 74.26/25.30  thf(590,axiom,((! [A:extended_enat]: ((minus_minus @ extended_enat @ (extended_enat2 @ (zero_zero @ nat)) @ A) = (extended_enat2 @ (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1685_idiff__enat__0)).
% 74.26/25.30  thf(2733,plain,((! [A:extended_enat]: ((minus_minus @ extended_enat @ (extended_enat2 @ (zero_zero @ nat)) @ A) = (extended_enat2 @ (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[590])).
% 74.26/25.30  thf(822,plain,((! [A:real,B:real]: ((A = B) => (! [C:real,D:real]: ((ord_less_eq @ real @ (abs_abs @ real @ C) @ D) => (ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (plus_plus @ real @ A @ C) @ B)) @ D)))))),inference(miniscope,[status(thm)],[821])).
% 74.26/25.30  thf(823,plain,(! [D:real,C:real,B:real,A:real] : ((~ (A = B)) | (~ (ord_less_eq @ real @ (abs_abs @ real @ C) @ D)) | (ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (plus_plus @ real @ A @ C) @ B)) @ D))),inference(cnf,[status(esa)],[822])).
% 74.26/25.30  thf(824,plain,(! [D:real,C:real,B:real,A:real] : ((A != B) | (~ (ord_less_eq @ real @ (abs_abs @ real @ C) @ D)) | (ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (plus_plus @ real @ A @ C) @ B)) @ D))),inference(lifteq,[status(thm)],[823])).
% 74.26/25.30  thf(825,plain,(! [C:real,B:real,A:real] : ((~ (ord_less_eq @ real @ (abs_abs @ real @ B) @ C)) | (ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (plus_plus @ real @ A @ B) @ A)) @ C))),inference(simp,[status(thm)],[824])).
% 74.26/25.30  thf(616,axiom,((! [TA: $tType]: ((semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ (plus_plus @ TA @ A @ B) @ C) = (plus_plus @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_distrib__right)).
% 74.26/25.30  thf(2805,plain,((! [TA: $tType]: ((semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ (plus_plus @ TA @ A @ B) @ C) = (plus_plus @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[616])).
% 74.26/25.30  thf(78,axiom,((linord715952674999750819strict @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semiring__1__strict)).
% 74.26/25.30  thf(1042,plain,((linord715952674999750819strict @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
% 74.26/25.30  thf(550,axiom,(((zero_zero @ extended_enat) != (one_one @ extended_enat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_zero__one__enat__neq_I1_J)).
% 74.26/25.30  thf(2539,plain,((~ ((zero_zero @ extended_enat) = (one_one @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[550])).
% 74.26/25.30  thf(2540,plain,((~ ((zero_zero @ extended_enat) = (one_one @ extended_enat)))),inference(polarity_switch,[status(thm)],[2539])).
% 74.26/25.30  thf(2541,plain,(((zero_zero @ extended_enat) != (one_one @ extended_enat))),inference(lifteq,[status(thm)],[2540])).
% 74.26/25.30  thf(284,axiom,((! [A:nat]: (ord_less @ nat @ A @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_lessI)).
% 74.26/25.30  thf(1751,plain,((! [A:nat]: (ord_less @ nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])).
% 74.26/25.30  thf(3,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ (abs_abs @ TA @ A) @ B) => ((ord_less @ TA @ (abs_abs @ TA @ C) @ D) => (ord_less @ TA @ (times_times @ TA @ (abs_abs @ TA @ A) @ (abs_abs @ TA @ C)) @ (times_times @ TA @ B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2630_abs__mult__less)).
% 74.26/25.30  thf(819,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ (abs_abs @ TA @ A) @ B) => ((ord_less @ TA @ (abs_abs @ TA @ C) @ D) => (ord_less @ TA @ (times_times @ TA @ (abs_abs @ TA @ A) @ (abs_abs @ TA @ C)) @ (times_times @ TA @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 74.26/25.30  thf(820,plain,(! [TA:$tType,D:TA,C:TA,B:TA,A:TA] : ((~ (linordered_idom @ TA)) | (~ (ord_less @ TA @ (abs_abs @ TA @ A) @ B)) | (~ (ord_less @ TA @ (abs_abs @ TA @ C) @ D)) | (ord_less @ TA @ (times_times @ TA @ (abs_abs @ TA @ A) @ (abs_abs @ TA @ C)) @ (times_times @ TA @ B @ D)))),inference(cnf,[status(esa)],[819])).
% 74.26/25.30  thf(716,axiom,((! [TA: $tType]: ((ordere8940638589300402666id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ B @ C) => (ord_less @ TA @ B @ (plus_plus @ TA @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_950_add__strict__increasing2)).
% 74.26/25.30  thf(3154,plain,((! [TA: $tType]: ((ordere8940638589300402666id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ B @ C) => (ord_less @ TA @ B @ (plus_plus @ TA @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[716])).
% 74.26/25.30  thf(711,axiom,((! [A:extended_enat]: ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ A) = (A != (zero_zero @ extended_enat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_i0__less)).
% 74.26/25.30  thf(3134,plain,((! [A:extended_enat]: ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ A) = (~ (A = (zero_zero @ extended_enat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[711])).
% 74.26/25.30  thf(194,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ((ord_max @ TA @ (numeral_numeral @ TA @ A) @ (one_one @ TA)) = (numeral_numeral @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4777_max__0__1_I6_J)).
% 74.26/25.30  thf(1423,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ((ord_max @ TA @ (numeral_numeral @ TA @ A) @ (one_one @ TA)) = (numeral_numeral @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
% 74.26/25.30  thf(700,axiom,((! [A:nat]: ~ (ord_less_eq @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_enat__ord__code_I5_J)).
% 74.26/25.30  thf(3090,plain,((! [A:nat]: ~ (ord_less_eq @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[700])).
% 74.26/25.30  thf(712,axiom,((! [TA: $tType,TB: $tType]: ((wellorder @ TB) => (! [A:(TA > TB),B:(TA > $o),C:TA]: ((! [D:TA]: ((! [E:TA]: ((ord_less @ TB @ (A @ E) @ (A @ D)) => (B @ E))) => (B @ D))) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_measure__induct__rule)).
% 74.26/25.30  thf(3137,plain,((! [TA: $tType,TB: $tType]: ((wellorder @ TB) => (! [A:(TA > TB),B:(TA > $o),C:TA]: ((! [D:TA]: ((! [E:TA]: ((ord_less @ TB @ (A @ E) @ (A @ D)) => (B @ E))) => (B @ D))) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[712])).
% 74.26/25.30  thf(634,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ E)) = (minus_minus @ nat @ D @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1764_nat__diff__add__eq2)).
% 74.26/25.30  thf(2872,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ E)) = (minus_minus @ nat @ D @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[634])).
% 74.26/25.30  thf(72,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ C) => ((ord_less_eq @ nat @ (minus_minus @ nat @ B @ A) @ (minus_minus @ nat @ C @ A)) = (ord_less_eq @ nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1720_le__diff__iff)).
% 74.26/25.30  thf(1027,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ C) => ((ord_less_eq @ nat @ (minus_minus @ nat @ B @ A) @ (minus_minus @ nat @ C @ A)) = (ord_less_eq @ nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
% 74.26/25.30  thf(681,axiom,((! [TA: $tType]: ((semiri3467727345109120633visors @ TA) => (! [A:TA,B:TA]: (((times_times @ TA @ A @ B) = (zero_zero @ TA)) => ((A = (zero_zero @ TA)) | (B = (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_divisors__zero)).
% 74.26/25.30  thf(3028,plain,((! [TA: $tType]: ((semiri3467727345109120633visors @ TA) => (! [A:TA,B:TA]: (((times_times @ TA @ A @ B) = (zero_zero @ TA)) => ((A = (zero_zero @ TA)) | (B = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[681])).
% 74.26/25.30  thf(428,axiom,((semigroup_mult @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Osemigroup__mult_302)).
% 74.26/25.30  thf(2211,plain,((semigroup_mult @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])).
% 74.26/25.30  thf(463,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less @ nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_Suc__less__eq2)).
% 74.26/25.30  thf(2313,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less @ nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[463])).
% 74.26/25.30  thf(593,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ C @ B)) = ((ord_less @ nat @ (zero_zero @ nat) @ B) => (ord_less_eq @ nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_mult__le__cancel2)).
% 74.26/25.30  thf(2741,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ C @ B)) = ((ord_less @ nat @ (zero_zero @ nat) @ B) => (ord_less_eq @ nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[593])).
% 74.26/25.30  thf(250,axiom,((monoid_add @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add_89)).
% 74.26/25.30  thf(1634,plain,((monoid_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])).
% 74.26/25.30  thf(102,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (times_times @ TA @ A @ B) @ (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_mult__neg__pos)).
% 74.26/25.30  thf(1106,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (times_times @ TA @ A @ B) @ (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])).
% 74.26/25.30  thf(33,axiom,((power @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Power_Opower_342)).
% 74.26/25.30  thf(916,plain,((power @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 74.26/25.30  thf(764,axiom,((ab_semigroup_mult @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_464)).
% 74.26/25.30  thf(3271,plain,((ab_semigroup_mult @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[764])).
% 74.26/25.30  thf(511,axiom,((complete_Inf @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Complete__Lattices_OInf_76)).
% 74.26/25.30  thf(2445,plain,((complete_Inf @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[511])).
% 74.26/25.30  thf(729,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B)) @ (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_955_sum__squares__le__zero__iff)).
% 74.26/25.30  thf(3191,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B)) @ (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[729])).
% 74.26/25.30  thf(338,axiom,((! [A:nat]: ((zero_zero @ nat) != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_nat_Odistinct_I1_J)).
% 74.26/25.30  thf(1938,plain,((! [A:nat]: ~ ((zero_zero @ nat) = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])).
% 74.26/25.30  thf(74,axiom,((! [A:nat,B:nat]: ((plus_plus @ nat @ (minus_minus @ nat @ A @ B) @ B) = (ord_max @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4839_nat__minus__add__max)).
% 74.26/25.30  thf(1032,plain,((! [A:nat,B:nat]: ((plus_plus @ nat @ (minus_minus @ nat @ A @ B) @ B) = (ord_max @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])).
% 74.26/25.30  thf(311,axiom,((! [A:nat,B:nat,C:nat]: (((times_times @ nat @ A @ B) = (times_times @ nat @ A @ C)) = ((B = C) | (A = (zero_zero @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_mult__cancel1)).
% 74.26/25.30  thf(1837,plain,((! [A:nat,B:nat,C:nat]: (((times_times @ nat @ A @ B) = (times_times @ nat @ A @ C)) = ((B = C) | (A = (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])).
% 74.26/25.30  thf(762,axiom,((semiri3467727345109120633visors @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring__no__zero__divisors_458)).
% 74.26/25.30  thf(3269,plain,((semiri3467727345109120633visors @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[762])).
% 74.26/25.30  thf(176,axiom,((semiring_0 @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__0_325)).
% 74.26/25.30  thf(1365,plain,((semiring_0 @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])).
% 74.26/25.30  thf(3808,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less_eq @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ extended_enat) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1256,2483])).
% 74.26/25.30  thf(3809,plain,(! [TA:$tType] : ((~ (ord_less_eq @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ extended_enat) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3808])).
% 74.26/25.30  thf(3810,plain,((~ (ord_less_eq @ extended_enat @ (one_one @ extended_enat) @ (zero_zero @ extended_enat)))),inference(pattern_uni,[status(thm)],[3809:[bind_type(TA,$thf(extended_enat))]])).
% 74.26/25.30  thf(506,axiom,((! [TA: $tType]: ((dvd @ TA) => (! [A:TA,B:TA]: ((dvd_dvd @ TA @ A @ B) => (~ (! [C:TA]: (B != (times_times @ TA @ A @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1371_dvdE)).
% 74.26/25.30  thf(2433,plain,((! [TA: $tType]: ((dvd @ TA) => (! [A:TA,B:TA]: ((dvd_dvd @ TA @ A @ B) => (~ (! [C:TA]: ~ (B = (times_times @ TA @ A @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])).
% 74.26/25.30  thf(527,axiom,((semigroup_add @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Osemigroup__add_307)).
% 74.26/25.30  thf(2477,plain,((semigroup_add @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[527])).
% 74.26/25.30  thf(852,plain,(! [C:(nat > int),B:nat,A:nat] : ((ord_less @ nat @ (sk2 @ (C) @ B @ A) @ B) | (sk1 @ A @ B @ C))),inference(cnfConj,[status(thm)],[851])).
% 74.26/25.30  thf(471,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => ((ord_max @ TA @ (one_one @ TA) @ (zero_zero @ TA)) = (one_one @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4774_max__0__1_I2_J)).
% 74.26/25.30  thf(2332,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => ((ord_max @ TA @ (one_one @ TA) @ (zero_zero @ TA)) = (one_one @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[471])).
% 74.26/25.30  thf(621,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_941_mult__right__le__imp__le)).
% 74.26/25.30  thf(2820,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[621])).
% 74.26/25.30  thf(323,axiom,((! [A:nat]: ((ord_max @ nat @ A @ (zero_zero @ nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4826_max__0R)).
% 74.26/25.30  thf(1888,plain,((! [A:nat]: ((ord_max @ nat @ A @ (zero_zero @ nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])).
% 74.26/25.30  thf(227,axiom,((zero_neq_one @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__neq__one_85)).
% 74.26/25.30  thf(1538,plain,((zero_neq_one @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])).
% 74.26/25.30  thf(3716,plain,(! [TA:$tType] : (((zero_zero @ TA) != (one_one @ TA)) | ~ (($true)) | ((zero_neq_one @ nat) != (zero_neq_one @ TA)))),inference(paramod_ordered,[status(thm)],[1538,2954])).
% 74.26/25.30  thf(3717,plain,(! [TA:$tType] : (((zero_zero @ TA) != (one_one @ TA)) | ((zero_neq_one @ nat) != (zero_neq_one @ TA)))),inference(simp,[status(thm)],[3716])).
% 74.26/25.30  thf(3718,plain,(((zero_zero @ nat) != (one_one @ nat))),inference(pattern_uni,[status(thm)],[3717:[bind_type(TA,$thf(nat))]])).
% 74.26/25.30  thf(155,axiom,((linord181362715937106298miring @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_41)).
% 74.26/25.30  thf(1301,plain,((linord181362715937106298miring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
% 74.26/25.30  thf(3544,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less @ TA @ (zero_zero @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ nat) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1301,2246])).
% 74.26/25.30  thf(3545,plain,(! [TA:$tType] : ((~ (ord_less @ TA @ (zero_zero @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ nat) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3544])).
% 74.26/25.30  thf(3546,plain,((~ (ord_less @ nat @ (zero_zero @ nat) @ (zero_zero @ nat)))),inference(pattern_uni,[status(thm)],[3545:[bind_type(TA,$thf(nat))]])).
% 74.26/25.30  thf(113,axiom,((plus @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oplus)).
% 74.26/25.30  thf(1159,plain,((plus @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
% 74.26/25.30  thf(800,axiom,((one @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oone_498)).
% 74.26/25.30  thf(3408,plain,((one @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[800])).
% 74.26/25.30  thf(282,axiom,((! [A:nat]: ((dvd_dvd @ nat @ A @ (one_one @ nat)) = (A = (one_one @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1323_nat__dvd__1__iff__1)).
% 74.26/25.30  thf(1740,plain,((! [A:nat]: ((dvd_dvd @ nat @ A @ (one_one @ nat)) = (A = (one_one @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])).
% 74.26/25.30  thf(332,axiom,((! [A:nat]: ((ord_less_eq @ nat @ A @ (zero_zero @ nat)) = (A = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_le__0__eq)).
% 74.26/25.30  thf(1910,plain,((! [A:nat]: ((ord_less_eq @ nat @ A @ (zero_zero @ nat)) = (A = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])).
% 74.26/25.30  thf(9,axiom,((! [A:int]: ((ord_less @ int @ (abs_abs @ int @ A) @ (one_one @ int)) = (A = (zero_zero @ int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2708_zabs__less__one__iff)).
% 74.26/25.30  thf(840,plain,((! [A:int]: ((ord_less @ int @ (abs_abs @ int @ A) @ (one_one @ int)) = (A = (zero_zero @ int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 74.26/25.30  thf(841,plain,(! [A:int] : (((ord_less @ int @ (abs_abs @ int @ A) @ (one_one @ int)) = (A = (zero_zero @ int))))),inference(cnf,[status(esa)],[840])).
% 74.26/25.30  thf(842,plain,(! [A:int] : (((ord_less @ int @ (abs_abs @ int @ A) @ (one_one @ int)) = (A = (zero_zero @ int))))),inference(lifteq,[status(thm)],[841])).
% 74.26/25.30  thf(186,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus @ nat @ A @ (ord_max @ nat @ B @ C)) = (ord_max @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4838_nat__add__max__right)).
% 74.26/25.30  thf(1402,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus @ nat @ A @ (ord_max @ nat @ B @ C)) = (ord_max @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])).
% 74.26/25.30  thf(67,axiom,((linord181362715937106298miring @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__nonzero__semiring)).
% 74.26/25.30  thf(1016,plain,((linord181362715937106298miring @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
% 74.26/25.30  thf(3465,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ int) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1016,1733])).
% 74.26/25.30  thf(3466,plain,(! [TA:$tType] : ((~ (ord_less @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ int) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3465])).
% 74.26/25.30  thf(3467,plain,((~ (ord_less @ int @ (one_one @ int) @ (zero_zero @ int)))),inference(pattern_uni,[status(thm)],[3466:[bind_type(TA,$thf(int))]])).
% 74.26/25.30  thf(168,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ C) => (((minus_minus @ nat @ B @ A) = (minus_minus @ nat @ C @ A)) = (B = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1721_eq__diff__iff)).
% 74.26/25.30  thf(1328,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ C) => (((minus_minus @ nat @ B @ A) = (minus_minus @ nat @ C @ A)) = (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])).
% 74.26/25.30  thf(663,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ B) = (((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ A @ (one_one @ TA))) & ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (one_one @ TA) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1040_mult__le__cancel__right2)).
% 74.26/25.30  thf(2973,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ B) = (((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ A @ (one_one @ TA))) & ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (one_one @ TA) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[663])).
% 74.26/25.30  thf(104,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ (suc @ (zero_zero @ nat)) @ (times_times @ nat @ A @ B)) = ((ord_less_eq @ nat @ (suc @ (zero_zero @ nat)) @ A) & (ord_less_eq @ nat @ (suc @ (zero_zero @ nat)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_one__le__mult__iff)).
% 74.26/25.30  thf(1111,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ (suc @ (zero_zero @ nat)) @ (times_times @ nat @ A @ B)) = ((ord_less_eq @ nat @ (suc @ (zero_zero @ nat)) @ A) & (ord_less_eq @ nat @ (suc @ (zero_zero @ nat)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
% 74.26/25.30  thf(739,axiom,((! [A:int,B:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => (((times_times @ int @ A @ B) = (one_one @ int)) = ((A = (one_one @ int)) & (B = (one_one @ int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1189_pos__zmult__eq__1__iff)).
% 74.26/25.30  thf(3218,plain,((! [A:int,B:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => (((times_times @ int @ A @ B) = (one_one @ int)) = ((A = (one_one @ int)) & (B = (one_one @ int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[739])).
% 74.26/25.30  thf(53,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (times_times @ nat @ (suc @ A) @ B) @ (times_times @ nat @ (suc @ A) @ C)) = (ord_less @ nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_806_Suc__mult__less__cancel1)).
% 74.26/25.30  thf(980,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (times_times @ nat @ (suc @ A) @ B) @ (times_times @ nat @ (suc @ A) @ C)) = (ord_less @ nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
% 74.26/25.30  thf(631,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ B @ (one_one @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ B @ A) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_954_mult__left__le__one__le)).
% 74.26/25.30  thf(2858,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ B @ (one_one @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ B @ A) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[631])).
% 74.26/25.30  thf(696,axiom,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: ((A != (top_top @ TA)) = (ord_less @ TA @ A @ (top_top @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6217_top_Onot__eq__extremum)).
% 74.26/25.30  thf(3078,plain,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: ((~ (A = (top_top @ TA))) = (ord_less @ TA @ A @ (top_top @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[696])).
% 74.26/25.30  thf(808,axiom,((zero_neq_one @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ozero__neq__one_482)).
% 74.26/25.30  thf(3440,plain,((zero_neq_one @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[808])).
% 74.26/25.30  thf(337,axiom,((! [A:int,B:int]: ((dvd_dvd @ int @ A @ B) => ((ord_less @ int @ (zero_zero @ int) @ B) => (ord_less_eq @ int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1464_zdvd__imp__le)).
% 74.26/25.30  thf(1936,plain,((! [A:int,B:int]: ((dvd_dvd @ int @ A @ B) => ((ord_less @ int @ (zero_zero @ int) @ B) => (ord_less_eq @ int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])).
% 74.26/25.30  thf(96,axiom,((! [A:nat,B:nat]: ((plus_plus @ nat @ (suc @ A) @ B) = (suc @ (plus_plus @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_725_add__Suc)).
% 74.26/25.30  thf(1089,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)],[96])).
% 74.26/25.30  thf(138,axiom,((strict7427464778891057005id_add @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ostrict__ordered__comm__monoid__add)).
% 74.26/25.30  thf(1234,plain,((strict7427464778891057005id_add @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
% 74.26/25.30  thf(19,axiom,((! [A:real,B:real,C:real]: ((ord_less @ real @ A @ B) => ((ord_less @ real @ B @ C) => (? [D:real]: ((ord_less @ real @ (zero_zero @ real) @ D) & ! [E:real]: ((ord_less @ real @ (abs_abs @ real @ (minus_minus @ real @ B @ E)) @ D) => ((ord_less_eq @ real @ A @ E) & (ord_less_eq @ real @ E @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2662_lemma__interval)).
% 74.26/25.30  thf(874,plain,((! [A:real,B:real,C:real]: ((ord_less @ real @ A @ B) => ((ord_less @ real @ B @ C) => (? [D:real]: ((ord_less @ real @ (zero_zero @ real) @ D) & ! [E:real]: ((ord_less @ real @ (abs_abs @ real @ (minus_minus @ real @ B @ E)) @ D) => ((ord_less_eq @ real @ A @ E) & (ord_less_eq @ real @ E @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 74.26/25.30  thf(109,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (plus_plus @ nat @ A @ B) @ C) => (ord_less @ nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_add__lessD1)).
% 74.26/25.30  thf(1143,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (plus_plus @ nat @ A @ B) @ C) => (ord_less @ nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
% 74.26/25.30  thf(289,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((dvd_dvd @ nat @ B @ A) => (ord_less @ nat @ (zero_zero @ nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1435_dvd__pos__nat)).
% 74.26/25.30  thf(1762,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((dvd_dvd @ nat @ B @ A) => (ord_less @ nat @ (zero_zero @ nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])).
% 74.26/25.30  thf(753,axiom,((comple592849572758109894attice @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__distrib__lattice_450)).
% 74.26/25.30  thf(3254,plain,((comple592849572758109894attice @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[753])).
% 74.26/25.30  thf(292,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_Suc__le__mono)).
% 74.26/25.30  thf(1772,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)],[292])).
% 74.26/25.30  thf(146,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ (zero_zero @ TA)) => (ord_less @ TA @ (times_times @ TA @ C @ B) @ (times_times @ TA @ C @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_858_mult__strict__left__mono__neg)).
% 74.26/25.30  thf(1259,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ (zero_zero @ TA)) => (ord_less @ TA @ (times_times @ TA @ C @ B) @ (times_times @ TA @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
% 74.26/25.30  thf(707,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (times_times @ TA @ B @ A)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ (one_one @ TA) @ B)) & ((ord_less @ TA @ A @ (zero_zero @ TA)) => (ord_less_eq @ TA @ B @ (one_one @ TA))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039_mult__le__cancel__right1)).
% 74.26/25.30  thf(3122,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (times_times @ TA @ B @ A)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ (one_one @ TA) @ B)) & ((ord_less @ TA @ A @ (zero_zero @ TA)) => (ord_less_eq @ TA @ B @ (one_one @ TA))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[707])).
% 74.26/25.30  thf(670,axiom,((! [A:extended_enat,B:nat]: ((ord_less @ extended_enat @ A @ (extended_enat2 @ B)) => (? [C:nat]: (A = (extended_enat2 @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_enat__iless)).
% 74.26/25.30  thf(2990,plain,((! [A:extended_enat,B:nat]: ((ord_less @ extended_enat @ A @ (extended_enat2 @ B)) => (? [C:nat]: (A = (extended_enat2 @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[670])).
% 74.26/25.30  thf(225,axiom,((! [A:nat,B:nat]: ((times_times @ nat @ A @ (suc @ B)) = (plus_plus @ nat @ A @ (times_times @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_mult__Suc__right)).
% 74.26/25.30  thf(1534,plain,((! [A:nat,B:nat]: ((times_times @ nat @ A @ (suc @ B)) = (plus_plus @ nat @ A @ (times_times @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
% 74.26/25.30  thf(295,axiom,((strict7427464778891057005id_add @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add_252)).
% 74.26/25.30  thf(1794,plain,((strict7427464778891057005id_add @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])).
% 74.26/25.30  thf(68,axiom,((! [A:nat,B:nat]: (((plus_plus @ nat @ A @ B) = A) => (B = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764_add__eq__self__zero)).
% 74.26/25.30  thf(1017,plain,((! [A:nat,B:nat]: (((plus_plus @ nat @ A @ B) = A) => (B = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
% 74.26/25.30  thf(562,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ A) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ B @ (one_one @ TA))) & ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => (ord_less @ TA @ (one_one @ TA) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_mult__less__cancel__left2)).
% 74.26/25.30  thf(2577,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ A) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ B @ (one_one @ TA))) & ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => (ord_less @ TA @ (one_one @ TA) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[562])).
% 74.26/25.30  thf(87,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less @ nat @ C @ (suc @ A)) => (B @ C))) = ((B @ (zero_zero @ nat)) & ! [C:nat]: ((ord_less @ nat @ C @ A) => (B @ (suc @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_All__less__Suc2)).
% 74.26/25.30  thf(1064,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less @ nat @ C @ (suc @ A)) => (B @ C))) = ((B @ (zero_zero @ nat)) & ! [C:nat]: ((ord_less @ nat @ C @ A) => (B @ (suc @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
% 74.26/25.30  thf(98,axiom,((! [TA: $tType]: ((dvd @ TA) => (! [A:TA,B:TA,C:TA]: ((A = (times_times @ TA @ B @ C)) => (dvd_dvd @ TA @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1372_dvdI)).
% 74.26/25.30  thf(1096,plain,((! [TA: $tType]: ((dvd @ TA) => (! [A:TA,B:TA,C:TA]: ((A = (times_times @ TA @ B @ C)) => (dvd_dvd @ TA @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
% 74.26/25.30  thf(260,axiom,((! [A:nat,B:nat]: (((zero_zero @ nat) = (ord_max @ nat @ A @ B)) = ((A = (zero_zero @ nat)) & (B = (zero_zero @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4829_max__nat_Oneutr__eq__iff)).
% 74.26/25.30  thf(1672,plain,((! [A:nat,B:nat]: (((zero_zero @ nat) = (ord_max @ nat @ A @ B)) = ((A = (zero_zero @ nat)) & (B = (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])).
% 74.26/25.30  thf(724,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ B) => (B != (zero_zero @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_gr__implies__not__zero)).
% 74.26/25.30  thf(3176,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ B) => (~ (B = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[724])).
% 74.26/25.30  thf(699,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ B) => (~ (! [C:TA]: (B != (plus_plus @ TA @ A @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_less__eqE)).
% 74.26/25.30  thf(3087,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ B) => (~ (! [C:TA]: ~ (B = (plus_plus @ TA @ A @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[699])).
