%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP216^2 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 08:07:13 AM UTC 2026
% Result : Theorem 178.23s 123.85s
% Output : Refutation 181.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP216^2 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n017.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 20:11:37 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 6.30/2.34 % [INFO] Parsing done (1546ms).
% 6.30/2.36 % [INFO] Running in sequential loop mode.
% 7.32/2.73 % [INFO] eprover registered as external prover.
% 7.32/2.74 % [INFO] Scanning for conjecture ...
% 9.55/3.30 % [INFO] Found a conjecture (or negated_conjecture) and 6698 axioms. Running axiom selection ...
% 12.73/5.08 % [INFO] Axiom selection finished. Selected 1029 axioms (removed 5669 axioms).
% 14.76/5.78 % [INFO] Problem is higher-order (TPTP THF).
% 15.18/5.84 % [INFO] Type checking passed.
% 15.18/5.85 % [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 ...
% 35.57/12.30 % [INFO] [Domain constraints] Detected constraint on product_unit
% 35.57/12.31 % [INFO] [Domain constraints] dom(product_unit) ⊆ {product_Unity}
% 178.23/123.83 % External prover 'e' found a proof!
% 178.23/123.83 % [INFO] Killing All external provers ...
% 178.23/123.84 % Time passed: 123481ms (effective reasoning time: 121473ms)
% 178.23/123.84 % 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)>
% 178.23/123.85 % Axioms used in derivation (1029): tcon_Option_Ooption___Lattices_Obounded__lattice__top_29, fact_559_map__comp__simps_I1_J, fact_3340_dom__def, fact_4102_execute__swap_I2_J, fact_549_add__diff__cancel__left_H, fact_969_Suc__eq__plus1__left, tcon_Set_Oset___Lattices_Osemilattice__inf_249, fact_143_Heap_Oexhaust, fact_1275_times__integer__code_I2_J, fact_478_less__eq__option__None, tcon_fun___Complete__Lattices_OInf, fact_4991_relpow__E, fact_13_heap_Oleq__trans, fact_1025_option_Osize__neq, fact_105_surj__pair, fact_1073_cond__case__prod__eta, fact_4899_relpowp__1, fact_2342_top__empty__eq2, fact_817_mod__by__1, fact_1067_split__cong, fact_3_execute__guard_I1_J, fact_306_lookup__chain, fact_5639_snga__assn__raw_Ocases, fact_4651_some__elem, fact_626_diff__diff__eq, tcon_Product__Type_Ounit___Orderings_Oorder__top_411, fact_4104_upd__def, fact_3312_fun__upd__None__if__notin__dom, fact_466_trans__le__add2, fact_892_mod__eq__nat1E, fact_400_effect__lookupI, fact_101_prod__induct4, tcon_Code__Numeral_Ointeger___Groups_Ocancel__semigroup__add_461, tcon_Set_Oset___Finite__Set_Ofinite_257, fact_3560_effect__makeI, tcon_Code__Numeral_Ointeger___Groups_Oab__semigroup__mult_464, fact_482_bind__eq__Some__conv, fact_86_success__bind__executeI, fact_696_less__diff__conv, tcon_fun___Lattices_Oinf, tfree_0, fact_5990_heap_Omono__body__fixp, fact_5982_option_Omono__body__fixp, fact_3405_map__leD, fact_104_prod__cases, fact_5055_option_Opred__inject_I2_J, fact_2862_refines__def, tcon_Product__Type_Ounit___Lattices_Osemilattice__inf_407, fact_496_add__mono__thms__linordered__field_I4_J, tcon_Heap_Oref___Countable_Ocountable_289, fact_223_ssubst__Pair__rhs, fact_884_nat__mod__eq__iff, tcon_Product__Type_Oprod___HOL_Oequal_400, fact_1026_Heap_Osize__neq, fact_397_execute__lookup, fact_3481_map__map, tcon_Nat_Onat___Rings_Osemiring__0_140, fact_268_zero__neq__one, fact_50_option_Oexhaust, fact_152_accp_Ocases, fact_3124_inf__Int__eq2, tcon_Nat_Onat___Typerep_Otyperep_55, tcon_Code__Numeral_Ointeger___Rings_Osemiring__modulo_470, fact_125_fold__atLeastAtMost__nat_Ocases, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, tcon_Code__Numeral_Onatural___Euclidean__Division_Ounique__euclidean__semiring_515, fact_520_add__strict__increasing2, fact_2739_sup__Un__eq2, fact_53_combine__options__cases, fact_4109_fails__array__upd, fact_598_ab__semigroup__mult__class_Omult_Ocommute, fact_529_ex__has__greatest__nat__lemma, tcon_Nat_Onat___Orderings_Oorder__bot_131, tcon_fun___Finite__Set_Ofinite, fact_2381_prod__decode__aux_Ocases, fact_57_the__default_Osimps_I1_J, fact_1169_case__prodD, fact_270_plus__nat_Oadd__0, tcon_Code__Numeral_Ointeger___Groups_Osemigroup__add_479, fact_133_add__right__imp__eq, fact_3324_nempty__dom, fact_963_less__add__Suc2, fact_301_pred__equals__eq2, fact_1274_times__integer__code_I1_J, fact_113_prod__induct7, tcon_List_Olist___Quickcheck__Exhaustive_Ofull__exhaustive_292, tcon_Nat_Onat___HOL_Oequal_156, fact_4218_exhaustive__fun_H_Ocases, fact_2736_map__upd__eqD1, fact_2679_sup__Some, tcon_Nat_Onat___Groups_Oab__semigroup__mult_113, tcon_Nat_Onat___GCD_Osemiring__Gcd_143, tcon_Product__Type_Ounit___Countable_Ocountable_413, tcon_Set_Oset___Lattices_Osemilattice__sup_248, fact_538_nat__1__eq__mult__iff, fact_2_execute__raise, fact_5985_heap_Oconst__mono, tcon_Nat_Onat___Quickcheck__Exhaustive_Ofull__exhaustive_92, tcon_Code__Numeral_Ointeger___Rings_Odvd_510, fact_185_add__mono__thms__linordered__field_I2_J, fact_2988_Ref__Time_Oupdate__def, fact_396_map__option__o__empty, tcon_HOL_Obool___Lattices_Obounded__lattice__top_45, tcon_HOL_Obool___HOL_Oequal_286, fact_58_Heap__cases, fact_3042_inter__eq__subsetI, tcon_Code__Numeral_Ointeger___Num_Osemiring__numeral_478, fact_3412_upd__None__map__le, fact_4272_Predicate_Oiterate__upto_Opinduct, fact_165_fold__atLeastAtMost__nat_Opinduct, tcon_Nat_Onat___Groups_Osemigroup__mult_122, fact_4126_fails__array__len, fact_298_disjE__realizer2, fact_3074_wait__def, fact_1273_full__exhaustive__integer_H_Ocases, fact_0_fails__def, fact_277_pos__add__strict, fact_4107_upd__ureturn, fact_40_effect__ifI, fact_99_prod__cases7, tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_396, tcon_Set_Oset___Countable_Ocountable_255, tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__comm__monoid__add_522, fact_4662_some__theI, tcon_Option_Ooption___Finite__Set_Ofinite_328, fact_4357_refl__on__init__seg__of, fact_2993_unit__abs__eta__conv, fact_1064_prod_Ocase__distrib, fact_15_assert__cong, fact_145_option_Osimps_I5_J, fact_703_map__comp__Some__iff, fact_276_guard__def, fact_957_one__is__add, fact_2717_fun__upd__upd, fact_2727_fun__upd__def, fact_5640_one__assn__raw_Ocases, fact_127_timeFrame_Opelims, fact_479_less__eq__option__None__is__None, fact_42_combine__options__commute, fact_2690_zero__int_Orsp, fact_178_fold__if__return, fact_1187_Heap__Time__Monad_Obind__def, fact_654_Nat_Odiff__add__assoc2, fact_3053_disjoint__alt__simp2, fact_147_effect__bindE, fact_120_timeFrame_Osimps_I1_J, fact_142_add__mono__thms__linordered__semiring_I4_J, fact_1122_case__prodI, fact_408_less__eq__option__None__code, fact_3534_slice__len, fact_3574_mergesort__by__rel_Ocases, fact_469_add__le__mono, fact_2234_top__option__def, fact_25_ureturn__bind, fact_958_add__is__1, fact_249_fun_Omap__ident, tcon_HOL_Obool___Quickcheck__Random_Orandom_268, tcon_Code__Numeral_Ointeger___Groups_Oordered__ab__semigroup__monoid__add__imp__le_430, fact_253_effect__LetI, fact_960_nat__in__between__eq_I1_J, fact_175_add_Oright__commute, fact_4080_execute__freeze, fact_3543_new__def, fact_61_some__opt__sym__eq__trivial, fact_642_crossproduct__eq, tcon_Heap_Oarray___Typerep_Otyperep_37, fact_3050_inf__option__def, fact_588_nat__eq__add__iff1, fact_464_exists__leI, fact_30_combine__options__simps_I2_J, fact_21_success__tapI, subcl_Heap_Oheap___Countable_Ocountable, fact_597_ab__semigroup__mult__class_Omult_Oleft__commute, fact_996_Suc__diff__eq__diff__pred, fact_14_heap_Oleq__antisym, fact_4074_length__def, tcon_HOL_Obool___Lattices_Obounded__lattice_271, fact_498_add__le__less__mono, fact_4985_relpow__Suc__E2, fact_3393_map__add__find__right, tcon_Product__Type_Ounit___Heap_Oheap_422, fact_19_fails__bind, fact_74_bex2I, fact_5988_refines__adm, tcon_Code__Numeral_Ointeger___Orderings_Opreorder_488, fact_5644_mod__h__bot__indep, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add_89, fact_293_return__bind, tcon_Set_Oset___Complete__Lattices_OInf_252, fact_2730_fun__upd__same, fact_3588_enumerate__map__upt, fact_3533_of__list__def, fact_959_nat__in__between__eq_I2_J, fact_2734_map__upd__Some__unfold, fact_997_Suc__pred_H, fact_4276_scomp__scomp, fact_39_effect__ifE, fact_259_combine__options__def, tcon_Option_Ooption___Lattices_Osup_331, fact_198_add__lessD1, fact_5722_effect__refE, fact_360_map__option_Ocompositionality, fact_3036_bot__unit__def, tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_537, fact_66_not__Some__eq2, fact_23_success__ureturnI, fact_189_add_Oright__assoc, tcon_fun___Lattices_Obounded__lattice__top_63, fact_16_success__ifI, fact_17_success__guardI, fact_473_le__add2, fact_55_effect__success, fact_4298_iterate_Ocases, tcon_Code__Numeral_Onatural___Rings_Osemiring__no__zero__divisors_528, fact_4278_Pair__scomp, fact_530_map__comp__def, tcon_Nat_Onat___Groups_Ocancel__semigroup__add_108, tcon_Set_Oset___Quickcheck__Exhaustive_Ofull__exhaustive_242, fact_972_diff__Suc__eq__diff__pred, fact_3564_enumerate__replicate__eq, fact_5719_effect__refI, tcon_List_Olist___Heap_Oheap_295, fact_594_bounded__Max__nat, fact_4076_effect__nthI, tcon_List_Olist___Typerep_Otyperep_39, tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__ab__semigroup__add_517, fact_420_le__add__same__cancel1, fact_5061_option_Omap__cong__pred, fact_27_success__bind__effectI, fact_4012_rotate__length01, tcon_Code__Numeral_Ointeger___Groups_Oone_509, tcon_Product__Type_Oprod___Heap_Oheap_399, fact_1484_effect__updateI, fact_701_mlex__bound, fact_129_add__left__cancel, fact_5664_case__option__rule, fact_472_add__leD1, fact_443_accp__subset, fact_4981_relpow__0__I, tcon_Heap__Time__Monad_OHeap___Quickcheck__Random_Orandom_573, fact_471_add__leD2, fact_1068_old_Oprod_Ocase, tcon_Product__Type_Ounit___Finite__Set_Ofinite_416, fact_983_nat__induct__non__zero, tcon_Code__Numeral_Onatural___Groups_Osemigroup__mult_548, fact_1126_case__prodI2_H, fact_3589_map__upt__eqI, fact_3542_Array__Time_Omake__def, fact_312_map__option__case, fact_2728_fun__upd__eqD, tcon_Code__Numeral_Ointeger___Groups_Ouminus_502, fact_228_not__gr__zero, fact_3117_inf__None__2, tcon_Nat_Onat___Groups_Olinordered__ab__semigroup__add_96, tcon_Product__Type_Ounit___Quickcheck__Exhaustive_Ofull__exhaustive_401, fact_4359_trans__init__seg__of, fact_2718_fun__upd__triv, fact_1500_the__res__def, tcon_Code__Numeral_Ointeger___Quickcheck__Random_Orandom_463, fact_294_bind__return, fact_648_diff__cancel2, fact_3394_map__add__eq__empty__iff, tcon_HOL_Obool___Countable_Ocountable_276, fact_3576_nth__enumerate__eq, fact_897_split__mod, tcon_HOL_Obool___Finite__Set_Ofinite_279, fact_248_zero__reorient, fact_639_distrib__left, fact_1021_Heap_Osize_I2_J, fact_1185_execute__bind__case, tcon_Set_Oset___Orderings_Opreorder_256, tcon_Nat_Onat___Orderings_Opreorder_135, tcon_HOL_Obool___Typerep_Otyperep_44, fact_2169_bot__empty__eq2, tcon_HOL_Obool___Lattices_Osup_283, tcon_Heap__Time__Monad_OHeap___Typerep_Otyperep, tcon_Heap_Oarray___HOL_Oequal_301, fact_3052_disjoint__mono, fact_4083_effect__freezeE, fact_131_Heap__execute, tcon_Option_Ooption___Enum_Oenum_27, fact_3323_domIff, tcon_Nat_Onat___Rings_Osemiring_145, fact_244_less__add__same__cancel1, fact_4283_iterate_Osimps, fact_4081_success__freezeI, tcon_Code__Numeral_Ointeger___Rings_Ozero__less__one_480, fact_93_old_Oprod_Oinject, fact_2680_intrel__iff, fact_716_nat__diff__split__asm, fact_5638_sngr__assn__raw_Ocases, tcon_Nat_Onat___Countable_Ocountable_133, fact_526_success__changeI, fact_999_Suc__n__minus__m__eq, fact_4029_listrel__iff__nth, tcon_Product__Type_Oprod___Enum_Oenum_12, fact_369_map__option__cong, fact_638_comm__semiring__class_Odistrib, fact_946_nat__arith_Osuc1, tcon_Code__Numeral_Ointeger___Groups_Ocancel__ab__semigroup__add_453, tcon_HOL_Obool___Lattices_Osemilattice__sup_269, fact_4082_success__map__entryI, tcon_Code__Numeral_Ointeger___Quickcheck__Exhaustive_Oexhaustive_447, fact_374_success__lookupI, fact_288_return__def, fact_444_le__some__optE, fact_460_subrelI, fact_3413_map__add__def, tcon_HOL_Obool___Orderings_Oorder__bot_275, tcon_Heap_Oarray___Countable_Ocountable_299, tcon_Nat_Onat___Euclidean__Division_Ounique__euclidean__semiring_85, fact_1170_case__prodE, fact_3316_dom__const_H, fact_12_heap_Oleq__refl, tcon_Option_Ooption___Lattices_Oinf_332, fact_184_add__mono__thms__linordered__field_I1_J, fact_2686_sup__option__def, tcon_Nat_Onat___Groups_Osemigroup__add_128, fact_1352_less__integer__code_I1_J, tcon_Heap_Oarray___Quickcheck__Random_Orandom_298, tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__monoid__add__imp__le_514, fact_558_map__comp__simps_I2_J, fact_49_option_OdiscI, tcon_Code__Numeral_Onatural___Quickcheck__Exhaustive_Ofull__exhaustive_521, fact_5992_admissible__heap, fact_79_execute__tap, fact_4110_effect__updE, fact_5968_Heap__lub__def, fact_401_effect__lookupE, fact_214_mlex__iff, fact_674_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, fact_539_nat__mult__eq__1__iff, fact_62_success__newI, fact_278_canonically__ordered__monoid__add__class_OlessE, fact_5690_in__range__subset, fact_657_add__mult__distrib2, fact_43_combine__options__left__commute, fact_1751_time__def, fact_6_success__def, fact_252_option_Ocase__distrib, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_88, fact_67_effect__tapE, fact_670_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, fact_262_gr__implies__not__zero, tcon_Product__Type_Ounit___Typerep_Otyperep_10, fact_5571_Option_Ois__none__def, tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_82, fact_2726_map__option__o__map__upd, fact_3535_slice__complete, fact_4101_success__swapI, fact_5693_in__range_Oelims_I1_J, fact_2721_empty__upd__none, fact_405_lookup__def, fact_4106_effect__updI, fact_202_less__option__None__Some__code, tcon_Option_Ooption___HOL_Oequal_334, fact_155_accp__induct, tcon_fun___Boolean__Algebras_Oboolean__algebra, fact_3419_map__le__imp__upd__le, fact_955_nat__compl__induct_H, fact_4149_effect__lengthI, fact_4656_split__paired__Eps, tcon_Heap_Oref___Quickcheck__Exhaustive_Ofull__exhaustive_287, tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff, fact_5991_heap_Ofixp__rule__uc, tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__0_547, fact_532_map__comp__empty_I1_J, fact_4982_relpow__Suc__E, fact_9_execute__bind_I2_J, fact_589_nat__eq__add__iff2, fact_5721_execute__ref, tcon_Option_Ooption___Heap_Oheap_333, fact_7_Heap__ordE, fact_5973_option_Oleq__trans, tcon_Product__Type_Ounit___Lattices_Obounded__lattice__top, fact_938_Suc__diff__1, fact_3575_map__eq__nth__eq, fact_4072_fails__array__nth, fact_182_add__strict__left__mono, tcon_fun___HOL_Oequal, fact_1_Heap__eqI, fact_3539_effect__of__listI, fact_570_diff__add__zero, fact_172_comp__apply__eq, fact_4007_nth__rotate, tcon_Code__Numeral_Onatural___Groups_Ocancel__ab__semigroup__add_531, tcon_Nat_Onat___Orderings_Ono__top_141, fact_153_accp_Osimps, fact_291_tap__def, fact_970_plus__1__eq__Suc, fact_3530_execute__of__list, fact_415_less__eq__option__Some__None, fact_115_prod__induct5, fact_640_distrib__right, tcon_Product__Type_Ounit___Lattices_Osup_420, tcon_Nat_Onat___Rings_Ocomm__semiring_130, tcon_Product__Type_Ounit___Complete__Partial__Order_Occpo_404, fact_132_timeFrame__assoc, fact_4979_relpow__Suc__D2_H, fact_2115_memb__imp__not__empty, fact_421_le__add__same__cancel2, fact_2863_refines__empty, subcl_Heap_Oheap___Typerep_Otyperep, tcon_Code__Evaluation_Oterm___Typerep_Otyperep_6, fact_4274_scomp__apply, tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_552, fact_98_prod__cases6, fact_697_add__diff__inverse__nat, fact_4989_relpowp__relpow__eq, tcon_Set_Oset___HOL_Oequal_263, fact_966_Suc__to__right, fact_475_add__leE, fact_5983_option_Opartial__function__definitions__axioms, help_If_1_1_T, tcon_Code__Numeral_Ointeger___Rings_Osemiring__0_494, fact_304_fails__wait, tcon_Code__Numeral_Onatural___Orderings_Opreorder_557, fact_1172_case__prodD_H, tcon_Code__Numeral_Onatural___Groups_Oplus_569, fact_204_less__option__None__is__Some, tcon_Heap__Time__Monad_OHeap___HOL_Oequal_574, tcon_Option_Ooption___Lattices_Osemilattice__inf_319, tcon_Set_Oset___Orderings_Oorder__bot_254, fact_5977_Partial__Function_Obind__mono, fact_610_nat__less__add__iff1, fact_5989_heap_Ofixp__induct__uc, fact_100_prod__induct3, fact_4902_funpow_Osimps_I2_J, fact_139_add_Oassoc, fact_695_diff__add__0, fact_2337_Collect__const__case__prod, tcon_Nat_Onat___Heap_Oheap_155, fact_455_le__iff__add, fact_458_accp__subset__induct, fact_2733_fun__upd__idem__iff, tcon_fun___Countable_Ocountable, fact_8_Heap__ordI, fact_210_trans__less__add1, fact_254_distrib__if__bind, tcon_fun___Lattices_Osemilattice__sup, fact_158_accp__induct__rule, fact_5057_option_Opred__inject_I1_J, fact_1013_power__eq__if, tcon_Nat_Onat___Rings_Osemiring__modulo_119, fact_673_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, fact_2719_fun__upd__apply, tcon_Nat_Onat___Lattices_Osup_147, fact_961_less__imp__Suc__add, fact_285_less__imp__add__positive, fact_445_pred__subset__eq2, fact_3480_map__comp__map, tcon_fun___Quickcheck__Exhaustive_Oexhaustive, tcon_Code__Numeral_Onatural___Euclidean__Division_Oeuclidean__semiring_524, fact_356_option_Omap__ident, tcon_Code__Numeral_Ointeger___Rings_Osemidom__divide_477, fact_556_Nat_Odiff__diff__right, fact_3578_obtain__list__from__elements, fact_225_Nat_Oadd__0__right, tcon_Code__Numeral_Onatural___Rings_Osemiring_564, fact_3395_map__add__None, fact_10_the__default_Osimps_I2_J, fact_156_accp__downward, tcon_Code__Numeral_Onatural___Rings_Odvd_571, fact_167_rewriteR__comp__comp2, fact_653_Nat_Odiff__add__assoc, fact_643_crossproduct__noteq, fact_2740_fun__upd__comp, fact_4849_Heap__lub__empty, tcon_HOL_Obool___Lattices_Oinf_284, fact_83_effectI, tcon_Heap_Oarray___Quickcheck__Exhaustive_Ofull__exhaustive_297, fact_48_option_Odistinct_I1_J, fact_295_add__0__iff, fact_4108_success__updI, tcon_Code__Numeral_Ointeger___Groups_Ozero_506, tcon_Product__Type_Ounit___Complete__Lattices_OSup_409, fact_944_add__Suc__shift, tcon_HOL_Obool___Complete__Lattices_OInf_273, fact_497_add__mono__thms__linordered__field_I3_J, fact_454_add__right__mono, fact_416_bind__runit, fact_4975_relpow__fun__conv, fact_1536_the__heap__def, fact_669_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, fact_3409_map__add__SomeD, tcon_Option_Ooption___Orderings_Opreorder_326, fact_146_option_Osimps_I4_J, fact_5694_in__range_Osimps, fact_509_nat__geq__1__eq__neqz, fact_930_Suc__diff, fact_3033_old_Ounit_Oexhaust, fact_398_change__def, fact_224_add__is__0, tcon_HOL_Obool___Complete__Partial__Order_Occpo_267, fact_2735_map__upd__triv, fact_4013_rotate__rotate, tcon_Nat_Onat___Rings_Odvd_154, fact_4014_rotate__add, tcon_Product__Type_Ounit___Lattices_Osemilattice__sup_406, tcon_Code__Numeral_Onatural___Rings_Osemiring__modulo_545, fact_4356_init__seg__of__def, fact_117_timeFrame_Oelims, fact_33_not__Some__