% 74.26/25.30  thf(263,axiom,((! [A:nat,B:nat]: ((ord_max @ nat @ (suc @ A) @ (suc @ B)) = (suc @ (ord_max @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4825_max__Suc__Suc)).
% 74.26/25.30  thf(1683,plain,((! [A:nat,B:nat]: ((ord_max @ nat @ (suc @ A) @ (suc @ B)) = (suc @ (ord_max @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])).
% 74.26/25.30  thf(114,axiom,((complete_Sup @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Complete__Lattices_OSup_9)).
% 74.26/25.30  thf(1160,plain,((complete_Sup @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
% 74.26/25.30  thf(713,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ E)) = (ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1773_nat__less__add__iff1)).
% 74.26/25.30  thf(3143,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ E)) = (ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[713])).
% 74.26/25.30  thf(799,axiom,((comm_semiring @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring_477)).
% 74.26/25.30  thf(3407,plain,((comm_semiring @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[799])).
% 74.26/25.30  thf(809,axiom,((comm_semiring_0 @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__0_470)).
% 74.26/25.30  thf(3441,plain,((comm_semiring_0 @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[809])).
% 74.26/25.30  thf(388,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ C) => ((ord_less @ nat @ (minus_minus @ nat @ B @ A) @ (minus_minus @ nat @ C @ A)) = (ord_less @ nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1735_less__diff__iff)).
% 74.26/25.30  thf(2080,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ C) => ((ord_less @ nat @ (minus_minus @ nat @ B @ A) @ (minus_minus @ nat @ C @ A)) = (ord_less @ nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])).
% 74.26/25.30  thf(439,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat]: (A @ D @ (zero_zero @ nat))) => ((! [D:nat]: (A @ (zero_zero @ nat) @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_diff__induct)).
% 74.26/25.30  thf(2240,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat]: (A @ D @ (zero_zero @ nat))) => ((! [D:nat]: (A @ (zero_zero @ nat) @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[439])).
% 74.26/25.30  thf(303,axiom,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_mult__nonpos__nonpos)).
% 74.26/25.30  thf(1810,plain,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])).
% 74.26/25.30  thf(730,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (one_one @ TA)) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ (times_times @ TA @ B @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_mult__left__le)).
% 74.26/25.30  thf(3194,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (one_one @ TA)) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ (times_times @ TA @ B @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[730])).
% 74.26/25.30  thf(376,axiom,((wellorder @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder)).
% 74.26/25.30  thf(2038,plain,((wellorder @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[376])).
% 74.26/25.30  thf(254,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(TA > nat),D:nat]: ((A @ B) => ((! [E:TA]: ((A @ E) => (ord_less @ nat @ (C @ E) @ D))) => (? [E:TA]: ((A @ E) & ! [F:TA]: ((A @ F) => (ord_less_eq @ nat @ (C @ F) @ (C @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_Lattices__Big_Oex__has__greatest__nat)).
% 74.26/25.30  thf(1644,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(TA > nat),D:nat]: ((A @ B) => ((! [E:TA]: ((A @ E) => (ord_less @ nat @ (C @ E) @ D))) => (? [E:TA]: ((A @ E) & ! [F:TA]: ((A @ F) => (ord_less_eq @ nat @ (C @ F) @ (C @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])).
% 74.26/25.30  thf(778,axiom,((! [A:extended_enat]: ((! [B:nat]: (A != (extended_enat2 @ B))) => (A = (extend4730790105801354508finity @ extended_enat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_enat_Oexhaust)).
% 74.26/25.30  thf(3294,plain,((! [A:extended_enat]: ((! [B:nat]: ~ (A = (extended_enat2 @ B))) => (A = (extend4730790105801354508finity @ extended_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[778])).
% 74.26/25.30  thf(607,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_945_add__neg__nonpos)).
% 74.26/25.30  thf(2781,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[607])).
% 74.26/25.30  thf(93,axiom,((! [A:nat,B:nat]: ((A != B) => ((~ (ord_less @ nat @ A @ B)) => (ord_less @ nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_linorder__neqE__nat)).
% 74.26/25.30  thf(1082,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)],[93])).
% 74.26/25.30  thf(369,axiom,((linordered_idom @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom_298)).
% 74.26/25.30  thf(2023,plain,((linordered_idom @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])).
% 74.26/25.30  thf(339,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (plus_plus @ nat @ C @ B) @ A) = (plus_plus @ nat @ C @ (minus_minus @ nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1741_Nat_Odiff__add__assoc)).
% 74.26/25.30  thf(1942,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (plus_plus @ nat @ C @ B) @ A) = (plus_plus @ nat @ C @ (minus_minus @ nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])).
% 74.26/25.30  thf(255,axiom,((mult_zero @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Omult__zero_95)).
% 74.26/25.30  thf(1659,plain,((mult_zero @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])).
% 74.26/25.30  thf(153,axiom,((! [TA: $tType]: (! [A:(nat > TA),B:(nat > TA),C:TA,D:nat]: ((! [E:nat]: ((A @ (suc @ E)) = (B @ E))) => (((A @ (zero_zero @ nat)) = C) => (((D = (zero_zero @ nat)) => ((A @ D) = C)) & ((D != (zero_zero @ nat)) => ((A @ D) = (B @ (minus_minus @ nat @ D @ (one_one @ nat))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1790_Suc__if__eq)).
% 74.26/25.30  thf(1292,plain,((! [TA: $tType]: (! [A:(nat > TA),B:(nat > TA),C:TA,D:nat]: ((! [E:nat]: ((A @ (suc @ E)) = (B @ E))) => (((A @ (zero_zero @ nat)) = C) => (((D = (zero_zero @ nat)) => ((A @ D) = C)) & ((~ (D = (zero_zero @ nat))) => ((A @ D) = (B @ (minus_minus @ nat @ D @ (one_one @ nat))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
% 74.26/25.30  thf(41,axiom,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ B @ C) @ (times_times @ TA @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_mult__right__mono__neg)).
% 74.26/25.30  thf(933,plain,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ B @ C) @ (times_times @ TA @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
% 74.26/25.30  thf(555,axiom,((! [TA: $tType,TB: $tType]: ((complete_Sup @ TA) => (complete_Sup @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_OSup)).
% 74.26/25.30  thf(2551,plain,((! [TA: $tType,TB: $tType]: ((complete_Sup @ TA) => (complete_Sup @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[555])).
% 74.26/25.30  thf(247,axiom,((linord8928482502909563296strict @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semiring__strict)).
% 74.26/25.30  thf(1612,plain,((linord8928482502909563296strict @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
% 74.26/25.30  thf(665,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ~ (ord_less @ TA @ A @ (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_not__less__zero)).
% 74.26/25.30  thf(2978,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ~ (ord_less @ TA @ A @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[665])).
% 74.26/25.30  thf(60,axiom,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ A @ (ord_max @ nat @ B @ C)) = (ord_max @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4836_nat__mult__max__right)).
% 74.26/25.30  thf(997,plain,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ A @ (ord_max @ nat @ B @ C)) = (ord_max @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
% 74.26/25.30  thf(544,axiom,((complete_Inf @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Complete__Lattices_OInf_10)).
% 74.26/25.30  thf(2519,plain,((complete_Inf @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[544])).
% 74.26/25.30  thf(549,axiom,((! [A:extended_enat]: ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ A) => ((times_times @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (extend4730790105801354508finity @ extended_enat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1033_imult__infinity)).
% 74.26/25.30  thf(2536,plain,((! [A:extended_enat]: ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ A) => ((times_times @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (extend4730790105801354508finity @ extended_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[549])).
% 74.26/25.30  thf(487,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ B @ C) => (ord_less @ nat @ (suc @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_less__trans__Suc)).
% 74.26/25.30  thf(2387,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ B @ C) => (ord_less @ nat @ (suc @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[487])).
% 74.26/25.30  thf(82,axiom,(((ord_less_eq @ nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus @ nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_nat__le__iff__add)).
% 74.26/25.30  thf(1050,plain,(((ord_less_eq @ nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus @ nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
% 74.26/25.30  thf(31,axiom,((! [A:nat]: ((times_times @ nat @ A @ (one_one @ nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_nat__mult__1__right)).
% 74.26/25.30  thf(911,plain,((! [A:nat]: ((times_times @ nat @ A @ (one_one @ nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 74.26/25.30  thf(706,axiom,((! [A:int,B:(int > $o),C:(int > $o)]: ((ord_less @ int @ (zero_zero @ int) @ A) => ((! [D:int,E:int]: ((B @ D) = (B @ (minus_minus @ int @ D @ (times_times @ int @ E @ A))))) => ((? [D:int]: ! [E:int]: ((ord_less @ int @ E @ D) => ((C @ E) = (B @ E)))) => ((? [D:int]: (B @ D)) => (? [D:int]: (C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1646_minusinfinity)).
% 74.26/25.30  thf(3115,plain,((! [A:int,B:(int > $o),C:(int > $o)]: ((ord_less @ int @ (zero_zero @ int) @ A) => ((! [D:int,E:int]: ((B @ D) = (B @ (minus_minus @ int @ D @ (times_times @ int @ E @ A))))) => ((? [D:int]: ! [E:int]: ((ord_less @ int @ E @ D) => ((C @ E) = (B @ E)))) => ((? [D:int]: (B @ D)) => (? [D:int]: (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[706])).
% 74.26/25.30  thf(801,axiom,((ordere6658533253407199908up_add @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_459)).
% 74.26/25.30  thf(3409,plain,((ordere6658533253407199908up_add @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[801])).
% 74.26/25.30  thf(273,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ C @ B)) = ((ord_less @ nat @ (zero_zero @ nat) @ B) & (ord_less @ nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_mult__less__cancel2)).
% 74.26/25.30  thf(1715,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ C @ B)) = ((ord_less @ nat @ (zero_zero @ nat) @ B) & (ord_less @ nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])).
% 74.26/25.30  thf(694,axiom,((! [A:nat]: ~ (ord_less @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_infinity__ilessE)).
% 74.26/25.30  thf(3064,plain,((! [A:nat]: ~ (ord_less @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[694])).
% 74.26/25.30  thf(353,axiom,((dvd @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Odvd_104)).
% 74.26/25.30  thf(1979,plain,((dvd @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])).
% 74.26/25.30  thf(449,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_mult__le__mono1)).
% 74.26/25.30  thf(2272,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[449])).
% 74.26/25.30  thf(598,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (times_times @ TA @ B @ A) @ (times_times @ TA @ C @ A)) = (ord_less_eq @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1191_mult__le__cancel__iff1)).
% 74.26/25.30  thf(2756,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (times_times @ TA @ B @ A) @ (times_times @ TA @ C @ A)) = (ord_less_eq @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[598])).
% 74.26/25.30  thf(738,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_less @ extended_enat @ (plus_plus @ extended_enat @ A @ B) @ (plus_plus @ extended_enat @ A @ C)) = ((A != (extend4730790105801354508finity @ extended_enat)) & (ord_less @ extended_enat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_enat__add__left__cancel__less)).
% 74.26/25.30  thf(3215,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_less @ extended_enat @ (plus_plus @ extended_enat @ A @ B) @ (plus_plus @ extended_enat @ A @ C)) = (~ (A = (extend4730790105801354508finity @ extended_enat)) & (ord_less @ extended_enat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[738])).
% 74.26/25.30  thf(105,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less @ nat @ A @ B) => ((! [D:nat]: ((B = (suc @ D)) => (C @ D))) => ((! [D:nat]: ((ord_less @ nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_strict__inc__induct)).
% 74.26/25.30  thf(1114,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less @ nat @ A @ B) => ((! [D:nat]: ((B = (suc @ D)) => (C @ D))) => ((! [D:nat]: ((ord_less @ nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
% 74.26/25.30  thf(165,axiom,((linordered_ring @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__ring)).
% 74.26/25.30  thf(1324,plain,((linordered_ring @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
% 74.26/25.30  thf(539,axiom,((! [A:nat]: ((! [B:nat]: (A != (plus_plus @ nat @ B @ B))) => (~ (! [B:nat]: (A != (plus_plus @ nat @ B @ (suc @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_even__odd__cases)).
% 74.26/25.30  thf(2504,plain,((! [A:nat]: ((! [B:nat]: ~ (A = (plus_plus @ nat @ B @ B))) => (~ (! [B:nat]: ~ (A = (plus_plus @ nat @ B @ (suc @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[539])).
% 74.26/25.30  thf(515,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (times_times @ nat @ C @ A) @ (times_times @ nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_mult__le__mono2)).
% 74.26/25.30  thf(2450,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (times_times @ nat @ C @ A) @ (times_times @ nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])).
% 74.26/25.30  thf(55,axiom,((zero_less_one @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ozero__less__one_310)).
% 74.26/25.30  thf(985,plain,((zero_less_one @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
% 74.26/25.30  thf(228,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ (suc @ B)) = ((A = (zero_zero @ nat)) | ? [C:nat]: ((A = (suc @ C)) & (ord_less @ nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_less__Suc__eq__0__disj)).
% 74.26/25.30  thf(1539,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ (suc @ B)) = ((A = (zero_zero @ nat)) | ? [C:nat]: ((A = (suc @ C)) & (ord_less @ nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
% 74.26/25.30  thf(182,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_less__not__refl3)).
% 74.26/25.30  thf(1382,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
% 74.26/25.30  thf(532,axiom,((! [A:nat]: ((A != (zero_zero @ nat)) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_old_Onat_Oexhaust)).
% 74.26/25.30  thf(2487,plain,((! [A:nat]: ((~ (A = (zero_zero @ nat))) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[532])).
% 74.26/25.30  thf(692,axiom,((! [TA: $tType]: ((semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ A @ (plus_plus @ TA @ B @ C)) = (plus_plus @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_distrib__left)).
% 74.26/25.30  thf(3059,plain,((! [TA: $tType]: ((semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ A @ (plus_plus @ TA @ B @ C)) = (plus_plus @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[692])).
% 74.26/25.30  thf(740,axiom,((! [A:nat,B:nat]: (((extended_enat2 @ A) = (extended_enat2 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_enat_Oinject)).
% 74.26/25.30  thf(3222,plain,((! [A:nat,B:nat]: (((extended_enat2 @ A) = (extended_enat2 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[740])).
% 74.26/25.30  thf(3538,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ nat) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1301,1733])).
% 74.26/25.30  thf(3539,plain,(! [TA:$tType] : ((~ (ord_less @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ nat) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3538])).
% 74.26/25.30  thf(3540,plain,((~ (ord_less @ nat @ (one_one @ nat) @ (zero_zero @ nat)))),inference(pattern_uni,[status(thm)],[3539:[bind_type(TA,$thf(nat))]])).
% 74.26/25.30  thf(536,axiom,((! [A:nat,B:nat]: ((~ (ord_less @ nat @ A @ B)) => ((ord_less @ nat @ A @ (suc @ B)) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_less__antisym)).
% 74.26/25.30  thf(2497,plain,((! [A:nat,B:nat]: ((~ (ord_less @ nat @ A @ B)) => ((ord_less @ nat @ A @ (suc @ B)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[536])).
% 74.26/25.30  thf(714,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ E)) = (minus_minus @ nat @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1763_nat__diff__add__eq1)).
% 74.26/25.30  thf(3147,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ E)) = (minus_minus @ nat @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[714])).
% 74.26/25.30  thf(199,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) | (ord_less_eq @ nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_nat__le__linear)).
% 74.26/25.30  thf(1434,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)],[199])).
% 74.26/25.30  thf(426,axiom,((! [A:nat]: (ord_less_eq @ nat @ (zero_zero @ nat) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_le0)).
% 74.26/25.30  thf(2208,plain,((! [A:nat]: (ord_less_eq @ nat @ (zero_zero @ nat) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[426])).
% 74.26/25.30  thf(387,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (plus_plus @ nat @ A @ B) @ C) => (~ ((ord_less_eq @ nat @ A @ C) => (~ (ord_less_eq @ nat @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__leE)).
% 74.26/25.30  thf(2076,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (plus_plus @ nat @ A @ B) @ C) => (~ ((ord_less_eq @ nat @ A @ C) => (~ (ord_less_eq @ nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])).
% 74.26/25.30  thf(75,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_721_le__SucI)).
% 74.26/25.30  thf(1035,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)],[75])).
% 74.26/25.30  thf(208,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less @ nat @ A @ B) => (((plus_plus @ nat @ C @ B) = (plus_plus @ nat @ A @ D)) => (ord_less @ nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_less__add__eq__less)).
% 74.26/25.30  thf(1466,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less @ nat @ A @ B) => (((plus_plus @ nat @ C @ B) = (plus_plus @ nat @ A @ D)) => (ord_less @ nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
% 74.26/25.30  thf(122,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) & (ord_less @ TA @ B @ C)) | ((ord_less @ TA @ A @ (zero_zero @ TA)) & (ord_less @ TA @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_860_mult__less__cancel__left__disj)).
% 74.26/25.30  thf(1187,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) & (ord_less @ TA @ B @ C)) | ((ord_less @ TA @ A @ (zero_zero @ TA)) & (ord_less @ TA @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
% 74.26/25.30  thf(119,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq @ nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq @ nat @ E @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_Nat_Oex__has__greatest__nat)).
% 74.26/25.30  thf(1167,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq @ nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq @ nat @ E @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
% 74.26/25.30  thf(420,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/sandbox2/benchmark/theBenchmark.p',fact_208_add__leD1)).
% 74.26/25.30  thf(2189,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)],[420])).
% 74.26/25.30  thf(306,axiom,((! [A:nat,B:nat]: (((ord_less @ nat @ A @ B) | (A = B)) => (ord_less_eq @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__or__eq__imp__le)).
% 74.26/25.30  thf(1814,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)],[306])).
% 74.26/25.30  thf(95,axiom,((! [A:nat]: ((times_times @ nat @ (one_one @ nat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_nat__mult__1)).
% 74.26/25.30  thf(1086,plain,((! [A:nat]: ((times_times @ nat @ (one_one @ nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])).
% 74.26/25.30  thf(741,axiom,((! [TA: $tType]: ((ab_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: ((plus_plus @ TA @ A @ (plus_plus @ TA @ B @ C)) = (plus_plus @ TA @ B @ (plus_plus @ TA @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_add_Oleft__commute)).
% 74.26/25.30  thf(3225,plain,((! [TA: $tType]: ((ab_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: ((plus_plus @ TA @ A @ (plus_plus @ TA @ B @ C)) = (plus_plus @ TA @ B @ (plus_plus @ TA @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[741])).
% 74.26/25.30  thf(142,axiom,((numeral @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Onumeral_343)).
% 74.26/25.30  thf(1241,plain,((numeral @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
% 74.26/25.30  thf(553,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: (((plus_plus @ TA @ A @ B) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_add__eq__0__iff__both__eq__0)).
% 74.26/25.30  thf(2546,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: (((plus_plus @ TA @ A @ B) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[553])).
% 74.26/25.30  thf(768,axiom,((ordered_semiring @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Oordered__semiring_467)).
% 74.26/25.30  thf(3279,plain,((ordered_semiring @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[768])).
% 74.26/25.30  thf(726,axiom,((! [A:extended_enat,B:extended_enat]: (((times_times @ extended_enat @ A @ B) = (zero_zero @ extended_enat)) = ((A = (zero_zero @ extended_enat)) | (B = (zero_zero @ extended_enat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_779_imult__is__0)).
% 74.26/25.30  thf(3183,plain,((! [A:extended_enat,B:extended_enat]: (((times_times @ extended_enat @ A @ B) = (zero_zero @ extended_enat)) = ((A = (zero_zero @ extended_enat)) | (B = (zero_zero @ extended_enat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[726])).
% 74.26/25.30  thf(379,axiom,((! [A:nat,B:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1725_diff__add__inverse2)).
% 74.26/25.30  thf(2057,plain,((! [A:nat,B:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])).
% 74.26/25.30  thf(783,axiom,((! [A:extended_enat]: ((plus_plus @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_plus__enat__simps_I2_J)).
% 74.26/25.30  thf(3306,plain,((! [A:extended_enat]: ((plus_plus @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[783])).
% 74.26/25.30  thf(496,axiom,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA]: ? [B:TA]: (ord_less @ TA @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_linordered__field__no__ub)).
% 74.26/25.30  thf(2408,plain,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA]: ? [B:TA]: (ord_less @ TA @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[496])).
% 74.26/25.30  thf(611,axiom,((! [TA: $tType]: ((zero_less_one @ TA) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_zero__less__one__class_Ozero__le__one)).
% 74.26/25.30  thf(2793,plain,((! [TA: $tType]: ((zero_less_one @ TA) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[611])).
% 74.26/25.30  thf(219,axiom,(((zero_zero @ extended_enat) = (extended_enat2 @ (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_zero__enat__def)).
% 74.26/25.30  thf(1515,plain,(((zero_zero @ extended_enat) = (extended_enat2 @ (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
% 74.26/25.30  thf(434,axiom,((! [A:nat,B:nat]: (ord_less_eq @ nat @ (minus_minus @ nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1717_diff__le__self)).
% 74.26/25.30  thf(2221,plain,((! [A:nat,B:nat]: (ord_less_eq @ nat @ (minus_minus @ nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[434])).
% 74.26/25.30  thf(473,axiom,((! [A:nat,B:(nat > $o),C:nat]: ((! [D:nat]: ((ord_less @ nat @ A @ D) => (B @ D))) => ((! [D:nat]: ((ord_less_eq @ nat @ D @ A) => ((! [E:nat]: ((ord_less @ nat @ D @ E) => (B @ E))) => (B @ D)))) => (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5382_nat__descend__induct)).
% 74.26/25.30  thf(2338,plain,((! [A:nat,B:(nat > $o),C:nat]: ((! [D:nat]: ((ord_less @ nat @ A @ D) => (B @ D))) => ((! [D:nat]: ((ord_less_eq @ nat @ D @ A) => ((! [E:nat]: ((ord_less @ nat @ D @ E) => (B @ E))) => (B @ D)))) => (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[473])).
% 74.26/25.30  thf(361,axiom,((complete_Inf @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Complete__Lattices_OInf_304)).
% 74.26/25.30  thf(1996,plain,((complete_Inf @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])).
% 74.26/25.30  thf(652,axiom,((! [TA: $tType]: ((mult_zero @ TA) => ((^ [A:TA]: (zero_zero @ TA)) = (times_times @ TA @ (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_lambda__zero)).
% 74.26/25.30  thf(2936,plain,((! [TA: $tType]: ((mult_zero @ TA) => ((^ [A:TA]: (zero_zero @ TA)) = (times_times @ TA @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[652])).
% 74.26/25.30  thf(277,axiom,(((one_one @ nat) = (suc @ (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_One__nat__def)).
% 74.26/25.30  thf(1727,plain,(((one_one @ nat) = (suc @ (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])).
% 74.26/25.30  thf(498,axiom,((! [A:nat]: ((minus_minus @ nat @ (zero_zero @ nat) @ A) = (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1681_diff__0__eq__0)).
% 74.26/25.30  thf(2413,plain,((! [A:nat]: ((minus_minus @ nat @ (zero_zero @ nat) @ A) = (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])).
% 74.26/25.30  thf(414,axiom,((zero @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero)).
% 74.26/25.30  thf(2176,plain,((zero @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[414])).
% 74.26/25.30  thf(262,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ B @ (suc @ A)) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_795_le__less__Suc__eq)).
% 74.26/25.30  thf(1680,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ B @ (suc @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])).
% 74.26/25.30  thf(100,axiom,((! [A:nat]: (ord_less_eq @ nat @ (zero_zero @ nat) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_bot__nat__0_Oextremum)).
% 74.26/25.30  thf(1103,plain,((! [A:nat]: (ord_less_eq @ nat @ (zero_zero @ nat) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])).
% 74.26/25.30  thf(450,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ A) => (ord_less @ nat @ (minus_minus @ nat @ A @ C) @ (minus_minus @ nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1734_diff__less__mono)).
% 74.26/25.30  thf(2275,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ A) => (ord_less @ nat @ (minus_minus @ nat @ A @ C) @ (minus_minus @ nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[450])).
% 74.26/25.30  thf(212,axiom,(((numeral_numeral @ extended_enat) = (^ [A:num]: (extended_enat2 @ (numeral_numeral @ nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_numeral__eq__enat)).
% 74.26/25.30  thf(1483,plain,(((numeral_numeral @ extended_enat) = (^ [A:num]: (extended_enat2 @ (numeral_numeral @ nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])).
% 74.26/25.30  thf(232,axiom,((ordere6911136660526730532id_add @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_48)).
% 74.26/25.30  thf(1548,plain,((ordere6911136660526730532id_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
% 74.26/25.30  thf(757,axiom,((zero_less_one @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ozero__less__one_476)).
% 74.26/25.30  thf(3262,plain,((zero_less_one @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[757])).
% 74.26/25.30  thf(773,axiom,((semiring_0 @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring__0_488)).
% 74.26/25.30  thf(3289,plain,((semiring_0 @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[773])).
% 74.26/25.30  thf(405,axiom,((numeral @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Onumeral)).
% 74.26/25.30  thf(2144,plain,((numeral @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[405])).
% 74.26/25.30  thf(29,axiom,((ordere6658533253407199908up_add @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_45)).
% 74.26/25.30  thf(906,plain,((ordere6658533253407199908up_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 74.26/25.30  thf(584,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ B @ (one_one @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_953_mult__right__le__one__le)).
% 74.26/25.30  thf(2717,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ B @ (one_one @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[584])).
% 74.26/25.30  thf(130,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ (suc @ B)) = (ord_less_eq @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_less__Suc__eq__le)).
% 74.26/25.30  thf(1219,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)],[130])).
% 74.26/25.30  thf(372,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) & (ord_less @ TA @ (zero_zero @ TA) @ B)) | ((ord_less @ TA @ A @ (zero_zero @ TA)) & (ord_less @ TA @ B @ (zero_zero @ TA))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_853_zero__less__mult__iff)).
% 74.26/25.30  thf(2028,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) & (ord_less @ TA @ (zero_zero @ TA) @ B)) | ((ord_less @ TA @ A @ (zero_zero @ TA)) & (ord_less @ TA @ B @ (zero_zero @ TA))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])).
% 74.26/25.30  thf(754,axiom,((! [TA: $tType]: (! [A:(nat > TA),B:TA]: ((extended_case_enat @ TA @ A @ B @ (extend4730790105801354508finity @ extended_enat)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_enat_Osimps_I5_J)).
% 74.26/25.30  thf(3255,plain,((! [TA: $tType]: (! [A:(nat > TA),B:TA]: ((extended_case_enat @ TA @ (A) @ B @ (extend4730790105801354508finity @ extended_enat)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[754])).
% 74.26/25.30  thf(747,axiom,((! [A:extended_enat,B:extended_enat]: (((plus_plus @ extended_enat @ A @ B) = (zero_zero @ extended_enat)) = ((A = (zero_zero @ extended_enat)) & (B = (zero_zero @ extended_enat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_iadd__is__0)).
% 74.26/25.30  thf(3240,plain,((! [A:extended_enat,B:extended_enat]: (((plus_plus @ extended_enat @ A @ B) = (zero_zero @ extended_enat)) = ((A = (zero_zero @ extended_enat)) & (B = (zero_zero @ extended_enat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[747])).
% 74.26/25.30  thf(10,axiom,((! [A:int,B:int,C:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => (ord_less @ int @ B @ (plus_plus @ int @ C @ (times_times @ int @ (plus_plus @ int @ (abs_abs @ int @ (minus_minus @ int @ C @ B)) @ (one_one @ int)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2785_incr__lemma)).
% 74.26/25.30  thf(843,plain,((! [A:int,B:int,C:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => (ord_less @ int @ B @ (plus_plus @ int @ C @ (times_times @ int @ (plus_plus @ int @ (abs_abs @ int @ (minus_minus @ int @ C @ B)) @ (one_one @ int)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 74.26/25.30  thf(419,axiom,((semigroup_mult @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult_74)).
% 74.26/25.30  thf(2188,plain,((semigroup_mult @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])).
% 74.26/25.30  thf(489,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (ord_less_eq @ nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_800_Suc__leI)).
% 74.26/25.30  thf(2393,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)],[489])).
% 74.26/25.30  thf(697,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_less_eq @ extended_enat @ A @ B) => ((plus_plus @ extended_enat @ C @ (minus_minus @ extended_enat @ B @ A)) = (minus_minus @ extended_enat @ (plus_plus @ extended_enat @ C @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1754_add__diff__assoc__enat)).
% 74.26/25.30  thf(3081,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_less_eq @ extended_enat @ A @ B) => ((plus_plus @ extended_enat @ C @ (minus_minus @ extended_enat @ B @ A)) = (minus_minus @ extended_enat @ (plus_plus @ extended_enat @ C @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[697])).
% 74.26/25.30  thf(765,axiom,((! [A:extended_enat]: ~ (ord_less @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_enat__ord__simps_I6_J)).
% 74.26/25.30  thf(3272,plain,((! [A:extended_enat]: ~ (ord_less @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[765])).
% 74.26/25.30  thf(5,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:num]: ((abs_abs @ TA @ (numeral_numeral @ TA @ A)) = (numeral_numeral @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2584_abs__numeral)).
% 74.26/25.30  thf(826,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:num]: ((abs_abs @ TA @ (numeral_numeral @ TA @ A)) = (numeral_numeral @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 74.26/25.30  thf(770,axiom,((comple5582772986160207858norder @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__linorder)).
% 74.26/25.30  thf(3283,plain,((comple5582772986160207858norder @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[770])).
% 74.26/25.30  thf(542,axiom,((! [A:nat,B:nat]: (ord_less_eq @ nat @ A @ (plus_plus @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_le__add1)).
% 74.26/25.30  thf(2514,plain,((! [A:nat,B:nat]: (ord_less_eq @ nat @ A @ (plus_plus @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[542])).
% 74.26/25.30  thf(296,axiom,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (order_mono @ nat @ nat @ (times_times @ nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8114_mono__times__nat)).
% 74.26/25.30  thf(1795,plain,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (order_mono @ nat @ nat @ (times_times @ nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])).
% 74.26/25.30  thf(491,axiom,(((ord_less @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_nat__less__le)).
% 74.26/25.30  thf(2398,plain,(((ord_less @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[491])).
% 74.26/25.30  thf(796,axiom,((order_bot @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder__bot_480)).
% 74.26/25.30  thf(3404,plain,((order_bot @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[796])).
% 74.26/25.30  thf(620,axiom,((! [A:nat]: ((minus_minus @ extended_enat @ (extended_enat2 @ A) @ (extend4730790105801354508finity @ extended_enat)) = (zero_zero @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1697_idiff__infinity__right)).
% 74.26/25.30  thf(2817,plain,((! [A:nat]: ((minus_minus @ extended_enat @ (extended_enat2 @ A) @ (extend4730790105801354508finity @ extended_enat)) = (zero_zero @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[620])).
% 74.26/25.30  thf(133,axiom,((! [A:nat]: (ord_less_eq @ nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_le__refl)).
% 74.26/25.30  thf(1226,plain,((! [A:nat]: (ord_less_eq @ nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
% 74.26/25.30  thf(659,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_add__nonpos__neg)).
% 74.26/25.30  thf(2959,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[659])).
% 74.26/25.30  thf(737,axiom,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounded_lattice @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_5)).
% 74.26/25.30  thf(3213,plain,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounded_lattice @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[737])).
% 74.26/25.30  thf(43,axiom,((! [A:nat]: ((A != (zero_zero @ nat)) => ((A != (suc @ (zero_zero @ nat))) => (~ (! [B:nat]: (A != (suc @ (suc @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_vebt__buildup_Ocases)).
% 74.26/25.30  thf(936,plain,((! [A:nat]: ((~ (A = (zero_zero @ nat))) => ((~ (A = (suc @ (zero_zero @ nat)))) => (~ (! [B:nat]: ~ (A = (suc @ (suc @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
% 74.26/25.30  thf(592,axiom,((! [TA: $tType]: ((semigroup_mult @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ (times_times @ TA @ A @ B) @ C) = (times_times @ TA @ A @ (times_times @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_mult_Oassoc)).
% 74.26/25.30  thf(2738,plain,((! [TA: $tType]: ((semigroup_mult @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ (times_times @ TA @ A @ B) @ C) = (times_times @ TA @ A @ (times_times @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[592])).
% 74.26/25.30  thf(735,axiom,((! [A:extended_enat]: ~ (ord_less @ extended_enat @ A @ (zero_zero @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_not__iless0)).
% 74.26/25.30  thf(3208,plain,((! [A:extended_enat]: ~ (ord_less @ extended_enat @ A @ (zero_zero @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[735])).
% 74.26/25.30  thf(85,axiom,((! [A:nat,B:nat]: ~ (ord_less @ nat @ (plus_plus @ nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_not__add__less1)).
% 74.26/25.30  thf(1058,plain,((! [A:nat,B:nat]: ~ (ord_less @ nat @ (plus_plus @ nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
% 74.26/25.30  thf(362,axiom,((! [A:nat,B:nat]: ((~ (ord_less @ nat @ A @ B)) => ((ord_less @ nat @ A @ (suc @ B)) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_not__less__less__Suc__eq)).
% 74.26/25.30  thf(1997,plain,((! [A:nat,B:nat]: ((~ (ord_less @ nat @ A @ B)) => ((ord_less @ nat @ A @ (suc @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])).
% 74.26/25.30  thf(169,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ B) => (ord_less @ nat @ A @ (times_times @ nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_n__less__m__mult__n)).
% 74.26/25.30  thf(1332,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ B) => (ord_less @ nat @ A @ (times_times @ nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
% 74.26/25.30  thf(97,axiom,((! [A:nat]: ((zero_zero @ nat) != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_Zero__neq__Suc)).
% 74.26/25.30  thf(1092,plain,((! [A:nat]: ~ ((zero_zero @ nat) = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
% 74.26/25.30  thf(503,axiom,((! [A:nat]: ((zero_zero @ nat) != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_old_Onat_Odistinct_I1_J)).
% 74.26/25.30  thf(2425,plain,((! [A:nat]: ~ ((zero_zero @ nat) = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[503])).
% 74.26/25.30  thf(526,axiom,((! [A:nat]: ((minus_minus @ nat @ A @ (zero_zero @ nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1711_minus__nat_Odiff__0)).
% 74.26/25.30  thf(2474,plain,((! [A:nat]: ((minus_minus @ nat @ A @ (zero_zero @ nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[526])).
% 74.26/25.30  thf(781,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((plus_plus @ extended_enat @ A @ B) = (plus_plus @ extended_enat @ A @ C)) = ((A = (extend4730790105801354508finity @ extended_enat)) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_enat__add__left__cancel)).
% 74.26/25.30  thf(3302,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((plus_plus @ extended_enat @ A @ B) = (plus_plus @ extended_enat @ A @ C)) = ((A = (extend4730790105801354508finity @ extended_enat)) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[781])).
% 74.26/25.30  thf(252,axiom,((! [A:nat]: ((A != (zero_zero @ nat)) = (ord_less @ nat @ (zero_zero @ nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_neq0__conv)).
% 74.26/25.30  thf(1638,plain,((! [A:nat]: ((~ (A = (zero_zero @ nat))) = (ord_less @ nat @ (zero_zero @ nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])).
% 74.26/25.30  thf(722,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ E)) = (ord_less_eq @ nat @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1761_nat__le__add__iff1)).
% 74.26/25.30  thf(3170,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ E)) = (ord_less_eq @ nat @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[722])).
% 74.26/25.30  thf(261,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_Suc__inject)).
% 74.26/25.30  thf(1675,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])).
% 74.26/25.30  thf(679,axiom,((! [TA: $tType,TB: $tType]: ((order_top @ TA) => (order_top @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top)).
% 74.26/25.30  thf(3023,plain,((! [TA: $tType,TB: $tType]: ((order_top @ TA) => (order_top @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[679])).
% 74.26/25.30  thf(259,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ (zero_zero @ nat) @ C) => (ord_less @ nat @ (times_times @ nat @ C @ A) @ (times_times @ nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_915_mult__less__mono2)).
% 74.26/25.30  thf(1669,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ (zero_zero @ nat) @ C) => (ord_less @ nat @ (times_times @ nat @ C @ A) @ (times_times @ nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])).
% 74.26/25.30  thf(270,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (zero_zero @ TA)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) & (ord_less @ TA @ B @ (zero_zero @ TA))) | ((ord_less @ TA @ A @ (zero_zero @ TA)) & (ord_less @ TA @ (zero_zero @ TA) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_848_mult__less__0__iff)).
% 74.26/25.30  thf(1707,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (zero_zero @ TA)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) & (ord_less @ TA @ B @ (zero_zero @ TA))) | ((ord_less @ TA @ A @ (zero_zero @ TA)) & (ord_less @ TA @ (zero_zero @ TA) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])).
% 74.26/25.30  thf(459,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ((ord_max @ TA @ (zero_zero @ TA) @ (numeral_numeral @ TA @ A)) = (numeral_numeral @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4772_max__0__1_I3_J)).
% 74.26/25.30  thf(2293,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ((ord_max @ TA @ (zero_zero @ TA) @ (numeral_numeral @ TA @ A)) = (numeral_numeral @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[459])).
% 74.26/25.30  thf(689,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ (one_one @ TA) @ (one_one @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_zero__less__two)).
% 74.26/25.30  thf(3051,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ (one_one @ TA) @ (one_one @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[689])).
% 74.26/25.30  thf(251,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ C @ D) => (ord_less @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_add__less__mono)).
% 74.26/25.30  thf(1635,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ C @ D) => (ord_less @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])).
% 74.26/25.30  thf(599,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ B @ C)) & ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => (ord_less @ TA @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_934_mult__less__cancel__left)).
% 74.26/25.30  thf(2759,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ B @ C)) & ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => (ord_less @ TA @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[599])).
% 74.26/25.30  thf(597,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) = (A = (zero_zero @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_le__zero__eq)).
% 74.26/25.30  thf(2753,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) = (A = (zero_zero @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[597])).
% 74.26/25.30  thf(410,axiom,((complete_Sup @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Complete__Lattices_OSup_303)).
% 74.26/25.30  thf(2166,plain,((complete_Sup @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[410])).
% 74.26/25.30  thf(290,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (minus_minus @ nat @ A @ C) @ (minus_minus @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1718_diff__le__mono)).
% 74.26/25.30  thf(1765,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (minus_minus @ nat @ A @ C) @ (minus_minus @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])).
% 74.26/25.30  thf(517,axiom,((semiri3467727345109120633visors @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__no__zero__divisors)).
% 74.26/25.30  thf(2457,plain,((semiri3467727345109120633visors @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[517])).
% 74.26/25.30  thf(36,axiom,((! [A:nat]: ((plus_plus @ nat @ (zero_zero @ nat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_plus__nat_Oadd__0)).
% 74.26/25.30  thf(919,plain,((! [A:nat]: ((plus_plus @ nat @ (zero_zero @ nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
% 74.26/25.30  thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_55_nat__add__left__cancel__less)).
% 74.26/25.30  thf(900,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)],[27])).
% 74.26/25.30  thf(830,plain,(! [TA:$tType,A:TA] : ((~ (linordered_idom @ TA)) | ((times_times @ TA @ (abs_abs @ TA @ A) @ (abs_abs @ TA @ A)) = (times_times @ TA @ A @ A)))),inference(cnf,[status(esa)],[829])).
% 74.26/25.30  thf(831,plain,(! [TA:$tType,A:TA] : (((times_times @ TA @ (abs_abs @ TA @ A) @ (abs_abs @ TA @ A)) = (times_times @ TA @ A @ A)) | (~ (linordered_idom @ TA)))),inference(lifteq,[status(thm)],[830])).
% 74.26/25.30  thf(188,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ A @ B) => ((dvd_dvd @ nat @ A @ C) => (dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1728_dvd__diff__nat)).
% 74.26/25.30  thf(1408,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ A @ B) => ((dvd_dvd @ nat @ A @ C) => (dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
% 74.26/25.30  thf(3813,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less_eq @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ int) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1016,2483])).
% 74.26/25.30  thf(3814,plain,(! [TA:$tType] : ((~ (ord_less_eq @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ int) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3813])).
% 74.26/25.30  thf(3815,plain,((~ (ord_less_eq @ int @ (one_one @ int) @ (zero_zero @ int)))),inference(pattern_uni,[status(thm)],[3814:[bind_type(TA,$thf(int))]])).
% 74.26/25.30  thf(65,axiom,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ C @ B) @ (times_times @ TA @ C @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_mult__left__mono__neg)).
% 74.26/25.30  thf(1011,plain,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ C @ B) @ (times_times @ TA @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
% 74.26/25.30  thf(763,axiom,((bounde4967611905675639751up_bot @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__sup__bot_454)).
% 74.26/25.30  thf(3270,plain,((bounde4967611905675639751up_bot @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[763])).
% 74.26/25.30  thf(58,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ A) => ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ B) => (ord_less @ nat @ (suc @ (zero_zero @ nat)) @ (times_times @ nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_one__less__mult)).
% 74.26/25.30  thf(990,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ A) => ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ B) => (ord_less @ nat @ (suc @ (zero_zero @ nat)) @ (times_times @ nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
% 74.26/25.30  thf(229,axiom,((! [A:nat,B:nat]: (ord_less_eq @ nat @ A @ (plus_plus @ nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_le__add2)).
% 74.26/25.30  thf(1542,plain,((! [A:nat,B:nat]: (ord_less_eq @ nat @ A @ (plus_plus @ nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])).
% 74.26/25.30  thf(654,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => (((plus_plus @ nat @ (times_times @ nat @ B @ C) @ D) = (plus_plus @ nat @ (times_times @ nat @ A @ C) @ E)) = ((plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ D) = E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1759_nat__eq__add__iff1)).
% 74.26/25.30  thf(2943,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => (((plus_plus @ nat @ (times_times @ nat @ B @ C) @ D) = (plus_plus @ nat @ (times_times @ nat @ A @ C) @ E)) = ((plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ D) = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[654])).
% 74.26/25.30  thf(482,axiom,((ordere6911136660526730532id_add @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_269)).
% 74.26/25.30  thf(2378,plain,((ordere6911136660526730532id_add @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[482])).
% 74.26/25.30  thf(238,axiom,((ab_semigroup_mult @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__semigroup__mult_289)).
% 74.26/25.30  thf(1571,plain,((ab_semigroup_mult @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
% 74.26/25.30  thf(383,axiom,((! [A:int,B:int,C:int]: ((A != (zero_zero @ int)) => ((dvd_dvd @ int @ B @ C) = (dvd_dvd @ int @ (times_times @ int @ A @ B) @ (times_times @ int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1437_zdvd__mono)).
% 74.26/25.30  thf(2065,plain,((! [A:int,B:int,C:int]: ((~ (A = (zero_zero @ int))) => ((dvd_dvd @ int @ B @ C) = (dvd_dvd @ int @ (times_times @ int @ A @ B) @ (times_times @ int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])).
% 74.26/25.30  thf(150,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ A @ B) => (~ (dvd_dvd @ nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1434_nat__dvd__not__less)).
% 74.26/25.30  thf(1282,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ A @ B) => (~ (dvd_dvd @ nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
% 74.26/25.30  thf(528,axiom,((semigroup_mult @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__mult)).
% 74.26/25.30  thf(2478,plain,((semigroup_mult @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[528])).
% 74.26/25.30  thf(389,axiom,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA]: (order_mono @ TA @ TA @ (plus_plus @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8115_mono__add)).
% 74.26/25.30  thf(2084,plain,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA]: (order_mono @ TA @ TA @ (plus_plus @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])).
% 74.26/25.30  thf(746,axiom,((! [TA: $tType,TB: $tType]: ((order_bot @ TA) => (order_bot @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot)).
% 74.26/25.30  thf(3238,plain,((! [TA: $tType,TB: $tType]: ((order_bot @ TA) => (order_bot @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[746])).
% 74.26/25.30  thf(430,axiom,((! [A:nat]: ((A != (zero_zero @ nat)) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_not0__implies__Suc)).
% 74.26/25.30  thf(2214,plain,((! [A:nat]: ((~ (A = (zero_zero @ nat))) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])).
% 74.26/25.30  thf(485,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less_eq @ TA @ (one_one @ TA) @ (one_one @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_le__numeral__extra_I4_J)).
% 74.26/25.30  thf(2383,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (ord_less_eq @ TA @ (one_one @ TA) @ (one_one @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[485])).
% 74.26/25.30  thf(325,axiom,((! [A:nat]: (dvd_dvd @ nat @ (suc @ (zero_zero @ nat)) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1327_dvd__1__left)).
% 74.26/25.30  thf(1894,plain,((! [A:nat]: (dvd_dvd @ nat @ (suc @ (zero_zero @ nat)) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])).
% 74.26/25.30  thf(669,axiom,((! [TA: $tType]: (! [A:(nat > TA),B:TA,C:nat]: ((extended_case_enat @ TA @ A @ B @ (extended_enat2 @ C)) = (A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_enat_Osimps_I4_J)).
% 74.26/25.30  thf(2987,plain,((! [TA: $tType]: (! [A:(nat > TA),B:TA,C:nat]: ((extended_case_enat @ TA @ (A) @ B @ (extended_enat2 @ C)) = (A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[669])).
% 74.26/25.30  thf(2605,plain,((((vEBT_Leaf @ ($false) @ ($true)) = (vEBT_Leaf @ ($true) @ ($true))) = ((($false) = ($true)) & (($true) = ($true))))),inference(instance,[status(thm)],[2602])).
% 74.26/25.30  thf(2606,plain,((~ ((vEBT_Leaf @ ($false) @ ($true)) = (vEBT_Leaf @ ($true) @ ($true))))),inference(simp,[status(thm)],[2605])).
% 74.26/25.30  thf(2637,plain,(((vEBT_Leaf @ ($false) @ ($true)) != (vEBT_Leaf @ ($true) @ ($true)))),inference(lifteq,[status(thm)],[2606])).
% 74.26/25.30  thf(502,axiom,((! [A:int,B:int,C:int]: ((times_times @ int @ (plus_plus @ int @ A @ B) @ C) = (plus_plus @ int @ (times_times @ int @ A @ C) @ (times_times @ int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1179_int__distrib_I1_J)).
% 74.26/25.30  thf(2422,plain,((! [A:int,B:int,C:int]: ((times_times @ int @ (plus_plus @ int @ A @ B) @ C) = (plus_plus @ int @ (times_times @ int @ A @ C) @ (times_times @ int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])).
% 74.26/25.30  thf(604,axiom,(((minus_minus @ extended_enat) = (^ [A:extended_enat,B:extended_enat]: (extended_case_enat @ extended_enat @ (^ [C:nat]: (extended_case_enat @ extended_enat @ (^ [D:nat]: (extended_enat2 @ (minus_minus @ nat @ C @ D))) @ (zero_zero @ extended_enat) @ B)) @ (extend4730790105801354508finity @ extended_enat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1753_diff__enat__def)).
% 74.26/25.30  thf(2774,plain,(((minus_minus @ extended_enat) = (^ [A:extended_enat,B:extended_enat]: (extended_case_enat @ extended_enat @ (^ [C:nat]: (extended_case_enat @ extended_enat @ (^ [D:nat]: (extended_enat2 @ (minus_minus @ nat @ C @ D))) @ (zero_zero @ extended_enat) @ B)) @ (extend4730790105801354508finity @ extended_enat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[604])).
% 74.26/25.30  thf(772,axiom,((! [A:extended_enat]: (ord_less_eq @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_enat__ord__code_I3_J)).
% 74.26/25.30  thf(3287,plain,((! [A:extended_enat]: (ord_less_eq @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[772])).
% 74.26/25.30  thf(221,axiom,((! [A:nat,B:nat]: (ord_less @ nat @ A @ (suc @ (plus_plus @ nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_803_less__add__Suc2)).
% 74.26/25.30  thf(1524,plain,((! [A:nat,B:nat]: (ord_less @ nat @ A @ (suc @ (plus_plus @ nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
% 74.26/25.30  thf(658,axiom,((! [A:extended_enat]: ((ord_less @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) => (~ (! [B:nat]: (A != (extended_enat2 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_less__infinityE)).
% 74.26/25.30  thf(2955,plain,((! [A:extended_enat]: ((ord_less @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) => (~ (! [B:nat]: ~ (A = (extended_enat2 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[658])).
% 74.26/25.30  thf(20,axiom,((! [A:int]: ((dvd_dvd @ int @ A @ (one_one @ int)) = ((abs_abs @ int @ A) = (one_one @ int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2693_zdvd1__eq)).
% 74.26/25.30  thf(880,plain,((! [A:int]: ((dvd_dvd @ int @ A @ (one_one @ int)) = ((abs_abs @ int @ A) = (one_one @ int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 74.26/25.30  thf(79,axiom,((! [A:real]: ((~ (ord_less @ real @ (zero_zero @ real) @ (times_times @ real @ A @ A))) = (A = (zero_zero @ real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_not__real__square__gt__zero)).
% 74.26/25.30  thf(1043,plain,((! [A:real]: ((~ (ord_less @ real @ (zero_zero @ real) @ (times_times @ real @ A @ A))) = (A = (zero_zero @ real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
% 74.26/25.30  thf(299,axiom,((ordere8940638589300402666id_add @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add_253)).
% 74.26/25.30  thf(1801,plain,((ordere8940638589300402666id_add @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])).
% 74.26/25.30  thf(615,axiom,((! [TA: $tType]: (((numeral @ TA) & (semiring @ TA)) => (! [A:num,B:TA,C:TA]: ((times_times @ TA @ (numeral_numeral @ TA @ A) @ (plus_plus @ TA @ B @ C)) = (plus_plus @ TA @ (times_times @ TA @ (numeral_numeral @ TA @ A) @ B) @ (times_times @ TA @ (numeral_numeral @ TA @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_distrib__left__numeral)).
% 74.26/25.30  thf(2802,plain,((! [TA: $tType]: (((numeral @ TA) & (semiring @ TA)) => (! [A:num,B:TA,C:TA]: ((times_times @ TA @ (numeral_numeral @ TA @ A) @ (plus_plus @ TA @ B @ C)) = (plus_plus @ TA @ (times_times @ TA @ (numeral_numeral @ TA @ A) @ B) @ (times_times @ TA @ (numeral_numeral @ TA @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[615])).
% 74.26/25.30  thf(3498,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less @ TA @ (one_one @ TA) @ (one_one @ TA))) | ((linord181362715937106298miring @ int) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1016,2146])).
% 74.26/25.30  thf(3499,plain,(! [TA:$tType] : ((~ (ord_less @ TA @ (one_one @ TA) @ (one_one @ TA))) | ((linord181362715937106298miring @ int) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3498])).
% 74.26/25.30  thf(3500,plain,((~ (ord_less @ int @ (one_one @ int) @ (one_one @ int)))),inference(pattern_uni,[status(thm)],[3499:[bind_type(TA,$thf(int))]])).
% 74.26/25.30  thf(349,axiom,((! [A:nat]: ((minus_minus @ nat @ A @ A) = (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1682_diff__self__eq__0)).
% 74.26/25.30  thf(1969,plain,((! [A:nat]: ((minus_minus @ nat @ A @ A) = (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])).
% 74.26/25.30  thf(158,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ B) => (ord_less @ nat @ A @ (times_times @ nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_n__less__n__mult__m)).
% 74.26/25.30  thf(1307,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ B) => (ord_less @ nat @ A @ (times_times @ nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
% 74.26/25.30  thf(92,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ C @ A) @ (times_times @ TA @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_mult__strict__left__mono)).
% 74.26/25.30  thf(1080,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ C @ A) @ (times_times @ TA @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
% 74.26/25.30  thf(691,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ E)) = (ord_less_eq @ nat @ D @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1762_nat__le__add__iff2)).
% 74.26/25.30  thf(3055,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ E)) = (ord_less_eq @ nat @ D @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[691])).
% 74.26/25.30  thf(398,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ~ (ord_less @ TA @ (numeral_numeral @ TA @ A) @ (one_one @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_not__numeral__less__one)).
% 74.26/25.30  thf(2111,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ~ (ord_less @ TA @ (numeral_numeral @ TA @ A) @ (one_one @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[398])).
% 74.26/25.30  thf(359,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) => ((ord_less @ nat @ (zero_zero @ nat) @ A) => (dvd_dvd @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1461_dvd__mult__cancel)).
% 74.26/25.30  thf(1993,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) => ((ord_less @ nat @ (zero_zero @ nat) @ A) => (dvd_dvd @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[359])).
% 74.26/25.30  thf(447,axiom,((! [A:nat]: ~ (ord_less @ nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__not__refl)).
% 74.26/25.30  thf(2267,plain,((! [A:nat]: ~ (ord_less @ nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[447])).
% 74.26/25.30  thf(512,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: (ord_less_eq @ TA @ (zero_zero @ TA) @ (numeral_numeral @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_zero__le__numeral)).
% 74.26/25.30  thf(2446,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: (ord_less_eq @ TA @ (zero_zero @ TA) @ (numeral_numeral @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[512])).
% 74.26/25.30  thf(720,axiom,((! [TA: $tType]: ((semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: ((plus_plus @ TA @ (plus_plus @ TA @ A @ B) @ C) = (plus_plus @ TA @ A @ (plus_plus @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_add_Oassoc)).
% 74.26/25.30  thf(3165,plain,((! [TA: $tType]: ((semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: ((plus_plus @ TA @ (plus_plus @ TA @ A @ B) @ C) = (plus_plus @ TA @ A @ (plus_plus @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[720])).
% 74.26/25.30  thf(847,plain,(! [TA:$tType,B:TA,A:TA] : ((~ (linordered_idom @ TA)) | (~ (ord_less_eq @ TA @ (zero_zero @ TA) @ A)) | ((times_times @ TA @ (abs_abs @ TA @ B) @ A) = (abs_abs @ TA @ (times_times @ TA @ B @ A))))),inference(cnf,[status(esa)],[846])).
% 74.26/25.30  thf(848,plain,(! [TA:$tType,B:TA,A:TA] : (((times_times @ TA @ (abs_abs @ TA @ B) @ A) = (abs_abs @ TA @ (times_times @ TA @ B @ A))) | (~ (linordered_idom @ TA)) | (~ (ord_less_eq @ TA @ (zero_zero @ TA) @ A)))),inference(lifteq,[status(thm)],[847])).
% 74.26/25.30  thf(3450,plain,((~ ((extend4730790105801354508finity @ extended_enat) = (zero_zero @ extended_enat)))),inference(polarity_switch,[status(thm)],[3449])).
% 74.26/25.30  thf(3451,plain,(((extend4730790105801354508finity @ extended_enat) != (zero_zero @ extended_enat))),inference(lifteq,[status(thm)],[3450])).
% 74.26/25.30  thf(520,axiom,((! [A:nat,B:nat]: (ord_less @ nat @ (minus_minus @ nat @ A @ B) @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1730_diff__less__Suc)).
% 74.26/25.30  thf(2461,plain,((! [A:nat,B:nat]: (ord_less @ nat @ (minus_minus @ nat @ A @ B) @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[520])).
% 74.26/25.30  thf(23,axiom,((ordere2520102378445227354miring @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__comm__semiring_56)).