eq, fact_548_add__diff__cancel__right, tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_529, fact_77_timeFrame_Ocases, fact_2864_refines__bind, tcon_Set_Oset___Lattices_Obounded__lattice__top_49, fact_659_nat__mult__1, fact_913_Suc__times__mod__eq, fact_1124_mem__case__prodI, fact_956_nat__compl__induct, fact_1168_mem__case__prodE, fact_4105_execute__upd_I2_J, fact_362_map__option_Ocomp, fact_4070_Array__Time_Onth__def, fact_2114_set__notEmptyE, tcon_Code__Numeral_Onatural___Rings_Ozero__less__one_553, fact_555_Nat_Oadd__diff__assoc2, fact_4148_effect__lengthE, fact_3552_map__add__upt_H, fact_698_less__diff__conv2, fact_994_nz__le__conv__less, fact_3314_dom__empty, tcon_Code__Numeral_Onatural___Groups_Oordered__cancel__comm__monoid__add_523, fact_4091_get__update__elem__neqIndex, fact_3408_map__add__Some__iff, tcon_Set_Oset___Boolean__Algebras_Oboolean__algebra_245, tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_94, fact_4145_len__def, tcon_Code__Numeral_Onatural___Rings_Osemiring__0_562, tcon_fun___Lattices_Osemilattice__inf, fact_590_nat__le__add__iff1, fact_5650_times__assn__raw_Oelims_I2_J, fact_73_comp__cong__left, tcon_Nat_Onat___Rings_Osemidom__modulo_125, fact_675_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_4089_length__update, fact_4980_relpow__0__E, fact_676_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, fact_652_Nat_Ole__diff__conv2, fact_3590_slice__nth, fact_4075_effect__nthE, tcon_Code__Numeral_Ointeger___Groups_Olinordered__ab__semigroup__add_444, fact_203_less__option__None__Some, fact_1123_case__prodI2, fact_108_comp__eq__dest__lhs, fact_542_zero__diff, fact_672_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, fact_651_le__diff__conv, fact_4078_freeze__def, fact_271_add__eq__self__zero, tcon_Product__Type_Ounit___Boolean__Algebras_Oboolean__algebra_403, fact_537_diff__diff__left, tcon_fun___Typerep_Otyperep_62, fact_173_effect__returnE, fact_238_add__gr__0, fact_4282_iterate_Oelims, fact_5685_in__range__dist__union, tcon_Set_Oset___Complete__Lattices_OSup_251, fact_188_fails__return, fact_5637_times__assn__raw_Ocases, fact_3400_map__add__upd__left, fact_449_add__mono__thms__linordered__semiring_I2_J, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_84, fact_5692_in__range_Oelims_I2_J, fact_647_Nat_Odiff__cancel, tcon_HOL_Obool___Lattices_Osemilattice__inf_270, fact_263_not__less__zero, fact_347_case__map__option, fact_92_prod_Oinject, tcon_Option_Ooption___Quickcheck__Exhaustive_Ofull__exhaustive_314, fact_2696_one__int_Orsp, fact_595_subset__Collect__conv, fact_169_rewriteR__comp__comp, fact_28_execute__guard_I2_J, tcon_HOL_Obool___Orderings_Oorder__top_274, fact_5649_times__assn__raw_Oelims_I3_J, fact_433_bind__option__cong__code, fact_5684_in__range__empty, fact_54_success__effectE, tcon_Code__Numeral_Ointeger___Rings_Ozero__neq__one_484, fact_928_diff__Suc__diff__eq2, fact_1023_option_Osize_I3_J, fact_495_zero__less__one__class_Ozero__le__one, tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_405, fact_130_Heap_Oinject, fact_300_K__record__comp, fact_191_less__option__Some, fact_1074_case__prod__eta, fact_968_mult__Suc, fact_230_zero__eq__add__iff__both__eq__0, fact_381_option_Orec__o__map, fact_290_effect__ureturnE, fact_226_timeFrame__zero, fact_20_success__of__listI, fact_3403_map__add__left__None, fact_484_map__option__bind, fact_1125_mem__case__prodI2, tcon_Heap_Oref___HOL_Oequal_291, tcon_Code__Numeral_Ointeger___Euclidean__Division_Ounique__euclidean__semiring_431, tcon_Code__Numeral_Ointeger___HOL_Oequal_511, fact_1270_less__eq__integer__code_I1_J, fact_5986_Heap__Time__Monad_Obind__mono, fact_451_add__mono, help_fChoice_1_1_T, fact_468_add__le__mono1, fact_3399_map__add__upd, tcon_Code__Numeral_Onatural___Num_Osemiring__numeral_551, tcon_Option_Ooption___Orderings_Oorder__top_323, fact_5724_next__present, fact_264_gr__zeroI, tcon_fun___Enum_Oenum_61, tcon_Code__Numeral_Ointeger___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_427, tcon_Code__Numeral_Ointeger___Typerep_Otyperep_4, tcon_Product__Type_Ounit___HOL_Oequal_423, fact_4_execute__assert_I2_J, tcon_Product__Type_Ounit___Complete__Lattices_OInf_410, tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__diff_541, fact_655_Nat_Ole__imp__diff__is__add, tcon_Set_Oset___Complete__Partial__Order_Occpo_246, fact_370_option_Osimps_I9_J, tcon_Nat_Onat___Quickcheck__Random_Orandom_110, fact_3414_map__add__left__comm, tcon_Nat_Onat___Groups_Oone_153, fact_700_mlex__fst__decrI, fact_282_zero__less__one, fact_240_some__opt__eq__trivial, tcon_Code__Numeral_Ointeger___Groups_Osemigroup__mult_475, tcon_Option_Ooption___Countable_Ocountable_325, fact_261_zero__less__iff__neq__zero, fact_5972_option_Oleq__antisym, fact_4125_success__lenI, fact_1173_case__prodE_H, tcon_fun___Complete__Lattices_OSup, fact_38_effect__deterministic_I1_J, fact_289_effect__ureturnI, fact_36_effect__deterministic_I3_J, tcon_Code__Numeral_Ointeger___Rings_Ocomm__semiring__0_474, fact_5981_option_Ofixp__rule__uc, fact_448_add__mono__thms__linordered__semiring_I3_J, tcon_Product__Type_Ounit___Lattices_Oinf_421, fact_660_nat__mult__1__right, tcon_Set_Oset___Lattices_Osup_261, fact_157_not__accp__down, fact_88_Eps__Opt__eq__Some, fact_3541_execute__new, fact_200_not__add__less1, fact_245_add__less__same__cancel2, fact_512_mlex__leq, tcon_Code__Numeral_Onatural___HOL_Oequal_572, fact_35_option_Osimps_I7_J, tcon_Code__Numeral_Ointeger___Groups_Oordered__cancel__ab__semigroup__add_436, fact_508_mono__nat__linear__lb, fact_3402_map__add__find__left, fact_24_bind__ureturn, fact_5558_is__none__code_I2_J, fact_110_comp__eq__dest, fact_534_map__comp__None__iff, fact_3311_dom__eq__empty__conv, fact_1253_prod_Odisc__eq__case, fact_3484_List_Omap_Ocomp, fact_5065_option_Opred__map, tcon_Product__Type_Oprod___Finite__Set_Ofinite_398, fact_465_nat__le__iff__add, tcon_Code__Numeral_Onatural___Groups_Olinordered__ab__semigroup__add_525, tcon_fun___Orderings_Oorder__bot, fact_4904_funpow__add, fact_450_add__mono__thms__linordered__semiring_I1_J, fact_3054_disjoint__alt__simp1, fact_4903_funpow__Suc__right, tcon_Set_Oset___Enum_Oenum_47, tcon_Nat_Onat___Groups_Oab__semigroup__add_116, fact_154_accpI, fact_964_less__add__Suc1, fact_410_le__zero__eq, tcon_Code__Numeral_Onatural___Rings_Osemidom__divide_550, fact_243_less__add__same__cancel2, tcon_Set_Oset___Typerep_Otyperep_48, tcon_Nat_Onat___Groups_Ozero_151, fact_52_split__option__all, fact_4219_Lazy__Sequence_Oiterate__upto_Ocases, fact_2732_fun__upd__twist, fact_183_add__strict__mono, fact_37_effect__deterministic_I2_J, fact_135_ab__semigroup__add__class_Oadd_Oleft__commute, fact_661_mult__eq__if, fact_3105_execute__update, fact_168_rewriteL__comp__comp2, fact_159_fun_Omap__comp, fact_4068_execute__nth_I1_J, tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_542, tcon_Code__Numeral_Ointeger___Groups_Oplus_507, tcon_Nat_Onat___Groups_Oplus_152, fact_208_less__add__eq__less, fact_11_raise__bind, fact_4220_iter_Ocases, fact_269_array__make, tcon_Code__Numeral_Ointeger___Rings_Osemidom__modulo_476, fact_4900_Suc__funpow, fact_407_nat__add__left__cancel__le, tcon_Nat_Onat___Lattices_Oinf_148, fact_3396_empty__map__add, tcon_Option_Ooption___Lattices_Obounded__lattice_320, fact_68_effect__tapI, fact_971_Suc__eq__plus1, tcon_Code__Numeral_Onatural___Groups_Oone_570, fact_187_success__returnI, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_103, tcon_Code__Numeral_Onatural___Rings_Osemidom__modulo_549, tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_93, fact_453_less__eqE, fact_63_success__makeI, fact_4901_comp__funpow, tcon_Set_Oset___Groups_Ouminus_260, fact_592_nat__diff__add__eq1, fact_4984_relpow__Suc__D2, tcon_Product__Type_Ounit___Orderings_Oorder__bot_412, fact_3322_domD, fact_3034_top__unit__def, fact_931_Suc__mod__mult__self4, tcon_HOL_Obool___Orderings_Opreorder_277, fact_114_prod__induct6, fact_4079_execute__map__entry_I2_J, fact_217_execute__return, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors_100, fact_692_add__scale__eq__noteq, fact_212_not__add__less2, tcon_fun___Quickcheck__Exhaustive_Ofull__exhaustive, tcon_Product__Type_Oprod___Countable_Ocountable_397, fact_4071_success__nthI, fact_4216_full__exhaustive__fun_H_Ocases, fact_4986_relpow__Suc__I2, tcon_Nat_Onat___Rings_Ozero__less__one_129, fact_3482_List_Omap_Ocompositionality, fact_678_ordered__cancel__comm__monoid__diff__class_Odiff__add, tcon_Set_Oset___Lattices_Oinf_262, tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_535, tcon_Set_Oset___Quickcheck__Exhaustive_Oexhaustive_244, tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring_554, fact_550_add__diff__cancel__left, fact_5720_ref__def, fact_5978_option_Oconst__mono, fact_5567_is__none__simps_I2_J, fact_406_map__conv__bind__option, fact_2866_refines__option, fact_121_heap__def, fact_414_less__eq__option__Some, tcon_Set_Oset___Lattices_Obounded__lattice_250, fact_3662_natural__zero__minus__one, fact_3398_empty__eq__map__add__iff, fact_95_prod__cases3, fact_715_nat__diff__split, fact_5658_bind__rule, tcon_Option_Ooption___Quickcheck__Random_Orandom_317, fact_1040_case__prod__conv, tcon_Option_Ooption___Typerep_Otyperep_28, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_101, fact_190_nat__add__left__cancel__less, fact_5560_is__none__map__option, tcon_Code__Numeral_Ointeger___Rings_Ocomm__semiring_481, tcon_fun___Orderings_Oorder__top, tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__mult_538, fact_3483_list_Omap__comp, fact_5651_times__assn__raw_Oelims_I1_J, tcon_Set_Oset___Quickcheck__Random_Orandom_247, fact_5979_option_Ofixp__induct__uc, tcon_fun___Orderings_Opreorder, fact_72_comp__cong__right, fact_649_diff__add__inverse, tcon_Nat_Onat___Num_Osemiring__numeral_127, fact_5663_hoare__triple__success, fact_5559_is__none__code_I1_J, tcon_Product__Type_Ounit___Orderings_Opreorder_414, tcon_HOL_Obool___Groups_Ouminus_282, fact_3407_map__le__empty, fact_45_Collect__mem__eq, tcon_Nat_Onat___Quickcheck__Exhaustive_Oexhaustive_99, tcon_HOL_Obool___Enum_Oenum_43, fact_3070_disjoint__alt__simp3, fact_31_option_Oinject, fact_1278_plus__integer__code_I1_J, tcon_Product__Type_Ounit___Lattices_Obounded__lattice_408, tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1__cancel_533, fact_399_fails__assert_H, fact_5691_in__range_Oelims_I3_J, fact_699_mlex__snd__decrI, tcon_Nat_Onat___Lattices_Osemilattice__sup_111, tcon_Nat_Onat___Rings_Ocomm__semiring__1__cancel_105, fact_56_effect__raiseE, fact_934_Suc__mod__mult__self1, fact_409_bind__assoc, tcon_Code__Numeral_Onatural___Power_Opower_566, fact_1070_case__prod__Pair__iden, tcon_Nat_Onat___Power_Opower_149, tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_556, fact_5662_case__prod__rule, fact_199_add__less__mono, fact_82_effect__def, fact_4037_listrel__eq__len, tcon_Nat_Onat___Rings_Osemidom__divide_126, tcon_Code__Numeral_Ointeger___Rings_Osemiring_500, fact_171_type__copy__map__cong0, fact_4983_relpow__Suc__I, fact_103_Pair__inject, fact_419_add__le__same__cancel2, fact_5058_option_Opred__True, tcon_Product__Type_Oprod___Typerep_Otyperep_13, fact_75_pairself_Ocases, tcon_Product__Type_Ounit___Enum_Oenum, fact_481_Option_Obind__cong, tcon_Code__Numeral_Ointeger___Groups_Ostrict__ordered__comm__monoid__add_440, fact_90_effect__assertE, fact_499_add__less__le__mono, tcon_Heap_Oheap_Oheap__ext___HOL_Oequal_425, fact_3569_nth__upt, fact_34_combine__options__simps_I3_J, fact_3041_disjointI, fact_3585_nth__map__upt, fact_920_mult__Suc__right, fact_106_old_Oprod_Oexhaust, fact_5980_fixp__induct__option, tcon_List_Olist___Quickcheck__Random_Orandom_293, fact_78_execute__assert_I1_J, fact_611_nat__less__add__iff2, fact_29_combine__options__simps_I1_J, fact_4094_update__swap__neqIndex, fact_5976_Heap__ord__def, tcon_HOL_Obool___Boolean__Algebras_Oboolean__algebra_266, fact_69_effect__assertI, fact_107_one__reorient, fact_227_Heap__Time__Monad_Obind__bind, fact_2741_map__upd__nonempty, fact_1248_mlex__eq, fact_134_add__left__imp__eq, tcon_Code__Numeral_Onatural___Typerep_Otyperep_2, fact_967_One__nat__def, fact_962_less__iff__Suc__add, fact_60_execute__heap, tcon_Nat_Onat___Complete__Lattices_OInf_124, fact_2685_set__diff__diff__left, fact_186_add__mono__thms__linordered__field_I5_J, fact_2834_time__refines, fact_3361_le__map__dom__mono, fact_51_split__option__ex, fact_519_add__strict__increasing, fact_239_less__one, fact_371_option_Osimps_I8_J, tcon_Heap_Oref___Typerep_Otyperep_41, fact_4279_scomp__def, fact_483_bind_Obind__lzero, fact_480_bind_Obind__lunit, fact_274_raise__def, fact_2722_sup__None__1, fact_255_success__LetI, fact_4073_execute__nth_I2_J, fact_5974_option_Oleq__refl, fact_4990_relpow__E2, fact_3215_The__split__eq, fact_511_bind__split, fact_1276_minus__integer__code_I1_J, fact_76_fails__array__new, fact_97_prod__cases5, fact_284_execute__ureturn, tcon_Code__Numeral_Onatural___Groups_Oordered__cancel__ab__semigroup__add_518, fact_3123_inf__unit__def, tcon_Code__Numeral_Ointeger___Groups_Oab__semigroup__add_467, fact_257_case__optionE, fact_929_diff__Suc__diff__eq1, fact_2702_intrel__def, fact_335_map__option__eq__Some, fact_1075_case__prodE2, tcon_HOL_Obool___Heap_Oheap_285, fact_2731_fun__upd__other, fact_3559_effect__newI, fact_96_prod__cases4, fact_933_Suc__mod__mult__self2, fact_181_add__strict__right__mono, fact_4215_full__exhaustive__natural_H_Ocases, fact_965_less__natE, fact_3397_map__add__empty, fact_18_success__assertI, fact_361_option_Omap__comp, fact_917_add__Suc__right, tcon_Product__Type_Oprod___Quickcheck__Exhaustive_Ofull__exhaustive_394, fact_215_mlex__less, fact_891_mod__eq__nat2E, fact_1063_nested__case__prod__simp, fact_921_diff__Suc__1, fact_5_successI, fact_338_option_Omap__disc__iff, fact_1485_effect__updateE, tcon_fun___Lattices_Obounded__lattice, tcon_Heap_Oref___Quickcheck__Random_Orandom_288, tcon_Code__Numeral_Ointeger___Power_Opower_504, fact_148_effect__bindI, fact_641_combine__common__factor, tcon_Code__Numeral_Ointeger___Rings_Osemiring__no__zero__divisors_448, tcon_Code__Numeral_Ointeger___Groups_Ostrict__ordered__ab__semigroup__add_435, fact_3112_default__unit__def, fact_4217_exhaustive__natural_H_Ocases, fact_94_execute__bind_I1_J, fact_3584_array__of__list__make, fact_609_left__add__mult__distrib, tcon_fun___Groups_Ouminus, fact_3118_inf__None__1, fact_22_success__heapI, fact_170_rewriteL__comp__comp, fact_4358_antisym__init__seg__of, fact_111_comp__assoc, fact_2729_fun__upd__idem, fact_417_bind__rzero, tcon_HOL_Obool___Complete__Lattices_OSup_272, tcon_Code__Numeral_Ointeger___Groups_Oordered__cancel__comm__monoid__add_441, fact_3090_execute__assert_H, fact_3404_map__leI, fact_5515_heap__interpretation, fact_32_not__None__eq, fact_599_mult_Oassoc, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_671_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, fact_3420_map__add__distinct__le, fact_547_add__diff__cancel__right_H, fact_418_add__le__same__cancel1, fact_998_add__eq__if, tcon_Nat_Onat___Rings_Osemidom__divide__unit__factor_98, fact_510_bind__split__asm, tcon_Heap_Oheap_Oheap__ext___Typerep_Otyperep_8, tcon_Heap_Oref___Heap_Oheap_290, fact_59_successE, fact_128_add__right__cancel, fact_533_map__comp__empty_I2_J, tcon_HOL_Obool___Quickcheck__Exhaustive_Ofull__exhaustive_264, fact_1272_exhaustive__integer_H_Ocases, fact_554_Nat_Oadd__diff__assoc, fact_591_nat__le__add__iff2, tcon_Option_Ooption___Lattices_Osemilattice__sup_318, fact_1030_option_Osize_I4_J, fact_3038_sup__unit__def, fact_337_map__option__is__None, fact_5570_is__none__simps_I1_J, tcon_Nat_Onat___Complete__Lattices_OSup_123, fact_452_add__left__mono, fact_2723_sup__None__2, fact_201_less__option__None, fact_3540_execute__make, fact_5987_fixp__induct__heap, tcon_Code__Numeral_Ointeger___Euclidean__Division_Oeuclidean__semiring_442, fact_336_None__eq__map__option__iff, fact_5969_heap__step__admissible, fact_702_mult__eq__self__implies__10, fact_593_nat__diff__add__eq2, fact_4084_effect__freezeI, tcon_List_Olist___Countable_Ocountable_294, fact_144_execute_Osimps, fact_5648_times__assn__raw_Osimps, fact_102_timeFrame_Osimps_I2_J, fact_677_le__add__diff, fact_246_add__less__same__cancel1, fact_3554_map__add__upt, tcon_Heap_Oarray___Heap_Oheap_300, fact_2994_inf__Some, fact_596_cancel__ab__semigroup__add__class_Odiff__right__commute, tcon_Code__Numeral_Ointeger___Groups_Oordered__ab__semigroup__add_449, tcon_Code__Numeral_Onatural___Groups_Ozero_568, fact_3321_domI, fact_467_trans__le__add1, fact_514_bind__map__option, fact_890_nat__mod__eq__lemma, fact_4646_Eps__Opt__def, tcon_Code__Numeral_Ointeger___Rings_Ocomm__semiring__1__cancel_457, fact_4277_scomp__Pair, fact_305_Euclid__induct, fact_1252_split__part, fact_470_le__Suc__ex, tcon_Nat_Onat___Euclidean__Division_Oeuclidean__semiring_95, fact_2851_fails__refines, tcon_Product__Type_Oprod___Quickcheck__Exhaustive_Oexhaustive_395, fact_118_execute__bind__eq__SomeI, fact_658_mlex__leI, fact_1177_Collect__case__prod__mono, fact_303_zero__natural_Orsp, tcon_List_Olist___HOL_Oequal_296, fact_447_zero__le, tcon_Set_Oset___Orderings_Oorder__top_253, fact_211_add__less__mono1, fact_231_add__eq__0__iff__both__eq__0, fact_5056_option_Opred__mono, fact_5632_pure__assn__raw_Ocases, fact_41_combine__options__assoc, tcon_Nat_Onat___Rings_Ozero__neq__one_134, fact_4361_initial__segment__of__Diff, fact_952_power__0, fact_112_comp__def, fact_174_effect__returnI, fact_945_add__Suc, fact_4112_execute__len, fact_91_comp__apply, fact_5970_option__admissible, fact_5723_next__fresh, fact_1277_plus__integer__code_I2_J, tcon_Code__Numeral_Onatural___Quickcheck__Exhaustive_Oexhaustive_527, tcon_Product__Type_Ounit___Groups_Ouminus_419, fact_46_Collect__cong, fact_474_le__add1, fact_4977_relpow__1, fact_26_option_Osimps_I6_J, fact_160_comp__cong, tcon_Nat_Onat___Rings_Ocomm__semiring__0_121, fact_136_ab__semigroup__add__class_Oadd_Ocommute, fact_273_ureturn__def, fact_71_fun__comp__eq__conv, fact_126_one__natural_Orsp, fact_2811_Eps__Opt__eq__None, fact_932_Suc__mod__mult__self3, fact_209_trans__less__add2, fact_87_Eps__Opt__eq__Some__implies, fact_109_comp__eq__elim, fact_650_diff__add__inverse2, tcon_Heap_Oheap_Oheap__ext___Quickcheck__Random_Orandom_424, fact_44_mem__Collect__eq, tcon_fun___Lattices_Osup, tcon_Code__Numeral_Ointeger___Quickcheck__Exhaustive_Ofull__exhaustive_439, fact_4649_Eps__case__prod__eq, fact_4221_log_Ocases, tcon_Nat_Onat___Lattices_Osemilattice__inf_112, fact_656_add__mult__distrib, fact_4103_execute__upd_I1_J, fact_2123_subset__minus__empty
% 178.23/123.85 % No. of inferences in proof: 2062
% 178.23/123.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 123481 ms resp. 121473 ms w/o parsing
% 181.68/124.51 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 181.68/124.51 thf(code_natural_type, type, code_natural: $tType).