% 74.26/25.30  thf(890,plain,((ordere2520102378445227354miring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 74.26/25.30  thf(258,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ B) => (ord_less @ TA @ (plus_plus @ TA @ A @ (one_one @ TA)) @ (plus_plus @ TA @ B @ (one_one @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_add__mono1)).
% 74.26/25.30  thf(1667,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ B) => (ord_less @ TA @ (plus_plus @ TA @ A @ (one_one @ TA)) @ (plus_plus @ TA @ B @ (one_one @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])).
% 74.26/25.30  thf(683,axiom,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ B) @ C) @ (plus_plus @ TA @ (times_times @ TA @ D @ B) @ E)) = (ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ (minus_minus @ TA @ A @ D) @ B) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1633_less__add__iff1)).
% 74.26/25.30  thf(3034,plain,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ B) @ C) @ (plus_plus @ TA @ (times_times @ TA @ D @ B) @ E)) = (ord_less @ TA @ (plus_plus @ TA @ (times_times @ TA @ (minus_minus @ TA @ A @ D) @ B) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[683])).
% 74.26/25.30  thf(497,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ A @ C)) = (ord_less_eq @ nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_nat__add__left__cancel__le)).
% 74.26/25.30  thf(2410,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ A @ C)) = (ord_less_eq @ nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[497])).
% 74.26/25.30  thf(166,axiom,(((one_one @ nat) = (one_one @ nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4546_one__natural_Orsp)).
% 74.26/25.30  thf(1325,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
% 74.26/25.30  thf(111,axiom,((! [A:nat]: ~ (ord_less_eq @ nat @ (suc @ A) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_Suc__n__not__le__n)).
% 74.26/25.30  thf(1149,plain,((! [A:nat]: ~ (ord_less_eq @ nat @ (suc @ A) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
% 74.26/25.30  thf(779,axiom,((! [A:extended_enat,B:extended_enat]: (((plus_plus @ extended_enat @ A @ B) = (extend4730790105801354508finity @ extended_enat)) = ((A = (extend4730790105801354508finity @ extended_enat)) | (B = (extend4730790105801354508finity @ extended_enat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_plus__eq__infty__iff__enat)).
% 74.26/25.30  thf(3298,plain,((! [A:extended_enat,B:extended_enat]: (((plus_plus @ extended_enat @ A @ B) = (extend4730790105801354508finity @ extended_enat)) = ((A = (extend4730790105801354508finity @ extended_enat)) | (B = (extend4730790105801354508finity @ extended_enat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[779])).
% 74.26/25.30  thf(235,axiom,((! [A:nat,B:nat]: ((dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ A)) = ((ord_less @ nat @ B @ A) | (dvd_dvd @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1745_dvd__minus__self)).
% 74.26/25.30  thf(1556,plain,((! [A:nat,B:nat]: ((dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ A)) = ((ord_less @ nat @ B @ A) | (dvd_dvd @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])).
% 74.26/25.30  thf(551,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less @ TA @ C @ D) => ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_942_mult__le__less__imp__less)).
% 74.26/25.30  thf(2542,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less @ TA @ C @ D) => ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[551])).
% 74.26/25.30  thf(572,axiom,((! [A:(int > $o),B:int,C:int]: ((A @ B) => ((! [D:int]: ((ord_less_eq @ int @ B @ D) => ((A @ D) => (A @ (plus_plus @ int @ D @ (one_one @ int)))))) => ((! [D:int]: ((ord_less_eq @ int @ D @ B) => ((A @ D) => (A @ (minus_minus @ int @ D @ (one_one @ int)))))) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1647_int__induct)).
% 74.26/25.30  thf(2647,plain,((! [A:(int > $o),B:int,C:int]: ((A @ B) => ((! [D:int]: ((ord_less_eq @ int @ B @ D) => ((A @ D) => (A @ (plus_plus @ int @ D @ (one_one @ int)))))) => ((! [D:int]: ((ord_less_eq @ int @ D @ B) => ((A @ D) => (A @ (minus_minus @ int @ D @ (one_one @ int)))))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[572])).
% 74.26/25.30  thf(451,axiom,((canoni5634975068530333245id_add @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add)).
% 74.26/25.30  thf(2278,plain,((canoni5634975068530333245id_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[451])).
% 74.26/25.30  thf(556,axiom,((! [TA: $tType]: ((strict7427464778891057005id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ B @ C) => (ord_less @ TA @ B @ (plus_plus @ TA @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_pos__add__strict)).
% 74.26/25.30  thf(2553,plain,((! [TA: $tType]: ((strict7427464778891057005id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ B @ C) => (ord_less @ TA @ B @ (plus_plus @ TA @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[556])).
% 74.26/25.30  thf(625,axiom,((! [TA: $tType,TB: $tType]: ((lattice @ TA) => (lattice @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice)).
% 74.26/25.30  thf(2842,plain,((! [TA: $tType,TB: $tType]: ((lattice @ TA) => (lattice @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[625])).
% 74.26/25.30  thf(86,axiom,((! [A:nat,B:nat]: ((ord_less @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (ord_less @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_enat__ord__simps_I2_J)).
% 74.26/25.30  thf(1061,plain,((! [A:nat,B:nat]: ((ord_less @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (ord_less @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
% 74.26/25.30  thf(342,axiom,(((ord_less_eq @ nat) = (^ [A:nat,B:nat]: ((ord_less @ nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_le__eq__less__or__eq)).
% 74.26/25.30  thf(1952,plain,(((ord_less_eq @ nat) = (^ [A:nat,B:nat]: ((ord_less @ nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])).
% 74.26/25.30  thf(581,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) => ((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_940_mult__left__le__imp__le)).
% 74.26/25.30  thf(2710,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) => ((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[581])).
% 74.26/25.30  thf(644,axiom,((! [TA: $tType,TB: $tType]: ((wellorder @ TB) => (! [A:(TA > TB),B:(TA > $o),C:TA]: ((! [D:TA]: ((! [E:TA]: ((ord_less @ TB @ (A @ E) @ (A @ D)) => (B @ E))) => (B @ D))) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_measure__induct)).
% 74.26/25.30  thf(2911,plain,((! [TA: $tType,TB: $tType]: ((wellorder @ TB) => (! [A:(TA > TB),B:(TA > $o),C:TA]: ((! [D:TA]: ((! [E:TA]: ((ord_less @ TB @ (A @ E) @ (A @ D)) => (B @ E))) => (B @ D))) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[644])).
% 74.26/25.30  thf(307,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => ((ord_max @ TA @ (zero_zero @ TA) @ (one_one @ TA)) = (one_one @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4775_max__0__1_I1_J)).
% 74.26/25.30  thf(1820,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => ((ord_max @ TA @ (zero_zero @ TA) @ (one_one @ TA)) = (one_one @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])).
% 74.26/25.30  thf(54,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ (suc @ A) @ B) => (ord_less @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_796_Suc__le__lessD)).
% 74.26/25.30  thf(983,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)],[54])).
% 74.26/25.30  thf(429,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_add__nonneg__nonneg)).
% 74.26/25.30  thf(2212,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])).
% 74.26/25.30  thf(128,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less @ nat @ A @ B) | (ord_less @ nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_nat__neq__iff)).
% 74.26/25.30  thf(1213,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)],[128])).
% 74.26/25.30  thf(201,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ (suc @ A) @ B) = (ord_less @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_Suc__le__eq)).
% 74.26/25.30  thf(1445,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)],[201])).
% 74.26/25.30  thf(390,axiom,((order_mono @ nat @ nat @ suc)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8116_mono__Suc)).
% 74.26/25.30  thf(2086,plain,((order_mono @ nat @ nat @ (suc))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])).
% 74.26/25.30  thf(21,axiom,((! [A:int,B:int]: ((A != (zero_zero @ int)) => ((dvd_dvd @ int @ (times_times @ int @ A @ B) @ A) = ((abs_abs @ int @ B) = (one_one @ int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2764_zdvd__mult__cancel1)).
% 74.26/25.30  thf(883,plain,((! [A:int,B:int]: ((~ (A = (zero_zero @ int))) => ((dvd_dvd @ int @ (times_times @ int @ A @ B) @ A) = ((abs_abs @ int @ B) = (one_one @ int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
% 74.26/25.30  thf(56,axiom,((linordered_semiring @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semiring)).
% 74.26/25.30  thf(986,plain,((linordered_semiring @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
% 74.26/25.30  thf(613,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq @ int @ (plus_plus @ int @ (times_times @ int @ A @ B) @ C) @ (plus_plus @ int @ (times_times @ int @ A @ D) @ E)) => ((ord_less_eq @ int @ (zero_zero @ int) @ C) => ((ord_less @ int @ C @ A) => ((ord_less @ int @ E @ A) => (ord_less_eq @ int @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_unique__quotient__lemma)).
% 74.26/25.30  thf(2797,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq @ int @ (plus_plus @ int @ (times_times @ int @ A @ B) @ C) @ (plus_plus @ int @ (times_times @ int @ A @ D) @ E)) => ((ord_less_eq @ int @ (zero_zero @ int) @ C) => ((ord_less @ int @ C @ A) => ((ord_less @ int @ E @ A) => (ord_less_eq @ int @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[613])).
% 74.26/25.30  thf(785,axiom,((! [A:extended_enat]: ((ord_max @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4819_max__enat__simps_I5_J)).
% 74.26/25.30  thf(3310,plain,((! [A:extended_enat]: ((ord_max @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[785])).
% 74.26/25.30  thf(673,axiom,((! [TA: $tType]: ((mult_zero @ TA) => (! [A:TA,B:TA]: (((times_times @ TA @ A @ B) != (zero_zero @ TA)) => ((A != (zero_zero @ TA)) & (B != (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_mult__not__zero)).
% 74.26/25.30  thf(2999,plain,((! [TA: $tType]: ((mult_zero @ TA) => (! [A:TA,B:TA]: ((~ ((times_times @ TA @ A @ B) = (zero_zero @ TA))) => (~ (A = (zero_zero @ TA)) & ~ (B = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[673])).
% 74.26/25.30  thf(301,axiom,(((ord_less @ nat) = (^ [A:nat]: (ord_less_eq @ nat @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_less__eq__Suc__le)).
% 74.26/25.30  thf(1805,plain,(((ord_less @ nat) = (^ [A:nat]: (ord_less_eq @ nat @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])).
% 74.26/25.30  thf(384,axiom,((! [A:nat,B:nat]: (((times_times @ nat @ A @ B) = (one_one @ nat)) = ((A = (one_one @ nat)) & (B = (one_one @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_nat__mult__eq__1__iff)).
% 74.26/25.30  thf(2069,plain,((! [A:nat,B:nat]: (((times_times @ nat @ A @ B) = (one_one @ nat)) = ((A = (one_one @ nat)) & (B = (one_one @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])).
% 74.26/25.30  thf(126,axiom,((zero_less_one @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ozero__less__one)).
% 74.26/25.30  thf(1198,plain,((zero_less_one @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
% 74.26/25.30  thf(508,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((dvd_dvd @ nat @ (times_times @ nat @ B @ A) @ A) = (B = (one_one @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1479_dvd__mult__cancel2)).
% 74.26/25.30  thf(2439,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((dvd_dvd @ nat @ (times_times @ nat @ B @ A) @ A) = (B = (one_one @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])).
% 74.26/25.30  thf(587,axiom,((! [A:num,B:nat]: ((ord_less @ extended_enat @ (numeral_numeral @ extended_enat @ A) @ (extended_enat2 @ B)) = (ord_less @ nat @ (numeral_numeral @ nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_numeral__less__enat__iff)).
% 74.26/25.30  thf(2725,plain,((! [A:num,B:nat]: ((ord_less @ extended_enat @ (numeral_numeral @ extended_enat @ A) @ (extended_enat2 @ B)) = (ord_less @ nat @ (numeral_numeral @ nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[587])).
% 74.26/25.30  thf(268,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (times_times @ nat @ (suc @ A) @ B) @ (times_times @ nat @ (suc @ A) @ C)) = (ord_less_eq @ nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_Suc__mult__le__cancel1)).
% 74.26/25.30  thf(1699,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (times_times @ nat @ (suc @ A) @ B) @ (times_times @ nat @ (suc @ A) @ C)) = (ord_less_eq @ nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])).
% 74.26/25.30  thf(718,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: ((zero @ TB) => (! [A:((TC > TB) > TA),B:TA]: ((A = (^ [C:(TC > TB)]: (B))) => ((A @ (^ [C:TC]: (zero_zero @ TB))) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3849_fun__cong__unused__0)).
% 74.26/25.30  thf(3159,plain,((! [TA: $tType,TB: $tType,TC: $tType]: ((zero @ TB) => (! [A:((TC > TB) > TA),B:TA]: (((A) = (^ [C:(TC > TB)]: (B))) => ((A @ (^ [C:TC]: (zero_zero @ TB))) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[718])).
% 74.26/25.30  thf(382,axiom,((lattice @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Olattice_93)).
% 74.26/25.30  thf(2064,plain,((lattice @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])).
% 74.26/25.30  thf(479,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_855_zero__less__mult__pos2)).
% 74.26/25.30  thf(2369,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])).
% 74.26/25.30  thf(293,axiom,((! [A:nat,B:nat]: ((A = (suc @ B)) => (A != (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_nat_OdiscI)).
% 74.26/25.30  thf(1775,plain,((! [A:nat,B:nat]: ((A = (suc @ B)) => (~ (A = (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])).
% 74.26/25.30  thf(61,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (minus_minus @ nat @ A @ B) @ C) = (minus_minus @ nat @ A @ (plus_plus @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1684_diff__diff__left)).
% 74.26/25.30  thf(1000,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (minus_minus @ nat @ A @ B) @ C) = (minus_minus @ nat @ A @ (plus_plus @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
% 74.26/25.30  thf(175,axiom,((complete_Sup @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Complete__Lattices_OSup_75)).
% 74.26/25.30  thf(1364,plain,((complete_Sup @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
% 74.26/25.30  thf(488,axiom,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((suc @ (minus_minus @ nat @ A @ (one_one @ nat))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1702_Suc__diff__1)).
% 74.26/25.30  thf(2390,plain,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((suc @ (minus_minus @ nat @ A @ (one_one @ nat))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[488])).
% 74.26/25.30  thf(267,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ B) => (~ (! [C:nat]: ((ord_less @ nat @ A @ C) => (B != (suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_Suc__lessE)).
% 74.26/25.30  thf(1694,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ B) => (~ (! [C:nat]: ((ord_less @ nat @ A @ C) => (~ (B = (suc @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])).
% 74.26/25.30  thf(37,axiom,((power @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Power_Opower)).
% 74.26/25.30  thf(922,plain,((power @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
% 74.26/25.30  thf(576,axiom,((! [TA: $tType]: ((ab_semigroup_add @ TA) => ((plus_plus @ TA) = (^ [A:TA,B:TA]: (plus_plus @ TA @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_add_Ocommute)).
% 74.26/25.30  thf(2693,plain,((! [TA: $tType]: ((ab_semigroup_add @ TA) => ((plus_plus @ TA) = (^ [A:TA,B:TA]: (plus_plus @ TA @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[576])).
% 74.26/25.30  thf(190,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ B @ C) => (ord_less_eq @ nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_le__trans)).
% 74.26/25.30  thf(1413,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ B @ C) => (ord_less_eq @ nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])).
% 74.26/25.30  thf(675,axiom,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add__mono)).
% 74.26/25.30  thf(3009,plain,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[675])).
% 74.26/25.30  thf(341,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ C @ (minus_minus @ nat @ B @ A)) = (minus_minus @ nat @ (plus_plus @ nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1693_Nat_Odiff__diff__right)).
% 74.26/25.30  thf(1948,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ C @ (minus_minus @ nat @ B @ A)) = (minus_minus @ nat @ (plus_plus @ nat @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])).
% 74.26/25.30  thf(811,axiom,(((vEBT_VEBT_elim_dead @ summarya @ (extend4730790105801354508finity @ extended_enat)) = summarya)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__C2_OIH_C_I2_J)).
% 74.26/25.30  thf(3444,plain,(((vEBT_VEBT_elim_dead @ summarya @ (extend4730790105801354508finity @ extended_enat)) = summarya)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[811])).
% 74.26/25.30  thf(682,axiom,((! [TA: $tType]: ((comm_monoid_diff @ TA) => (! [A:TA,B:TA]: ((minus_minus @ TA @ A @ (plus_plus @ TA @ A @ B)) = (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1537_diff__add__zero)).
% 74.26/25.30  thf(3031,plain,((! [TA: $tType]: ((comm_monoid_diff @ TA) => (! [A:TA,B:TA]: ((minus_minus @ TA @ A @ (plus_plus @ TA @ A @ B)) = (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[682])).
% 74.26/25.30  thf(318,axiom,((! [A:num,B:num]: ((ord_less_eq @ extended_enat @ (numeral_numeral @ extended_enat @ A) @ (numeral_numeral @ extended_enat @ B)) = (ord_less_eq @ nat @ (numeral_numeral @ nat @ A) @ (numeral_numeral @ nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_enat__ord__number_I1_J)).
% 74.26/25.30  thf(1873,plain,((! [A:num,B:num]: ((ord_less_eq @ extended_enat @ (numeral_numeral @ extended_enat @ A) @ (numeral_numeral @ extended_enat @ B)) = (ord_less_eq @ nat @ (numeral_numeral @ nat @ A) @ (numeral_numeral @ nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])).
% 74.26/25.30  thf(46,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ (zero_zero @ TA)) => (ord_less @ TA @ (times_times @ TA @ B @ C) @ (times_times @ TA @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_mult__strict__right__mono__neg)).
% 74.26/25.30  thf(944,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ (zero_zero @ TA)) => (ord_less @ TA @ (times_times @ TA @ B @ C) @ (times_times @ TA @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
% 74.26/25.30  thf(671,axiom,((! [TA: $tType]: ((monoid_add @ TA) => (! [A:TA]: ((plus_plus @ TA @ (zero_zero @ TA) @ A) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_add__0)).
% 74.26/25.30  thf(2994,plain,((! [TA: $tType]: ((monoid_add @ TA) => (! [A:TA]: ((plus_plus @ TA @ (zero_zero @ TA) @ A) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[671])).
% 74.26/25.30  thf(39,axiom,((! [A:nat,B:nat,C:nat]: (((times_times @ nat @ A @ B) = (times_times @ nat @ A @ C)) = ((A = (zero_zero @ nat)) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_765_nat__mult__eq__cancel__disj)).
% 74.26/25.30  thf(927,plain,((! [A:nat,B:nat,C:nat]: (((times_times @ nat @ A @ B) = (times_times @ nat @ A @ C)) = ((A = (zero_zero @ nat)) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
% 74.26/25.30  thf(538,axiom,((zero_neq_one @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ozero__neq__one)).
% 74.26/25.30  thf(2503,plain,((zero_neq_one @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[538])).
% 74.26/25.30  thf(106,axiom,((! [A:nat]: ((ord_less_eq @ nat @ A @ (zero_zero @ nat)) = (A = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_bot__nat__0_Oextremum__unique)).
% 74.26/25.30  thf(1134,plain,((! [A:nat]: ((ord_less_eq @ nat @ A @ (zero_zero @ nat)) = (A = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
% 74.26/25.30  thf(649,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less_eq @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_939_mult__le__cancel__left__pos)).
% 74.26/25.30  thf(2927,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less_eq @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[649])).
% 74.26/25.30  thf(688,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (times_times @ TA @ A @ B)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ (one_one @ TA) @ B)) & ((ord_less @ TA @ A @ (zero_zero @ TA)) => (ord_less_eq @ TA @ B @ (one_one @ TA))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1037_mult__le__cancel__left1)).
% 74.26/25.30  thf(3048,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (times_times @ TA @ A @ B)) = (((ord_less @ TA @ (zero_zero @ TA) @ A) => (ord_less_eq @ TA @ (one_one @ TA) @ B)) & ((ord_less @ TA @ A @ (zero_zero @ TA)) => (ord_less_eq @ TA @ B @ (one_one @ TA))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[688])).
% 74.26/25.30  thf(110,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (suc @ (minus_minus @ nat @ B @ A)) @ C) = (minus_minus @ nat @ (suc @ B) @ (plus_plus @ nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1701_diff__Suc__diff__eq2)).
% 74.26/25.30  thf(1145,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ (suc @ (minus_minus @ nat @ B @ A)) @ C) = (minus_minus @ nat @ (suc @ B) @ (plus_plus @ nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
% 74.26/25.30  thf(51,axiom,((! [A:nat,B:(nat > int),C:int]: ((! [D:nat]: ((ord_less @ nat @ D @ A) => (ord_less_eq @ int @ (abs_abs @ int @ (minus_minus @ int @ (B @ (plus_plus @ nat @ D @ (one_one @ nat))) @ (B @ D))) @ (one_one @ int)))) => ((ord_less_eq @ int @ (B @ (zero_zero @ nat)) @ C) => ((ord_less_eq @ int @ C @ (B @ A)) => (? [D:nat]: ((ord_less_eq @ nat @ D @ A) & ((B @ D) = C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2801_nat0__intermed__int__val)).
% 74.26/25.30  thf(968,plain,((! [A:nat,B:(nat > int),C:int]: ((! [D:nat]: ((ord_less @ nat @ D @ A) => (ord_less_eq @ int @ (abs_abs @ int @ (minus_minus @ int @ (B @ (plus_plus @ nat @ D @ (one_one @ nat))) @ (B @ D))) @ (one_one @ int)))) => ((ord_less_eq @ int @ (B @ (zero_zero @ nat)) @ C) => ((ord_less_eq @ int @ C @ (B @ A)) => (? [D:nat]: ((ord_less_eq @ nat @ D @ A) & ((B @ D) = C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
% 74.26/25.30  thf(8,axiom,((! [A:int,B:int]: ((A != (zero_zero @ int)) => ((dvd_dvd @ int @ B @ A) => (ord_less_eq @ int @ (abs_abs @ int @ B) @ (abs_abs @ int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2754_dvd__imp__le__int)).
% 74.76/25.30  thf(836,plain,((! [A:int,B:int]: ((~ (A = (zero_zero @ int))) => ((dvd_dvd @ int @ B @ A) => (ord_less_eq @ int @ (abs_abs @ int @ B) @ (abs_abs @ int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 74.76/25.30  thf(81,axiom,((ordere2520102378445227354miring @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oordered__comm__semiring_279)).
% 74.76/25.30  thf(1049,plain,((ordere2520102378445227354miring @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
% 74.76/25.30  thf(287,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)) => ((ord_less @ TA @ A @ (zero_zero @ TA)) | (ord_less @ TA @ B @ (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_add__less__zeroD)).
% 74.76/25.30  thf(1758,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)) => ((ord_less @ TA @ A @ (zero_zero @ TA)) | (ord_less @ TA @ B @ (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])).
% 74.76/25.30  thf(118,axiom,((ab_semigroup_mult @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__mult)).
% 74.76/25.30  thf(1166,plain,((ab_semigroup_mult @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
% 74.76/25.30  thf(465,axiom,((! [A:nat,B:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1724_diff__add__inverse)).
% 74.76/25.30  thf(2318,plain,((! [A:nat,B:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])).
% 74.76/25.30  thf(734,axiom,((! [TA: $tType,TB: $tType]: ((complete_Inf @ TA) => (complete_Inf @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_OInf)).
% 74.76/25.30  thf(3206,plain,((! [TA: $tType,TB: $tType]: ((complete_Inf @ TA) => (complete_Inf @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[734])).
% 74.76/25.30  thf(777,axiom,((semigroup_add @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_475)).
% 74.76/25.30  thf(3293,plain,((semigroup_add @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[777])).
% 74.76/25.30  thf(525,axiom,((! [A:nat,B:nat]: ((A = (times_times @ nat @ A @ B)) => ((B = (one_one @ nat)) | (A = (zero_zero @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_919_mult__eq__self__implies__10)).
% 74.76/25.30  thf(2471,plain,((! [A:nat,B:nat]: ((A = (times_times @ nat @ A @ B)) => ((B = (one_one @ nat)) | (A = (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[525])).
% 74.76/25.30  thf(330,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (ord_less_eq @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_less__imp__le__nat)).
% 74.76/25.30  thf(1905,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (ord_less_eq @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])).
% 74.76/25.30  thf(193,axiom,((! [A:nat,B:nat,C:nat]: (((times_times @ nat @ (suc @ A) @ B) = (times_times @ nat @ (suc @ A) @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_727_Suc__mult__cancel1)).
% 74.76/25.30  thf(1420,plain,((! [A:nat,B:nat,C:nat]: (((times_times @ nat @ (suc @ A) @ B) = (times_times @ nat @ (suc @ A) @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
% 74.76/25.30  thf(514,axiom,((semiring @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring)).
% 74.76/25.30  thf(2449,plain,((semiring @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[514])).
% 74.76/25.30  thf(217,axiom,((! [A:nat]: ((ord_less @ nat @ A @ (one_one @ nat)) = (A = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_less__one)).
% 74.76/25.30  thf(1509,plain,((! [A:nat]: ((ord_less @ nat @ A @ (one_one @ nat)) = (A = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])).
% 74.76/25.30  thf(767,axiom,((ordere2520102378445227354miring @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Oordered__comm__semiring_461)).
% 74.76/25.30  thf(3278,plain,((ordere2520102378445227354miring @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[767])).
% 74.76/25.30  thf(569,axiom,((! [A:int,B:int]: ((ord_less @ int @ A @ (plus_plus @ int @ B @ (one_one @ int))) = (ord_less_eq @ int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_zle__add1__eq__le)).
% 74.76/25.30  thf(2597,plain,((! [A:int,B:int]: ((ord_less @ int @ A @ (plus_plus @ int @ B @ (one_one @ int))) = (ord_less_eq @ int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[569])).
% 74.76/25.30  thf(345,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ C)) => ((dvd_dvd @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ B) => (dvd_dvd @ nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1747_dvd__diffD1)).
% 74.76/25.30  thf(1958,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ C)) => ((dvd_dvd @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ B) => (dvd_dvd @ nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])).
% 74.76/25.30  thf(776,axiom,((mult_zero @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Omult__zero_490)).
% 74.76/25.30  thf(3292,plain,((mult_zero @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[776])).
% 74.76/25.30  thf(640,axiom,((! [A:int]: ((ord_less_eq @ int @ (one_one @ int) @ A) = (ord_less @ int @ (zero_zero @ int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_int__one__le__iff__zero__less)).
% 74.76/25.30  thf(2899,plain,((! [A:int]: ((ord_less_eq @ int @ (one_one @ int) @ A) = (ord_less @ int @ (zero_zero @ int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[640])).
% 74.76/25.30  thf(559,axiom,((! [A:extended_enat,B:extended_enat]: ((A != (extend4730790105801354508finity @ extended_enat)) => ((minus_minus @ extended_enat @ (plus_plus @ extended_enat @ A @ B) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1689_add__diff__cancel__enat)).
% 74.76/25.30  thf(2567,plain,((! [A:extended_enat,B:extended_enat]: ((~ (A = (extend4730790105801354508finity @ extended_enat))) => ((minus_minus @ extended_enat @ (plus_plus @ extended_enat @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[559])).
% 74.76/25.30  thf(231,axiom,((linord4710134922213307826strict @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__ring__strict_275)).
% 74.76/25.30  thf(1547,plain,((linord4710134922213307826strict @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])).
% 74.76/25.30  thf(461,axiom,((! [A:int]: ((plus_plus @ int @ (plus_plus @ int @ (one_one @ int) @ A) @ A) != (zero_zero @ int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_odd__nonzero)).
% 74.76/25.30  thf(2298,plain,((! [A:int]: ~ ((plus_plus @ int @ (plus_plus @ int @ (one_one @ int) @ A) @ A) = (zero_zero @ int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[461])).
% 74.76/25.30  thf(62,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (plus_plus @ nat @ A @ B) @ C) => (ord_less_eq @ nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_add__leD2)).
% 74.76/25.30  thf(1003,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (plus_plus @ nat @ A @ B) @ C) => (ord_less_eq @ nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
% 74.76/25.30  thf(566,axiom,((! [TA: $tType]: ((ab_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: ((plus_plus @ TA @ (plus_plus @ TA @ A @ B) @ C) = (plus_plus @ TA @ A @ (plus_plus @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_ab__semigroup__add__class_Oadd__ac_I1_J)).
% 74.76/25.30  thf(2588,plain,((! [TA: $tType]: ((ab_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: ((plus_plus @ TA @ (plus_plus @ TA @ A @ B) @ C) = (plus_plus @ TA @ A @ (plus_plus @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[566])).
% 74.76/25.30  thf(709,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) = (A != (zero_zero @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_zero__less__iff__neq__zero)).
% 74.76/25.30  thf(3129,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) = (~ (A = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[709])).
% 74.76/25.30  thf(294,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ (zero_zero @ nat))) => (? [C:nat]: ((ord_less @ nat @ C @ B) & ! [D:nat]: ((ord_less_eq @ nat @ D @ C) => (~ (A @ D))) & (A @ (suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_ex__least__nat__less)).
% 74.76/25.30  thf(1780,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ (zero_zero @ nat))) => (? [C:nat]: ((ord_less @ nat @ C @ B) & ! [D:nat]: ((ord_less_eq @ nat @ D @ C) => (~ (A @ D))) & (A @ (suc @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])).
% 74.76/25.30  thf(224,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ A @ (plus_plus @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_trans__le__add1)).
% 74.76/25.30  thf(1531,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ A @ (plus_plus @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
% 74.76/25.30  thf(639,axiom,((! [A:int,B:(int > $o),C:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => ((! [D:int]: ((B @ D) => (B @ (minus_minus @ int @ D @ A)))) => ((ord_less_eq @ int @ (zero_zero @ int) @ C) => (! [D:int]: ((B @ D) => (B @ (minus_minus @ int @ D @ (times_times @ int @ C @ A)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1652_decr__mult__lemma)).
% 74.76/25.30  thf(2888,plain,((! [A:int,B:(int > $o),C:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => ((! [D:int]: ((B @ D) => (B @ (minus_minus @ int @ D @ A)))) => ((ord_less_eq @ int @ (zero_zero @ int) @ C) => (! [D:int]: ((B @ D) => (B @ (minus_minus @ int @ D @ (times_times @ int @ C @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[639])).
% 74.76/25.30  thf(637,axiom,((! [TA: $tType]: ((ab_semigroup_mult @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ A @ (times_times @ TA @ B @ C)) = (times_times @ TA @ B @ (times_times @ TA @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_mult_Oleft__commute)).
% 74.76/25.30  thf(2882,plain,((! [TA: $tType]: ((ab_semigroup_mult @ TA) => (! [A:TA,B:TA,C:TA]: ((times_times @ TA @ A @ (times_times @ TA @ B @ C)) = (times_times @ TA @ B @ (times_times @ TA @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[637])).
% 74.76/25.30  thf(89,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less @ nat @ C @ (suc @ A)) & (B @ C))) = ((B @ (zero_zero @ nat)) | ? [C:nat]: ((ord_less @ nat @ C @ A) & (B @ (suc @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_Ex__less__Suc2)).
% 74.76/25.30  thf(1070,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less @ nat @ C @ (suc @ A)) & (B @ C))) = ((B @ (zero_zero @ nat)) | ? [C:nat]: ((ord_less @ nat @ C @ A) & (B @ (suc @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
% 74.76/25.30  thf(705,axiom,((! [A:num,B:nat]: ((ord_less_eq @ extended_enat @ (numeral_numeral @ extended_enat @ A) @ (extended_enat2 @ B)) = (ord_less_eq @ nat @ (numeral_numeral @ nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_numeral__le__enat__iff)).
% 74.76/25.30  thf(3112,plain,((! [A:num,B:nat]: ((ord_less_eq @ extended_enat @ (numeral_numeral @ extended_enat @ A) @ (extended_enat2 @ B)) = (ord_less_eq @ nat @ (numeral_numeral @ nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[705])).
% 74.76/25.30  thf(18,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA]: (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ (one_one @ TA) @ (abs_abs @ TA @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2658_abs__add__one__gt__zero)).
% 74.76/25.30  thf(872,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA]: (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ (one_one @ TA) @ (abs_abs @ TA @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 74.76/25.30  thf(132,axiom,((semiring @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring_97)).
% 74.76/25.30  thf(1225,plain,((semiring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
% 74.76/25.30  thf(380,axiom,((! [A:nat,B:nat]: ((ord_max @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (extended_enat2 @ (ord_max @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4832_max__enat__simps_I1_J)).
% 74.76/25.30  thf(2060,plain,((! [A:nat,B:nat]: ((ord_max @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (extended_enat2 @ (ord_max @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])).
% 74.76/25.30  thf(283,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less @ nat @ A @ B) => ((! [D:nat]: (C @ D @ (suc @ D))) => ((! [D:nat,E:nat,F:nat]: ((ord_less @ nat @ D @ E) => ((ord_less @ nat @ E @ F) => ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))))) => (C @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_less__Suc__induct)).
% 74.76/25.30  thf(1743,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less @ nat @ A @ B) => ((! [D:nat]: (C @ D @ (suc @ D))) => ((! [D:nat,E:nat,F:nat]: ((ord_less @ nat @ D @ E) => ((ord_less @ nat @ E @ F) => ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))))) => (C @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])).
% 74.76/25.30  thf(422,axiom,((! [A:int,B:int,C:$o,D:$o]: ((A = B) => (((ord_less_eq @ int @ (zero_zero @ int) @ B) => (C = D)) => (((ord_less_eq @ int @ (zero_zero @ int) @ A) => (C)) = ((ord_less_eq @ int @ (zero_zero @ int) @ B) => (D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1175_imp__le__cong)).
% 74.76/25.30  thf(2192,plain,((! [A:int,B:int,C:$o,D:$o]: ((A = B) => (((ord_less_eq @ int @ (zero_zero @ int) @ B) => (C = D)) => (((ord_less_eq @ int @ (zero_zero @ int) @ A) => (C)) = ((ord_less_eq @ int @ (zero_zero @ int) @ B) => (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])).
% 74.76/25.30  thf(22,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (abs_abs @ TA @ (minus_minus @ TA @ A @ B)) @ C) = ((ord_less_eq @ TA @ (minus_minus @ TA @ B @ C) @ A) & (ord_less_eq @ TA @ A @ (plus_plus @ TA @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2653_abs__diff__le__iff)).
% 74.76/25.30  thf(887,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (abs_abs @ TA @ (minus_minus @ TA @ A @ B)) @ C) = ((ord_less_eq @ TA @ (minus_minus @ TA @ B @ C) @ A) & (ord_less_eq @ TA @ A @ (plus_plus @ TA @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 74.76/25.30  thf(179,axiom,((! [A:nat,B:(nat > int),C:int]: ((! [D:nat]: ((ord_less @ nat @ D @ A) => (ord_less_eq @ int @ (abs_abs @ int @ (minus_minus @ int @ (B @ (suc @ D)) @ (B @ D))) @ (one_one @ int)))) => ((ord_less_eq @ int @ (B @ (zero_zero @ nat)) @ C) => ((ord_less_eq @ int @ C @ (B @ A)) => (? [D:nat]: ((ord_less_eq @ nat @ D @ A) & ((B @ D) = C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2796_nat__ivt__aux)).
% 74.76/25.30  thf(1368,plain,((! [A:nat,B:(nat > int),C:int]: ((! [D:nat]: ((ord_less @ nat @ D @ A) => (ord_less_eq @ int @ (abs_abs @ int @ (minus_minus @ int @ (B @ (suc @ D)) @ (B @ D))) @ (one_one @ int)))) => ((ord_less_eq @ int @ (B @ (zero_zero @ nat)) @ C) => ((ord_less_eq @ int @ C @ (B @ A)) => (? [D:nat]: ((ord_less_eq @ nat @ D @ A) & ((B @ D) = C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
% 74.76/25.30  thf(742,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_less_eq @ extended_enat @ (plus_plus @ extended_enat @ A @ B) @ (plus_plus @ extended_enat @ A @ C)) = ((A = (extend4730790105801354508finity @ extended_enat)) | (ord_less_eq @ extended_enat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_enat__add__left__cancel__le)).
% 74.76/25.30  thf(3228,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_less_eq @ extended_enat @ (plus_plus @ extended_enat @ A @ B) @ (plus_plus @ extended_enat @ A @ C)) = ((A = (extend4730790105801354508finity @ extended_enat)) | (ord_less_eq @ extended_enat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[742])).
% 74.76/25.30  thf(285,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (((times_times @ nat @ A @ B) = (times_times @ nat @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_914_nat__mult__eq__cancel1)).
% 74.76/25.30  thf(1753,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (((times_times @ nat @ A @ B) = (times_times @ nat @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])).
% 74.76/25.30  thf(495,axiom,((ab_semigroup_mult @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult_63)).
% 74.76/25.30  thf(2407,plain,((ab_semigroup_mult @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[495])).
% 74.76/25.30  thf(149,axiom,((! [A:int,B:int,C:(int > $o)]: ((ord_less_eq @ int @ A @ B) => ((C @ B) => ((! [D:int]: ((ord_less_eq @ int @ D @ B) => ((C @ D) => (C @ (minus_minus @ int @ D @ (one_one @ int)))))) => (C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1627_int__le__induct)).
% 74.76/25.30  thf(1267,plain,((! [A:int,B:int,C:(int > $o)]: ((ord_less_eq @ int @ A @ B) => ((C @ B) => ((! [D:int]: ((ord_less_eq @ int @ D @ B) => ((C @ D) => (C @ (minus_minus @ int @ D @ (one_one @ int)))))) => (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
% 74.76/25.30  thf(136,axiom,((! [A:nat,B:nat]: (((plus_plus @ nat @ A @ B) = (zero_zero @ nat)) = ((A = (zero_zero @ nat)) & (B = (zero_zero @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_add__is__0)).
% 74.76/25.30  thf(1230,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)],[136])).
% 74.76/25.30  thf(628,axiom,((! [TA: $tType]: ((mult_zero @ TA) => (! [A:TA]: ((times_times @ TA @ (zero_zero @ TA) @ A) = (zero_zero @ TA)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_mult__zero__left)).
% 74.76/25.30  thf(2850,plain,((! [TA: $tType]: ((mult_zero @ TA) => (! [A:TA]: ((times_times @ TA @ (zero_zero @ TA) @ A) = (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[628])).
% 74.76/25.30  thf(59,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = (ord_less @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_913_nat__mult__less__cancel1)).
% 74.76/25.30  thf(993,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = (ord_less @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
% 74.76/25.30  thf(574,axiom,((! [TA: $tType]: ((ordere8940638589300402666id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ B @ C) => (ord_less @ TA @ B @ (plus_plus @ TA @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_949_add__strict__increasing)).
% 74.76/25.30  thf(2689,plain,((! [TA: $tType]: ((ordere8940638589300402666id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ B @ C) => (ord_less @ TA @ B @ (plus_plus @ TA @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[574])).
% 74.76/25.30  thf(595,axiom,((! [A:extended_enat]: ((ord_max @ extended_enat @ (zero_zero @ extended_enat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4821_max__enat__simps_I3_J)).
% 74.76/25.30  thf(2747,plain,((! [A:extended_enat]: ((ord_max @ extended_enat @ (zero_zero @ extended_enat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[595])).
% 74.76/25.30  thf(749,axiom,((! [TA: $tType]: ((ordere2520102378445227354miring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ C @ A) @ (times_times @ TA @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_816_ordered__comm__semiring__class_Ocomm__mult__left__mono)).
% 74.76/25.30  thf(3246,plain,((! [TA: $tType]: ((ordere2520102378445227354miring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ C @ A) @ (times_times @ TA @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[749])).
% 74.76/25.30  thf(813,axiom,((bounde4346867609351753570nf_top @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__inf__top_455)).
% 74.76/25.30  thf(3448,plain,((bounde4346867609351753570nf_top @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[813])).
% 74.76/25.30  thf(121,axiom,((semiring_numeral @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Osemiring__numeral_306)).
% 74.76/25.30  thf(1186,plain,((semiring_numeral @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
% 74.76/25.30  thf(77,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ (times_times @ nat @ C @ D)) => ((dvd_dvd @ nat @ D @ (minus_minus @ nat @ B @ A)) = (dvd_dvd @ nat @ D @ (plus_plus @ nat @ B @ (minus_minus @ nat @ (times_times @ nat @ C @ D) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1776_dvd__minus__add)).
% 74.76/25.30  thf(1038,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ A @ (times_times @ nat @ C @ D)) => ((dvd_dvd @ nat @ D @ (minus_minus @ nat @ B @ A)) = (dvd_dvd @ nat @ D @ (plus_plus @ nat @ B @ (minus_minus @ nat @ (times_times @ nat @ C @ D) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
% 74.76/25.30  thf(317,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((plus_plus @ nat @ (minus_minus @ nat @ B @ A) @ C) = (minus_minus @ nat @ (plus_plus @ nat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1694_Nat_Oadd__diff__assoc2)).
% 74.76/25.30  thf(1869,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((plus_plus @ nat @ (minus_minus @ nat @ B @ A) @ C) = (minus_minus @ nat @ (plus_plus @ nat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])).
% 74.76/25.30  thf(504,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ C)) => ((dvd_dvd @ nat @ A @ C) => ((ord_less_eq @ nat @ C @ B) => (dvd_dvd @ nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1746_dvd__diffD)).
% 74.76/25.30  thf(2429,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ A @ (minus_minus @ nat @ B @ C)) => ((dvd_dvd @ nat @ A @ C) => ((ord_less_eq @ nat @ C @ B) => (dvd_dvd @ nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[504])).
% 74.76/25.30  thf(139,axiom,((lattice @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Lattices_Olattice_12)).
% 74.76/25.30  thf(1235,plain,((lattice @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
% 74.76/25.30  thf(162,axiom,((! [A:nat]: ((suc @ A) != (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_old_Onat_Odistinct_I2_J)).
% 74.76/25.30  thf(1317,plain,((! [A:nat]: ~ ((suc @ A) = (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
% 74.76/25.30  thf(328,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ (minus_minus @ nat @ A @ B)) = (ord_less @ nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1690_zero__less__diff)).
% 74.76/25.30  thf(1901,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ (minus_minus @ nat @ A @ B)) = (ord_less @ nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])).
% 74.76/25.30  thf(723,axiom,((! [TA: $tType,TB: $tType]: ((counta3822494911875563373attice @ TA) => (counta3822494911875563373attice @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Countable__Complete__Lattices_Ocountable__complete__lattice)).
% 74.76/25.30  thf(3174,plain,((! [TA: $tType,TB: $tType]: ((counta3822494911875563373attice @ TA) => (counta3822494911875563373attice @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[723])).
% 74.76/25.30  thf(241,axiom,((! [TA: $tType]: ((dvd @ TA) => ((dvd_dvd @ TA) = (^ [A:TA,B:TA]: ? [C:TA]: (B = (times_times @ TA @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1373_dvd__def)).
% 74.76/25.30  thf(1579,plain,((! [TA: $tType]: ((dvd @ TA) => ((dvd_dvd @ TA) = (^ [A:TA,B:TA]: ? [C:TA]: (B = (times_times @ TA @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
% 74.76/25.30  thf(151,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (? [C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ C) & ((plus_plus @ nat @ A @ C) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_912_less__imp__add__positive)).
% 74.76/25.30  thf(1285,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (? [C:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ C) & ((plus_plus @ nat @ A @ C) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
% 74.76/25.30  thf(171,axiom,((! [TA: $tType]: ((linordered_ring @ TA) => (! [A:TA]: (ord_less_eq @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_830_zero__le__square)).
% 74.76/25.30  thf(1336,plain,((! [TA: $tType]: ((linordered_ring @ TA) => (! [A:TA]: (ord_less_eq @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
% 74.76/25.30  thf(30,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((dvd_dvd @ int @ A @ B) => ((dvd_dvd @ int @ A @ (plus_plus @ int @ C @ D)) = (dvd_dvd @ int @ A @ (plus_plus @ int @ (plus_plus @ int @ C @ (times_times @ int @ E @ B)) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1442_zdvd__period)).
% 74.76/25.30  thf(907,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((dvd_dvd @ int @ A @ B) => ((dvd_dvd @ int @ A @ (plus_plus @ int @ C @ D)) = (dvd_dvd @ int @ A @ (plus_plus @ int @ (plus_plus @ int @ C @ (times_times @ int @ E @ B)) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 74.76/25.30  thf(782,axiom,((semiring_numeral @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_474)).
% 74.76/25.30  thf(3305,plain,((semiring_numeral @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[782])).
% 74.76/25.30  thf(409,axiom,((strict9044650504122735259up_add @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_26)).
% 74.76/25.30  thf(2165,plain,((strict9044650504122735259up_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[409])).
% 74.76/25.30  thf(3816,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less_eq @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ nat) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1301,2483])).
% 74.76/25.30  thf(3817,plain,(! [TA:$tType] : ((~ (ord_less_eq @ TA @ (one_one @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ nat) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3816])).
% 74.76/25.30  thf(3818,plain,((~ (ord_less_eq @ nat @ (one_one @ nat) @ (zero_zero @ nat)))),inference(pattern_uni,[status(thm)],[3817:[bind_type(TA,$thf(nat))]])).
% 74.76/25.30  thf(305,axiom,((ab_semigroup_add @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__add)).
% 74.76/25.30  thf(1813,plain,((ab_semigroup_add @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])).
% 74.76/25.30  thf(154,axiom,((plus @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oplus_102)).
% 74.76/25.30  thf(1300,plain,((plus @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
% 74.76/25.30  thf(203,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: (ord_less_eq @ TA @ (one_one @ TA) @ (numeral_numeral @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_one__le__numeral)).
% 74.76/25.30  thf(1452,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: (ord_less_eq @ TA @ (one_one @ TA) @ (numeral_numeral @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
% 74.76/25.30  thf(433,axiom,((suc = (plus_plus @ nat @ (one_one @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_Suc__eq__plus1__left)).
% 74.76/25.30  thf(2219,plain,(((suc) = (plus_plus @ nat @ (one_one @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[433])).
% 74.76/25.30  thf(354,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less @ nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_792_le__imp__less__Suc)).
% 74.76/25.30  thf(1980,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less @ nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])).
% 74.76/25.30  thf(94,axiom,((comm_semiring_0 @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__0_73)).
% 74.76/25.30  thf(1085,plain,((comm_semiring_0 @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
% 74.76/25.30  thf(467,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_851_mult__pos__pos)).
% 74.76/25.30  thf(2322,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])).
% 74.76/25.30  thf(49,axiom,((! [A:int,B:int,C:(int > $o)]: ((ord_less_eq @ int @ A @ B) => ((C @ A) => ((! [D:int]: ((ord_less_eq @ int @ A @ D) => ((C @ D) => (C @ (plus_plus @ int @ D @ (one_one @ int)))))) => (C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1183_int__ge__induct)).
% 74.76/25.30  thf(951,plain,((! [A:int,B:int,C:(int > $o)]: ((ord_less_eq @ int @ A @ B) => ((C @ A) => ((! [D:int]: ((ord_less_eq @ int @ A @ D) => ((C @ D) => (C @ (plus_plus @ int @ D @ (one_one @ int)))))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
% 74.76/25.30  thf(441,axiom,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus @ nat @ B @ C)) => ((suc @ A) = (plus_plus @ nat @ B @ (suc @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_nat__arith_Osuc1)).
% 74.76/25.30  thf(2247,plain,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus @ nat @ B @ C)) => ((suc @ A) = (plus_plus @ nat @ B @ (suc @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])).
% 74.76/25.30  thf(336,axiom,(((ord_less @ nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (suc @ (plus_plus @ nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_less__iff__Suc__add)).
% 74.76/25.30  thf(1934,plain,(((ord_less @ nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (suc @ (plus_plus @ nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])).
% 74.76/25.30  thf(537,axiom,((! [A:nat,B:nat]: ((minus_minus @ nat @ (suc @ A) @ (suc @ B)) = (minus_minus @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1680_diff__Suc__Suc)).
% 74.76/25.30  thf(2500,plain,((! [A:nat,B:nat]: ((minus_minus @ nat @ (suc @ A) @ (suc @ B)) = (minus_minus @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[537])).
% 74.76/25.30  thf(300,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ (suc @ B)) => ((~ (ord_less @ nat @ A @ B)) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_less__SucE)).
% 74.76/25.30  thf(1802,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)],[300])).
% 74.76/25.30  thf(196,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) & (ord_less_eq @ TA @ (zero_zero @ TA) @ B)) | ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) & (ord_less_eq @ TA @ B @ (zero_zero @ TA))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_zero__le__mult__iff)).
% 74.76/25.30  thf(1427,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ (times_times @ TA @ A @ B)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) & (ord_less_eq @ TA @ (zero_zero @ TA) @ B)) | ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) & (ord_less_eq @ TA @ B @ (zero_zero @ TA))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
% 74.76/25.30  thf(297,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ A @ (plus_plus @ nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_trans__less__add2)).
% 74.76/25.30  thf(1797,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ A @ (plus_plus @ nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])).
% 74.76/25.30  thf(588,axiom,((! [A:extended_enat]: (ord_less_eq @ extended_enat @ (zero_zero @ extended_enat) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_776_i0__lb)).
% 74.76/25.30  thf(2728,plain,((! [A:extended_enat]: (ord_less_eq @ extended_enat @ (zero_zero @ extended_enat) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[588])).
% 74.76/25.30  thf(653,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ (minus_minus @ nat @ B @ A) @ C) = (ord_less @ nat @ B @ (plus_plus @ nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1758_less__diff__conv2)).
% 74.76/25.30  thf(2939,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ (minus_minus @ nat @ B @ A) @ C) = (ord_less @ nat @ B @ (plus_plus @ nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[653])).
% 74.76/25.30  thf(717,axiom,((! [TA: $tType]: ((wellorder @ TA) => (((?) @ TA) = (^ [A:(TA > $o)]: ? [B:TA]: ((A @ B) & ! [C:TA]: ((ord_less @ TA @ C @ B) => (~ (A @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1251_exists__least__iff)).
% 74.76/25.30  thf(3156,plain,((! [TA: $tType]: ((wellorder @ TA) => (((?) @ TA) = (^ [A:(TA > $o)]: ? [B:TA]: ((A @ B) & ! [C:TA]: ((ord_less @ TA @ C @ B) => (~ (A @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[717])).
% 74.76/25.30  thf(793,axiom,(((extend4730790105801354508finity @ extended_enat) != (one_one @ extended_enat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_infinity__ne__i1)).
% 74.76/25.30  thf(3398,plain,((~ ((extend4730790105801354508finity @ extended_enat) = (one_one @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[793])).
% 74.76/25.30  thf(13,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (abs_abs @ TA @ (minus_minus @ TA @ A @ B)) @ C) = ((ord_less @ TA @ (minus_minus @ TA @ B @ C) @ A) & (ord_less @ TA @ A @ (plus_plus @ TA @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2654_abs__diff__less__iff)).
% 74.76/25.30  thf(859,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (abs_abs @ TA @ (minus_minus @ TA @ A @ B)) @ C) = ((ord_less @ TA @ (minus_minus @ TA @ B @ C) @ A) & (ord_less @ TA @ A @ (plus_plus @ TA @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 74.76/25.30  thf(327,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = ((ord_less @ nat @ (zero_zero @ nat) @ A) & (ord_less @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_nat__mult__less__cancel__disj)).
% 74.76/25.30  thf(1898,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = ((ord_less @ nat @ (zero_zero @ nat) @ A) & (ord_less @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])).
% 74.76/25.30  thf(145,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_add__pos__pos)).
% 74.76/25.30  thf(1257,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
% 74.76/25.30  thf(558,axiom,((! [A:nat]: (((A = (zero_zero @ nat)) => ((times_times @ extended_enat @ (extended_enat2 @ A) @ (extend4730790105801354508finity @ extended_enat)) = (zero_zero @ extended_enat))) & ((A != (zero_zero @ nat)) => ((times_times @ extended_enat @ (extended_enat2 @ A) @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_times__enat__simps_I4_J)).
% 74.76/25.30  thf(2558,plain,((! [A:nat]: (((A = (zero_zero @ nat)) => ((times_times @ extended_enat @ (extended_enat2 @ A) @ (extend4730790105801354508finity @ extended_enat)) = (zero_zero @ extended_enat))) & ((~ (A = (zero_zero @ nat))) => ((times_times @ extended_enat @ (extended_enat2 @ A) @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[558])).
% 74.76/25.30  thf(399,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (((minus_minus @ nat @ B @ A) = C) = (B = (plus_plus @ nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1739_Nat_Ole__imp__diff__is__add)).
% 74.76/25.30  thf(2113,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (((minus_minus @ nat @ B @ A) = C) = (B = (plus_plus @ nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])).
% 74.76/25.30  thf(269,axiom,((! [A:extended_enat,B:nat]: ((ord_less @ extended_enat @ A @ (extended_enat2 @ B)) => (~ (! [C:nat]: ((A = (extended_enat2 @ C)) => (~ (ord_less @ nat @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_less__enatE)).
% 74.76/25.30  thf(1702,plain,((! [A:extended_enat,B:nat]: ((ord_less @ extended_enat @ A @ (extended_enat2 @ B)) => (~ (! [C:nat]: ((A = (extended_enat2 @ C)) => (~ (ord_less @ nat @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])).
% 74.76/25.30  thf(483,axiom,((power @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Power_Opower_99)).
% 74.76/25.30  thf(2379,plain,((power @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[483])).
% 74.76/25.30  thf(452,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: (((plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B)) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_sum__squares__eq__zero__iff)).
% 74.76/25.30  thf(2279,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: (((plus_plus @ TA @ (times_times @ TA @ A @ A) @ (times_times @ TA @ B @ B)) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[452])).
% 74.76/25.30  thf(476,axiom,((! [A:nat]: ((~ (ord_less @ nat @ (zero_zero @ nat) @ A)) = (A = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_753_not__gr0)).
% 74.76/25.30  thf(2357,plain,((! [A:nat]: ((~ (ord_less @ nat @ (zero_zero @ nat) @ A)) = (A = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[476])).
% 74.76/25.30  thf(344,axiom,((! [A:nat,B:nat]: ((dvd_dvd @ nat @ A @ B) => ((dvd_dvd @ nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1558_dvd__antisym)).
% 74.76/25.30  thf(1955,plain,((! [A:nat,B:nat]: ((dvd_dvd @ nat @ A @ B) => ((dvd_dvd @ nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])).
% 74.76/25.30  thf(213,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_eq__imp__le)).
% 74.76/25.30  thf(1485,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
% 74.76/25.30  thf(350,axiom,((! [A:num,B:num]: ((ord_less @ extended_enat @ (numeral_numeral @ extended_enat @ A) @ (numeral_numeral @ extended_enat @ B)) = (ord_less @ nat @ (numeral_numeral @ nat @ A) @ (numeral_numeral @ nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_enat__ord__number_I2_J)).
% 74.76/25.30  thf(1972,plain,((! [A:num,B:num]: ((ord_less @ extended_enat @ (numeral_numeral @ extended_enat @ A) @ (numeral_numeral @ extended_enat @ B)) = (ord_less @ nat @ (numeral_numeral @ nat @ A) @ (numeral_numeral @ nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])).
% 74.76/25.30  thf(83,axiom,((! [A:nat]: ((ord_less_eq @ nat @ A @ (zero_zero @ nat)) => (A = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_760_bot__nat__0_Oextremum__uniqueI)).