% 181.68/124.51 thf(code_integer_type, type, code_integer: $tType).
% 181.68/124.51 thf(code_term_type, type, code_term: $tType).
% 181.68/124.51 thf(product_unit_type, type, product_unit: $tType).
% 181.68/124.51 thf(typerep_type, type, typerep: $tType).
% 181.68/124.51 thf(assn_type, type, assn: $tType).
% 181.68/124.51 thf(char_type, type, char: $tType).
% 181.68/124.51 thf(rat_type, type, rat: $tType).
% 181.68/124.51 thf(num_type, type, num: $tType).
% 181.68/124.51 thf(nat_type, type, nat: $tType).
% 181.68/124.51 thf(int_type, type, int: $tType).
% 181.68/124.51 thf(a_type, type, a: $tType).
% 181.68/124.51 thf(bounded_lattice_top_decl, type, bounded_lattice_top: !> [TA: $tType]: $o).
% 181.68/124.51 thf(typerep2_decl, type, typerep2: !> [TA: $tType]: $o).
% 181.68/124.51 thf(enum_decl, type, enum: !> [TA: $tType]: $o).
% 181.68/124.51 thf(cl_HOL_Oequal_decl, type, cl_HOL_Oequal: !> [TA: $tType]: $o).
% 181.68/124.51 thf(heap_decl, type, heap: !> [TA: $tType]: $o).
% 181.68/124.51 thf(dvd_decl, type, dvd: !> [TA: $tType]: $o).
% 181.68/124.51 thf(one_decl, type, one: !> [TA: $tType]: $o).
% 181.68/124.51 thf(plus_decl, type, plus: !> [TA: $tType]: $o).
% 181.68/124.51 thf(zero_decl, type, zero: !> [TA: $tType]: $o).
% 181.68/124.51 thf(power_decl, type, power: !> [TA: $tType]: $o).
% 181.68/124.51 thf(inf_decl, type, inf: !> [TA: $tType]: $o).
% 181.68/124.51 thf(sup_decl, type, sup: !> [TA: $tType]: $o).
% 181.68/124.51 thf(uminus_decl, type, uminus: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semiring_decl, type, semiring: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semiring_Gcd_decl, type, semiring_Gcd: !> [TA: $tType]: $o).
% 181.68/124.51 thf(no_top_decl, type, no_top: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semiring_0_decl, type, semiring_0: !> [TA: $tType]: $o).
% 181.68/124.51 thf(finite_finite_decl, type, finite_finite: !> [TA: $tType]: $o).
% 181.68/124.51 thf(preorder_decl, type, preorder: !> [TA: $tType]: $o).
% 181.68/124.51 thf(zero_neq_one_decl, type, zero_neq_one: !> [TA: $tType]: $o).
% 181.68/124.51 thf(countable_decl, type, countable: !> [TA: $tType]: $o).
% 181.68/124.51 thf(order_bot_decl, type, order_bot: !> [TA: $tType]: $o).
% 181.68/124.51 thf(order_top_decl, type, order_top: !> [TA: $tType]: $o).
% 181.68/124.51 thf(comm_semiring_decl, type, comm_semiring: !> [TA: $tType]: $o).
% 181.68/124.51 thf(zero_less_one_decl, type, zero_less_one: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semigroup_add_decl, type, semigroup_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semiring_numeral_decl, type, semiring_numeral: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semidom_divide_decl, type, semidom_divide: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semidom_modulo_decl, type, semidom_modulo: !> [TA: $tType]: $o).
% 181.68/124.51 thf(complete_Inf_decl, type, complete_Inf: !> [TA: $tType]: $o).
% 181.68/124.51 thf(complete_Sup_decl, type, complete_Sup: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semigroup_mult_decl, type, semigroup_mult: !> [TA: $tType]: $o).
% 181.68/124.51 thf(comm_semiring_0_decl, type, comm_semiring_0: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semiring_modulo_decl, type, semiring_modulo: !> [TA: $tType]: $o).
% 181.68/124.51 thf(ab_semigroup_add_decl, type, ab_semigroup_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(comm_monoid_diff_decl, type, comm_monoid_diff: !> [TA: $tType]: $o).
% 181.68/124.51 thf(ab_semigroup_mult_decl, type, ab_semigroup_mult: !> [TA: $tType]: $o).
% 181.68/124.51 thf(bounded_lattice_decl, type, bounded_lattice: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semilattice_inf_decl, type, semilattice_inf: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semilattice_sup_decl, type, semilattice_sup: !> [TA: $tType]: $o).
% 181.68/124.51 thf(quickcheck_random_decl, type, quickcheck_random: !> [TA: $tType]: $o).
% 181.68/124.51 thf(comple9053668089753744459l_ccpo_decl, type, comple9053668089753744459l_ccpo: !> [TA: $tType]: $o).
% 181.68/124.51 thf(cancel_semigroup_add_decl, type, cancel_semigroup_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(comm_s4317794764714335236cancel_decl, type, comm_s4317794764714335236cancel: !> [TA: $tType]: $o).
% 181.68/124.51 thf(cancel2418104881723323429up_add_decl, type, cancel2418104881723323429up_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(ordere6658533253407199908up_add_decl, type, ordere6658533253407199908up_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semiri3467727345109120633visors_decl, type, semiri3467727345109120633visors: !> [TA: $tType]: $o).
% 181.68/124.51 thf(boolea8198339166811842893lgebra_decl, type, boolea8198339166811842893lgebra: !> [TA: $tType]: $o).
% 181.68/124.51 thf(quickc658316121487927005ustive_decl, type, quickc658316121487927005ustive: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semido2269285787275462019factor_decl, type, semido2269285787275462019factor: !> [TA: $tType]: $o).
% 181.68/124.51 thf(linord4140545234300271783up_add_decl, type, linord4140545234300271783up_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(euclid3725896446679973847miring_decl, type, euclid3725896446679973847miring: !> [TA: $tType]: $o).
% 181.68/124.51 thf(canoni5634975068530333245id_add_decl, type, canoni5634975068530333245id_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(ordere8940638589300402666id_add_decl, type, ordere8940638589300402666id_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(strict7427464778891057005id_add_decl, type, strict7427464778891057005id_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(quickc3360725361186068524ustive_decl, type, quickc3360725361186068524ustive: !> [TA: $tType]: $o).
% 181.68/124.51 thf(ordere580206878836729694up_add_decl, type, ordere580206878836729694up_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(ordere1170586879665033532d_diff_decl, type, ordere1170586879665033532d_diff: !> [TA: $tType]: $o).
% 181.68/124.51 thf(strict9044650504122735259up_add_decl, type, strict9044650504122735259up_add: !> [TA: $tType]: $o).
% 181.68/124.51 thf(euclid3128863361964157862miring_decl, type, euclid3128863361964157862miring: !> [TA: $tType]: $o).
% 181.68/124.51 thf(ordere1937475149494474687imp_le_decl, type, ordere1937475149494474687imp_le: !> [TA: $tType]: $o).
% 181.68/124.51 thf(semiri1453513574482234551roduct_decl, type, semiri1453513574482234551roduct: !> [TA: $tType]: $o).
% 181.68/124.51 thf(array_alloc_decl, type, array_alloc: !> [TA: $tType]: ((list @ TA) > ((heap_ext @ product_unit) > (product_prod @ (array @ TA) @ (heap_ext @ product_unit))))).
% 181.68/124.51 thf(array_freeze_decl, type, array_freeze: !> [TA: $tType]: ((array @ TA) > (heap_Time_Heap @ (list @ TA)))).
% 181.68/124.51 thf(array_get_decl, type, array_get: !> [TA: $tType]: ((heap_ext @ product_unit) > ((array @ TA) > (list @ TA)))).
% 181.68/124.51 thf(array_len_decl, type, array_len: !> [TA: $tType]: ((array @ TA) > (heap_Time_Heap @ nat))).
% 181.68/124.51 thf(array_length_decl, type, array_length: !> [TA: $tType]: ((heap_ext @ product_unit) > ((array @ TA) > nat))).
% 181.68/124.51 thf(array_make_decl, type, array_make: !> [TA: $tType]: (nat > ((nat > TA) > (heap_Time_Heap @ (array @ TA))))).
% 181.68/124.51 thf(array_map_entry_decl, type, array_map_entry: !> [TA: $tType]: (nat > ((TA > TA) > ((array @ TA) > (heap_Time_Heap @ (array @ TA)))))).
% 181.68/124.51 thf(array_new_decl, type, array_new: !> [TA: $tType]: (nat > (TA > (heap_Time_Heap @ (array @ TA))))).
% 181.68/124.51 thf(array_nth_decl, type, array_nth: !> [TA: $tType]: ((array @ TA) > (nat > (heap_Time_Heap @ TA)))).
% 181.68/124.51 thf(array_of_list_decl, type, array_of_list: !> [TA: $tType]: ((list @ TA) > (heap_Time_Heap @ (array @ TA)))).
% 181.68/124.51 thf(array_swap_decl, type, array_swap: !> [TA: $tType]: (nat > (TA > ((array @ TA) > (heap_Time_Heap @ TA))))).
% 181.68/124.51 thf(array_upd_decl, type, array_upd: !> [TA: $tType]: (nat > (TA > ((array @ TA) > (heap_Time_Heap @ (array @ TA)))))).
% 181.68/124.51 thf(array_update_decl, type, array_update: !> [TA: $tType]: ((array @ TA) > (nat > (TA > ((heap_ext @ product_unit) > (heap_ext @ product_unit)))))).
% 181.68/124.51 thf(rep_assn_decl, type, rep_assn: (assn > ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o))).
% 181.68/124.51 thf(in_range_decl, type, in_range: ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o)).
% 181.68/124.51 thf(times_assn_raw_decl, type, times_assn_raw: (((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) > (((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) > ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o)))).
% 181.68/124.51 thf(comple1908693960933563346ssible_decl, type, comple1908693960933563346ssible: !> [TA: $tType]: (((set @ TA) > TA) > ((TA > (TA > $o)) > ((TA > $o) > $o)))).
% 181.68/124.51 thf(comple187402453842119260l_fixp_decl, type, comple187402453842119260l_fixp: !> [TA: $tType]: (((set @ TA) > TA) > ((TA > (TA > $o)) > ((TA > TA) > TA)))).
% 181.68/124.51 thf(comple7038119648293358887notone_decl, type, comple7038119648293358887notone: !> [TA: $tType,TB: $tType]: ((TB > (TB > $o)) > ((TA > (TA > $o)) > ((TB > TA) > $o)))).
% 181.68/124.51 thf(comp_decl, type, comp: !> [TA: $tType,TB: $tType,TC: $tType]: ((TC > TB) > ((TA > TC) > (TA > TB)))).
% 181.68/124.51 thf(fun_upd_decl, type, fun_upd: !> [TA: $tType,TB: $tType]: ((TB > TA) > (TB > (TA > (TB > TA))))).
% 181.68/124.51 thf(minus_minus_decl, type, minus_minus: !> [TA: $tType]: (TA > (TA > TA))).
% 181.68/124.51 thf(one_one_decl, type, one_one: !> [TA: $tType]: TA).
% 181.68/124.51 thf(plus_plus_decl, type, plus_plus: !> [TA: $tType]: (TA > (TA > TA))).
% 181.68/124.51 thf(times_times_decl, type, times_times: !> [TA: $tType]: (TA > (TA > TA))).
% 181.68/124.51 thf(zero_zero_decl, type, zero_zero: !> [TA: $tType]: TA).
% 181.68/124.51 thf(the_decl, type, the: !> [TA: $tType]: ((TA > $o) > TA)).
% 181.68/124.51 thf(default_default_decl, type, default_default: !> [TA: $tType]: TA).
% 181.68/124.51 thf(undefined_decl, type, undefined: !> [TA: $tType]: TA).
% 181.68/124.51 thf(lim_decl, type, lim: !> [TA: $tType]: ((heap_ext @ TA) > nat)).
% 181.68/124.51 thf(heap_Time_Heap2_decl, type, heap_Time_Heap2: !> [TA: $tType]: (((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) > (heap_Time_Heap @ TA))).
% 181.68/124.51 thf(heap_Time_Heap_lub_decl, type, heap_Time_Heap_lub: !> [TA: $tType]: ((set @ (heap_Time_Heap @ TA)) > (heap_Time_Heap @ TA))).
% 181.68/124.51 thf(heap_Time_Heap_ord_decl, type, heap_Time_Heap_ord: !> [TA: $tType]: ((heap_Time_Heap @ TA) > ((heap_Time_Heap @ TA) > $o))).
% 181.68/124.51 thf(heap_Time_assert_decl, type, heap_Time_assert: !> [TA: $tType]: ((TA > $o) > (TA > (heap_Time_Heap @ TA)))).
% 181.68/124.51 thf(heap_Time_bind_decl, type, heap_Time_bind: !> [TA: $tType,TB: $tType]: ((heap_Time_Heap @ TB) > ((TB > (heap_Time_Heap @ TA)) > (heap_Time_Heap @ TA)))).
% 181.68/124.51 thf(heap_Time_effect_decl, type, heap_Time_effect: !> [TA: $tType]: ((heap_Time_Heap @ TA) > ((heap_ext @ product_unit) > ((heap_ext @ product_unit) > (TA > (nat > $o)))))).
% 181.68/124.51 thf(heap_Time_execute_decl, type, heap_Time_execute: !> [TA: $tType]: ((heap_Time_Heap @ TA) > ((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))).
% 181.68/124.51 thf(heap_Time_guard_decl, type, heap_Time_guard: !> [TA: $tType]: (((heap_ext @ product_unit) > $o) > (((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) > (heap_Time_Heap @ TA)))).
% 181.68/124.51 thf(heap_Time_heap_decl, type, heap_Time_heap: !> [TA: $tType]: (((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) > (heap_Time_Heap @ TA))).
% 181.68/124.51 thf(heap_Time_raise_decl, type, heap_Time_raise: !> [TA: $tType]: ((list @ char) > (heap_Time_Heap @ TA))).
% 181.68/124.51 thf(heap_Time_return_decl, type, heap_Time_return: !> [TA: $tType]: (TA > (heap_Time_Heap @ TA))).
% 181.68/124.51 thf(heap_Time_success_decl, type, heap_Time_success: !> [TA: $tType]: ((heap_Time_Heap @ TA) > ((heap_ext @ product_unit) > $o))).
% 181.68/124.51 thf(heap_Time_tap_decl, type, heap_Time_tap: !> [TA: $tType]: (((heap_ext @ product_unit) > TA) > (heap_Time_Heap @ TA))).
% 181.68/124.51 thf(heap_Time_timeFrame_decl, type, heap_Time_timeFrame: !> [TA: $tType]: (nat > ((option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))).
% 181.68/124.51 thf(heap_T5500966940807335491me_rel_decl, type, heap_T5500966940807335491me_rel: !> [TA: $tType]: ((product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) > ((product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) > $o))).
% 181.68/124.51 thf(heap_Time_ureturn_decl, type, heap_Time_ureturn: !> [TA: $tType]: (TA > (heap_Time_Heap @ TA))).
% 181.68/124.51 thf(heap_Time_wait_decl, type, heap_Time_wait: (nat > (heap_Time_Heap @ product_unit))).
% 181.68/124.51 thf(hoare_hoare_triple_decl, type, hoare_hoare_triple: !> [TA: $tType]: (assn > ((heap_Time_Heap @ TA) > ((TA > assn) > $o)))).
% 181.68/124.51 thf(if_decl, type, if: !> [TA: $tType]: ($o > (TA > (TA > TA)))).
% 181.68/124.51 thf(intrel_decl, type, intrel: ((product_prod @ nat @ nat) > ((product_prod @ nat @ nat) > $o))).
% 181.68/124.51 thf(inf_inf_decl, type, inf_inf: !> [TA: $tType]: (TA > (TA > TA))).
% 181.68/124.51 thf(sup_sup_decl, type, sup_sup: !> [TA: $tType]: (TA > (TA > TA))).
% 181.68/124.51 thf(enumerate_decl, type, enumerate: !> [TA: $tType]: (nat > ((list @ TA) > (list @ (product_prod @ nat @ TA))))).
% 181.68/124.51 thf(map_decl, type, map: !> [TA: $tType,TB: $tType]: ((TB > TA) > ((list @ TB) > (list @ TA)))).
% 181.68/124.51 thf(listrel_decl, type, listrel: !> [TA: $tType,TB: $tType]: ((set @ (product_prod @ TB @ TA)) > (set @ (product_prod @ (list @ TB) @ (list @ TA))))).
% 181.68/124.51 thf(nth_decl, type, nth: !> [TA: $tType]: ((list @ TA) > (nat > TA))).
% 181.68/124.51 thf(replicate_decl, type, replicate: !> [TA: $tType]: (nat > (TA > (list @ TA)))).
% 181.68/124.51 thf(rotate_decl, type, rotate: !> [TA: $tType]: (nat > ((list @ TA) > (list @ TA)))).
% 181.68/124.51 thf(upt_decl, type, upt: (nat > (nat > (list @ nat)))).
% 181.68/124.51 thf(dom_decl, type, dom: !> [TA: $tType,TB: $tType]: ((TB > (option @ TA)) > (set @ TB))).
% 181.68/124.51 thf(map_add_decl, type, map_add: !> [TA: $tType,TB: $tType]: ((TB > (option @ TA)) > ((TB > (option @ TA)) > (TB > (option @ TA))))).
% 181.68/124.51 thf(map_comp_decl, type, map_comp: !> [TA: $tType,TB: $tType,TC: $tType]: ((TC > (option @ TB)) > ((TA > (option @ TC)) > (TA > (option @ TB))))).
% 181.68/124.51 thf(map_le_decl, type, map_le: !> [TA: $tType,TB: $tType]: ((TB > (option @ TA)) > ((TB > (option @ TA)) > $o))).
% 181.68/124.51 thf(eps_Opt_decl, type, eps_Opt: !> [TA: $tType]: ((TA > $o) > (option @ TA))).
% 181.68/124.51 thf(slice_decl, type, slice: !> [TA: $tType]: (nat > (nat > ((list @ TA) > (list @ TA))))).
% 181.68/124.51 thf(the_default_decl, type, the_default: !> [TA: $tType]: (TA > ((option @ TA) > TA))).
% 181.68/124.51 thf(suc_decl, type, suc: (nat > nat)).
% 181.68/124.51 thf(compow_decl, type, compow: !> [TA: $tType]: (nat > (TA > TA))).
% 181.68/124.51 thf(size_size_decl, type, size_size: !> [TA: $tType]: (TA > nat)).
% 181.68/124.51 thf(bind_decl, type, bind: !> [TA: $tType,TB: $tType]: ((option @ TB) > ((TB > (option @ TA)) > (option @ TA)))).
% 181.68/124.51 thf(combine_options_decl, type, combine_options: !> [TA: $tType]: ((TA > (TA > TA)) > ((option @ TA) > ((option @ TA) > (option @ TA))))).
% 181.68/124.51 thf(is_none_decl, type, is_none: !> [TA: $tType]: ((option @ TA) > $o)).
% 181.68/124.51 thf(none_decl, type, none: !> [TA: $tType]: (option @ TA)).
% 181.68/124.51 thf(some_decl, type, some: !> [TA: $tType]: (TA > (option @ TA))).
% 181.68/124.51 thf(case_option_decl, type, case_option: !> [TA: $tType,TB: $tType]: (TB > ((TA > TB) > ((option @ TA) > TB)))).
% 181.68/124.51 thf(map_option_decl, type, map_option: !> [TA: $tType,TB: $tType]: ((TB > TA) > ((option @ TB) > (option @ TA)))).
% 181.68/124.51 thf(pred_option_decl, type, pred_option: !> [TA: $tType]: ((TA > $o) > ((option @ TA) > $o))).
% 181.68/124.51 thf(rec_option_decl, type, rec_option: !> [TA: $tType,TB: $tType]: (TB > ((TA > TB) > ((option @ TA) > TB)))).
% 181.68/124.51 thf(bot_bot_decl, type, bot_bot: !> [TA: $tType]: TA).
% 181.68/124.51 thf(ord_less_decl, type, ord_less: !> [TA: $tType]: (TA > (TA > $o))).
% 181.68/124.51 thf(ord_less_eq_decl, type, ord_less_eq: !> [TA: $tType]: (TA > (TA > $o))).
% 181.68/124.51 thf(top_top_decl, type, top_top: !> [TA: $tType]: TA).
% 181.68/124.51 thf(partial_flat_lub_decl, type, partial_flat_lub: !> [TA: $tType]: (TA > ((set @ TA) > TA))).
% 181.68/124.51 thf(partial_flat_ord_decl, type, partial_flat_ord: !> [TA: $tType]: (TA > (TA > (TA > $o)))).
% 181.68/124.51 thf(partial_fun_lub_decl, type, partial_fun_lub: !> [TA: $tType,TB: $tType,TC: $tType]: (((set @ TC) > TB) > ((set @ (TA > TC)) > (TA > TB)))).
% 181.68/124.51 thf(partial_fun_ord_decl, type, partial_fun_ord: !> [TA: $tType,TB: $tType,TC: $tType]: ((TC > (TB > $o)) > ((TA > TC) > ((TA > TB) > $o)))).
% 181.68/124.51 thf(partial_img_lub_decl, type, partial_img_lub: !> [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: ((TD > TC) > ((TB > TA) > (((set @ TC) > TB) > ((set @ TD) > TA))))).
% 181.68/124.51 thf(partial_img_ord_decl, type, partial_img_ord: !> [TA: $tType,TB: $tType,TC: $tType]: ((TC > TB) > ((TB > (TB > TA)) > (TC > (TC > TA))))).
% 181.68/124.51 thf(partia7178651479351089652itions_decl, type, partia7178651479351089652itions: !> [TA: $tType]: ((TA > (TA > $o)) > (((set @ TA) > TA) > $o))).
% 181.68/124.51 thf(power_power_decl, type, power_power: !> [TA: $tType]: (TA > (nat > TA))).
% 181.68/124.51 thf(iterate_upto_rel_decl, type, iterate_upto_rel: !> [TA: $tType]: ((product_prod @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural)) > ((product_prod @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural)) > $o))).
% 181.68/124.51 thf(product_Pair_decl, type, product_Pair: !> [TA: $tType,TB: $tType]: (TB > (TA > (product_prod @ TB @ TA)))).
% 181.68/124.51 thf(product_Unity_decl, type, product_Unity: product_unit).
% 181.68/124.51 thf(product_case_prod_decl, type, product_case_prod: !> [TA: $tType,TB: $tType,TC: $tType]: ((TC > (TB > TA)) > ((product_prod @ TC @ TB) > TA))).
% 181.68/124.51 thf(product_scomp_decl, type, product_scomp: !> [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: ((TD > (product_prod @ TC @ TB)) > ((TC > (TB > TA)) > (TD > TA)))).
% 181.68/124.51 thf(iterate_decl, type, iterate: !> [TA: $tType,TB: $tType]: (code_natural > ((TB > (TA > (product_prod @ TB @ TA))) > (TB > (TA > (product_prod @ TB @ TA)))))).
% 181.68/124.51 thf(ref_alloc_decl, type, ref_alloc: !> [TA: $tType]: (TA > ((heap_ext @ product_unit) > (product_prod @ (ref @ TA) @ (heap_ext @ product_unit))))).
% 181.68/124.51 thf(ref_change_decl, type, ref_change: !> [TA: $tType]: ((TA > TA) > ((ref @ TA) > (heap_Time_Heap @ TA)))).
% 181.68/124.51 thf(ref_get_decl, type, ref_get: !> [TA: $tType]: ((heap_ext @ product_unit) > ((ref @ TA) > TA))).
% 181.68/124.51 thf(ref_lookup_decl, type, ref_lookup: !> [TA: $tType]: ((ref @ TA) > (heap_Time_Heap @ TA))).
% 181.68/124.51 thf(ref_present_decl, type, ref_present: !> [TA: $tType]: ((heap_ext @ product_unit) > ((ref @ TA) > $o))).
% 181.68/124.51 thf(ref_ref_decl, type, ref_ref: !> [TA: $tType]: (TA > (heap_Time_Heap @ (ref @ TA)))).
% 181.68/124.51 thf(ref_set_decl, type, ref_set: !> [TA: $tType]: ((ref @ TA) > (TA > ((heap_ext @ product_unit) > (heap_ext @ product_unit))))).
% 181.68/124.51 thf(ref_update_decl, type, ref_update: !> [TA: $tType]: ((ref @ TA) > (TA > (heap_Time_Heap @ product_unit)))).
% 181.68/124.51 thf(refine_Imp_assert_decl, type, refine_Imp_assert: ($o > (heap_Time_Heap @ product_unit))).
% 181.68/124.51 thf(refine_Imp_refines_decl, type, refine_Imp_refines: !> [TA: $tType]: ((heap_Time_Heap @ TA) > ((heap_Time_Heap @ TA) > $o))).
% 181.68/124.51 thf(modulo_modulo_decl, type, modulo_modulo: !> [TA: $tType]: (TA > (TA > TA))).
% 181.68/124.51 thf(collect_decl, type, collect: !> [TA: $tType]: ((TA > $o) > (set @ TA))).
% 181.68/124.51 thf(set_fo1817059534552279752at_rel_decl, type, set_fo1817059534552279752at_rel: !> [TA: $tType]: ((product_prod @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA))) > ((product_prod @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA))) > $o))).
% 181.68/124.51 thf(time_fails_decl, type, time_fails: !> [TA: $tType]: ((heap_Time_Heap @ TA) > ((heap_ext @ product_unit) > $o))).
% 181.68/124.51 thf(time_the_heap_decl, type, time_the_heap: !> [TA: $tType]: ((heap_Time_Heap @ TA) > ((heap_ext @ product_unit) > (heap_ext @ product_unit)))).
% 181.68/124.51 thf(time_the_res_decl, type, time_the_res: !> [TA: $tType]: ((heap_Time_Heap @ TA) > ((heap_ext @ product_unit) > TA))).
% 181.68/124.51 thf(time_time_decl, type, time_time: !> [TA: $tType]: ((heap_Time_Heap @ TA) > ((heap_ext @ product_unit) > nat))).
% 181.68/124.51 thf(accp_decl, type, accp: !> [TA: $tType]: ((TA > (TA > $o)) > (TA > $o))).
% 181.68/124.51 thf(mlex_prod_decl, type, mlex_prod: !> [TA: $tType]: ((TA > nat) > ((set @ (product_prod @ TA @ TA)) > (set @ (product_prod @ TA @ TA))))).
% 181.68/124.51 thf(init_seg_of_decl, type, init_seg_of: !> [TA: $tType]: (set @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))))).
% 181.68/124.51 thf(fChoice_decl, type, fChoice: !> [TA: $tType]: ((TA > $o) > TA)).
% 181.68/124.51 thf(member_decl, type, member: !> [TA: $tType]: (TA > ((set @ TA) > $o))).
% 181.68/124.51 thf(h_decl, type, h: (heap_ext @ product_unit)).
% 181.68/124.51 thf(xs_decl, type, xs: (list @ a)).
% 181.68/124.51 thf(651,axiom,((! [TA: $tType]: (! [A:TA,B:TA]: (((some @ TA @ A) = (some @ TA @ B)) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_option_Oinject)).
% 181.68/124.51 thf(3021,plain,((! [TA: $tType]: (! [A:TA,B:TA]: (((some @ TA @ A) = (some @ TA @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[651])).
% 181.68/124.51 thf(530,axiom,((! [TA: $tType,TB: $tType]: (((cl_HOL_Oequal @ TB) & (quickc658316121487927005ustive @ TB) & (quickc658316121487927005ustive @ TA)) => (quickc658316121487927005ustive @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Quickcheck__Exhaustive_Oexhaustive)).
% 181.68/124.51 thf(2630,plain,((! [TA: $tType,TB: $tType]: (((cl_HOL_Oequal @ TB) & (quickc658316121487927005ustive @ TB) & (quickc658316121487927005ustive @ TA)) => (quickc658316121487927005ustive @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[530])).
% 181.68/124.51 thf(523,axiom,((heap @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Heap_Oheap_422)).
% 181.68/124.51 thf(2612,plain,((heap @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[523])).
% 181.68/124.51 thf(153,axiom,((semigroup_mult @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Osemigroup__mult_475)).
% 181.68/124.51 thf(1454,plain,((semigroup_mult @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
% 181.68/124.51 thf(920,axiom,((! [TA: $tType]: (! [A:(product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: ((! [B:nat,C:TA,D:(heap_ext @ product_unit),E:nat]: (A != (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ B @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))))) => (~ (! [B:nat]: (A != (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ B @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_timeFrame_Ocases)).
% 181.68/124.51 thf(3798,plain,((! [TA: $tType]: (! [A:(product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: ((! [B:nat,C:TA,D:(heap_ext @ product_unit),E:nat]: ~ (A = (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ B @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))))) => (~ (! [B:nat]: ~ (A = (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ B @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[920])).
% 181.68/124.51 thf(882,axiom,((typerep2 @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Typerep_Otyperep_44)).
% 181.68/124.51 thf(3698,plain,((typerep2 @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[882])).
% 181.68/124.51 thf(473,axiom,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less_eq @ TA @ A @ B) & (ord_less @ TA @ C @ D)) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_add__mono__thms__linordered__field_I4_J)).
% 181.68/124.51 thf(2463,plain,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less_eq @ 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)],[473])).
% 181.68/124.51 thf(1005,axiom,((! [TA: $tType]: ((time_the_heap @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: (case_option @ (heap_ext @ product_unit) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (undefined @ (heap_ext @ product_unit)) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (heap_ext @ product_unit) @ (^ [C:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ (heap_ext @ product_unit) @ (^ [D:(heap_ext @ product_unit),E:nat]: (D))))) @ (heap_Time_execute @ TA @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1536_the__heap__def)).
% 181.68/124.51 thf(3969,plain,((! [TA: $tType]: ((time_the_heap @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: (case_option @ (heap_ext @ product_unit) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (undefined @ (heap_ext @ product_unit)) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (heap_ext @ product_unit) @ (^ [C:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ (heap_ext @ product_unit) @ (^ [D:(heap_ext @ product_unit),E:nat]: (D))))) @ (heap_Time_execute @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005])).
% 181.68/124.51 thf(499,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit)]: ((refine_Imp_refines @ TA @ A @ B) => ((~ (time_fails @ TA @ B @ C)) => (ord_less_eq @ nat @ (time_time @ TA @ A @ C) @ (time_time @ TA @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2834_time__refines)).
% 181.68/124.51 thf(2544,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit)]: ((refine_Imp_refines @ TA @ A @ B) => ((~ (time_fails @ TA @ B @ C)) => (ord_less_eq @ nat @ (time_time @ TA @ A @ C) @ (time_time @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])).
% 181.68/124.51 thf(306,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(list @ TA)]: ((map @ TC @ TB @ A @ (map @ TA @ TC @ B @ C)) = (map @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3481_map__map)).
% 181.68/124.51 thf(1950,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(list @ TA)]: ((map @ TC @ TB @ (A) @ (map @ TA @ TC @ (B) @ C)) = (map @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])).
% 181.68/124.51 thf(124,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/sandbox/benchmark/theBenchmark.p',fact_958_add__is__1)).
% 181.68/124.51 thf(1369,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)],[124])).
% 181.68/124.51 thf(607,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ (product_prod @ TA @ TB))]: ((! [B:TA,C:TB]: (A != (some @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ B @ C)))) = (A = (none @ (product_prod @ TA @ TB))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_not__Some__eq2)).
% 181.68/124.51 thf(2889,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ (product_prod @ TA @ TB))]: ((! [B:TA,C:TB]: ~ (A = (some @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ B @ C)))) = (A = (none @ (product_prod @ TA @ TB))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[607])).
% 181.68/124.51 thf(414,axiom,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_add__strict__right__mono)).
% 181.68/124.51 thf(2295,plain,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[414])).
% 181.68/124.51 thf(663,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:TA]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => (heap_Time_success @ (array @ TA) @ (array_upd @ TA @ A @ D @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4108_success__updI)).
% 181.68/124.51 thf(3053,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:TA]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => (heap_Time_success @ (array @ TA) @ (array_upd @ TA @ A @ D @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[663])).
% 181.68/124.51 thf(1015,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType]: (! [A:(TF > (product_prod @ TA @ TB)),B:(TA > (TB > (product_prod @ TE @ TD))),C:(TE > (TD > TC))]: ((product_scomp @ TF @ TE @ TD @ TC @ (product_scomp @ TF @ TA @ TB @ (product_prod @ TE @ TD) @ A @ B) @ C) = (product_scomp @ TF @ TA @ TB @ TC @ A @ (^ [D:TA]: (product_scomp @ TB @ TE @ TD @ TC @ (B @ D) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4276_scomp__scomp)).
% 181.68/124.51 thf(4005,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType]: (! [A:(TF > (product_prod @ TA @ TB)),B:(TA > (TB > (product_prod @ TE @ TD))),C:(TE > (TD > TC))]: ((product_scomp @ TF @ TE @ TD @ TC @ (product_scomp @ TF @ TA @ TB @ (product_prod @ TE @ TD) @ A @ B) @ C) = (product_scomp @ TF @ TA @ TB @ TC @ A @ (^ [D:TA]: (product_scomp @ TB @ TE @ TD @ TC @ (B @ D) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015])).
% 181.68/124.51 thf(212,axiom,((! [A:(product_prod @ code_natural @ code_natural)]: ~ (! [B:code_natural,C:code_natural]: (A != (product_Pair @ code_natural @ code_natural @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4221_log_Ocases)).
% 181.68/124.51 thf(1633,plain,((! [A:(product_prod @ code_natural @ code_natural)]: ~ (! [B:code_natural,C:code_natural]: ~ (A = (product_Pair @ code_natural @ code_natural @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])).
% 181.68/124.51 thf(574,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/sandbox/benchmark/theBenchmark.p',fact_449_add__mono__thms__linordered__semiring_I2_J)).
% 181.68/124.51 thf(2778,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)],[574])).
% 181.68/124.51 thf(792,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/sandbox/benchmark/theBenchmark.p',fact_469_add__le__mono)).
% 181.68/124.51 thf(3399,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)],[792])).
% 181.68/124.51 thf(407,axiom,(((inf_inf @ product_unit) = (^ [A:product_unit,B:product_unit]: (product_Unity)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3123_inf__unit__def)).
% 181.68/124.51 thf(2263,plain,(((inf_inf @ product_unit) = (^ [A:product_unit,B:product_unit]: (product_Unity)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])).
% 181.68/124.51 thf(989,axiom,((! [TA: $tType]: ((time_fails @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ TA @ A @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_fails__def)).
% 181.68/124.51 thf(3930,plain,((! [TA: $tType]: ((time_fails @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ TA @ A @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[989])).
% 181.68/124.51 thf(954,axiom,((ordere580206878836729694up_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add_89)).
% 181.68/124.51 thf(3863,plain,((ordere580206878836729694up_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[954])).
% 181.68/124.51 thf(938,axiom,((! [TA: $tType]: ((heap_Time_raise @ TA) = (^ [A:(list @ char)]: (heap_Time_Heap2 @ TA @ (^ [B:(heap_ext @ product_unit)]: (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_raise__def)).
% 181.68/124.51 thf(3830,plain,((! [TA: $tType]: ((heap_Time_raise @ TA) = (^ [A:(list @ char)]: (heap_Time_Heap2 @ TA @ (^ [B:(heap_ext @ product_unit)]: (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[938])).
% 181.68/124.51 thf(578,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TC @ TB),B:(TC > (TB > (TA > $o))),C:TA]: ((! [D:TC,E:TB]: (((product_Pair @ TC @ TB @ D @ E) = A) => (B @ D @ E @ C))) => (product_case_prod @ TC @ TB @ (TA > $o) @ B @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_case__prodI2_H)).
% 181.68/124.51 thf(2787,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TC @ TB),B:(TC > (TB > (TA > $o))),C:TA]: ((! [D:TC,E:TB]: (((product_Pair @ TC @ TB @ D @ E) = A) => (B @ D @ E @ C))) => (product_case_prod @ TC @ TB @ (TA > $o) @ (B) @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[578])).
% 181.68/124.51 thf(809,axiom,((! [TA: $tType]: (heap @ (array @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oarray___Heap_Oheap_300)).
% 181.68/124.51 thf(3449,plain,((! [TA: $tType]: (heap @ (array @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[809])).
% 181.68/124.51 thf(1021,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > $o),B:(heap_ext @ product_unit),C:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((~ (A @ B)) => ((heap_Time_execute @ TA @ (heap_Time_guard @ TA @ A @ C) @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_execute__guard_I1_J)).
% 181.68/124.51 thf(4015,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > $o),B:(heap_ext @ product_unit),C:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((~ (A @ B)) => ((heap_Time_execute @ TA @ (heap_Time_guard @ TA @ (A) @ (C)) @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021])).
% 181.68/124.51 thf(52,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB)]: ((dom @ TA @ TB @ (^ [B:TA]: (some @ TB @ (A @ B)))) = (top_top @ (set @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3316_dom__const_H)).
% 181.68/124.51 thf(1179,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB)]: ((dom @ TA @ TB @ (^ [B:TA]: (some @ TB @ (A @ B)))) = (top_top @ (set @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
% 181.68/124.51 thf(427,axiom,((quickcheck_random @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_537)).
% 181.68/124.51 thf(2331,plain,((quickcheck_random @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])).
% 181.68/124.51 thf(265,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/sandbox/benchmark/theBenchmark.p',fact_651_le__diff__conv)).
% 181.68/124.51 thf(1818,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)],[265])).
% 181.68/124.51 thf(97,axiom,((! [TA: $tType]: (! [A:nat,B:(nat > TA),C:nat]: ((enumerate @ TA @ A @ (map @ nat @ TA @ B @ (upt @ A @ C))) = (map @ nat @ (product_prod @ nat @ TA) @ (^ [D:nat]: (product_Pair @ nat @ TA @ D @ (B @ D))) @ (upt @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3588_enumerate__map__upt)).