% 74.76/25.30  thf(1052,plain,((! [A:nat]: ((ord_less_eq @ nat @ A @ (zero_zero @ nat)) => (A = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
% 74.76/25.30  thf(216,axiom,((! [A:int,B:int,C:int]: ((times_times @ int @ A @ (plus_plus @ int @ B @ C)) = (plus_plus @ int @ (times_times @ int @ A @ B) @ (times_times @ int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1180_int__distrib_I2_J)).
% 74.76/25.30  thf(1506,plain,((! [A:int,B:int,C:int]: ((times_times @ int @ A @ (plus_plus @ int @ B @ C)) = (plus_plus @ int @ (times_times @ int @ A @ B) @ (times_times @ int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
% 74.76/25.30  thf(108,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ A @ (plus_plus @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_trans__less__add1)).
% 74.76/25.30  thf(1140,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ A @ (plus_plus @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
% 74.76/25.30  thf(541,axiom,((! [A:int]: ((times_times @ int @ (zero_zero @ int) @ A) = (zero_zero @ int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1178_times__int__code_I2_J)).
% 74.76/25.30  thf(2511,plain,((! [A:int]: ((times_times @ int @ (zero_zero @ int) @ A) = (zero_zero @ int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[541])).
% 74.76/25.30  thf(632,axiom,((! [A:nat]: (((A = (zero_zero @ nat)) => ((times_times @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)) = (zero_zero @ extended_enat))) & ((A != (zero_zero @ nat)) => ((times_times @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)) = (extend4730790105801354508finity @ extended_enat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_times__enat__simps_I3_J)).
% 74.76/25.30  thf(2860,plain,((! [A:nat]: (((A = (zero_zero @ nat)) => ((times_times @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)) = (zero_zero @ extended_enat))) & ((~ (A = (zero_zero @ nat))) => ((times_times @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ (extended_enat2 @ A)) = (extend4730790105801354508finity @ extended_enat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[632])).
% 74.76/25.30  thf(586,axiom,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: ((ord_less_eq @ TA @ (top_top @ TA) @ A) => (A = (top_top @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6213_top_Oextremum__uniqueI)).
% 74.76/25.30  thf(2722,plain,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: ((ord_less_eq @ TA @ (top_top @ TA) @ A) => (A = (top_top @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[586])).
% 74.76/25.30  thf(64,axiom,((! [A:nat]: ~ (ord_less @ nat @ A @ (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_not__less0)).
% 74.76/25.30  thf(1008,plain,((! [A:nat]: ~ (ord_less @ nat @ A @ (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
% 74.76/25.30  thf(674,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ D) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_933_mult__strict__mono)).
% 74.76/25.30  thf(3007,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ D) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[674])).
% 74.76/25.30  thf(446,axiom,((ab_semigroup_add @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__semigroup__add_292)).
% 74.76/25.30  thf(2266,plain,((ab_semigroup_add @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[446])).
% 74.76/25.30  thf(721,axiom,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounde4346867609351753570nf_top @ (TB > TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__inf__top)).
% 74.76/25.30  thf(3168,plain,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounde4346867609351753570nf_top @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[721])).
% 74.76/25.30  thf(475,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less @ nat @ D @ E) => (ord_less @ nat @ (A @ D) @ (A @ E)))) => (ord_less_eq @ nat @ (plus_plus @ nat @ (A @ B) @ C) @ (A @ (plus_plus @ nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_mono__nat__linear__lb)).
% 74.76/25.30  thf(2352,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less @ nat @ D @ E) => (ord_less @ nat @ (A @ D) @ (A @ E)))) => (ord_less_eq @ nat @ (plus_plus @ nat @ (A @ B) @ C) @ (A @ (plus_plus @ nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[475])).
% 74.76/25.30  thf(529,axiom,((! [A:nat]: (((one_one @ extended_enat) = (extended_enat2 @ A)) = (A = (one_one @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_enat__1__iff_I2_J)).
% 74.76/25.30  thf(2479,plain,((! [A:nat]: (((one_one @ extended_enat) = (extended_enat2 @ A)) = (A = (one_one @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[529])).
% 74.76/25.30  thf(794,axiom,((bounded_lattice @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Obounded__lattice_1)).
% 74.76/25.30  thf(3401,plain,((bounded_lattice @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[794])).
% 74.76/25.30  thf(205,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (zero_zero @ TA)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) & (ord_less_eq @ TA @ B @ (zero_zero @ TA))) | ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) & (ord_less_eq @ TA @ (zero_zero @ TA) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_mult__le__0__iff)).
% 74.76/25.30  thf(1459,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (zero_zero @ TA)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) & (ord_less_eq @ TA @ B @ (zero_zero @ TA))) | ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) & (ord_less_eq @ TA @ (zero_zero @ TA) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
% 74.76/25.30  thf(695,axiom,((! [A:int,B:(int > $o),C:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => ((! [D:int]: ((B @ D) => (B @ (plus_plus @ int @ D @ A)))) => ((ord_less_eq @ int @ (zero_zero @ int) @ C) => (! [D:int]: ((B @ D) => (B @ (plus_plus @ int @ D @ (times_times @ int @ C @ A)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_incr__mult__lemma)).
% 74.76/25.30  thf(3067,plain,((! [A:int,B:(int > $o),C:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => ((! [D:int]: ((B @ D) => (B @ (plus_plus @ int @ D @ A)))) => ((ord_less_eq @ int @ (zero_zero @ int) @ C) => (! [D:int]: ((B @ D) => (B @ (plus_plus @ int @ D @ (times_times @ int @ C @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[695])).
% 74.76/25.30  thf(348,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ C @ B)) = (minus_minus @ nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1723_diff__cancel2)).
% 74.76/25.30  thf(1966,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ C @ B)) = (minus_minus @ nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])).
% 74.76/25.30  thf(638,axiom,((! [TA: $tType]: ((one @ TA) => (! [A:TA]: (((one_one @ TA) = A) = (A = (one_one @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_one__reorient)).
% 74.76/25.30  thf(2885,plain,((! [TA: $tType]: ((one @ TA) => (! [A:TA]: (((one_one @ TA) = A) = (A = (one_one @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[638])).
% 74.76/25.30  thf(624,axiom,((! [A:real,B:real,C:(real > (real > $o))]: ((ord_less_eq @ real @ A @ B) => ((! [D:real,E:real,F:real]: ((C @ D @ E) => ((C @ E @ F) => ((ord_less_eq @ real @ D @ E) => ((ord_less_eq @ real @ E @ F) => (C @ D @ F)))))) => ((! [D:real]: ((ord_less_eq @ real @ A @ D) => ((ord_less_eq @ real @ D @ B) => (? [E:real]: ((ord_less @ real @ (zero_zero @ real) @ E) & ! [F:real,G:real]: (((ord_less_eq @ real @ F @ D) & (ord_less_eq @ real @ D @ G) & (ord_less @ real @ (minus_minus @ real @ G @ F) @ E)) => (C @ F @ G))))))) => (C @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1792_Bolzano)).
% 74.76/25.30  thf(2828,plain,((! [A:real,B:real,C:(real > (real > $o))]: ((ord_less_eq @ real @ A @ B) => ((! [D:real,E:real,F:real]: ((C @ D @ E) => ((C @ E @ F) => ((ord_less_eq @ real @ D @ E) => ((ord_less_eq @ real @ E @ F) => (C @ D @ F)))))) => ((! [D:real]: ((ord_less_eq @ real @ A @ D) => ((ord_less_eq @ real @ D @ B) => (? [E:real]: ((ord_less @ real @ (zero_zero @ real) @ E) & ! [F:real,G:real]: (((ord_less_eq @ real @ F @ D) & (ord_less_eq @ real @ D @ G) & (ord_less @ real @ (minus_minus @ real @ G @ F) @ E)) => (C @ F @ G))))))) => (C @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[624])).
% 74.76/25.30  thf(728,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less_eq @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1192_mult__le__cancel__iff2)).
% 74.76/25.30  thf(3188,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less_eq @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[728])).
% 74.76/25.30  thf(220,axiom,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd @ nat @ C @ A) & (dvd_dvd @ nat @ C @ B) & (((times_times @ nat @ A @ D) = (plus_plus @ nat @ (times_times @ nat @ B @ E) @ C)) | ((times_times @ nat @ B @ D) = (plus_plus @ nat @ (times_times @ nat @ A @ E) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1439_bezout__add__nat)).
% 74.76/25.30  thf(1517,plain,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd @ nat @ C @ A) & (dvd_dvd @ nat @ C @ B) & (((times_times @ nat @ A @ D) = (plus_plus @ nat @ (times_times @ nat @ B @ E) @ C)) | ((times_times @ nat @ B @ D) = (plus_plus @ nat @ (times_times @ nat @ A @ E) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])).
% 74.76/25.30  thf(469,axiom,((! [A:nat]: ((ord_max @ nat @ (zero_zero @ nat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4827_max__0L)).
% 74.76/25.30  thf(2325,plain,((! [A:nat]: ((ord_max @ nat @ (zero_zero @ nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])).
% 74.76/25.30  thf(436,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (B != (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_gr__implies__not0)).
% 74.76/25.30  thf(2226,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (~ (B = (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[436])).
% 74.76/25.30  thf(316,axiom,((! [A:int,B:int]: ((ord_less @ int @ A @ (plus_plus @ int @ B @ (one_one @ int))) = ((ord_less @ int @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1185_zless__add1__eq)).
% 74.76/25.30  thf(1866,plain,((! [A:int,B:int]: ((ord_less @ int @ A @ (plus_plus @ int @ B @ (one_one @ int))) = ((ord_less @ int @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])).
% 74.76/25.30  thf(103,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_720_Suc__le__D)).
% 74.76/25.30  thf(1108,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
% 74.76/25.30  thf(771,axiom,((~ (? [A:nat]: (vEBT_V8194947554948674370ptions @ summarya @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__C2_Ohyps_C_I5_J)).
% 74.76/25.30  thf(3284,plain,((~ (? [A:nat]: (vEBT_V8194947554948674370ptions @ summarya @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[771])).
% 74.76/25.30  thf(844,plain,((! [A:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => (! [B:int,C:int]: (ord_less @ int @ B @ (plus_plus @ int @ C @ (times_times @ int @ (plus_plus @ int @ (abs_abs @ int @ (minus_minus @ int @ C @ B)) @ (one_one @ int)) @ A))))))),inference(miniscope,[status(thm)],[843])).
% 74.76/25.30  thf(845,plain,(! [C:int,B:int,A:int] : ((~ (ord_less @ int @ (zero_zero @ int) @ A)) | (ord_less @ int @ B @ (plus_plus @ int @ C @ (times_times @ int @ (plus_plus @ int @ (abs_abs @ int @ (minus_minus @ int @ C @ B)) @ (one_one @ int)) @ A))))),inference(cnf,[status(esa)],[844])).
% 74.76/25.30  thf(365,axiom,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (? [C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ C) & (ord_less @ TA @ C @ A) & (ord_less @ TA @ C @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_field__lbound__gt__zero)).
% 74.76/25.30  thf(2013,plain,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (? [C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ C) & (ord_less @ TA @ C @ A) & (ord_less @ TA @ C @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])).
% 74.76/25.30  thf(3399,plain,((~ ((extend4730790105801354508finity @ extended_enat) = (one_one @ extended_enat)))),inference(polarity_switch,[status(thm)],[3398])).
% 74.76/25.30  thf(3400,plain,(((extend4730790105801354508finity @ extended_enat) != (one_one @ extended_enat))),inference(lifteq,[status(thm)],[3399])).
% 74.76/25.30  thf(648,axiom,((! [A:extended_enat]: ((minus_minus @ extended_enat @ A @ (zero_zero @ extended_enat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1678_idiff__0__right)).
% 74.76/25.30  thf(2924,plain,((! [A:extended_enat]: ((minus_minus @ extended_enat @ A @ (zero_zero @ extended_enat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[648])).
% 74.76/25.30  thf(815,axiom,((complete_Sup @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_OSup_472)).
% 74.76/25.30  thf(3452,plain,((complete_Sup @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[815])).
% 74.76/25.30  thf(518,axiom,((strict9044650504122735259up_add @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ostrict__ordered__ab__semigroup__add)).
% 74.76/25.30  thf(2458,plain,((strict9044650504122735259up_add @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[518])).
% 74.76/25.30  thf(577,axiom,((! [A:extended_enat]: ((minus_minus @ extended_enat @ (zero_zero @ extended_enat) @ A) = (zero_zero @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1677_idiff__0)).
% 74.76/25.30  thf(2696,plain,((! [A:extended_enat]: ((minus_minus @ extended_enat @ (zero_zero @ extended_enat) @ A) = (zero_zero @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[577])).
% 74.76/25.30  thf(234,axiom,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ (ord_max @ nat @ A @ B) @ C) = (ord_max @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4835_nat__mult__max__left)).
% 74.76/25.30  thf(1553,plain,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ (ord_max @ nat @ A @ B) @ C) = (ord_max @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])).
% 74.76/25.30  thf(163,axiom,((! [A:nat]: (ord_less_eq @ nat @ A @ (times_times @ nat @ A @ (times_times @ nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_le__cube)).
% 74.76/25.30  thf(1321,plain,((! [A:nat]: (ord_less_eq @ nat @ A @ (times_times @ nat @ A @ (times_times @ nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
% 74.76/25.30  thf(333,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((minus_minus @ nat @ (suc @ B) @ A) = (minus_minus @ nat @ B @ (minus_minus @ nat @ A @ (one_one @ nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1768_Suc__diff__eq__diff__pred)).
% 74.76/25.30  thf(1913,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((minus_minus @ nat @ (suc @ B) @ A) = (minus_minus @ nat @ B @ (minus_minus @ nat @ A @ (one_one @ nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])).
% 74.76/25.30  thf(314,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq @ nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq @ nat @ A @ D) => ((ord_less @ nat @ D @ B) => ((C @ D) => (C @ (suc @ D)))))) => (C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_dec__induct)).
% 74.76/25.30  thf(1844,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq @ nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq @ nat @ A @ D) => ((ord_less @ nat @ D @ B) => ((C @ D) => (C @ (suc @ D)))))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])).
% 74.76/25.30  thf(28,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ B @ (minus_minus @ nat @ B @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1683_diff__diff__cancel)).
% 74.76/25.30  thf(903,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ B @ (minus_minus @ nat @ B @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 74.76/25.30  thf(129,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less @ TA @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_856_mult__less__cancel__left__neg)).
% 74.76/25.30  thf(1216,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less @ TA @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
% 74.76/25.30  thf(24,axiom,((! [A:int,B:int,C:int]: ((times_times @ int @ A @ (minus_minus @ int @ B @ C)) = (minus_minus @ int @ (times_times @ int @ A @ B) @ (times_times @ int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1593_int__distrib_I4_J)).
% 74.76/25.30  thf(891,plain,((! [A:int,B:int,C:int]: ((times_times @ int @ A @ (minus_minus @ int @ B @ C)) = (minus_minus @ int @ (times_times @ int @ A @ B) @ (times_times @ int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 74.76/25.30  thf(672,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_add__pos__nonneg)).
% 74.76/25.30  thf(2997,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[672])).
% 74.76/25.30  thf(202,axiom,((! [A:nat]: ((zero_zero @ nat) != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_Zero__not__Suc)).
% 74.76/25.30  thf(1448,plain,((! [A:nat]: ~ ((zero_zero @ nat) = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
% 74.76/25.30  thf(788,axiom,((! [A:extended_enat]: ((minus_minus @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1676_idiff__infinity)).
% 74.76/25.30  thf(3320,plain,((! [A:extended_enat]: ((minus_minus @ extended_enat @ (extend4730790105801354508finity @ extended_enat) @ A) = (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[788])).
% 74.76/25.30  thf(646,axiom,((! [A:nat]: (ord_less @ extended_enat @ (extended_enat2 @ A) @ (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_enat__ord__code_I4_J)).
% 74.76/25.30  thf(2919,plain,((! [A:nat]: (ord_less @ extended_enat @ (extended_enat2 @ A) @ (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[646])).
% 74.76/25.30  thf(280,axiom,((! [A:nat,B:nat]: (((plus_plus @ nat @ A @ B) = (suc @ (zero_zero @ nat))) = (((A = (suc @ (zero_zero @ nat))) & (B = (zero_zero @ nat))) | ((A = (zero_zero @ nat)) & (B = (suc @ (zero_zero @ nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_add__is__1)).
% 74.76/25.30  thf(1734,plain,((! [A:nat,B:nat]: (((plus_plus @ nat @ A @ B) = (suc @ (zero_zero @ nat))) = (((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)],[280])).
% 74.76/25.30  thf(302,axiom,((! [A:nat,B:nat]: (((times_times @ nat @ A @ B) = (suc @ (zero_zero @ nat))) = ((A = (suc @ (zero_zero @ nat))) & (B = (suc @ (zero_zero @ nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_mult__eq__1__iff)).
% 74.76/25.30  thf(1807,plain,((! [A:nat,B:nat]: (((times_times @ nat @ A @ B) = (suc @ (zero_zero @ nat))) = ((A = (suc @ (zero_zero @ nat))) & (B = (suc @ (zero_zero @ nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])).
% 74.76/25.30  thf(567,axiom,((! [TA: $tType]: ((linord6961819062388156250ring_1 @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ E) => (((plus_plus @ TA @ D @ E) = (one_one @ TA)) => (ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ D @ A) @ (times_times @ TA @ E @ C)) @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_convex__bound__le)).
% 74.76/25.30  thf(2591,plain,((! [TA: $tType]: ((linord6961819062388156250ring_1 @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ E) => (((plus_plus @ TA @ D @ E) = (one_one @ TA)) => (ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ D @ A) @ (times_times @ TA @ E @ C)) @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[567])).
% 74.76/25.30  thf(509,axiom,((numeral @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Onumeral_495)).
% 74.76/25.30  thf(2443,plain,((numeral @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])).
% 74.76/25.30  thf(167,axiom,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA]: ? [B:TA]: (ord_less @ TA @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_linordered__field__no__lb)).
% 74.76/25.30  thf(1326,plain,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA]: ? [B:TA]: (ord_less @ TA @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
% 74.76/25.30  thf(580,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) = (((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ A @ C)) & ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less_eq @ TA @ C @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_931_mult__le__cancel__right)).
% 74.76/25.30  thf(2707,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) = (((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less_eq @ TA @ A @ C)) & ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less_eq @ TA @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[580])).
% 74.76/25.30  thf(411,axiom,((! [A:nat]: ((A != (zero_zero @ nat)) = (ord_less @ nat @ (zero_zero @ nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_bot__nat__0_Onot__eq__extremum)).
% 74.76/25.30  thf(2167,plain,((! [A:nat]: ((~ (A = (zero_zero @ nat))) = (ord_less @ nat @ (zero_zero @ nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[411])).
% 74.76/25.30  thf(454,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (minus_minus @ nat @ A @ B) @ C) = (ord_less_eq @ nat @ A @ (plus_plus @ nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1743_le__diff__conv)).
% 74.76/25.30  thf(2283,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (minus_minus @ nat @ A @ B) @ C) = (ord_less_eq @ nat @ A @ (plus_plus @ nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])).
% 74.76/25.30  thf(395,axiom,((comm_semiring_0 @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__semiring__0_300)).
% 74.76/25.30  thf(2098,plain,((comm_semiring_0 @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])).
% 74.76/25.30  thf(630,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less_eq @ TA @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_938_mult__le__cancel__left__neg)).
% 74.76/25.30  thf(2855,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ A @ C)) = (ord_less_eq @ TA @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[630])).
% 74.76/25.30  thf(47,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add__le__mono1)).
% 74.76/25.30  thf(946,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => (ord_less_eq @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
% 74.76/25.30  thf(662,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (one_one @ TA)) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ B @ (one_one @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (one_one @ TA))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_952_mult__le__one)).
% 74.76/25.30  thf(2971,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (one_one @ TA)) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => ((ord_less_eq @ TA @ B @ (one_one @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ A @ B) @ (one_one @ TA))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[662])).
% 74.76/25.30  thf(601,axiom,((! [A:extended_enat,B:nat]: ((ord_less_eq @ extended_enat @ A @ (extended_enat2 @ B)) => (? [C:nat]: (A = (extended_enat2 @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_enat__ile)).
% 74.76/25.30  thf(2764,plain,((! [A:extended_enat,B:nat]: ((ord_less_eq @ extended_enat @ A @ (extended_enat2 @ B)) => (? [C:nat]: (A = (extended_enat2 @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[601])).
% 74.76/25.30  thf(443,axiom,((semiri3467727345109120633visors @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors_44)).
% 74.76/25.30  thf(2262,plain,((semiri3467727345109120633visors @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[443])).
% 74.76/25.30  thf(698,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_936_mult__strict__mono_H)).
% 74.76/25.30  thf(3085,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[698])).
% 74.76/25.30  thf(568,axiom,((! [TA: $tType]: ((semiri3467727345109120633visors @ TA) => (! [A:TA,B:TA]: ((A != (zero_zero @ TA)) => ((B != (zero_zero @ TA)) => ((times_times @ TA @ A @ B) != (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_no__zero__divisors)).
% 74.76/25.30  thf(2594,plain,((! [TA: $tType]: ((semiri3467727345109120633visors @ TA) => (! [A:TA,B:TA]: ((~ (A = (zero_zero @ TA))) => ((~ (B = (zero_zero @ TA))) => (~ ((times_times @ TA @ A @ B) = (zero_zero @ TA))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[568])).
% 74.76/25.30  thf(275,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((A != B) => ((~ (ord_less @ TA @ A @ B)) => (ord_less @ TA @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_linorder__neqE__linordered__idom)).
% 74.76/25.30  thf(1721,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((~ (A = B)) => ((~ (ord_less @ TA @ A @ B)) => (ord_less @ TA @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])).
% 74.76/25.30  thf(629,axiom,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_mult__mono_H)).
% 74.76/25.30  thf(2853,plain,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[629])).
% 74.76/25.30  thf(457,axiom,(((one_one @ int) = (one_one @ int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4545_one__integer_Orsp)).
% 74.76/25.30  thf(2290,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])).
% 74.76/25.30  thf(442,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ (suc @ D)) => (A @ D))) => (A @ (minus_minus @ nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1707_zero__induct__lemma)).
% 74.76/25.30  thf(2251,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ (suc @ D)) => (A @ D))) => (A @ (minus_minus @ nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[442])).
% 74.76/25.30  thf(402,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus @ nat @ (times_times @ nat @ A @ B) @ (plus_plus @ nat @ (times_times @ nat @ C @ B) @ D)) = (plus_plus @ nat @ (times_times @ nat @ (plus_plus @ nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_left__add__mult__distrib)).
% 74.76/25.30  thf(2135,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus @ nat @ (times_times @ nat @ A @ B) @ (plus_plus @ nat @ (times_times @ nat @ C @ B) @ D)) = (plus_plus @ nat @ (times_times @ nat @ (plus_plus @ nat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])).
% 74.76/25.30  thf(494,axiom,((linord4710134922213307826strict @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__ring__strict)).
% 74.76/25.30  thf(2406,plain,((linord4710134922213307826strict @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[494])).
% 74.76/25.30  thf(618,axiom,((! [A:int,B:int]: ((ord_less_eq @ int @ A @ (minus_minus @ int @ B @ (one_one @ int))) = (ord_less @ int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1549_zle__diff1__eq)).
% 74.76/25.30  thf(2811,plain,((! [A:int,B:int]: ((ord_less_eq @ int @ A @ (minus_minus @ int @ B @ (one_one @ int))) = (ord_less @ int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[618])).
% 74.76/25.30  thf(364,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_eq @ nat @ (suc @ D) @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_full__nat__induct)).
% 74.76/25.30  thf(2004,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_eq @ nat @ (suc @ D) @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])).
% 74.76/25.30  thf(745,axiom,((! [TA: $tType]: (! [A:(nat > TA),B:TA,C:nat]: ((extended_rec_enat @ TA @ A @ B @ (extended_enat2 @ C)) = (A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_enat_Osimps_I6_J)).
% 74.76/25.30  thf(3235,plain,((! [TA: $tType]: (! [A:(nat > TA),B:TA,C:nat]: ((extended_rec_enat @ TA @ (A) @ B @ (extended_enat2 @ C)) = (A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[745])).
% 74.76/25.30  thf(505,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ C) => (ord_less_eq @ TA @ (plus_plus @ TA @ B @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_add__decreasing2)).
% 74.76/25.30  thf(2431,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ C) => (ord_less_eq @ TA @ (plus_plus @ TA @ B @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])).
% 74.76/25.30  thf(547,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ E)) = (ord_less @ nat @ D @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1774_nat__less__add__iff2)).
% 74.76/25.30  thf(2526,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ C) @ D) @ (plus_plus @ nat @ (times_times @ nat @ B @ C) @ E)) = (ord_less @ nat @ D @ (plus_plus @ nat @ (times_times @ nat @ (minus_minus @ nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[547])).
% 74.76/25.30  thf(499,axiom,((ring_1 @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oring__1)).
% 74.76/25.30  thf(2416,plain,((ring_1 @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])).
% 74.76/25.30  thf(215,axiom,((! [A:int,B:int,C:(int > $o)]: ((ord_less @ int @ A @ B) => ((C @ (plus_plus @ int @ A @ (one_one @ int))) => ((! [D:int]: ((ord_less @ int @ A @ D) => ((C @ D) => (C @ (plus_plus @ int @ D @ (one_one @ int)))))) => (C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1184_int__gr__induct)).
% 74.76/25.30  thf(1491,plain,((! [A:int,B:int,C:(int > $o)]: ((ord_less @ int @ A @ B) => ((C @ (plus_plus @ int @ A @ (one_one @ int))) => ((! [D:int]: ((ord_less @ int @ A @ D) => ((C @ D) => (C @ (plus_plus @ int @ D @ (one_one @ int)))))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])).
% 74.76/25.30  thf(265,axiom,((! [A:nat]: (ord_less_eq @ nat @ A @ (times_times @ nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_le__square)).
% 74.76/25.30  thf(1689,plain,((! [A:nat]: (ord_less_eq @ nat @ A @ (times_times @ nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])).
% 74.76/25.30  thf(609,axiom,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((A = B) & (ord_less_eq @ TA @ C @ D)) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_add__mono__thms__linordered__semiring_I2_J)).
% 74.76/25.30  thf(2786,plain,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((A = B) & (ord_less_eq @ TA @ C @ D)) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[609])).
% 74.76/25.30  thf(32,axiom,(((one_one @ extended_enat) = (extended_enat2 @ (one_one @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_one__enat__def)).
% 74.76/25.30  thf(914,plain,(((one_one @ extended_enat) = (extended_enat2 @ (one_one @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
% 74.76/25.30  thf(760,axiom,((canoni5634975068530333245id_add @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_453)).
% 74.76/25.30  thf(3267,plain,((canoni5634975068530333245id_add @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[760])).
% 74.76/25.30  thf(124,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (times_times @ TA @ B @ A) @ (times_times @ TA @ C @ A)) = (ord_less @ TA @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1313_mult__less__iff1)).
% 74.76/25.30  thf(1193,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (times_times @ TA @ B @ A) @ (times_times @ TA @ C @ A)) = (ord_less @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])).
% 74.76/25.30  thf(641,axiom,((! [A:nat,B:extended_enat]: ((ord_less_eq @ extended_enat @ (extended_enat2 @ (suc @ A)) @ B) = (ord_less @ extended_enat @ (extended_enat2 @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1032_Suc__ile__eq)).
% 74.76/25.30  thf(2902,plain,((! [A:nat,B:extended_enat]: ((ord_less_eq @ extended_enat @ (extended_enat2 @ (suc @ A)) @ B) = (ord_less @ extended_enat @ (extended_enat2 @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[641])).