% 181.68/124.51 thf(1295,plain,((! [TA: $tType]: (! [A:nat,B:(nat > TA),C:nat]: ((enumerate @ TA @ A @ (map @ nat @ TA @ (B) @ (upt @ A @ C))) = (map @ nat @ (product_prod @ nat @ TA) @ (^ [D:nat]: (product_Pair @ nat @ TA @ D @ (B @ D))) @ (upt @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
% 181.68/124.51 thf(247,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: ((ord_less_eq @ (option @ TA) @ A @ (none @ TA)) => (A = (none @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_less__eq__option__None__is__None)).
% 181.68/124.51 thf(1750,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: ((ord_less_eq @ (option @ TA) @ A @ (none @ TA)) => (A = (none @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
% 181.68/124.51 thf(671,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_of_list @ TA) = (^ [A:(list @ TA)]: (heap_Time_heap @ (array @ TA) @ (^ [B:(heap_ext @ product_unit)]: (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [C:(array @ TA),D:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ (plus_plus @ nat @ (one_one @ nat) @ (size_size @ (list @ TA) @ A))))) @ (array_alloc @ TA @ A @ B))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3533_of__list__def)).
% 181.68/124.51 thf(3072,plain,((! [TA: $tType]: ((heap @ TA) => ((array_of_list @ TA) = (^ [A:(list @ TA)]: (heap_Time_heap @ (array @ TA) @ (^ [B:(heap_ext @ product_unit)]: (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [C:(array @ TA),D:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ (plus_plus @ nat @ (one_one @ nat) @ (size_size @ (list @ TA) @ A))))) @ (array_alloc @ TA @ A @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[671])).
% 181.68/124.51 thf(766,axiom,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Typerep_Otyperep_28)).
% 181.68/124.51 thf(3317,plain,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[766])).
% 181.68/124.51 thf(285,axiom,((semiri3467727345109120633visors @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Osemiring__no__zero__divisors_528)).
% 181.68/124.51 thf(1882,plain,((semiri3467727345109120633visors @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])).
% 181.68/124.51 thf(483,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/sandbox/benchmark/theBenchmark.p',fact_529_ex__has__greatest__nat__lemma)).
% 181.68/124.51 thf(2495,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)],[483])).
% 181.68/124.51 thf(798,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/sandbox/benchmark/theBenchmark.p',fact_570_diff__add__zero)).
% 181.68/124.51 thf(3417,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)],[798])).
% 181.68/124.51 thf(754,axiom,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ (TA > TB) @ (product_prod @ TA @ TA))]: ~ (! [B:(TA > TB),C:TA,D:TA]: (A != (product_Pair @ (TA > TB) @ (product_prod @ TA @ TA) @ B @ (product_Pair @ TA @ TA @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_pairself_Ocases)).
% 181.68/124.51 thf(3285,plain,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ (TA > TB) @ (product_prod @ TA @ TA))]: ~ (! [B:(TA > TB),C:TA,D:TA]: ~ (A = (product_Pair @ (TA > TB) @ (product_prod @ TA @ TA) @ (B) @ (product_Pair @ TA @ TA @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[754])).
% 181.68/124.51 thf(542,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG)))))) > $o),B:(product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG))))))]: ((! [C:TA,D:TB,E:TC,F:TD,G:TE,H:TF,I:TG]: (A @ (product_Pair @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG))))) @ C @ (product_Pair @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG)))) @ D @ (product_Pair @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG))) @ E @ (product_Pair @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG)) @ F @ (product_Pair @ TE @ (product_prod @ TF @ TG) @ G @ (product_Pair @ TF @ TG @ H @ I)))))))) => (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_prod__induct7)).
% 181.68/124.51 thf(2676,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG)))))) > $o),B:(product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG))))))]: ((! [C:TA,D:TB,E:TC,F:TD,G:TE,H:TF,I:TG]: (A @ (product_Pair @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG))))) @ C @ (product_Pair @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG)))) @ D @ (product_Pair @ TC @ (product_prod @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG))) @ E @ (product_Pair @ TD @ (product_prod @ TE @ (product_prod @ TF @ TG)) @ F @ (product_Pair @ TE @ (product_prod @ TF @ TG) @ G @ (product_Pair @ TF @ TG @ H @ I)))))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[542])).
% 181.68/124.51 thf(198,axiom,((! [TA: $tType,TB: $tType]: ((top_top @ (TA > (TB > $o))) = (^ [A:TA,B:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ A @ B) @ (top_top @ (set @ (product_prod @ TA @ TB)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2342_top__empty__eq2)).
% 181.68/124.51 thf(1591,plain,((! [TA: $tType,TB: $tType]: ((top_top @ (TA > (TB > $o))) = (^ [A:TA,B:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ A @ B) @ (top_top @ (set @ (product_prod @ TA @ TB)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
% 181.68/124.51 thf(821,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: ((product_scomp @ TA @ TB @ TC @ TD) = (^ [A:(TA > (product_prod @ TB @ TC)),B:(TB > (TC > TD)),C:TA]: (product_case_prod @ TB @ TC @ TD @ B @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4274_scomp__apply)).
% 181.68/124.51 thf(3498,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: ((product_scomp @ TA @ TB @ TC @ TD) = (^ [A:(TA > (product_prod @ TB @ TC)),B:(TB > (TC > TD)),C:TA]: (product_case_prod @ TB @ TC @ TD @ B @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[821])).
% 181.68/124.51 thf(793,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/sandbox/benchmark/theBenchmark.p',fact_142_add__mono__thms__linordered__semiring_I4_J)).
% 181.68/124.51 thf(3402,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)],[793])).
% 181.68/124.51 thf(229,axiom,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((minus_minus @ TA @ (plus_plus @ TA @ A @ B) @ (plus_plus @ TA @ A @ C)) = (minus_minus @ TA @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_add__diff__cancel__left)).
% 181.68/124.51 thf(1692,plain,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((minus_minus @ TA @ (plus_plus @ TA @ A @ B) @ (plus_plus @ TA @ A @ C)) = (minus_minus @ TA @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])).
% 181.68/124.51 thf(5,axiom,((uminus @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Ouminus_502)).
% 181.68/124.51 thf(1041,plain,((uminus @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 181.68/124.51 thf(440,axiom,((! [TA: $tType]: (! [A:assn,B:(heap_Time_Heap @ TA),C:(TA > assn),D:(heap_ext @ product_unit),E:(set @ nat)]: ((hoare_hoare_triple @ TA @ A @ B @ C) => ((rep_assn @ A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E)) => (heap_Time_success @ TA @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5663_hoare__triple__success)).
% 181.68/124.51 thf(2363,plain,((! [TA: $tType]: (! [A:assn,B:(heap_Time_Heap @ TA),C:(TA > assn),D:(heap_ext @ product_unit),E:(set @ nat)]: ((hoare_hoare_triple @ TA @ A @ B @ (C)) => ((rep_assn @ A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E)) => (heap_Time_success @ TA @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[440])).
% 181.68/124.51 thf(876,axiom,((! [TA: $tType]: (! [A:(list @ char),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ~ (heap_Time_effect @ TA @ (heap_Time_raise @ TA @ A) @ B @ C @ D @ E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_effect__raiseE)).
% 181.68/124.51 thf(3680,plain,((! [TA: $tType]: (! [A:(list @ char),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ~ (heap_Time_effect @ TA @ (heap_Time_raise @ TA @ A) @ B @ C @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[876])).
% 181.68/124.51 thf(61,axiom,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA))]: (member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ A) @ (init_seg_of @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4357_refl__on__init__seg__of)).
% 181.68/124.51 thf(1200,plain,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA))]: (member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ A) @ (init_seg_of @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
% 181.68/124.51 thf(351,axiom,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: ((sup_sup @ (TA > (TB > $o)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) = (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ (sup_sup @ (set @ (product_prod @ TA @ TB)) @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2739_sup__Un__eq2)).
% 181.68/124.51 thf(2077,plain,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: ((sup_sup @ (TA > (TB > $o)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) = (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ (sup_sup @ (set @ (product_prod @ TA @ TB)) @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])).
% 181.68/124.51 thf(1030,axiom,((semiring_Gcd @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___GCD_Osemiring__Gcd_143)).
% 181.68/124.51 thf(4037,plain,((semiring_Gcd @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030])).
% 181.68/124.51 thf(638,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/sandbox/benchmark/theBenchmark.p',fact_135_ab__semigroup__add__class_Oadd_Oleft__commute)).
% 181.68/124.51 thf(2976,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)],[638])).
% 181.68/124.51 thf(363,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TB,C:(TB > TA),D:TA,E:TA]: ((A != B) => ((fun_upd @ TB @ TA @ (fun_upd @ TB @ TA @ C @ A @ D) @ B @ E) = (fun_upd @ TB @ TA @ (fun_upd @ TB @ TA @ C @ B @ E) @ A @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2732_fun__upd__twist)).
% 181.68/124.51 thf(2117,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TB,C:(TB > TA),D:TA,E:TA]: ((~ (A = B)) => ((fun_upd @ TB @ TA @ (fun_upd @ TB @ TA @ C @ A @ D) @ B @ E) = (fun_upd @ TB @ TA @ (fun_upd @ TB @ TA @ C @ B @ E) @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[363])).
% 181.68/124.51 thf(623,axiom,((! [TA: $tType,TB: $tType]: (((finite_finite @ TB) & (countable @ TA)) => (countable @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Countable_Ocountable)).
% 181.68/124.51 thf(2940,plain,((! [TA: $tType,TB: $tType]: (((finite_finite @ TB) & (countable @ TA)) => (countable @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[623])).
% 181.68/124.51 thf(137,axiom,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA)),B:(set @ (product_prod @ TA @ TA)),C:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ B) @ (init_seg_of @ TA)) => ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ B @ C) @ (init_seg_of @ TA)) => (member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ C) @ (init_seg_of @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4359_trans__init__seg__of)).
% 181.68/124.51 thf(1406,plain,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA)),B:(set @ (product_prod @ TA @ TA)),C:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ B) @ (init_seg_of @ TA)) => ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ B @ C) @ (init_seg_of @ TA)) => (member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ C) @ (init_seg_of @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
% 181.68/124.51 thf(527,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(heap_Time_Heap @ TA)]: ((heap_Time_Heap_ord @ TA @ A @ B) => ((heap_Time_Heap_ord @ TA @ B @ C) => (heap_Time_Heap_ord @ TA @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_heap_Oleq__trans)).
% 181.68/124.51 thf(2622,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(heap_Time_Heap @ TA)]: ((heap_Time_Heap_ord @ TA @ A @ B) => ((heap_Time_Heap_ord @ TA @ B @ C) => (heap_Time_Heap_ord @ TA @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[527])).
% 181.68/124.51 thf(952,axiom,((! [A:(product_prod @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))))]: ~ (! [B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),D:(heap_ext @ product_unit),E:(set @ nat)]: (A != (product_Pair @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))) @ B @ (product_Pair @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat)) @ C @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5637_times__assn__raw_Ocases)).
% 181.68/124.51 thf(3858,plain,((! [A:(product_prod @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))))]: ~ (! [B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),D:(heap_ext @ product_unit),E:(set @ nat)]: ~ (A = (product_Pair @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))) @ (B) @ (product_Pair @ ((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat)) @ (C) @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[952])).
% 181.68/124.51 thf(977,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:TB,D:(heap_ext @ product_unit),E:nat,F:(TB > (heap_Time_Heap @ TA))]: (((heap_Time_execute @ TB @ A @ B) = (some @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))) => ((heap_Time_success @ TA @ (F @ C) @ D) => (heap_Time_success @ TA @ (heap_Time_bind @ TB @ TA @ A @ F) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_success__bind__executeI)).
% 181.68/124.51 thf(3905,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:TB,D:(heap_ext @ product_unit),E:nat,F:(TB > (heap_Time_Heap @ TA))]: (((heap_Time_execute @ TB @ A @ B) = (some @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))) => ((heap_Time_success @ TA @ (F @ C) @ D) => (heap_Time_success @ TA @ (heap_Time_bind @ TB @ TA @ A @ (F)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[977])).
% 181.68/124.51 thf(904,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA))]: ((bind @ TB @ TA @ (none @ TB) @ A) = (none @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_bind_Obind__lzero)).
% 181.68/124.51 thf(3762,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA))]: ((bind @ TB @ TA @ (none @ TB) @ (A)) = (none @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[904])).
% 181.68/124.51 thf(190,axiom,((! [A:(heap_ext @ product_unit),B:(set @ nat)]: ((in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ B)) = (! [C:nat]: ((member @ nat @ C @ B) => (ord_less @ nat @ C @ (lim @ product_unit @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5694_in__range_Osimps)).
% 181.68/124.51 thf(1569,plain,((! [A:(heap_ext @ product_unit),B:(set @ nat)]: ((in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ B)) = (! [C:nat]: ((member @ nat @ C @ B) => (ord_less @ nat @ C @ (lim @ product_unit @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])).
% 181.68/124.51 thf(405,axiom,((ordere8940638589300402666id_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oordered__cancel__comm__monoid__add_523)).
% 181.68/124.51 thf(2248,plain,((ordere8940638589300402666id_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[405])).
% 181.68/124.51 thf(682,axiom,((! [TA: $tType,TB: $tType]: ((semilattice_inf @ TA) => (semilattice_inf @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf)).
% 181.68/124.51 thf(3098,plain,((! [TA: $tType,TB: $tType]: ((semilattice_inf @ TA) => (semilattice_inf @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[682])).
% 181.68/124.51 thf(18,axiom,((euclid3128863361964157862miring @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Euclidean__Division_Ounique__euclidean__semiring_431)).
% 181.68/124.51 thf(1073,plain,((euclid3128863361964157862miring @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 181.68/124.51 thf(240,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:(nat > TA),D:nat,E:(heap_ext @ product_unit)]: (((product_Pair @ (array @ TA) @ (heap_ext @ product_unit) @ A @ B) = (array_alloc @ TA @ (map @ nat @ TA @ C @ (upt @ (zero_zero @ nat) @ D)) @ E)) => (heap_Time_effect @ (array @ TA) @ (array_make @ TA @ D @ C) @ E @ B @ A @ (plus_plus @ nat @ D @ (one_one @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3560_effect__makeI)).
% 181.68/124.51 thf(1728,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:(nat > TA),D:nat,E:(heap_ext @ product_unit)]: (((product_Pair @ (array @ TA) @ (heap_ext @ product_unit) @ A @ B) = (array_alloc @ TA @ (map @ nat @ TA @ (C) @ (upt @ (zero_zero @ nat) @ D)) @ E)) => (heap_Time_effect @ (array @ TA) @ (array_make @ TA @ D @ (C)) @ E @ B @ A @ (plus_plus @ nat @ D @ (one_one @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
% 181.68/124.51 thf(686,axiom,((! [TA: $tType]: ((enum @ TA) => (enum @ (set @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Enum_Oenum_47)).
% 181.68/124.51 thf(3108,plain,((! [TA: $tType]: ((enum @ TA) => (enum @ (set @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[686])).
% 181.68/124.51 thf(648,axiom,((! [TA: $tType]: ((cancel_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: (((plus_plus @ TA @ A @ B) = (plus_plus @ TA @ C @ B)) => (A = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_add__right__imp__eq)).
% 181.68/124.51 thf(3012,plain,((! [TA: $tType]: ((cancel_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: (((plus_plus @ TA @ A @ B) = (plus_plus @ TA @ C @ B)) => (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[648])).
% 181.68/124.51 thf(63,axiom,((! [TA: $tType,TB: $tType]: (! [A:(list @ TB),B:(list @ TA),C:(set @ (product_prod @ TB @ TA))]: ((member @ (product_prod @ (list @ TB) @ (list @ TA)) @ (product_Pair @ (list @ TB) @ (list @ TA) @ A @ B) @ (listrel @ TB @ TA @ C)) => ((size_size @ (list @ TB) @ A) = (size_size @ (list @ TA) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4037_listrel__eq__len)).
% 181.68/124.51 thf(1205,plain,((! [TA: $tType,TB: $tType]: (! [A:(list @ TB),B:(list @ TA),C:(set @ (product_prod @ TB @ TA))]: ((member @ (product_prod @ (list @ TB) @ (list @ TA)) @ (product_Pair @ (list @ TB) @ (list @ TA) @ A @ B) @ (listrel @ TB @ TA @ C)) => ((size_size @ (list @ TB) @ A) = (size_size @ (list @ TA) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
% 181.68/124.51 thf(362,axiom,((! [TA: $tType]: (! [A:(option @ TA)]: ((size_size @ (option @ TA) @ A) != (zero_zero @ nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_option_Osize__neq)).
% 181.68/124.51 thf(2114,plain,((! [TA: $tType]: (! [A:(option @ TA)]: ~ ((size_size @ (option @ TA) @ A) = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])).
% 181.68/124.51 thf(87,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:(TA > (option @ TB)),C:(TA > (option @ TB))]: (((inf_inf @ (set @ TA) @ (dom @ TA @ TB @ A) @ (dom @ TA @ TB @ B)) = (bot_bot @ (set @ TA))) => ((map_add @ TA @ TB @ A @ (map_add @ TA @ TB @ B @ C)) = (map_add @ TA @ TB @ B @ (map_add @ TA @ TB @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3414_map__add__left__comm)).
% 181.68/124.51 thf(1269,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:(TA > (option @ TB)),C:(TA > (option @ TB))]: (((inf_inf @ (set @ TA) @ (dom @ TA @ TB @ (A)) @ (dom @ TA @ TB @ (B))) = (bot_bot @ (set @ TA))) => ((map_add @ TA @ TB @ A @ (map_add @ TA @ TB @ B @ C)) = (map_add @ TA @ TB @ B @ (map_add @ TA @ TB @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
% 181.68/124.51 thf(50,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/sandbox/benchmark/theBenchmark.p',fact_640_distrib__right)).
% 181.68/124.51 thf(1173,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)],[50])).
% 181.68/124.51 thf(162,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: ((size_size @ (heap_Time_Heap @ TA) @ (heap_Time_Heap2 @ TA @ A)) = (suc @ (zero_zero @ nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_Heap_Osize_I2_J)).
% 181.68/124.51 thf(1486,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: ((size_size @ (heap_Time_Heap @ TA) @ (heap_Time_Heap2 @ TA @ (A))) = (suc @ (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
% 181.68/124.51 thf(946,axiom,((semiring_numeral @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Osemiring__numeral_127)).
% 181.68/124.51 thf(3848,plain,((semiring_numeral @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[946])).
% 181.68/124.51 thf(224,axiom,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((minus_minus @ TA @ (minus_minus @ TA @ A @ B) @ C) = (minus_minus @ TA @ A @ (plus_plus @ TA @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_diff__diff__eq)).
% 181.68/124.51 thf(1671,plain,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((minus_minus @ TA @ (minus_minus @ TA @ A @ B) @ C) = (minus_minus @ TA @ A @ (plus_plus @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
% 181.68/124.51 thf(218,axiom,((! [TA: $tType]: (heap @ (ref @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oref___Heap_Oheap_290)).
% 181.68/124.51 thf(1655,plain,((! [TA: $tType]: (heap @ (ref @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
% 181.68/124.51 thf(691,axiom,((complete_Sup @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Lattices_OSup_272)).
% 181.68/124.51 thf(3120,plain,((complete_Sup @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[691])).
% 181.68/124.51 thf(249,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/sandbox/benchmark/theBenchmark.p',fact_698_less__diff__conv2)).
% 181.68/124.51 thf(1756,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)],[249])).
% 181.68/124.51 thf(660,axiom,((! [TA: $tType]: ((power @ TA) => (! [A:TA]: ((power_power @ TA @ A @ (zero_zero @ nat)) = (one_one @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_power__0)).
% 181.68/124.51 thf(3044,plain,((! [TA: $tType]: ((power @ TA) => (! [A:TA]: ((power_power @ TA @ A @ (zero_zero @ nat)) = (one_one @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[660])).
% 181.68/124.51 thf(808,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (TA > TB)),B:TC,C:TA]: ((product_case_prod @ TC @ TA @ TB @ A @ (product_Pair @ TC @ TA @ B @ C)) = (A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_old_Oprod_Ocase)).
% 181.68/124.51 thf(3446,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (TA > TB)),B:TC,C:TA]: ((product_case_prod @ TC @ TA @ TB @ (A) @ (product_Pair @ TC @ TA @ B @ C)) = (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[808])).
% 181.68/124.51 thf(280,axiom,((semiring_numeral @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Num_Osemiring__numeral_551)).
% 181.68/124.51 thf(1872,plain,((semiring_numeral @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])).
% 181.68/124.51 thf(852,axiom,((typerep2 @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Typerep_Otyperep_10)).
% 181.68/124.51 thf(3616,plain,((typerep2 @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[852])).
% 181.68/124.51 thf(110,axiom,((! [A:nat]: ((times_times @ nat @ (one_one @ nat) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_nat__mult__1)).
% 181.68/124.51 thf(1327,plain,((! [A:nat]: ((times_times @ nat @ (one_one @ nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
% 181.68/124.51 thf(214,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:TA,C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:product_unit,F:nat]: ((heap_Time_effect @ product_unit @ (ref_update @ TA @ A @ B) @ C @ D @ E @ F) => (~ ((D = (ref_set @ TA @ A @ B @ C)) => (F != (one_one @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1485_effect__updateE)).
% 181.68/124.51 thf(1640,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:TA,C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:product_unit,F:nat]: ((heap_Time_effect @ product_unit @ (ref_update @ TA @ A @ B) @ C @ D @ E @ F) => (~ ((D = (ref_set @ TA @ A @ B @ C)) => (~ (F = (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
% 181.68/124.51 thf(764,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat,F:(TA > (heap_Time_Heap @ TB)),G:(heap_ext @ product_unit),H:TB,I:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => ((heap_Time_effect @ TB @ (F @ D) @ C @ G @ H @ I) => (heap_Time_effect @ TB @ (heap_Time_bind @ TA @ TB @ A @ F) @ B @ G @ H @ (plus_plus @ nat @ E @ I))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_effect__bindI)).
% 181.68/124.51 thf(3313,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat,F:(TA > (heap_Time_Heap @ TB)),G:(heap_ext @ product_unit),H:TB,I:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => ((heap_Time_effect @ TB @ (F @ D) @ C @ G @ H @ I) => (heap_Time_effect @ TB @ (heap_Time_bind @ TA @ TB @ A @ (F)) @ B @ G @ H @ (plus_plus @ nat @ E @ I))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[764])).
% 181.68/124.51 thf(840,axiom,((! [TA: $tType]: (! [A:(option @ TA)]: ((bind @ TA @ TA @ A @ (some @ TA)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_bind__runit)).
% 181.68/124.51 thf(3577,plain,((! [TA: $tType]: (! [A:(option @ TA)]: ((bind @ TA @ TA @ A @ (some @ TA)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[840])).
% 181.68/124.51 thf(21,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (? [C:nat]: (B = (suc @ (plus_plus @ nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_less__imp__Suc__add)).
% 181.68/124.51 thf(1078,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)],[21])).
% 181.68/124.51 thf(729,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TB > $o))]: (comple1908693960933563346ssible @ (TA > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (^ [B:(TA > (option @ TB))]: ! [C:TA,D:TB]: (((B @ C) = (some @ TB @ D)) => (A @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5970_option__admissible)).
% 181.68/124.51 thf(3217,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TB > $o))]: (comple1908693960933563346ssible @ (TA > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (^ [B:(TA > (option @ TB))]: ! [C:TA,D:TB]: (((B @ C) = (some @ TB @ D)) => (A @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[729])).
% 181.68/124.51 thf(662,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TB),B:(TA > TD),C:(TA > TB),D:(TB > TC)]: (((comp @ TD @ TB @ TA @ A @ B) = C) => ((comp @ TD @ TC @ TA @ (comp @ TB @ TC @ TD @ D @ A) @ B) = (comp @ TB @ TC @ TA @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_rewriteR__comp__comp)).
% 181.68/124.51 thf(3049,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TB),B:(TA > TD),C:(TA > TB),D:(TB > TC)]: (((comp @ TD @ TB @ TA @ A @ B) = (C)) => ((comp @ TD @ TC @ TA @ (comp @ TB @ TC @ TD @ D @ A) @ B) = (comp @ TB @ TC @ TA @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[662])).
% 181.68/124.51 thf(894,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: (((heap_Time_execute @ TA @ A @ B) != (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => (heap_Time_success @ TA @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_successI)).
% 181.68/124.51 thf(3745,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((~ ((heap_Time_execute @ TA @ A @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))) => (heap_Time_success @ TA @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[894])).
% 181.68/124.51 thf(770,axiom,((! [TA: $tType]: ((heap_Time_tap @ TA) = (^ [A:((heap_ext @ product_unit) > TA)]: (heap_Time_Heap2 @ TA @ (^ [B:(heap_ext @ product_unit)]: (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (A @ B) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_tap__def)).
% 181.68/124.51 thf(3332,plain,((! [TA: $tType]: ((heap_Time_tap @ TA) = (^ [A:((heap_ext @ product_unit) > TA)]: (heap_Time_Heap2 @ TA @ (^ [B:(heap_ext @ product_unit)]: (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (A @ B) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[770])).
% 181.68/124.51 thf(782,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/sandbox/benchmark/theBenchmark.p',fact_139_add_Oassoc)).
% 181.68/124.51 thf(3367,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)],[782])).
% 181.68/124.51 thf(864,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TB,E:nat,F:(TB > (heap_Time_Heap @ TA))]: ((heap_Time_effect @ TB @ A @ B @ C @ D @ E) => ((heap_Time_success @ TA @ (F @ D) @ C) => (heap_Time_success @ TA @ (heap_Time_bind @ TB @ TA @ A @ F) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_success__bind__effectI)).
% 181.68/124.51 thf(3648,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TB,E:nat,F:(TB > (heap_Time_Heap @ TA))]: ((heap_Time_effect @ TB @ A @ B @ C @ D @ E) => ((heap_Time_success @ TA @ (F @ D) @ C) => (heap_Time_success @ TA @ (heap_Time_bind @ TB @ TA @ A @ (F)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[864])).
% 181.68/124.51 thf(995,axiom,((comm_semiring_0 @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__0_121)).
% 181.68/124.51 thf(3942,plain,((comm_semiring_0 @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[995])).
% 181.68/124.51 thf(1019,axiom,((semilattice_inf @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Osemilattice__inf_407)).
% 181.68/124.51 thf(4011,plain,((semilattice_inf @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019])).
% 181.68/124.51 thf(278,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA,B:TA]: ((ord_less @ (option @ TA) @ (some @ TA @ A) @ (some @ TA @ B)) = (ord_less @ TA @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_less__option__Some)).
% 181.68/124.51 thf(1867,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA,B:TA]: ((ord_less @ (option @ TA) @ (some @ TA @ A) @ (some @ TA @ B)) = (ord_less @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])).
% 181.68/124.51 thf(382,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TA > (heap_Time_Heap @ TB))]: ((heap_Time_bind @ TA @ TB @ (heap_Time_ureturn @ TA @ A) @ B) = (B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_ureturn__bind)).
% 181.68/124.51 thf(2184,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TA > (heap_Time_Heap @ TB))]: ((heap_Time_bind @ TA @ TB @ (heap_Time_ureturn @ TA @ A) @ (B)) = (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])).
% 181.68/124.51 thf(713,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > (TC > (TA > $o))),B:TB,C:TC,D:TA]: ((product_case_prod @ TB @ TC @ (TA > $o) @ A @ (product_Pair @ TB @ TC @ B @ C) @ D) => (A @ B @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_case__prodD_H)).
% 181.68/124.51 thf(3175,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > (TC > (TA > $o))),B:TB,C:TC,D:TA]: ((product_case_prod @ TB @ TC @ (TA > $o) @ (A) @ (product_Pair @ TB @ TC @ B @ C) @ D) => (A @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[713])).
% 181.68/124.51 thf(479,axiom,((! [TA: $tType]: ((heap @ TA) => ((ref_lookup @ TA) = (^ [A:(ref @ TA)]: (heap_Time_tap @ TA @ (^ [B:(heap_ext @ product_unit)]: (ref_get @ TA @ B @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_lookup__def)).
% 181.68/124.51 thf(2476,plain,((! [TA: $tType]: ((heap @ TA) => ((ref_lookup @ TA) = (^ [A:(ref @ TA)]: (heap_Time_tap @ TA @ (^ [B:(heap_ext @ product_unit)]: (ref_get @ TA @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])).
% 181.68/124.51 thf(529,axiom,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA),C:(option @ TA),D:(option @ TA)]: ((! [E:TA,F:TA]: ((A @ E @ F) = (A @ F @ E))) => ((! [E:TA,F:TA,G:TA]: ((A @ (A @ E @ F) @ G) = (A @ E @ (A @ F @ G)))) => ((combine_options @ TA @ A @ B @ (combine_options @ TA @ A @ C @ D)) = (combine_options @ TA @ A @ C @ (combine_options @ TA @ A @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_combine__options__left__commute)).
% 181.68/124.51 thf(2627,plain,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA),C:(option @ TA),D:(option @ TA)]: ((! [E:TA,F:TA]: ((A @ E @ F) = (A @ F @ E))) => ((! [E:TA,F:TA,G:TA]: ((A @ (A @ E @ F) @ G) = (A @ E @ (A @ F @ G)))) => ((combine_options @ TA @ (A) @ B @ (combine_options @ TA @ (A) @ C @ D)) = (combine_options @ TA @ (A) @ C @ (combine_options @ TA @ (A) @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[529])).
% 181.68/124.51 thf(380,axiom,((! [TA: $tType,TB: $tType]: (! [A:code_natural,B:(TA > (TB > (product_prod @ TA @ TB))),C:TA,D:(TB > (product_prod @ TA @ TB))]: (((iterate @ TA @ TB @ A @ B @ C) = D) => (((A = (zero_zero @ code_natural)) => (D = (product_Pair @ TA @ TB @ C))) & ((A != (zero_zero @ code_natural)) => (D = (product_scomp @ TB @ TA @ TB @ (product_prod @ TA @ TB) @ (B @ C) @ (iterate @ TA @ TB @ (minus_minus @ code_natural @ A @ (one_one @ code_natural)) @ B))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4282_iterate_Oelims)).
% 181.68/124.51 thf(2168,plain,((! [TA: $tType,TB: $tType]: (! [A:code_natural,B:(TA > (TB > (product_prod @ TA @ TB))),C:TA,D:(TB > (product_prod @ TA @ TB))]: (((iterate @ TA @ TB @ A @ B @ C) = (D)) => (((A = (zero_zero @ code_natural)) => ((D) = (product_Pair @ TA @ TB @ C))) & ((~ (A = (zero_zero @ code_natural))) => ((D) = (product_scomp @ TB @ TA @ TB @ (product_prod @ TA @ TB) @ (B @ C) @ (iterate @ TA @ TB @ (minus_minus @ code_natural @ A @ (one_one @ code_natural)) @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])).
% 181.68/124.51 thf(297,axiom,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA]: ((minus_minus @ TA @ (plus_plus @ TA @ A @ B) @ A) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_add__diff__cancel__left_H)).
% 181.68/124.51 thf(1919,plain,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA]: ((minus_minus @ TA @ (plus_plus @ TA @ A @ B) @ A) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])).
% 181.68/124.51 thf(319,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((plus_plus @ TA @ C @ (minus_minus @ TA @ B @ A)) = (minus_minus @ TA @ (plus_plus @ TA @ C @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc)).
% 181.68/124.51 thf(1988,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((plus_plus @ TA @ C @ (minus_minus @ TA @ B @ A)) = (minus_minus @ TA @ (plus_plus @ TA @ C @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])).
% 181.68/124.51 thf(797,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TA > TB),C:(TA > TC)]: (((comp @ TB @ TC @ TA @ A @ B) = C) = (! [D:TA]: ((A @ (B @ D)) = (C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_fun__comp__eq__conv)).
% 181.68/124.51 thf(3414,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TA > TB),C:(TA > TC)]: (((comp @ TB @ TC @ TA @ A @ B) = (C)) = (! [D:TA]: ((A @ (B @ D)) = (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[797])).
% 181.68/124.51 thf(692,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_nth @ TA) = (^ [A:(array @ TA),B:nat]: (heap_Time_guard @ TA @ (^ [C:(heap_ext @ product_unit)]: (ord_less @ nat @ B @ (array_length @ TA @ C @ A))) @ (^ [C:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (nth @ TA @ (array_get @ TA @ C @ A) @ B) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4070_Array__Time_Onth__def)).
% 181.68/124.51 thf(3121,plain,((! [TA: $tType]: ((heap @ TA) => ((array_nth @ TA) = (^ [A:(array @ TA),B:nat]: (heap_Time_guard @ TA @ (^ [C:(heap_ext @ product_unit)]: (ord_less @ nat @ B @ (array_length @ TA @ C @ A))) @ (^ [C:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (nth @ TA @ (array_get @ TA @ C @ A) @ B) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[692])).
% 181.68/124.51 thf(820,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ TB),B:((option @ TB) > ((option @ TA) > $o)),C:(option @ TA)]: (((A = (none @ TB)) => (B @ A @ C)) => (((C = (none @ TA)) => (B @ A @ C)) => ((! [D:TB,E:TA]: ((A = (some @ TB @ D)) => ((C = (some @ TA @ E)) => (B @ A @ C)))) => (B @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_combine__options__cases)).
% 181.68/124.51 thf(3481,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ TB),B:((option @ TB) > ((option @ TA) > $o)),C:(option @ TA)]: (((A = (none @ TB)) => (B @ A @ C)) => (((C = (none @ TA)) => (B @ A @ C)) => ((! [D:TB,E:TA]: ((A = (some @ TB @ D)) => ((C = (some @ TA @ E)) => (B @ A @ C)))) => (B @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[820])).
% 181.68/124.51 thf(169,axiom,((! [TA: $tType]: (cl_HOL_Oequal @ (ref @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oref___HOL_Oequal_291)).
% 181.68/124.51 thf(1507,plain,((! [TA: $tType]: (cl_HOL_Oequal @ (ref @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
% 181.68/124.51 thf(970,axiom,((semigroup_mult @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult_122)).
% 181.68/124.51 thf(3895,plain,((semigroup_mult @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[970])).
% 181.68/124.51 thf(888,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TC > (heap_Time_Heap @ TB))),B:(TA > TA),C:((TC > (heap_Time_Heap @ TB)) > TA),D:TA,E:((TC > (heap_Time_Heap @ TB)) > $o)]: ((! [F:TC]: (comple7038119648293358887notone @ (TC > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TB) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TB) @ (^ [G:(TC > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ G)) @ F)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TC > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ (^ [F:(TC > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ F))))))) => ((! [F:(TC > (heap_Time_Heap @ TB))]: ((A @ (C @ F)) = F)) => ((comple1908693960933563346ssible @ (TC > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ E) => ((E @ (^ [F:TC]: (heap_Time_Heap2 @ TB @ (^ [G:(heap_ext @ product_unit)]: (none @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))))))) => ((! [F:TA]: ((E @ (A @ F)) => (E @ (A @ (B @ F))))) => (E @ (A @ D))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5989_heap_Ofixp__induct__uc)).
% 181.68/124.51 thf(3717,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TC > (heap_Time_Heap @ TB))),B:(TA > TA),C:((TC > (heap_Time_Heap @ TB)) > TA),D:TA,E:((TC > (heap_Time_Heap @ TB)) > $o)]: ((! [F:TC]: (comple7038119648293358887notone @ (TC > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TB) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TB) @ (^ [G:(TC > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ G)) @ F)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TC > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ (^ [F:(TC > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ F))))))) => ((! [F:(TC > (heap_Time_Heap @ TB))]: ((A @ (C @ F)) = (F))) => ((comple1908693960933563346ssible @ (TC > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ (E)) => ((E @ (^ [F:TC]: (heap_Time_Heap2 @ TB @ (^ [G:(heap_ext @ product_unit)]: (none @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))))))) => ((! [F:TA]: ((E @ (A @ F)) => (E @ (A @ (B @ F))))) => (E @ (A @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[888])).
% 181.68/124.51 thf(439,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ A @ (plus_plus @ nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_trans__less__add1)).
% 181.68/124.51 thf(2360,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)],[439])).
% 181.68/124.51 thf(783,axiom,((! [TA: $tType]: (! [A:(option @ TA)]: ((! [B:TA]: (A != (some @ TA @ B))) = (A = (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_not__Some__eq)).
% 181.68/124.51 thf(3370,plain,((! [TA: $tType]: (! [A:(option @ TA)]: ((! [B:TA]: ~ (A = (some @ TA @ B))) = (A = (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[783])).
% 181.68/124.51 thf(771,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/sandbox/benchmark/theBenchmark.p',fact_450_add__mono__thms__linordered__semiring_I1_J)).
% 181.68/124.51 thf(3335,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)],[771])).
% 181.68/124.51 thf(684,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit)]: ((A @ B) => (heap_Time_success @ TA @ (heap_Time_assert @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_success__assertI)).
% 181.68/124.51 thf(3103,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit)]: ((A @ B) => (heap_Time_success @ TA @ (heap_Time_assert @ TA @ (A) @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[684])).
% 181.68/124.51 thf(434,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA,B:(option @ TA)]: ((ord_less_eq @ (option @ TA) @ (some @ TA @ A) @ B) => (~ (! [C:TA]: ((B = (some @ TA @ C)) => (~ (ord_less_eq @ TA @ A @ C)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_le__some__optE)).
% 181.68/124.51 thf(2348,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA,B:(option @ TA)]: ((ord_less_eq @ (option @ TA) @ (some @ TA @ A) @ B) => (~ (! [C:TA]: ((B = (some @ TA @ C)) => (~ (ord_less_eq @ TA @ A @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[434])).
% 181.68/124.51 thf(678,axiom,((! [TA: $tType,TB: $tType]: (((heap @ TB) & (heap @ TA)) => (heap @ (product_prod @ TB @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Heap_Oheap_399)).
% 181.68/124.51 thf(3088,plain,((! [TA: $tType,TB: $tType]: (((heap @ TB) & (heap @ TA)) => (heap @ (product_prod @ TB @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[678])).
% 181.68/124.51 thf(206,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/sandbox/benchmark/theBenchmark.p',fact_208_less__add__eq__less)).
% 181.68/124.51 thf(1613,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)],[206])).
% 181.68/124.51 thf(973,axiom,((ordere1937475149494474687imp_le @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_84)).
% 181.68/124.51 thf(3898,plain,((ordere1937475149494474687imp_le @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[973])).
% 181.68/124.51 thf(1026,axiom,((! [TA: $tType]: (is_none @ TA @ (none @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5570_is__none__simps_I1_J)).
% 181.68/124.51 thf(4030,plain,((! [TA: $tType]: (is_none @ TA @ (none @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026])).
% 181.68/124.51 thf(487,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TA @ TB),B:TC,C:(TA > (TB > (set @ TC)))]: ((! [D:TA,E:TB]: ((A = (product_Pair @ TA @ TB @ D @ E)) => (member @ TC @ B @ (C @ D @ E)))) => (member @ TC @ B @ (product_case_prod @ TA @ TB @ (set @ TC) @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_mem__case__prodI2)).
% 181.68/124.51 thf(2516,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TA @ TB),B:TC,C:(TA > (TB > (set @ TC)))]: ((! [D:TA,E:TB]: ((A = (product_Pair @ TA @ TB @ D @ E)) => (member @ TC @ B @ (C @ D @ E)))) => (member @ TC @ B @ (product_case_prod @ TA @ TB @ (set @ TC) @ (C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[487])).
% 181.68/124.51 thf(454,axiom,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA),C:(set @ TA),D:(set @ TA)]: ((ord_less_eq @ (set @ TA) @ A @ B) => (((inf_inf @ (set @ TA) @ C @ B) = (inf_inf @ (set @ TA) @ D @ B)) => ((inf_inf @ (set @ TA) @ C @ A) = (inf_inf @ (set @ TA) @ D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3042_inter__eq__subsetI)).
% 181.68/124.51 thf(2400,plain,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA),C:(set @ TA),D:(set @ TA)]: ((ord_less_eq @ (set @ TA) @ A @ B) => (((inf_inf @ (set @ TA) @ C @ B) = (inf_inf @ (set @ TA) @ D @ B)) => ((inf_inf @ (set @ TA) @ C @ A) = (inf_inf @ (set @ TA) @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])).
% 181.68/124.51 thf(456,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TB,B:(TC > TB),C:(TA > TC),D:(option @ TA)]: ((case_option @ TB @ TC @ A @ B @ (map_option @ TA @ TC @ C @ D)) = (case_option @ TB @ TA @ A @ (comp @ TC @ TB @ TA @ B @ C) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_case__map__option)).
% 181.68/124.51 thf(2405,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TB,B:(TC > TB),C:(TA > TC),D:(option @ TA)]: ((case_option @ TB @ TC @ A @ (B) @ (map_option @ TA @ TC @ (C) @ D)) = (case_option @ TB @ TA @ A @ (comp @ TC @ TB @ TA @ B @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[456])).
% 181.68/124.51 thf(600,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TB > TC),C:(TA > TB)]: ((A = B) => ((comp @ TB @ TC @ TA @ A @ C) = (comp @ TB @ TC @ TA @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_comp__cong__left)).
% 181.68/124.51 thf(2869,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TB > TC),C:(TA > TB)]: (((A) = (B)) => ((comp @ TB @ TC @ TA @ A @ C) = (comp @ TB @ TC @ TA @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[600])).
% 181.68/124.51 thf(631,axiom,((! [TA: $tType]: ((zero_neq_one @ TA) => ((zero_zero @ TA) != (one_one @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_zero__neq__one)).
% 181.68/124.51 thf(2957,plain,((! [TA: $tType]: ((zero_neq_one @ TA) => (~ ((zero_zero @ TA) = (one_one @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[631])).
% 181.68/124.51 thf(940,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(product_prod @ (array @ TA) @ (product_prod @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))))]: ~ (! [B:(array @ TA),C:(list @ TA),D:(heap_ext @ product_unit),E:(set @ nat)]: (A != (product_Pair @ (array @ TA) @ (product_prod @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))) @ B @ (product_Pair @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat)) @ C @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5639_snga__assn__raw_Ocases)).
% 181.68/124.51 thf(3836,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(product_prod @ (array @ TA) @ (product_prod @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))))]: ~ (! [B:(array @ TA),C:(list @ TA),D:(heap_ext @ product_unit),E:(set @ nat)]: ~ (A = (product_Pair @ (array @ TA) @ (product_prod @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))) @ B @ (product_Pair @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat)) @ C @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[940])).