% 74.76/25.30  thf(437,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ (zero_zero @ nat) @ B) => (ord_less @ nat @ (minus_minus @ nat @ B @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1732_diff__less)).
% 74.76/25.30  thf(2230,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less @ nat @ (zero_zero @ nat) @ B) => (ord_less @ nat @ (minus_minus @ nat @ B @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[437])).
% 74.76/25.30  thf(645,axiom,((! [TA: $tType]: ((zero_less_one @ TA) => (ord_less @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_867_zero__less__one)).
% 74.76/25.30  thf(2917,plain,((! [TA: $tType]: ((zero_less_one @ TA) => (ord_less @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[645])).
% 74.76/25.30  thf(115,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_add__less__mono1)).
% 74.76/25.30  thf(1161,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
% 74.76/25.30  thf(91,axiom,((! [A:nat]: ((times_times @ nat @ A @ (zero_zero @ nat)) = (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_mult__0__right)).
% 74.76/25.30  thf(1077,plain,((! [A:nat]: ((times_times @ nat @ A @ (zero_zero @ nat)) = (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])).
% 74.76/25.30  thf(408,axiom,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ (plus_plus @ nat @ A @ B) @ C) = (plus_plus @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_add__mult__distrib)).
% 74.76/25.30  thf(2162,plain,((! [A:nat,B:nat,C:nat]: ((times_times @ nat @ (plus_plus @ nat @ A @ B) @ C) = (plus_plus @ nat @ (times_times @ nat @ A @ C) @ (times_times @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])).
% 74.76/25.30  thf(394,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (((suc @ A) != B) => (ord_less @ nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_Suc__lessI)).
% 74.76/25.30  thf(2095,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => ((~ ((suc @ A) = B)) => (ord_less @ nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])).
% 74.76/25.30  thf(7,axiom,((! [A:int,B:int]: (((abs_abs @ int @ (times_times @ int @ A @ B)) = (one_one @ int)) => ((abs_abs @ int @ A) = (one_one @ int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2742_abs__zmult__eq__1)).
% 74.76/25.30  thf(832,plain,((! [A:int,B:int]: (((abs_abs @ int @ (times_times @ int @ A @ B)) = (one_one @ int)) => ((abs_abs @ int @ A) = (one_one @ int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 74.76/25.30  thf(481,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((plus_plus @ nat @ C @ (minus_minus @ nat @ B @ A)) = (minus_minus @ nat @ (plus_plus @ nat @ C @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1695_Nat_Oadd__diff__assoc)).
% 74.76/25.30  thf(2374,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((plus_plus @ nat @ C @ (minus_minus @ nat @ B @ A)) = (minus_minus @ nat @ (plus_plus @ nat @ C @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])).
% 74.76/25.30  thf(456,axiom,((! [A:nat,B:nat]: (((suc @ (zero_zero @ nat)) = (times_times @ nat @ A @ B)) = ((A = (suc @ (zero_zero @ nat))) & (B = (suc @ (zero_zero @ nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_one__eq__mult__iff)).
% 74.76/25.30  thf(2287,plain,((! [A:nat,B:nat]: (((suc @ (zero_zero @ nat)) = (times_times @ nat @ A @ B)) = ((A = (suc @ (zero_zero @ nat))) & (B = (suc @ (zero_zero @ nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[456])).
% 74.76/25.30  thf(218,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ (times_times @ nat @ A @ B)) = ((ord_less @ nat @ (zero_zero @ nat) @ A) & (ord_less @ nat @ (zero_zero @ nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_nat__0__less__mult__iff)).
% 74.76/25.30  thf(1512,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ (times_times @ 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)],[218])).
% 74.76/25.30  thf(462,axiom,((! [A:(nat > $o),B:nat]: ((A @ (zero_zero @ nat)) => ((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_nat__induct)).
% 74.76/25.30  thf(2302,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)],[462])).
% 74.76/25.30  thf(486,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_add__nonpos__nonpos)).
% 74.76/25.30  thf(2385,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ B) @ (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])).
% 74.76/25.30  thf(775,axiom,((complete_Inf @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_OInf_473)).
% 74.76/25.30  thf(3291,plain,((complete_Inf @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[775])).
% 74.76/25.30  thf(833,plain,((! [A:int]: ((? [B:int]: ((abs_abs @ int @ (times_times @ int @ A @ B)) = (one_one @ int))) => ((abs_abs @ int @ A) = (one_one @ int))))),inference(miniscope,[status(thm)],[832])).
% 74.76/25.30  thf(834,plain,(! [B:int,A:int] : ((~ ((abs_abs @ int @ (times_times @ int @ A @ B)) = (one_one @ int))) | ((abs_abs @ int @ A) = (one_one @ int)))),inference(cnf,[status(esa)],[833])).
% 74.76/25.30  thf(835,plain,(! [B:int,A:int] : (((abs_abs @ int @ (times_times @ int @ A @ B)) != (one_one @ int)) | ((abs_abs @ int @ A) = (one_one @ int)))),inference(lifteq,[status(thm)],[834])).
% 74.76/25.30  thf(703,axiom,((! [TA: $tType]: (((dvd @ TA) & (semiring_0 @ TA)) => (! [A:(TA > $o),B:TA]: ((? [C:TA]: (A @ (times_times @ TA @ B @ C))) = (? [C:TA]: ((dvd_dvd @ TA @ B @ (plus_plus @ TA @ C @ (zero_zero @ TA))) & (A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1444_unity__coeff__ex)).
% 74.76/25.30  thf(3100,plain,((! [TA: $tType]: (((dvd @ TA) & (semiring_0 @ TA)) => (! [A:(TA > $o),B:TA]: ((? [C:TA]: (A @ (times_times @ TA @ B @ C))) = (? [C:TA]: ((dvd_dvd @ TA @ B @ (plus_plus @ TA @ C @ (zero_zero @ TA))) & (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[703])).
% 74.76/25.30  thf(243,axiom,((! [A:nat]: ((ord_max @ nat @ A @ (zero_zero @ nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4828_max__nat_Oright__neutral)).
% 74.76/25.30  thf(1593,plain,((! [A:nat]: ((ord_max @ nat @ A @ (zero_zero @ nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])).
% 74.76/25.30  thf(319,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ A @ B) = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1691_diff__is__0__eq_H)).
% 74.76/25.30  thf(1876,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((minus_minus @ nat @ A @ B) = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])).
% 74.76/25.30  thf(710,axiom,((! [TA: $tType]: ((strict9044650504122735259up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ D) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_add__strict__mono)).
% 74.76/25.30  thf(3132,plain,((! [TA: $tType]: ((strict9044650504122735259up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ C @ D) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[710])).
% 74.76/25.30  thf(650,axiom,((! [TA: $tType]: ((extended_case_enat @ TA) = (extended_rec_enat @ TA)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_case__enat__def)).
% 74.76/25.30  thf(2930,plain,((! [TA: $tType]: ((extended_case_enat @ TA) = (extended_rec_enat @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[650])).
% 74.76/25.30  thf(432,axiom,((order_bot @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder__bot_83)).
% 74.76/25.30  thf(2218,plain,((order_bot @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[432])).
% 74.76/25.30  thf(667,axiom,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_mult__right__mono)).
% 74.76/25.30  thf(2983,plain,((! [TA: $tType]: ((ordered_semiring @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ C) => (ord_less_eq @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[667])).
% 74.76/25.30  thf(585,axiom,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((plus_plus @ int @ (times_times @ int @ A @ B) @ C) = (plus_plus @ int @ (times_times @ int @ D @ E) @ F)) => ((ord_less_eq @ int @ (zero_zero @ int) @ (plus_plus @ int @ (times_times @ int @ D @ E) @ F)) => ((ord_less @ int @ F @ D) => ((ord_less_eq @ int @ (zero_zero @ int) @ C) => ((ord_less @ int @ (zero_zero @ int) @ D) => ((ord_less_eq @ int @ D @ A) => (ord_less_eq @ int @ B @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_zdiv__mono2__lemma)).
% 74.76/25.30  thf(2719,plain,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((plus_plus @ int @ (times_times @ int @ A @ B) @ C) = (plus_plus @ int @ (times_times @ int @ D @ E) @ F)) => ((ord_less_eq @ int @ (zero_zero @ int) @ (plus_plus @ int @ (times_times @ int @ D @ E) @ F)) => ((ord_less @ int @ F @ D) => ((ord_less_eq @ int @ (zero_zero @ int) @ C) => ((ord_less @ int @ (zero_zero @ int) @ D) => ((ord_less_eq @ int @ D @ A) => (ord_less_eq @ int @ B @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[585])).
% 74.76/25.30  thf(135,axiom,((strict9044650504122735259up_add @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_248)).
% 74.76/25.30  thf(1229,plain,((strict9044650504122735259up_add @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])).
% 74.76/25.30  thf(438,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(TA > nat)]: ((A @ B) => (? [D:TA]: ((A @ D) & ! [E:TA]: ((A @ E) => (ord_less_eq @ nat @ (C @ D) @ (C @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1020_ex__has__least__nat)).
% 74.76/25.30  thf(2233,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(TA > nat)]: ((A @ B) => (? [D:TA]: ((A @ D) & ! [E:TA]: ((A @ E) => (ord_less_eq @ nat @ (C @ D) @ (C @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])).
% 74.76/25.30  thf(818,plain,(((vEBT_VEBT_elim_dead @ summarya @ (extend4730790105801354508finity @ extended_enat)) != summarya)),inference(lifteq,[status(thm)],[817])).
% 74.76/25.30  thf(759,axiom,((! [A:extended_enat]: ((! [B:nat]: (A != (extended_enat2 @ B))) = (A = (extend4730790105801354508finity @ extended_enat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_not__enat__eq)).
% 74.76/25.30  thf(3264,plain,((! [A:extended_enat]: ((! [B:nat]: ~ (A = (extended_enat2 @ B))) = (A = (extend4730790105801354508finity @ extended_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[759])).
% 74.76/25.30  thf(591,axiom,((! [A:int,B:int]: ((ord_less @ int @ A @ B) => (ord_less_eq @ int @ (plus_plus @ int @ A @ (one_one @ int)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_zless__imp__add1__zle)).
% 74.76/25.30  thf(2736,plain,((! [A:int,B:int]: ((ord_less @ int @ A @ B) => (ord_less_eq @ int @ (plus_plus @ int @ A @ (one_one @ int)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[591])).
% 74.76/25.30  thf(854,plain,(! [D:int,C:(nat > int),B:nat,A:nat] : ((~ (sk1 @ A @ B @ C)) | (~ (ord_less_eq @ nat @ A @ B)) | (~ (ord_less_eq @ int @ (C @ A) @ D)) | (~ (ord_less_eq @ int @ D @ (C @ B))) | (ord_less_eq @ nat @ (sk3 @ D @ (C) @ B @ A) @ B))),inference(cnfConj,[status(thm)],[851])).
% 74.76/25.30  thf(356,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (((plus_plus @ TA @ A @ B) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_844_add__nonneg__eq__0__iff)).
% 74.76/25.30  thf(1986,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (((plus_plus @ TA @ A @ B) = (zero_zero @ TA)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])).
% 74.76/25.30  thf(16,axiom,((! [A:int,B:int,C:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => (ord_less @ int @ (minus_minus @ int @ B @ (times_times @ int @ (plus_plus @ int @ (abs_abs @ int @ (minus_minus @ int @ B @ C)) @ (one_one @ int)) @ A)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2786_decr__lemma)).
% 74.76/25.30  thf(867,plain,((! [A:int,B:int,C:int]: ((ord_less @ int @ (zero_zero @ int) @ A) => (ord_less @ int @ (minus_minus @ int @ B @ (times_times @ int @ (plus_plus @ int @ (abs_abs @ int @ (minus_minus @ int @ B @ C)) @ (one_one @ int)) @ A)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 74.76/25.30  thf(286,axiom,((comm_semiring @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__semiring)).
% 74.76/25.30  thf(1757,plain,((comm_semiring @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])).
% 74.76/25.30  thf(602,axiom,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ B) @ C) @ (plus_plus @ TA @ (times_times @ TA @ D @ B) @ E)) = (ord_less_eq @ TA @ C @ (plus_plus @ TA @ (times_times @ TA @ (minus_minus @ TA @ D @ A) @ B) @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1630_ordered__ring__class_Ole__add__iff2)).
% 74.76/25.30  thf(2768,plain,((! [TA: $tType]: ((ordered_ring @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ (times_times @ TA @ A @ B) @ C) @ (plus_plus @ TA @ (times_times @ TA @ D @ B) @ E)) = (ord_less_eq @ TA @ C @ (plus_plus @ TA @ (times_times @ TA @ (minus_minus @ TA @ D @ A) @ B) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[602])).
% 74.76/25.30  thf(15,axiom,(((times_times @ nat) = (^ [A:nat,B:nat]: (if @ nat @ (A = (zero_zero @ nat)) @ (zero_zero @ nat) @ (plus_plus @ nat @ B @ (times_times @ nat @ (minus_minus @ nat @ A @ (one_one @ nat)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1775_mult__eq__if)).
% 74.76/25.30  thf(865,plain,(((times_times @ nat) = (^ [A:nat,B:nat]: (if @ nat @ (A = (zero_zero @ nat)) @ (zero_zero @ nat) @ (plus_plus @ nat @ B @ (times_times @ nat @ (minus_minus @ nat @ A @ (one_one @ nat)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 74.76/25.30  thf(211,axiom,((! [A:nat,B:nat]: ((plus_plus @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (extended_enat2 @ (plus_plus @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_plus__enat__simps_I1_J)).
% 74.76/25.30  thf(1480,plain,((! [A:nat,B:nat]: ((plus_plus @ extended_enat @ (extended_enat2 @ A) @ (extended_enat2 @ B)) = (extended_enat2 @ (plus_plus @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])).
% 74.76/25.30  thf(733,axiom,((! [A:extended_enat]: ((ord_less_eq @ extended_enat @ A @ (zero_zero @ extended_enat)) = (A = (zero_zero @ extended_enat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_ile0__eq)).
% 74.76/25.30  thf(3203,plain,((! [A:extended_enat]: ((ord_less_eq @ extended_enat @ A @ (zero_zero @ extended_enat)) = (A = (zero_zero @ extended_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[733])).
% 74.76/25.30  thf(693,axiom,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_add__nonneg__pos)).
% 74.76/25.30  thf(3062,plain,((! [TA: $tType]: ((ordere6911136660526730532id_add @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ (zero_zero @ TA) @ (plus_plus @ TA @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[693])).
% 74.76/25.30  thf(677,axiom,((! [TA: $tType]: ((wellorder @ TA) => (! [A:(TA > $o),B:TA]: ((! [C:TA]: ((! [D:TA]: ((ord_less @ TA @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1256_less__induct)).
% 74.76/25.30  thf(3015,plain,((! [TA: $tType]: ((wellorder @ TA) => (! [A:(TA > $o),B:TA]: ((! [C:TA]: ((! [D:TA]: ((ord_less @ TA @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[677])).
% 74.76/25.30  thf(200,axiom,((! [A:nat,B:nat]: ((A != (zero_zero @ nat)) => (? [C:nat,D:nat,E:nat]: ((dvd_dvd @ nat @ C @ A) & (dvd_dvd @ nat @ C @ B) & ((times_times @ nat @ A @ D) = (plus_plus @ nat @ (times_times @ nat @ B @ E) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1463_bezout__add__strong__nat)).
% 74.76/25.30  thf(1436,plain,((! [A:nat,B:nat]: ((~ (A = (zero_zero @ nat))) => (? [C:nat,D:nat,E:nat]: ((dvd_dvd @ nat @ C @ A) & (dvd_dvd @ nat @ C @ B) & ((times_times @ nat @ A @ D) = (plus_plus @ nat @ (times_times @ nat @ B @ E) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
% 74.76/25.30  thf(791,axiom,((! [A:$o,B:$o,C:extended_enat]: ((vEBT_VEBT_elim_dead @ (vEBT_Leaf @ A @ B) @ C) = (vEBT_Leaf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_VEBT__internal_Oelim__dead_Osimps_I1_J)).
% 74.76/25.30  thf(3328,plain,((! [A:$o,B:$o,C:extended_enat]: ((vEBT_VEBT_elim_dead @ (vEBT_Leaf @ A @ B) @ C) = (vEBT_Leaf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[791])).
% 74.76/25.30  thf(161,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less @ nat @ C @ (suc @ A)) => (B @ C))) = ((B @ A) & ! [C:nat]: ((ord_less @ nat @ C @ A) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_All__less__Suc)).
% 74.76/25.30  thf(1314,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less @ nat @ C @ (suc @ A)) => (B @ C))) = ((B @ A) & ! [C:nat]: ((ord_less @ nat @ C @ A) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
% 74.76/25.30  thf(418,axiom,((! [A:nat]: (ord_less @ nat @ (zero_zero @ nat) @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_zero__less__Suc)).
% 74.76/25.30  thf(2186,plain,((! [A:nat]: (ord_less @ nat @ (zero_zero @ nat) @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[418])).
% 74.76/25.30  thf(170,axiom,((monoid_add @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__add_323)).
% 74.76/25.30  thf(1335,plain,((monoid_add @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
% 74.76/25.30  thf(579,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: (((zero_zero @ TA) = (plus_plus @ TA @ A @ B)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_zero__eq__add__iff__both__eq__0)).
% 74.76/25.30  thf(2704,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: (((zero_zero @ TA) = (plus_plus @ TA @ A @ B)) = ((A = (zero_zero @ TA)) & (B = (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[579])).
% 74.76/25.30  thf(478,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ (suc @ B)) = (ord_less @ nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_Suc__less__eq)).
% 74.76/25.30  thf(2366,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ A) @ (suc @ B)) = (ord_less @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])).
% 74.76/25.30  thf(789,axiom,((! [A:nat]: ((extended_enat2 @ A) != (extend4730790105801354508finity @ extended_enat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_enat_Odistinct_I1_J)).
% 74.76/25.30  thf(3323,plain,((! [A:nat]: ~ ((extended_enat2 @ A) = (extend4730790105801354508finity @ extended_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[789])).
% 74.76/25.30  thf(827,plain,(! [TA:$tType,A:num] : ((~ (linordered_idom @ TA)) | ((abs_abs @ TA @ (numeral_numeral @ TA @ A)) = (numeral_numeral @ TA @ A)))),inference(cnf,[status(esa)],[826])).
% 74.76/25.30  thf(828,plain,(! [TA:$tType,A:num] : (((abs_abs @ TA @ (numeral_numeral @ TA @ A)) = (numeral_numeral @ TA @ A)) | (~ (linordered_idom @ TA)))),inference(lifteq,[status(thm)],[827])).
% 74.76/25.30  thf(117,axiom,((unique1627219031080169319umeral @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Divides_Ounique__euclidean__semiring__numeral_24)).
% 74.76/25.30  thf(1165,plain,((unique1627219031080169319umeral @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
% 74.76/25.30  thf(687,axiom,((! [A:extended_enat,B:extended_enat,C:nat]: ((ord_less_eq @ extended_enat @ (plus_plus @ extended_enat @ A @ B) @ (extended_enat2 @ C)) = (? [D:nat,E:nat]: ((A = (extended_enat2 @ E)) & (B = (extended_enat2 @ D)) & (ord_less_eq @ nat @ (plus_plus @ nat @ E @ D) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_iadd__le__enat__iff)).
% 74.76/25.30  thf(3045,plain,((! [A:extended_enat,B:extended_enat,C:nat]: ((ord_less_eq @ extended_enat @ (plus_plus @ extended_enat @ A @ B) @ (extended_enat2 @ C)) = (? [D:nat,E:nat]: ((A = (extended_enat2 @ E)) & (B = (extended_enat2 @ D)) & (ord_less_eq @ nat @ (plus_plus @ nat @ E @ D) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[687])).
% 74.76/25.30  thf(608,axiom,((! [TA: $tType]: ((ab_semigroup_mult @ TA) => ((times_times @ TA) = (^ [A:TA,B:TA]: (times_times @ TA @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_mult_Ocommute)).
% 74.76/25.30  thf(2783,plain,((! [TA: $tType]: ((ab_semigroup_mult @ TA) => ((times_times @ TA) = (^ [A:TA,B:TA]: (times_times @ TA @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[608])).
% 74.76/25.30  thf(554,axiom,(((plus_plus @ extended_enat) = (^ [A:extended_enat,B:extended_enat]: (extended_case_enat @ extended_enat @ (^ [C:nat]: (extended_case_enat @ extended_enat @ (^ [D:nat]: (extended_enat2 @ (plus_plus @ nat @ C @ D))) @ (extend4730790105801354508finity @ extended_enat) @ B)) @ (extend4730790105801354508finity @ extended_enat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_plus__enat__def)).
% 74.76/25.30  thf(2549,plain,(((plus_plus @ extended_enat) = (^ [A:extended_enat,B:extended_enat]: (extended_case_enat @ extended_enat @ (^ [C:nat]: (extended_case_enat @ extended_enat @ (^ [D:nat]: (extended_enat2 @ (plus_plus @ nat @ C @ D))) @ (extend4730790105801354508finity @ extended_enat) @ B)) @ (extend4730790105801354508finity @ extended_enat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[554])).
% 74.76/25.30  thf(784,axiom,((zero @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_496)).
% 74.76/25.30  thf(3309,plain,((zero @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[784])).
% 74.76/25.30  thf(2617,plain,((((vEBT_Leaf @ ($true) @ ($true)) = (vEBT_Leaf @ ($true) @ ($false))) = ((($true) = ($true)) & (($true) = ($false))))),inference(instance,[status(thm)],[2602])).
% 74.76/25.30  thf(2618,plain,((~ ((vEBT_Leaf @ ($true) @ ($true)) = (vEBT_Leaf @ ($true) @ ($false))))),inference(simp,[status(thm)],[2617])).
% 74.76/25.30  thf(2636,plain,(((vEBT_Leaf @ ($true) @ ($false)) != (vEBT_Leaf @ ($true) @ ($true)))),inference(lifteq,[status(thm)],[2618])).
% 74.76/25.30  thf(423,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq @ nat @ A @ B)) = (ord_less_eq @ nat @ (suc @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_not__less__eq__eq)).
% 74.76/25.30  thf(2201,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)],[423])).
% 74.76/25.30  thf(35,axiom,((ord_less_eq @ int @ (zero_zero @ int) @ (zero_zero @ int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_less__eq__int__code_I1_J)).
% 74.76/25.30  thf(918,plain,((ord_less_eq @ int @ (zero_zero @ int) @ (zero_zero @ int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 74.76/25.30  thf(357,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ (minus_minus @ nat @ B @ C)) = (ord_less @ nat @ (plus_plus @ nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1737_less__diff__conv)).
% 74.76/25.30  thf(1989,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ (minus_minus @ nat @ B @ C)) = (ord_less @ nat @ (plus_plus @ nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])).
% 74.76/25.30  thf(26,axiom,((! [A:nat,B:nat]: ~ (ord_less @ nat @ (plus_plus @ nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_not__add__less2)).
% 74.76/25.30  thf(897,plain,((! [A:nat,B:nat]: ~ (ord_less @ nat @ (plus_plus @ nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 74.76/25.30  thf(500,axiom,((! [A:nat]: ~ (ord_less @ nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_less__irrefl__nat)).
% 74.76/25.30  thf(2417,plain,((! [A:nat]: ~ (ord_less @ nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[500])).
% 74.76/25.30  thf(660,axiom,((! [A:int]: ((ord_less @ int @ (plus_plus @ int @ (plus_plus @ int @ (one_one @ int) @ A) @ A) @ (zero_zero @ int)) = (ord_less @ int @ A @ (zero_zero @ int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1149_odd__less__0__iff)).
% 74.76/25.30  thf(2961,plain,((! [A:int]: ((ord_less @ int @ (plus_plus @ int @ (plus_plus @ int @ (one_one @ int) @ A) @ A) @ (zero_zero @ int)) = (ord_less @ int @ A @ (zero_zero @ int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[660])).
% 74.76/25.30  thf(271,axiom,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) = (((ord_less @ TA @ (zero_zero @ TA) @ B) & (ord_less @ TA @ A @ C)) | ((ord_less @ TA @ B @ (zero_zero @ TA)) & (ord_less @ TA @ C @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_mult__less__cancel__right__disj)).
% 74.76/25.30  thf(1710,plain,((! [TA: $tType]: ((linord4710134922213307826strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ B)) = (((ord_less @ TA @ (zero_zero @ TA) @ B) & (ord_less @ TA @ A @ C)) | ((ord_less @ TA @ B @ (zero_zero @ TA)) & (ord_less @ TA @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])).
% 74.76/25.30  thf(583,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (times_times @ TA @ B @ A)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ (one_one @ TA) @ B)) & ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => (ord_less @ TA @ B @ (one_one @ TA))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_mult__less__cancel__right1)).
% 74.76/25.30  thf(2714,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (times_times @ TA @ B @ A)) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ A) => (ord_less @ TA @ (one_one @ TA) @ B)) & ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) => (ord_less @ TA @ B @ (one_one @ TA))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[583])).
% 74.76/25.30  thf(731,axiom,((! [TA: $tType]: ((ab_semigroup_mult @ TA) => (! [A:TA]: ((^ [B:TA]: (times_times @ TA @ B @ A)) = (times_times @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2086_mult__commute__abs)).
% 74.76/25.30  thf(3196,plain,((! [TA: $tType]: ((ab_semigroup_mult @ TA) => (! [A:TA]: ((^ [B:TA]: (times_times @ TA @ B @ A)) = (times_times @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[731])).
% 74.76/25.30  thf(324,axiom,((! [A:nat]: (((extended_enat2 @ A) = (one_one @ extended_enat)) = (A = (one_one @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_enat__1__iff_I1_J)).
% 74.76/25.30  thf(1891,plain,((! [A:nat]: (((extended_enat2 @ A) = (one_one @ extended_enat)) = (A = (one_one @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])).
% 74.76/25.30  thf(435,axiom,((! [A:nat]: ((ord_less @ nat @ A @ (suc @ (zero_zero @ nat))) = (A = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_less__Suc0)).
% 74.76/25.30  thf(2223,plain,((! [A:nat]: ((ord_less @ nat @ A @ (suc @ (zero_zero @ nat))) = (A = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[435])).
% 74.76/25.30  thf(612,axiom,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => (ord_less_eq @ TA @ (plus_plus @ TA @ C @ A) @ (plus_plus @ TA @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_add__left__mono)).
% 74.76/25.30  thf(2795,plain,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => (ord_less_eq @ TA @ (plus_plus @ TA @ C @ A) @ (plus_plus @ TA @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[612])).
% 74.76/25.30  thf(368,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (times_times @ TA @ A @ B) @ (zero_zero @ TA)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_mult__pos__neg)).
% 74.76/25.30  thf(2021,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) => ((ord_less @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (times_times @ TA @ A @ B) @ (zero_zero @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])).
% 74.76/25.30  thf(381,axiom,((lattice @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Olattice_328)).
% 74.76/25.30  thf(2063,plain,((lattice @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])).
% 74.76/25.30  thf(837,plain,((! [A:int]: ((~ (A = (zero_zero @ int))) => (! [B:int]: ((dvd_dvd @ int @ B @ A) => (ord_less_eq @ int @ (abs_abs @ int @ B) @ (abs_abs @ int @ A))))))),inference(miniscope,[status(thm)],[836])).
% 74.76/25.30  thf(838,plain,(! [B:int,A:int] : ((A = (zero_zero @ int)) | (~ (dvd_dvd @ int @ B @ A)) | (ord_less_eq @ int @ (abs_abs @ int @ B) @ (abs_abs @ int @ A)))),inference(cnf,[status(esa)],[837])).