% 181.68/124.51 thf(393,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:TA,C:TB]: (((A @ B) = C) => ((fun_upd @ TA @ TB @ A @ B @ C) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2729_fun__upd__idem)).
% 181.68/124.51 thf(2216,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:TA,C:TB]: (((A @ B) = C) => ((fun_upd @ TA @ TB @ A @ B @ C) = (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[393])).
% 181.68/124.51 thf(858,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => (? [C:nat]: (B = (plus_plus @ nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_le__Suc__ex)).
% 181.68/124.51 thf(3629,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)],[858])).
% 181.68/124.51 thf(569,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(option @ TA),B:(TA > (option @ TC)),C:(TC > (option @ TB))]: ((bind @ TC @ TB @ (bind @ TA @ TC @ A @ B) @ C) = (bind @ TA @ TB @ A @ (^ [D:TA]: (bind @ TC @ TB @ (B @ D) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_bind__assoc)).
% 181.68/124.51 thf(2763,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(option @ TA),B:(TA > (option @ TC)),C:(TC > (option @ TB))]: ((bind @ TC @ TB @ (bind @ TA @ TC @ A @ (B)) @ (C)) = (bind @ TA @ TB @ A @ (^ [D:TA]: (bind @ TC @ TB @ (B @ D) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[569])).
% 181.68/124.51 thf(980,axiom,((! [TA: $tType]: ((heap_Time_Heap_ord @ TA) = (partial_img_ord @ (heap_Time_Heap @ TA) @ ((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ $o @ (heap_Time_execute @ TA) @ (partial_fun_ord @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (partial_flat_ord @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5976_Heap__ord__def)).
% 181.68/124.51 thf(3915,plain,((! [TA: $tType]: ((heap_Time_Heap_ord @ TA) = (partial_img_ord @ (heap_Time_Heap @ TA) @ ((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ $o @ (heap_Time_execute @ TA) @ (partial_fun_ord @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (partial_flat_ord @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[980])).
% 181.68/124.51 thf(397,axiom,((! [TA: $tType,TB: $tType]: ((bot_bot @ (TA > (TB > $o))) = (^ [A:TA,B:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ A @ B) @ (bot_bot @ (set @ (product_prod @ TA @ TB)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2169_bot__empty__eq2)).
% 181.68/124.51 thf(2227,plain,((! [TA: $tType,TB: $tType]: ((bot_bot @ (TA > (TB > $o))) = (^ [A:TA,B:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ A @ B) @ (bot_bot @ (set @ (product_prod @ TA @ TB)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[397])).
% 181.68/124.51 thf(192,axiom,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (plus_plus @ TA @ A @ B) @ B) = (ord_less @ TA @ A @ (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__less__same__cancel2)).
% 181.68/124.51 thf(1576,plain,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (plus_plus @ TA @ A @ B) @ B) = (ord_less @ TA @ A @ (zero_zero @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
% 181.68/124.51 thf(762,axiom,((! [TA: $tType]: ((countable @ TA) => (countable @ (list @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Countable_Ocountable_294)).
% 181.68/124.51 thf(3308,plain,((! [TA: $tType]: ((countable @ TA) => (countable @ (list @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[762])).
% 181.68/124.51 thf(326,axiom,((semigroup_mult @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Osemigroup__mult_548)).
% 181.68/124.51 thf(2010,plain,((semigroup_mult @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])).
% 181.68/124.51 thf(302,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ((heap_Time_bind @ TA @ TA @ A @ (heap_Time_return @ TA)) = (heap_Time_bind @ product_unit @ TA @ (heap_Time_wait @ (one_one @ nat)) @ (^ [B:product_unit]: (A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_bind__return)).
% 181.68/124.51 thf(1935,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ((heap_Time_bind @ TA @ TA @ A @ (heap_Time_return @ TA)) = (heap_Time_bind @ product_unit @ TA @ (heap_Time_wait @ (one_one @ nat)) @ (^ [B:product_unit]: (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])).
% 181.68/124.51 thf(202,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > $o),B:(TA > TB),C:(option @ TA)]: ((pred_option @ TB @ A @ (map_option @ TA @ TB @ B @ C)) = (pred_option @ TA @ (comp @ TB @ $o @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5065_option_Opred__map)).
% 181.68/124.51 thf(1601,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > $o),B:(TA > TB),C:(option @ TA)]: ((pred_option @ TB @ (A) @ (map_option @ TA @ TB @ (B) @ C)) = (pred_option @ TA @ (comp @ TB @ $o @ TA @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
% 181.68/124.51 thf(130,axiom,((! [A:nat,B:nat]: ((plus_plus @ nat @ (suc @ A) @ B) = (plus_plus @ nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_add__Suc__shift)).
% 181.68/124.51 thf(1386,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)],[130])).
% 181.68/124.51 thf(926,axiom,((strict7427464778891057005id_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_93)).
% 181.68/124.51 thf(3809,plain,((strict7427464778891057005id_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[926])).
% 181.68/124.51 thf(122,axiom,((semiri1453513574482234551roduct @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_427)).
% 181.68/124.51 thf(1366,plain,((semiri1453513574482234551roduct @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
% 181.68/124.51 thf(591,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TE > (TA > (TC > (TB > (TD > $o))))),B:TE]: (comple1908693960933563346ssible @ (TA > (option @ (product_prod @ TB @ (product_prod @ TC @ TD)))) @ (partial_fun_lub @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ TA @ (partial_flat_lub @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ (none @ (product_prod @ TB @ (product_prod @ TC @ TD))))) @ (partial_fun_ord @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ TA @ (partial_flat_ord @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ (none @ (product_prod @ TB @ (product_prod @ TC @ TD))))) @ (^ [C:(TA > (option @ (product_prod @ TB @ (product_prod @ TC @ TD))))]: ! [D:TA,E:TC,F:TB,G:TD]: (((C @ D) = (some @ (product_prod @ TB @ (product_prod @ TC @ TD)) @ (product_Pair @ TB @ (product_prod @ TC @ TD) @ F @ (product_Pair @ TC @ TD @ E @ G)))) => (A @ B @ D @ E @ F @ G))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5969_heap__step__admissible)).
% 181.68/124.51 thf(2819,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TE > (TA > (TC > (TB > (TD > $o))))),B:TE]: (comple1908693960933563346ssible @ (TA > (option @ (product_prod @ TB @ (product_prod @ TC @ TD)))) @ (partial_fun_lub @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ TA @ (partial_flat_lub @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ (none @ (product_prod @ TB @ (product_prod @ TC @ TD))))) @ (partial_fun_ord @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ TA @ (partial_flat_ord @ (option @ (product_prod @ TB @ (product_prod @ TC @ TD))) @ (none @ (product_prod @ TB @ (product_prod @ TC @ TD))))) @ (^ [C:(TA > (option @ (product_prod @ TB @ (product_prod @ TC @ TD))))]: ! [D:TA,E:TC,F:TB,G:TD]: (((C @ D) = (some @ (product_prod @ TB @ (product_prod @ TC @ TD)) @ (product_Pair @ TB @ (product_prod @ TC @ TD) @ F @ (product_Pair @ TC @ TD @ E @ G)))) => (A @ B @ D @ E @ F @ G))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[591])).
% 181.68/124.51 thf(261,axiom,((! [TA: $tType,TB: $tType]: (((heap @ TA) & (heap @ TB)) => (! [A:(array @ TB),B:nat,C:TB,D:(heap_ext @ product_unit)]: ((array_length @ TA @ (array_update @ TB @ A @ B @ C @ D)) = (array_length @ TA @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4089_length__update)).
% 181.68/124.51 thf(1803,plain,((! [TA: $tType,TB: $tType]: (((heap @ TA) & (heap @ TB)) => (! [A:(array @ TB),B:nat,C:TB,D:(heap_ext @ product_unit)]: ((array_length @ TA @ (array_update @ TB @ A @ B @ C @ D)) = (array_length @ TA @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])).
% 181.68/124.51 thf(962,axiom,((semido2269285787275462019factor @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__divide__unit__factor_98)).
% 181.68/124.51 thf(3880,plain,((semido2269285787275462019factor @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[962])).
% 181.68/124.51 thf(293,axiom,((semiring_0 @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Osemiring__0_562)).
% 181.68/124.51 thf(1904,plain,((semiring_0 @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])).
% 181.68/124.51 thf(173,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ A @ B) => (ord_less @ nat @ A @ (plus_plus @ nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_trans__less__add2)).
% 181.68/124.51 thf(1518,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)],[173])).
% 181.68/124.51 thf(73,axiom,((one @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Oone_509)).
% 181.68/124.51 thf(1228,plain,((one @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
% 181.68/124.51 thf(209,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA),C:TB]: (((map_option @ TA @ TB @ A @ B) = (some @ TB @ C)) = (? [D:TA]: ((B = (some @ TA @ D)) & ((A @ D) = C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_map__option__eq__Some)).
% 181.68/124.51 thf(1623,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA),C:TB]: (((map_option @ TA @ TB @ (A) @ B) = (some @ TB @ C)) = (? [D:TA]: ((B = (some @ TA @ D)) & ((A @ D) = C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
% 181.68/124.51 thf(968,axiom,((semilattice_inf @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__inf_112)).
% 181.68/124.51 thf(3891,plain,((semilattice_inf @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[968])).
% 181.68/124.51 thf(94,axiom,((preorder @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Orderings_Opreorder_488)).
% 181.68/124.51 thf(1287,plain,((preorder @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
% 181.68/124.51 thf(750,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(heap_Time_Heap @ TA),B:(TA > (heap_Time_Heap @ TC)),C:(TC > (heap_Time_Heap @ TB))]: ((heap_Time_bind @ TC @ TB @ (heap_Time_bind @ TA @ TC @ A @ B) @ C) = (heap_Time_bind @ TA @ TB @ A @ (^ [D:TA]: (heap_Time_bind @ TC @ TB @ (B @ D) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Heap__Time__Monad_Obind__bind)).
% 181.68/124.51 thf(3275,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(heap_Time_Heap @ TA),B:(TA > (heap_Time_Heap @ TC)),C:(TC > (heap_Time_Heap @ TB))]: ((heap_Time_bind @ TC @ TB @ (heap_Time_bind @ TA @ TC @ A @ (B)) @ (C)) = (heap_Time_bind @ TA @ TB @ A @ (^ [D:TA]: (heap_Time_bind @ TC @ TB @ (B @ D) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[750])).
% 181.68/124.51 thf(539,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TB > TD),C:(TA > TB)]: ((comp @ TD @ TC @ TA @ A @ (comp @ TB @ TD @ TA @ B @ C)) = (comp @ TB @ TC @ TA @ (comp @ TD @ TC @ TB @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_fun_Omap__comp)).
% 181.68/124.51 thf(2667,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TB > TD),C:(TA > TB)]: ((comp @ TD @ TC @ TA @ A @ (comp @ TB @ TD @ TA @ B @ C)) = (comp @ TB @ TC @ TA @ (comp @ TD @ TC @ TB @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[539])).
% 181.68/124.51 thf(839,axiom,((! [TA: $tType]: (! [A:TA]: ((none @ TA) != (some @ TA @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_option_Odistinct_I1_J)).
% 181.68/124.51 thf(3574,plain,((! [TA: $tType]: (! [A:TA]: ~ ((none @ TA) = (some @ TA @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[839])).
% 181.68/124.51 thf(544,axiom,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Quickcheck__Random_Orandom_317)).
% 181.68/124.51 thf(2682,plain,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[544])).
% 181.68/124.51 thf(154,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/sandbox/benchmark/theBenchmark.p',fact_589_nat__eq__add__iff2)).
% 181.68/124.51 thf(1455,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)],[154])).
% 181.68/124.51 thf(39,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) => (((C = (zero_zero @ nat)) => (A != B)) => (~ (! [E:TA,F:nat]: ((C = (suc @ F)) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ (compow @ (set @ (product_prod @ TA @ TA)) @ F @ D)) => (~ (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ D))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4991_relpow__E)).
% 181.68/124.51 thf(1132,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) => (((C = (zero_zero @ nat)) => (~ (A = B))) => (~ (! [E:TA,F:nat]: ((C = (suc @ F)) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ (compow @ (set @ (product_prod @ TA @ TA)) @ F @ D)) => (~ (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
% 181.68/124.51 thf(510,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TE > TB),B:(TA > TE),C:TA,D:(TD > TB),E:(TA > TD),F:(TB > TC)]: (((A @ (B @ C)) = (D @ (E @ C))) => ((comp @ TE @ TC @ TA @ (comp @ TB @ TC @ TE @ F @ A) @ B @ C) = (comp @ TD @ TC @ TA @ (comp @ TB @ TC @ TD @ F @ D) @ E @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_type__copy__map__cong0)).
% 181.68/124.51 thf(2571,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TE > TB),B:(TA > TE),C:TA,D:(TD > TB),E:(TA > TD),F:(TB > TC)]: (((A @ (B @ C)) = (D @ (E @ C))) => ((comp @ TE @ TC @ TA @ (comp @ TB @ TC @ TE @ F @ A) @ (B) @ C) = (comp @ TD @ TC @ TA @ (comp @ TB @ TC @ TD @ F @ D) @ (E) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[510])).
% 181.68/124.51 thf(11,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo @ nat @ (suc @ (plus_plus @ nat @ (times_times @ nat @ A @ B) @ C)) @ B) = (modulo_modulo @ nat @ (suc @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_Suc__mod__mult__self3)).
% 181.68/124.51 thf(1055,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo @ nat @ (suc @ (plus_plus @ nat @ (times_times @ nat @ A @ B) @ C)) @ B) = (modulo_modulo @ nat @ (suc @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 181.68/124.51 thf(139,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo @ nat @ A @ B) = (modulo_modulo @ nat @ C @ B)) => ((ord_less_eq @ nat @ C @ A) => (~ (! [D:nat]: (A != (plus_plus @ nat @ C @ (times_times @ nat @ B @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_mod__eq__nat1E)).
% 181.68/124.51 thf(1409,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo @ nat @ A @ B) = (modulo_modulo @ nat @ C @ B)) => ((ord_less_eq @ nat @ C @ A) => (~ (! [D:nat]: ~ (A = (plus_plus @ nat @ C @ (times_times @ nat @ B @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
% 181.68/124.51 thf(993,axiom,((! [TA: $tType]: ((heap_Time_success @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ TA @ A @ B) != (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_success__def)).
% 181.68/124.51 thf(3938,plain,((! [TA: $tType]: ((heap_Time_success @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ~ ((heap_Time_execute @ TA @ A @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[993])).
% 181.68/124.51 thf(719,axiom,((! [TA: $tType]: (! [A:TA]: ((eps_Opt @ TA @ ((=) @ TA @ A)) = (some @ TA @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_some__opt__sym__eq__trivial)).
% 181.68/124.51 thf(3195,plain,((! [TA: $tType]: (! [A:TA]: ((eps_Opt @ TA @ ((=) @ TA @ A)) = (some @ TA @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[719])).
% 181.68/124.51 thf(250,axiom,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => (ord_less @ TA @ (plus_plus @ TA @ C @ A) @ (plus_plus @ TA @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_add__strict__left__mono)).
% 181.68/124.51 thf(1760,plain,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less @ TA @ A @ B) => (ord_less @ TA @ (plus_plus @ TA @ C @ A) @ (plus_plus @ TA @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])).
% 181.68/124.51 thf(220,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/sandbox/benchmark/theBenchmark.p',fact_647_Nat_Odiff__cancel)).
% 181.68/124.51 thf(1660,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)],[220])).
% 181.68/124.51 thf(98,axiom,((! [TA: $tType]: ((size_size @ (option @ TA) @ (none @ TA)) = (suc @ (zero_zero @ nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_option_Osize_I3_J)).
% 181.68/124.51 thf(1298,plain,((! [TA: $tType]: ((size_size @ (option @ TA) @ (none @ TA)) = (suc @ (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
% 181.68/124.51 thf(853,axiom,((! [TA: $tType]: ((heap_Time_return @ TA) = (^ [A:TA]: (heap_Time_heap @ TA @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ A @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_return__def)).
% 181.68/124.51 thf(3617,plain,((! [TA: $tType]: ((heap_Time_return @ TA) = (^ [A:TA]: (heap_Time_heap @ TA @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ A @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[853])).
% 181.68/124.51 thf(111,axiom,((ordere8940638589300402666id_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Oordered__cancel__comm__monoid__add_441)).
% 181.68/124.51 thf(1330,plain,((ordere8940638589300402666id_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
% 181.68/124.51 thf(468,axiom,((! [TA: $tType]: ((init_seg_of @ TA) = (collect @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_case_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ $o @ (^ [A:(set @ (product_prod @ TA @ TA)),B:(set @ (product_prod @ TA @ TA))]: ((ord_less_eq @ (set @ (product_prod @ TA @ TA)) @ A @ B) & ! [C:TA,D:TA,E:TA]: (((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ B) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ D @ E) @ A)) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ A))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4356_init__seg__of__def)).
% 181.68/124.51 thf(2444,plain,((! [TA: $tType]: ((init_seg_of @ TA) = (collect @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_case_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ $o @ (^ [A:(set @ (product_prod @ TA @ TA)),B:(set @ (product_prod @ TA @ TA))]: ((ord_less_eq @ (set @ (product_prod @ TA @ TA)) @ A @ B) & ! [C:TA,D:TA,E:TA]: (((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ B) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ D @ E) @ A)) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])).
% 181.68/124.51 thf(108,axiom,((! [TA: $tType,TB: $tType]: ((dom @ TA @ TB @ (^ [A:TA]: (none @ TB))) = (bot_bot @ (set @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3314_dom__empty)).
% 181.68/124.51 thf(1323,plain,((! [TA: $tType,TB: $tType]: ((dom @ TA @ TB @ (^ [A:TA]: (none @ TB))) = (bot_bot @ (set @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
% 181.68/124.51 thf(866,axiom,((! [TA: $tType]: (! [A:TA]: ~ (is_none @ TA @ (some @ TA @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5558_is__none__code_I2_J)).
% 181.68/124.51 thf(3653,plain,((! [TA: $tType]: (! [A:TA]: ~ (is_none @ TA @ (some @ TA @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[866])).
% 181.68/124.51 thf(104,axiom,((plus @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Oplus_507)).
% 181.68/124.51 thf(1313,plain,((plus @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
% 181.68/124.51 thf(91,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ A @ B) => (~ (! [C:nat]: (B != (suc @ (plus_plus @ nat @ A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_965_less__natE)).
% 181.68/124.51 thf(1279,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)],[91])).
% 181.68/124.51 thf(896,axiom,((semidom_divide @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__divide_126)).
% 181.68/124.51 thf(3749,plain,((semidom_divide @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[896])).
% 181.68/124.51 thf(506,axiom,((! [TA: $tType]: ((quickc658316121487927005ustive @ TA) => (quickc658316121487927005ustive @ (set @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Quickcheck__Exhaustive_Oexhaustive_244)).
% 181.68/124.51 thf(2562,plain,((! [TA: $tType]: ((quickc658316121487927005ustive @ TA) => (quickc658316121487927005ustive @ (set @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])).
% 181.68/124.51 thf(610,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat,F:(heap_ext @ product_unit),G:TA,H:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => ((heap_Time_effect @ TA @ A @ B @ F @ G @ H) => (C = F)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_effect__deterministic_I2_J)).
% 181.68/124.51 thf(2897,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat,F:(heap_ext @ product_unit),G:TA,H:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => ((heap_Time_effect @ TA @ A @ B @ F @ G @ H) => (C = F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[610])).
% 181.68/124.51 thf(58,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/sandbox/benchmark/theBenchmark.p',fact_609_left__add__mult__distrib)).
% 181.68/124.51 thf(1191,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)],[58])).
% 181.68/124.51 thf(366,axiom,((! [TA: $tType,TB: $tType]: ((iterate @ TB @ TA) = (^ [A:code_natural,B:(TB > (TA > (product_prod @ TB @ TA))),C:TB]: (if @ (TA > (product_prod @ TB @ TA)) @ (A = (zero_zero @ code_natural)) @ (product_Pair @ TB @ TA @ C) @ (product_scomp @ TA @ TB @ TA @ (product_prod @ TB @ TA) @ (B @ C) @ (iterate @ TB @ TA @ (minus_minus @ code_natural @ A @ (one_one @ code_natural)) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4283_iterate_Osimps)).
% 181.68/124.51 thf(2126,plain,((! [TA: $tType,TB: $tType]: ((iterate @ TB @ TA) = (^ [A:code_natural,B:(TB > (TA > (product_prod @ TB @ TA))),C:TB]: (if @ (TA > (product_prod @ TB @ TA)) @ (A = (zero_zero @ code_natural)) @ (product_Pair @ TB @ TA @ C) @ (product_scomp @ TA @ TB @ TA @ (product_prod @ TB @ TA) @ (B @ C) @ (iterate @ TB @ TA @ (minus_minus @ code_natural @ A @ (one_one @ code_natural)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])).
% 181.68/124.51 thf(923,axiom,((order_bot @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder__bot_131)).
% 181.68/124.51 thf(3803,plain,((order_bot @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[923])).