% 74.76/25.30  thf(839,plain,(! [B:int,A:int] : ((A = (zero_zero @ int)) | (~ (dvd_dvd @ int @ B @ A)) | (ord_less_eq @ int @ (abs_abs @ int @ B) @ (abs_abs @ int @ A)))),inference(lifteq,[status(thm)],[838])).
% 74.76/25.30  thf(3541,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less @ TA @ (one_one @ TA) @ (one_one @ TA))) | ((linord181362715937106298miring @ nat) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1301,2146])).
% 74.76/25.30  thf(3542,plain,(! [TA:$tType] : ((~ (ord_less @ TA @ (one_one @ TA) @ (one_one @ TA))) | ((linord181362715937106298miring @ nat) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3541])).
% 74.76/25.30  thf(3543,plain,((~ (ord_less @ nat @ (one_one @ nat) @ (one_one @ nat)))),inference(pattern_uni,[status(thm)],[3542:[bind_type(TA,$thf(nat))]])).
% 74.76/25.30  thf(112,axiom,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd @ nat @ C @ A) & (dvd_dvd @ nat @ C @ B) & (((minus_minus @ nat @ (times_times @ nat @ A @ D) @ (times_times @ nat @ B @ E)) = C) | ((minus_minus @ nat @ (times_times @ nat @ B @ D) @ (times_times @ nat @ A @ E)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1749_bezout1__nat)).
% 74.76/25.30  thf(1152,plain,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd @ nat @ C @ A) & (dvd_dvd @ nat @ C @ B) & (((minus_minus @ nat @ (times_times @ nat @ A @ D) @ (times_times @ nat @ B @ E)) = C) | ((minus_minus @ nat @ (times_times @ nat @ B @ D) @ (times_times @ nat @ A @ E)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
% 74.76/25.30  thf(627,axiom,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: ((ord_less_eq @ TA @ (top_top @ TA) @ A) = (A = (top_top @ TA))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6212_top_Oextremum__unique)).
% 74.76/25.30  thf(2847,plain,((! [TA: $tType]: ((order_top @ TA) => (! [A:TA]: ((ord_less_eq @ TA @ (top_top @ TA) @ A) = (A = (top_top @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[627])).
% 74.76/25.30  thf(523,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (? [C:nat]: (B = (suc @ (plus_plus @ nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_less__imp__Suc__add)).
% 74.76/25.30  thf(2467,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)],[523])).
% 74.76/25.30  thf(352,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd @ int @ (times_times @ int @ A @ B) @ (times_times @ int @ A @ C)) => ((A != (zero_zero @ int)) => (dvd_dvd @ int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1438_zdvd__mult__cancel)).
% 74.76/25.30  thf(1976,plain,((! [A:int,B:int,C:int]: ((dvd_dvd @ int @ (times_times @ int @ A @ B) @ (times_times @ int @ A @ C)) => ((~ (A = (zero_zero @ int))) => (dvd_dvd @ int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])).
% 74.76/25.30  thf(564,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus @ nat @ B @ C)) = (~ (((ord_less @ nat @ B @ C) & ~ (A @ (zero_zero @ nat))) | ? [D:nat]: ((B = (plus_plus @ nat @ C @ D)) & ~ (A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1757_nat__diff__split__asm)).
% 74.76/25.30  thf(2583,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus @ nat @ B @ C)) = (~ (((ord_less @ nat @ B @ C) & ~ (A @ (zero_zero @ nat))) | ? [D:nat]: ((B = (plus_plus @ nat @ C @ D)) & ~ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[564])).
% 74.76/25.30  thf(140,axiom,((linord8928482502909563296strict @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__semiring__strict_264)).
% 74.76/25.30  thf(1236,plain,((linord8928482502909563296strict @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
% 74.76/25.30  thf(57,axiom,((! [A:nat,B:nat]: ((minus_minus @ nat @ A @ (plus_plus @ nat @ A @ B)) = (zero_zero @ nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1736_diff__add__0)).
% 74.76/25.30  thf(987,plain,((! [A:nat,B:nat]: ((minus_minus @ nat @ A @ (plus_plus @ nat @ A @ B)) = (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
% 74.76/25.30  thf(680,axiom,((! [A:extended_enat]: ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ A) => ((times_times @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1034_imult__infinity__right)).
% 74.76/25.30  thf(3025,plain,((! [A:extended_enat]: ((ord_less @ extended_enat @ (zero_zero @ extended_enat) @ A) => ((times_times @ extended_enat @ A @ (extend4730790105801354508finity @ extended_enat)) = (extend4730790105801354508finity @ extended_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[680])).
% 74.76/25.30  thf(147,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus @ nat @ (ord_max @ nat @ A @ B) @ C) = (ord_max @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4837_nat__add__max__left)).
% 74.76/25.30  thf(1261,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus @ nat @ (ord_max @ nat @ A @ B) @ C) = (ord_max @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
% 74.76/25.30  thf(570,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq @ int @ (zero_zero @ int) @ (plus_plus @ int @ (times_times @ int @ A @ B) @ C)) => ((ord_less @ int @ C @ A) => ((ord_less @ int @ (zero_zero @ int) @ A) => (ord_less_eq @ int @ (zero_zero @ int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_q__pos__lemma)).
% 74.76/25.30  thf(2600,plain,((! [A:int,B:int,C:int]: ((ord_less_eq @ int @ (zero_zero @ int) @ (plus_plus @ int @ (times_times @ int @ A @ B) @ C)) => ((ord_less @ int @ C @ A) => ((ord_less @ int @ (zero_zero @ int) @ A) => (ord_less_eq @ int @ (zero_zero @ int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[570])).
% 74.76/25.30  thf(803,axiom,((! [A:extended_enat]: ((A != (extend4730790105801354508finity @ extended_enat)) = (? [B:nat]: (A = (extended_enat2 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_not__infinity__eq)).
% 74.76/25.30  thf(3411,plain,((! [A:extended_enat]: ((~ (A = (extend4730790105801354508finity @ extended_enat))) = (? [B:nat]: (A = (extended_enat2 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[803])).
% 74.76/25.30  thf(226,axiom,((linord8928482502909563296strict @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semiring__strict_43)).
% 74.76/25.30  thf(1537,plain,((linord8928482502909563296strict @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
% 74.76/25.30  thf(242,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((! [C:nat]: ((A @ (suc @ C)) => (A @ C))) => (A @ (zero_zero @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_zero__induct)).
% 74.76/25.30  thf(1582,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((! [C:nat]: ((A @ (suc @ C)) => (A @ C))) => (A @ (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
% 74.76/25.30  thf(445,axiom,((semigroup_add @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__add)).
% 74.76/25.30  thf(2265,plain,((semigroup_add @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[445])).
% 74.76/25.30  thf(272,axiom,((! [A:nat,B:nat]: ((dvd_dvd @ nat @ A @ B) => ((ord_less @ nat @ (zero_zero @ nat) @ B) => (ord_less_eq @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1460_dvd__imp__le)).
% 74.76/25.30  thf(1713,plain,((! [A:nat,B:nat]: ((dvd_dvd @ nat @ A @ B) => ((ord_less @ nat @ (zero_zero @ nat) @ B) => (ord_less_eq @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])).
% 74.76/25.30  thf(245,axiom,((! [A:nat,B:nat]: ((minus_minus @ nat @ A @ (suc @ B)) = (minus_minus @ nat @ (minus_minus @ nat @ A @ (one_one @ nat)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1744_diff__Suc__eq__diff__pred)).
% 74.76/25.30  thf(1597,plain,((! [A:nat,B:nat]: ((minus_minus @ nat @ A @ (suc @ B)) = (minus_minus @ nat @ (minus_minus @ nat @ A @ (one_one @ nat)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
% 74.76/25.30  thf(198,axiom,((! [A:nat]: (((zero_zero @ extended_enat) = (extended_enat2 @ A)) = (A = (zero_zero @ nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_enat__0__iff_I2_J)).
% 74.76/25.30  thf(1431,plain,((! [A:nat]: (((zero_zero @ extended_enat) = (extended_enat2 @ A)) = (A = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
% 74.76/25.30  thf(531,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((A != B) => (ord_less @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_le__neq__implies__less)).
% 74.76/25.30  thf(2484,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)],[531])).
% 74.76/25.30  thf(322,axiom,((! [A:nat,B:nat]: ((plus_plus @ nat @ (suc @ A) @ B) = (plus_plus @ nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_add__Suc__shift)).
% 74.76/25.30  thf(1885,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)],[322])).
% 74.76/25.30  thf(578,axiom,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA,B:TA]: ((! [C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ C) => ((ord_less @ TA @ C @ (one_one @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ C @ A) @ B)))) => (ord_less_eq @ TA @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1036_field__le__mult__one__interval)).
% 74.76/25.30  thf(2699,plain,((! [TA: $tType]: ((linordered_field @ TA) => (! [A:TA,B:TA]: ((! [C:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ C) => ((ord_less @ TA @ C @ (one_one @ TA)) => (ord_less_eq @ TA @ (times_times @ TA @ C @ A) @ B)))) => (ord_less_eq @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[578])).
% 74.76/25.30  thf(185,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ D) => (ord_less_eq @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_add__le__mono)).
% 74.76/25.30  thf(1399,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ D) => (ord_less_eq @ nat @ (plus_plus @ nat @ A @ C) @ (plus_plus @ nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
% 74.76/25.30  thf(448,axiom,(((ord_less_eq @ real) = (^ [A:real,B:real]: ((ord_less @ real @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_less__eq__real__def)).
% 74.76/25.30  thf(2270,plain,(((ord_less_eq @ real) = (^ [A:real,B:real]: ((ord_less @ real @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[448])).
% 74.76/25.30  thf(403,axiom,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ((ord_max @ TA @ (one_one @ TA) @ (numeral_numeral @ TA @ A)) = (numeral_numeral @ TA @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4776_max__0__1_I5_J)).
% 74.76/25.30  thf(2138,plain,((! [TA: $tType]: ((linord181362715937106298miring @ TA) => (! [A:num]: ((ord_max @ TA @ (one_one @ TA) @ (numeral_numeral @ TA @ A)) = (numeral_numeral @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[403])).
% 74.76/25.30  thf(792,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((? [D:nat]: (A = (extended_enat2 @ D))) => ((? [D:nat]: (B = (extended_enat2 @ D))) => (! [D:nat]: (C != (extended_enat2 @ D))))) => (((? [D:nat]: (A = (extended_enat2 @ D))) => ((? [D:nat]: (B = (extended_enat2 @ D))) => (C != (extend4730790105801354508finity @ extended_enat)))) => (((? [D:nat]: (A = (extended_enat2 @ D))) => ((B = (extend4730790105801354508finity @ extended_enat)) => (! [D:nat]: (C != (extended_enat2 @ D))))) => (((? [D:nat]: (A = (extended_enat2 @ D))) => ((B = (extend4730790105801354508finity @ extended_enat)) => (C != (extend4730790105801354508finity @ extended_enat)))) => (((A = (extend4730790105801354508finity @ extended_enat)) => ((? [D:nat]: (B = (extended_enat2 @ D))) => (! [D:nat]: (C != (extended_enat2 @ D))))) => (((A = (extend4730790105801354508finity @ extended_enat)) => ((? [D:nat]: (B = (extended_enat2 @ D))) => (C != (extend4730790105801354508finity @ extended_enat)))) => (((A = (extend4730790105801354508finity @ extended_enat)) => ((B = (extend4730790105801354508finity @ extended_enat)) => (! [D:nat]: (C != (extended_enat2 @ D))))) => (~ ((A = (extend4730790105801354508finity @ extended_enat)) => ((B = (extend4730790105801354508finity @ extended_enat)) => (C != (extend4730790105801354508finity @ extended_enat)))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_enat3__cases)).
% 74.76/25.30  thf(3341,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((? [D:nat]: (A = (extended_enat2 @ D))) => ((? [D:nat]: (B = (extended_enat2 @ D))) => (! [D:nat]: ~ (C = (extended_enat2 @ D))))) => (((? [D:nat]: (A = (extended_enat2 @ D))) => ((? [D:nat]: (B = (extended_enat2 @ D))) => (~ (C = (extend4730790105801354508finity @ extended_enat))))) => (((? [D:nat]: (A = (extended_enat2 @ D))) => ((B = (extend4730790105801354508finity @ extended_enat)) => (! [D:nat]: ~ (C = (extended_enat2 @ D))))) => (((? [D:nat]: (A = (extended_enat2 @ D))) => ((B = (extend4730790105801354508finity @ extended_enat)) => (~ (C = (extend4730790105801354508finity @ extended_enat))))) => (((A = (extend4730790105801354508finity @ extended_enat)) => ((? [D:nat]: (B = (extended_enat2 @ D))) => (! [D:nat]: ~ (C = (extended_enat2 @ D))))) => (((A = (extend4730790105801354508finity @ extended_enat)) => ((? [D:nat]: (B = (extended_enat2 @ D))) => (~ (C = (extend4730790105801354508finity @ extended_enat))))) => (((A = (extend4730790105801354508finity @ extended_enat)) => ((B = (extend4730790105801354508finity @ extended_enat)) => (! [D:nat]: ~ (C = (extended_enat2 @ D))))) => (~ ((A = (extend4730790105801354508finity @ extended_enat)) => ((B = (extend4730790105801354508finity @ extended_enat)) => (~ (C = (extend4730790105801354508finity @ extended_enat))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[792])).
% 74.76/25.30  thf(3524,plain,(! [TA:$tType] : (~ (($true)) | (~ (ord_less @ TA @ (zero_zero @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ int) != (linord181362715937106298miring @ TA)))),inference(paramod_ordered,[status(thm)],[1016,2246])).
% 74.76/25.30  thf(3525,plain,(! [TA:$tType] : ((~ (ord_less @ TA @ (zero_zero @ TA) @ (zero_zero @ TA))) | ((linord181362715937106298miring @ int) != (linord181362715937106298miring @ TA)))),inference(simp,[status(thm)],[3524])).
% 74.76/25.30  thf(3526,plain,((~ (ord_less @ int @ (zero_zero @ int) @ (zero_zero @ int)))),inference(pattern_uni,[status(thm)],[3525:[bind_type(TA,$thf(int))]])).
% 74.76/25.30  thf(42,axiom,((comm_semiring @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring_82)).
% 74.76/25.30  thf(935,plain,((comm_semiring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
% 74.76/25.30  thf(797,axiom,((dvd @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Odvd_499)).
% 74.76/25.30  thf(3405,plain,((dvd @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[797])).
% 74.76/25.30  thf(366,axiom,((! [A:nat,B:nat]: (ord_less @ nat @ A @ (suc @ (plus_plus @ nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_802_less__add__Suc1)).
% 74.76/25.30  thf(2018,plain,((! [A:nat,B:nat]: (ord_less @ nat @ A @ (suc @ (plus_plus @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])).
% 74.76/25.30  thf(507,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = ((A = (zero_zero @ nat)) | (dvd_dvd @ nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1329_nat__mult__dvd__cancel__disj)).
% 74.76/25.30  thf(2436,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd @ nat @ (times_times @ nat @ A @ B) @ (times_times @ nat @ A @ C)) = ((A = (zero_zero @ nat)) | (dvd_dvd @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])).
% 74.76/25.30  thf(76,axiom,((semiring @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring_335)).
% 74.76/25.30  thf(1037,plain,((semiring @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
% 74.76/25.30  thf(191,axiom,((linord6961819062388156250ring_1 @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__semiring__1_280)).
% 74.76/25.30  thf(1416,plain,((linord6961819062388156250ring_1 @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])).
% 74.76/25.30  thf(334,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_Suc__mono)).
% 74.76/25.30  thf(1917,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)],[334])).
% 74.76/25.30  thf(516,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ B) => ((ord_less_eq @ nat @ (minus_minus @ nat @ B @ A) @ (minus_minus @ nat @ B @ C)) = (ord_less_eq @ nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1716_le__diff__iff_H)).
% 74.76/25.30  thf(2453,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ B) => ((ord_less_eq @ nat @ (minus_minus @ nat @ B @ A) @ (minus_minus @ nat @ B @ C)) = (ord_less_eq @ nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[516])).
% 74.76/25.30  thf(391,axiom,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_gr0__implies__Suc)).
% 74.76/25.30  thf(2087,plain,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[391])).
% 74.76/25.30  thf(524,axiom,((ordere6911136660526730532id_add @ extended_enat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oordered__comm__monoid__add_460)).
% 74.76/25.30  thf(2470,plain,((ordere6911136660526730532id_add @ extended_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[524])).
% 74.76/25.30  thf(666,axiom,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ B) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ A @ (one_one @ TA))) & ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (one_one @ TA) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1044_mult__less__cancel__right2)).
% 74.76/25.30  thf(2980,plain,((! [TA: $tType]: ((linordered_idom @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (times_times @ TA @ A @ B) @ B) = (((ord_less_eq @ TA @ (zero_zero @ TA) @ B) => (ord_less @ TA @ A @ (one_one @ TA))) & ((ord_less_eq @ TA @ B @ (zero_zero @ TA)) => (ord_less @ TA @ (one_one @ TA) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[666])).
% 74.76/25.30  thf(415,axiom,((comm_semiring @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__semiring_311)).
% 74.76/25.30  thf(2177,plain,((comm_semiring @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])).
% 74.76/25.30  thf(466,axiom,((ordered_semiring @ nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__semiring_68)).
% 74.76/25.30  thf(2321,plain,((ordered_semiring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[466])).
% 74.76/25.30  thf(178,axiom,((ordered_ring @ real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oordered__ring_316)).
% 74.76/25.30  thf(1367,plain,((ordered_ring @ real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
% 74.76/25.30  thf(44,axiom,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_mult__strict__right__mono)).
% 74.76/25.30  thf(940,plain,((! [TA: $tType]: ((linord8928482502909563296strict @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => ((ord_less @ TA @ (zero_zero @ TA) @ C) => (ord_less @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
% 74.76/25.30  thf(38,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_n__not__Suc__n)).
% 74.76/25.30  thf(923,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
% 74.76/25.30  thf(702,axiom,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less_eq @ TA @ A @ B) & (C = D)) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_add__mono__thms__linordered__semiring_I3_J)).
% 74.76/25.30  thf(3096,plain,((! [TA: $tType]: ((ordere6658533253407199908up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less_eq @ TA @ A @ B) & (C = D)) => (ord_less_eq @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[702])).
% 74.76/25.30  thf(281,axiom,((! [A:int,B:int,C:int]: ((ord_less @ int @ A @ B) => ((ord_less @ int @ (zero_zero @ int) @ C) => (ord_less @ int @ (times_times @ int @ C @ A) @ (times_times @ int @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1181_zmult__zless__mono2)).
% 74.76/25.30  thf(1737,plain,((! [A:int,B:int,C:int]: ((ord_less @ int @ A @ B) => ((ord_less @ int @ (zero_zero @ int) @ C) => (ord_less @ int @ (times_times @ int @ C @ A) @ (times_times @ int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])).
% 74.76/25.30  thf(412,axiom,((! [A:int,B:int,C:int]: ((times_times @ int @ (minus_minus @ int @ A @ B) @ C) = (minus_minus @ int @ (times_times @ int @ A @ C) @ (times_times @ int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1594_int__distrib_I3_J)).
% 74.76/25.30  thf(2170,plain,((! [A:int,B:int,C:int]: ((times_times @ int @ (minus_minus @ int @ A @ B) @ C) = (minus_minus @ int @ (times_times @ int @ A @ C) @ (times_times @ int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])).
% 74.76/25.30  thf(474,axiom,((ordered_semiring @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oordered__semiring)).
% 74.76/25.30  thf(2351,plain,((ordered_semiring @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[474])).
% 74.76/25.30  thf(421,axiom,((ordere6658533253407199908up_add @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add)).
% 74.76/25.30  thf(2191,plain,((ordere6658533253407199908up_add @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[421])).
% 74.76/25.30  thf(304,axiom,((dvd @ int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Odvd)).
% 74.76/25.30  thf(1812,plain,((dvd @ int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])).
% 74.76/25.30  thf(192,axiom,((! [A:nat]: ((dvd_dvd @ nat @ A @ (suc @ (zero_zero @ nat))) = (A = (suc @ (zero_zero @ nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1326_dvd__1__iff__1)).
% 74.76/25.30  thf(1417,plain,((! [A:nat]: ((dvd_dvd @ nat @ A @ (suc @ (zero_zero @ nat))) = (A = (suc @ (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
% 74.76/25.30  thf(603,axiom,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((plus_plus @ int @ (times_times @ int @ A @ B) @ C) = (plus_plus @ int @ (times_times @ int @ D @ E) @ F)) => ((ord_less @ int @ (plus_plus @ int @ (times_times @ int @ D @ E) @ F) @ (zero_zero @ int)) => ((ord_less @ int @ C @ A) => ((ord_less_eq @ int @ (zero_zero @ int) @ F) => ((ord_less @ int @ (zero_zero @ int) @ D) => ((ord_less_eq @ int @ D @ A) => (ord_less_eq @ int @ E @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_zdiv__mono2__neg__lemma)).
% 74.76/25.30  thf(2771,plain,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((plus_plus @ int @ (times_times @ int @ A @ B) @ C) = (plus_plus @ int @ (times_times @ int @ D @ E) @ F)) => ((ord_less @ int @ (plus_plus @ int @ (times_times @ int @ D @ E) @ F) @ (zero_zero @ int)) => ((ord_less @ int @ C @ A) => ((ord_less_eq @ int @ (zero_zero @ int) @ F) => ((ord_less @ int @ (zero_zero @ int) @ D) => ((ord_less_eq @ int @ D @ A) => (ord_less_eq @ int @ E @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[603])).
% 74.76/25.30  thf(4520,plain,(($false)),inference(e,[status(thm)],[3021,2822,1411,1024,3053,2778,2072,1729,3434,2463,1840,1982,3449,2544,1549,1686,1879,1718,2744,1823,1190,2109,1454,2031,1995,2263,1559,1105,2876,1237,846,2921,1031,3534,977,2976,3317,2808,2495,2776,3040,2947,1073,1544,2380,3402,1305,1005,2210,2117,1596,1290,1882,2395,2908,2099,2282,1426,3439,1137,2686,1310,2035,2141,2712,1233,2580,3313,2042,2146,1164,2316,3446,2448,2933,1919,3253,2459,3414,1342,1954,2844,1222,930,2360,829,1196,3103,2491,2020,1046,1613,1386,1724,2516,1904,1228,2869,2985,1576,2173,1366,2400,2825,1529,3263,2328,1430,2814,1907,1323,917,1992,2466,3248,1055,3442,2039,3275,1760,1660,2444,1264,2217,3125,1826,3410,2185,3280,1462,3043,949,2571,2420,1800,853,1379,2403,870,1479,1572,1013,1398,2635,1568,1963,3180,3231,1100,817,2691,2520,2730,2024,1641,3268,3258,2178,3199,2090,3163,3453,2880,1828,2034,821,1489,2950,1946,1465,1302,1664,2324,2027,2291,1020,1960,3093,2555,3290,2335,966,1183,2073,1843,3537,1377,1896,2483,2371,1526,3243,3327,1600,3211,2586,1975,2762,2508,2964,2523,2530,1345,2799,2286,2750,1405,1242,849,3406,2205,2954,3151,3011,942,1691,2574,3186,2118,1338,2000,3037,1863,3435,3301,2204,3531,1199,1470,2093,1311,2296,1067,2496,2790,1768,2905,1021,862,2147,3233,1619,3250,3261,894,2733,825,2805,1042,2541,1751,820,3154,3134,1423,3090,3137,2872,1027,3028,2211,2313,2741,1634,1106,916,3271,2445,3191,1938,1032,1837,3269,1365,3810,2433,2477,852,2332,2820,1888,3718,3546,1159,3408,1740,1910,842,1402,3467,1328,2973,1111,3218,980,2858,3078,3440,2245,1936,1089,1234,874,1143,1762,3254,1772,1259,3122,2990,1534,1794,1017,2577,1064,1096,1672,3176,3087,1683,1160,3143,3407,3441,2080,2240,1810,3194,2038,1644,3294,2781,1082,2023,1942,1659,1292,933,2551,1016,1612,2978,997,2519,2536,2387,1050,911,3115,3409,2482,1715,3064,1979,2272,2756,3215,1114,1324,2504,2450,985,1539,1382,2487,3059,3222,3540,2497,3147,1434,2208,2076,1035,1466,1187,1167,2189,1732,1814,1086,3225,1241,2546,3279,3183,2057,3306,2408,2793,1515,2221,2338,1996,2936,1727,2413,2176,1680,1103,2275,1483,1548,3262,3289,2602,2144,906,2717,1219,2028,1301,819,3255,3240,843,2188,2393,3081,3272,826,3283,2514,1795,2398,3404,2817,1256,1226,2959,3213,936,2738,3208,1058,1997,1332,1092,2425,2474,3302,1638,3170,1675,3023,1669,1707,2293,3051,1635,1733,2759,2753,2166,1765,2457,919,900,831,1408,3815,1011,3270,990,1542,2943,2378,1571,2065,1282,2478,2084,3238,2214,2383,1894,2987,2637,2422,2774,3287,1524,2955,2246,880,1043,1801,2802,3500,1969,1307,1080,3055,2111,1993,2267,2446,3165,848,3451,2461,890,1667,3034,2410,1325,1149,3298,1556,2542,2647,2278,2553,2842,1061,1952,2710,2911,1820,983,2212,1213,1445,2086,883,986,2797,3310,2999,1805,2069,1198,2439,2725,1699,3159,2064,2369,1775,1000,1364,2390,1694,922,2693,1413,3009,1948,3444,3031,2952,1873,944,2994,927,2503,1134,2927,3048,1145,968,836,1049,1758,1166,2318,3206,3293,2471,1905,1420,2449,1509,3278,2597,1958,3292,2899,2567,1547,2298,1003,2588,3129,1780,1531,2888,2882,1070,3112,872,1225,2060,1743,2192,887,1368,3228,1753,2407,1267,1230,2850,993,2689,2747,3246,3448,1186,1038,1869,840,2429,1235,1317,1901,3174,1579,1285,1336,907,3305,2165,3818,1813,1300,1452,2219,1980,1085,2322,1538,951,2247,1934,2500,1802,1427,1797,2728,2939,3156,3398,859,1898,1257,2558,2113,1702,2379,2279,2357,1955,2145,1485,1972,1052,1506,1140,2511,2860,2722,1008,3007,2266,3168,2352,2479,3401,1459,3067,1966,2885,2828,3188,1517,2325,2226,1866,1108,3284,845,2013,3400,2924,3452,2458,2696,1553,1321,1913,1844,903,1216,891,2997,1448,3320,2919,1734,1807,2591,2443,1326,2707,2167,2283,2098,2855,946,2971,2764,2262,3085,2594,1721,2853,2290,2251,2135,2406,2811,2004,3235,2431,2526,2416,1491,1689,2786,914,3267,1193,2902,2230,2917,1161,1077,2162,2095,832,2374,2287,1512,2302,2385,3291,835,3100,1593,1876,3132,2930,2218,2983,2719,1229,2233,818,3264,2736,854,1986,867,1757,2768,865,1480,3203,3062,3015,1436,3328,1314,2186,1335,2704,2366,3323,828,1165,3045,2783,2549,3309,2636,2201,918,1989,897,2417,2961,1710,2714,3196,1891,2223,2795,2021,2063,839,3543,1152,2847,2467,1976,2583,1236,987,3025,1261,2600,3411,1537,1582,2265,2539,1713,1597,1431,2484,1885,2699,1399,2270,2138,3341,3526,935,3405,2018,2436,1037,1416,1917,2453,2087,2470,2980,2177,2321,1367,940,923,3096,1737,2170,2351,2191,1812,1417,2771])).
% 74.76/25.30  % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 74.76/25.30  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------