% 181.68/124.51 thf(475,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:TA,D:(ref @ TA),E:nat]: ((A = B) => ((C = (ref_get @ TA @ B @ D)) => ((E = (one_one @ nat)) => (heap_Time_effect @ TA @ (ref_lookup @ TA @ D) @ B @ A @ C @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_effect__lookupI)).
% 181.68/124.51 thf(2466,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:TA,D:(ref @ TA),E:nat]: ((A = B) => ((C = (ref_get @ TA @ B @ D)) => ((E = (one_one @ nat)) => (heap_Time_effect @ TA @ (ref_lookup @ TA @ D) @ B @ A @ C @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[475])).
% 181.68/124.51 thf(183,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA]: (ord_less @ (option @ TA) @ (none @ TA) @ (some @ TA @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_less__option__None__Some__code)).
% 181.68/124.51 thf(1545,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA]: (ord_less @ (option @ TA) @ (none @ TA) @ (some @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
% 181.68/124.51 thf(298,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ B) => (B != (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_gr__implies__not__zero)).
% 181.68/124.51 thf(1922,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)],[298])).
% 181.68/124.51 thf(260,axiom,((! [TA: $tType]: (! [A:(set @ TA),B:(TA > $o)]: ((ord_less_eq @ (set @ TA) @ A @ (collect @ TA @ B)) = (! [C:TA]: ((member @ TA @ C @ A) => (B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_subset__Collect__conv)).
% 181.68/124.51 thf(1800,plain,((! [TA: $tType]: (! [A:(set @ TA),B:(TA > $o)]: ((ord_less_eq @ (set @ TA) @ A @ (collect @ TA @ (B))) = (! [C:TA]: ((member @ TA @ C @ A) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])).
% 181.68/124.51 thf(1012,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:(TA > (option @ TB))]: (((^ [C:TA]: (none @ TB)) = (map_add @ TA @ TB @ A @ B)) = ((A = (^ [C:TA]: (none @ TB))) & (B = (^ [C:TA]: (none @ TB)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3398_empty__eq__map__add__iff)).
% 181.68/124.51 thf(3998,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:(TA > (option @ TB))]: (((^ [C:TA]: (none @ TB)) = (map_add @ TA @ TB @ A @ B)) = (((A) = (^ [C:TA]: (none @ TB))) & ((B) = (^ [C:TA]: (none @ TB)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012])).
% 181.68/124.51 thf(455,axiom,((! [TA: $tType]: ((typerep2 @ TA) => (quickcheck_random @ (ref @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oref___Quickcheck__Random_Orandom_288)).
% 181.68/124.51 thf(2403,plain,((! [TA: $tType]: ((typerep2 @ TA) => (quickcheck_random @ (ref @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])).
% 181.68/124.51 thf(41,axiom,((! [A:nat,B:nat]: (((one_one @ nat) = (times_times @ nat @ A @ B)) = ((A = (one_one @ nat)) & (B = (one_one @ nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_nat__1__eq__mult__iff)).
% 181.68/124.51 thf(1147,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)],[41])).
% 181.68/124.51 thf(339,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ (minus_minus @ TA @ B @ A)) = (ord_less_eq @ TA @ (plus_plus @ TA @ C @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2)).
% 181.68/124.51 thf(2049,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ (minus_minus @ TA @ B @ A)) = (ord_less_eq @ TA @ (plus_plus @ TA @ C @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])).
% 181.68/124.51 thf(233,axiom,((! [TA: $tType]: (! [A:nat,B:(list @ TA),C:nat]: ((ord_less @ nat @ A @ (size_size @ (list @ TA) @ B)) => ((nth @ (product_prod @ nat @ TA) @ (enumerate @ TA @ C @ B) @ A) = (product_Pair @ nat @ TA @ (plus_plus @ nat @ C @ A) @ (nth @ TA @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3576_nth__enumerate__eq)).
% 181.68/124.51 thf(1704,plain,((! [TA: $tType]: (! [A:nat,B:(list @ TA),C:nat]: ((ord_less @ nat @ A @ (size_size @ (list @ TA) @ B)) => ((nth @ (product_prod @ nat @ TA) @ (enumerate @ TA @ C @ B) @ A) = (product_Pair @ nat @ TA @ (plus_plus @ nat @ C @ A) @ (nth @ TA @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
% 181.68/124.51 thf(676,axiom,((! [TA: $tType,TB: $tType]: (! [A:((TA > (heap_Time_Heap @ TB)) > (TA > (heap_Time_Heap @ TB)))]: ((! [B:TA]: (comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TB) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TB) @ (^ [C:(TA > (heap_Time_Heap @ TB))]: (A @ C @ B)))) => ((comple187402453842119260l_fixp @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ A) = (A @ (comple187402453842119260l_fixp @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5990_heap_Omono__body__fixp)).
% 181.68/124.51 thf(3084,plain,((! [TA: $tType,TB: $tType]: (! [A:((TA > (heap_Time_Heap @ TB)) > (TA > (heap_Time_Heap @ TB)))]: ((! [B:TA]: (comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TB) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TB) @ (^ [C:(TA > (heap_Time_Heap @ TB))]: (A @ C @ B)))) => ((comple187402453842119260l_fixp @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (A)) = (A @ (comple187402453842119260l_fixp @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[676])).
% 181.68/124.51 thf(376,axiom,((! [TA: $tType]: ((comm_monoid_diff @ TA) => (! [A:TA]: ((minus_minus @ TA @ (zero_zero @ TA) @ A) = (zero_zero @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_zero__diff)).
% 181.68/124.51 thf(2158,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)],[376])).
% 181.68/124.51 thf(885,axiom,((! [TA: $tType]: ((order_top @ TA) => ((top_top @ (option @ TA)) = (some @ TA @ (top_top @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2234_top__option__def)).
% 181.68/124.51 thf(3708,plain,((! [TA: $tType]: ((order_top @ TA) => ((top_top @ (option @ TA)) = (some @ TA @ (top_top @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[885])).
% 181.68/124.51 thf(264,axiom,((! [TA: $tType]: ((heap @ TA) => ((ref_change @ TA) = (^ [A:(TA > TA),B:(ref @ TA)]: (heap_Time_bind @ TA @ TA @ (ref_lookup @ TA @ B) @ (^ [C:TA]: (heap_Time_bind @ product_unit @ TA @ (ref_update @ TA @ B @ (A @ C)) @ (^ [D:product_unit]: (heap_Time_return @ TA @ (A @ C))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_change__def)).
% 181.68/124.51 thf(1815,plain,((! [TA: $tType]: ((heap @ TA) => ((ref_change @ TA) = (^ [A:(TA > TA),B:(ref @ TA)]: (heap_Time_bind @ TA @ TA @ (ref_lookup @ TA @ B) @ (^ [C:TA]: (heap_Time_bind @ product_unit @ TA @ (ref_update @ TA @ B @ (A @ C)) @ (^ [D:product_unit]: (heap_Time_return @ TA @ (A @ C))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])).
% 181.68/124.51 thf(120,axiom,((ab_semigroup_mult @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Oab__semigroup__mult_464)).
% 181.68/124.51 thf(1362,plain,((ab_semigroup_mult @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
% 181.68/124.51 thf(715,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(array @ TA),D:(heap_ext @ product_unit),E:(heap_ext @ product_unit),F:(array @ TA),G:nat]: ((heap_Time_effect @ (array @ TA) @ (array_upd @ TA @ A @ B @ C) @ D @ E @ F @ G) => (~ ((F = C) => ((E = (array_update @ TA @ C @ A @ B @ D)) => ((ord_less @ nat @ A @ (array_length @ TA @ D @ C)) => (G != (one_one @ nat))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4110_effect__updE)).
% 181.68/124.51 thf(3180,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(array @ TA),D:(heap_ext @ product_unit),E:(heap_ext @ product_unit),F:(array @ TA),G:nat]: ((heap_Time_effect @ (array @ TA) @ (array_upd @ TA @ A @ B @ C) @ D @ E @ F @ G) => (~ ((F = C) => ((E = (array_update @ TA @ C @ A @ B @ D)) => ((ord_less @ nat @ A @ (array_length @ TA @ D @ C)) => (~ (G = (one_one @ nat)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[715])).
% 181.68/124.51 thf(734,axiom,((! [TA: $tType,TB: $tType]: ((semilattice_inf @ TA) => (inf @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oinf)).
% 181.68/124.51 thf(3231,plain,((! [TA: $tType,TB: $tType]: ((semilattice_inf @ TA) => (inf @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[734])).
% 181.68/124.51 thf(942,axiom,((order_bot @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__bot_412)).
% 181.68/124.51 thf(3840,plain,((order_bot @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[942])).
% 181.68/124.51 thf(815,axiom,((semilattice_inf @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_270)).
% 181.68/124.51 thf(3463,plain,((semilattice_inf @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[815])).
% 181.68/124.51 thf(128,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 @ (times_times @ nat @ A @ D) @ C) @ (times_times @ nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_mlex__bound)).
% 181.68/124.51 thf(1379,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 @ (times_times @ nat @ A @ D) @ C) @ (times_times @ nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])).
% 181.68/124.51 thf(191,axiom,((! [TA: $tType]: (! [A:nat,B:(set @ (product_prod @ TA @ TA)),C:TA,D:TA,E:TA]: (((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ (compow @ (set @ (product_prod @ TA @ TA)) @ A @ B)) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ D @ E) @ B)) => (? [F:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ F) @ B) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ F @ E) @ (compow @ (set @ (product_prod @ TA @ TA)) @ A @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4979_relpow__Suc__D2_H)).
% 181.68/124.51 thf(1572,plain,((! [TA: $tType]: (! [A:nat,B:(set @ (product_prod @ TA @ TA)),C:TA,D:TA,E:TA]: (((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ (compow @ (set @ (product_prod @ TA @ TA)) @ A @ B)) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ D @ E) @ B)) => (? [F:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ F) @ B) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ F @ E) @ (compow @ (set @ (product_prod @ TA @ TA)) @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])).
% 181.68/124.51 thf(982,axiom,((semiring_0 @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__0_140)).
% 181.68/124.51 thf(3919,plain,((semiring_0 @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[982])).
% 181.68/124.51 thf(532,axiom,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (plus_plus @ TA @ B @ A)) = (ord_less_eq @ TA @ (zero_zero @ TA) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_le__add__same__cancel2)).
% 181.68/124.51 thf(2635,plain,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (plus_plus @ TA @ B @ A)) = (ord_less_eq @ TA @ (zero_zero @ TA) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[532])).
% 181.68/124.51 thf(619,axiom,((! [TA: $tType,TB: $tType]: ((semilattice_sup @ TA) => (semilattice_sup @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup)).
% 181.68/124.51 thf(2929,plain,((! [TA: $tType,TB: $tType]: ((semilattice_sup @ TA) => (semilattice_sup @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[619])).
% 181.68/124.51 thf(976,axiom,((! [TA: $tType]: ((time_the_res @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: (case_option @ TA @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (undefined @ TA) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ TA @ (^ [C:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ TA @ (^ [D:(heap_ext @ product_unit),E:nat]: (C))))) @ (heap_Time_execute @ TA @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1500_the__res__def)).
% 181.68/124.51 thf(3902,plain,((! [TA: $tType]: ((time_the_res @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: (case_option @ TA @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (undefined @ TA) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ TA @ (^ [C:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ TA @ (^ [D:(heap_ext @ product_unit),E:nat]: (C))))) @ (heap_Time_execute @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[976])).
% 181.68/124.51 thf(301,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/sandbox/benchmark/theBenchmark.p',fact_654_Nat_Odiff__add__assoc2)).
% 181.68/124.51 thf(1931,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)],[301])).
% 181.68/124.51 thf(449,axiom,((semidom_divide @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Osemidom__divide_550)).
% 181.68/124.51 thf(2388,plain,((semidom_divide @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[449])).
% 181.68/124.51 thf(494,axiom,((! [TA: $tType]: (sup @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osup_261)).
% 181.68/124.51 thf(2533,plain,((! [TA: $tType]: (sup @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[494])).
% 181.68/124.51 thf(75,axiom,((! [TA: $tType]: (! [A:nat,B:(TA > TA)]: ((compow @ (TA > TA) @ (suc @ A) @ B) = (comp @ TA @ TA @ TA @ B @ (compow @ (TA > TA) @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4902_funpow_Osimps_I2_J)).
% 181.68/124.51 thf(1232,plain,((! [TA: $tType]: (! [A:nat,B:(TA > TA)]: ((compow @ (TA > TA) @ (suc @ A) @ B) = (comp @ TA @ TA @ TA @ B @ (compow @ (TA > TA) @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])).
% 181.68/124.51 thf(746,axiom,((heap @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Heap_Oheap_155)).
% 181.68/124.51 thf(3268,plain,((heap @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[746])).
% 181.68/124.51 thf(1016,axiom,((one @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone_153)).
% 181.68/124.51 thf(4008,plain,((one @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016])).
% 181.68/124.51 thf(325,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > TB),B:(option @ TA),C:(TB > (option @ TC))]: ((bind @ TB @ TC @ (map_option @ TA @ TB @ A @ B) @ C) = (bind @ TA @ TC @ B @ (comp @ TB @ (option @ TC) @ TA @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_bind__map__option)).
% 181.68/124.51 thf(2007,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > TB),B:(option @ TA),C:(TB > (option @ TC))]: ((bind @ TB @ TC @ (map_option @ TA @ TB @ (A) @ B) @ (C)) = (bind @ TA @ TC @ B @ (comp @ TB @ (option @ TC) @ TA @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])).
% 181.68/124.51 thf(525,axiom,((! [TA: $tType,TB: $tType]: ((map_add @ TA @ TB) = (^ [A:(TA > (option @ TB)),B:(TA > (option @ TB)),C:TA]: (case_option @ (option @ TB) @ TB @ (A @ C) @ (some @ TB) @ (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3413_map__add__def)).
% 181.68/124.51 thf(2616,plain,((! [TA: $tType,TB: $tType]: ((map_add @ TA @ TB) = (^ [A:(TA > (option @ TB)),B:(TA > (option @ TB)),C:TA]: (case_option @ (option @ TB) @ TB @ (A @ C) @ (some @ TB) @ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[525])).
% 181.68/124.51 thf(672,axiom,((countable @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Countable_Ocountable_276)).
% 181.68/124.51 thf(3075,plain,((countable @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[672])).
% 181.68/124.51 thf(1022,axiom,((! [TA: $tType]: ((is_none @ TA) = (^ [A:(option @ TA)]: (A = (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5571_Option_Ois__none__def)).
% 181.68/124.51 thf(4018,plain,((! [TA: $tType]: ((is_none @ TA) = (^ [A:(option @ TA)]: (A = (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022])).
% 181.68/124.51 thf(575,axiom,((quickcheck_random @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_405)).
% 181.68/124.51 thf(2782,plain,((quickcheck_random @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[575])).
% 181.68/124.51 thf(709,axiom,((! [TA: $tType]: (! [A:TA]: ((heap_Time_execute @ TA @ (heap_Time_ureturn @ TA @ A)) = (comp @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ A @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (zero_zero @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_execute__ureturn)).
% 181.68/124.51 thf(3163,plain,((! [TA: $tType]: (! [A:TA]: ((heap_Time_execute @ TA @ (heap_Time_ureturn @ TA @ A)) = (comp @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ A @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (zero_zero @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[709])).
% 181.68/124.51 thf(604,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TD > TC),B:(TE > TD),C:(TB > TC),D:(TE > TB),E:(TA > TE),F:(TA > TB)]: (((comp @ TD @ TC @ TE @ A @ B) = (comp @ TB @ TC @ TE @ C @ D)) => (((comp @ TE @ TB @ TA @ D @ E) = F) => ((comp @ TD @ TC @ TA @ A @ (comp @ TE @ TD @ TA @ B @ E)) = (comp @ TB @ TC @ TA @ C @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_rewriteL__comp__comp2)).
% 181.68/124.51 thf(2880,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TD > TC),B:(TE > TD),C:(TB > TC),D:(TE > TB),E:(TA > TE),F:(TA > TB)]: (((comp @ TD @ TC @ TE @ A @ B) = (comp @ TB @ TC @ TE @ C @ D)) => (((comp @ TE @ TB @ TA @ D @ E) = (F)) => ((comp @ TD @ TC @ TA @ A @ (comp @ TE @ TD @ TA @ B @ E)) = (comp @ TB @ TC @ TA @ C @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[604])).
% 181.68/124.51 thf(805,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ TA @ (ref_lookup @ TA @ A) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (ref_get @ TA @ B @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_execute__lookup)).
% 181.68/124.51 thf(3438,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ TA @ (ref_lookup @ TA @ A) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (ref_get @ TA @ B @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[805])).
% 181.68/124.51 thf(497,axiom,((! [TA: $tType]: ((heap @ TA) => (heap @ (list @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Heap_Oheap_295)).
% 181.68/124.51 thf(2540,plain,((! [TA: $tType]: ((heap @ TA) => (heap @ (list @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[497])).
% 181.68/124.51 thf(429,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > $o)),B:(heap_Time_Heap @ TB)]: (comple7038119648293358887notone @ TA @ (heap_Time_Heap @ TB) @ A @ (heap_Time_Heap_ord @ TB) @ (^ [C:TA]: (B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5985_heap_Oconst__mono)).
% 181.68/124.51 thf(2335,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > $o)),B:(heap_Time_Heap @ TB)]: (comple7038119648293358887notone @ TA @ (heap_Time_Heap @ TB) @ (A) @ (heap_Time_Heap_ord @ TB) @ (^ [C:TA]: (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])).
% 181.68/124.51 thf(92,axiom,((semiring_0 @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Osemiring__0_494)).
% 181.68/124.51 thf(1283,plain,((semiring_0 @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
% 181.68/124.51 thf(907,axiom,((semigroup_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_128)).
% 181.68/124.51 thf(3771,plain,((semigroup_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[907])).
% 181.68/124.51 thf(163,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/sandbox/benchmark/theBenchmark.p',fact_593_nat__diff__add__eq2)).
% 181.68/124.51 thf(1489,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)],[163])).
% 181.68/124.51 thf(627,axiom,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounded_lattice @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice)).
% 181.68/124.51 thf(2950,plain,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounded_lattice @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[627])).
% 181.68/124.51 thf(965,axiom,((complete_Sup @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Complete__Lattices_OSup_409)).
% 181.68/124.51 thf(3887,plain,((complete_Sup @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[965])).
% 181.68/124.51 thf(331,axiom,((euclid3725896446679973847miring @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Euclidean__Division_Oeuclidean__semiring_524)).
% 181.68/124.51 thf(2027,plain,((euclid3725896446679973847miring @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])).
% 181.68/124.51 thf(721,axiom,((! [TA: $tType]: ((finite_finite @ TA) => (finite_finite @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Finite__Set_Ofinite_328)).
% 181.68/124.51 thf(3199,plain,((! [TA: $tType]: ((finite_finite @ TA) => (finite_finite @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[721])).
% 181.68/124.51 thf(991,axiom,((sup @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osup_147)).
% 181.68/124.51 thf(3934,plain,((sup @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[991])).
% 181.68/124.51 thf(873,axiom,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: ((! [C:TA,D:TB]: ((member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A) => (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) => (ord_less_eq @ (set @ (product_prod @ TA @ TB)) @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_subrelI)).
% 181.68/124.51 thf(3670,plain,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: ((! [C:TA,D:TB]: ((member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A) => (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) => (ord_less_eq @ (set @ (product_prod @ TA @ TB)) @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[873])).
% 181.68/124.51 thf(1013,axiom,((countable @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Countable_Ocountable_413)).
% 181.68/124.51 thf(4001,plain,((countable @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013])).
% 181.68/124.51 thf(142,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TB > (option @ TA)),C:(TB > (option @ TA)),D:TA]: ((~ (member @ TB @ A @ (dom @ TB @ TA @ B))) => ((map_add @ TB @ TA @ (fun_upd @ TB @ (option @ TA) @ C @ A @ (some @ TA @ D)) @ B) = (fun_upd @ TB @ (option @ TA) @ (map_add @ TB @ TA @ C @ B) @ A @ (some @ TA @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3400_map__add__upd__left)).
% 181.68/124.51 thf(1418,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TB > (option @ TA)),C:(TB > (option @ TA)),D:TA]: ((~ (member @ TB @ A @ (dom @ TB @ TA @ (B)))) => ((map_add @ TB @ TA @ (fun_upd @ TB @ (option @ TA) @ C @ A @ (some @ TA @ D)) @ B) = (fun_upd @ TB @ (option @ TA) @ (map_add @ TB @ TA @ C @ B) @ A @ (some @ TA @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
% 181.68/124.51 thf(811,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/sandbox/benchmark/theBenchmark.p',fact_189_add_Oright__assoc)).
% 181.68/124.51 thf(3453,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)],[811])).
% 181.68/124.51 thf(470,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((minus_minus @ TA @ C @ (minus_minus @ TA @ B @ A)) = (minus_minus @ TA @ (plus_plus @ TA @ C @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right)).
% 181.68/124.51 thf(2451,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((minus_minus @ TA @ C @ (minus_minus @ TA @ B @ A)) = (minus_minus @ TA @ (plus_plus @ TA @ C @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[470])).
% 181.68/124.51 thf(400,axiom,((! [TA: $tType]: ((ordere580206878836729694up_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/sandbox/benchmark/theBenchmark.p',fact_186_add__mono__thms__linordered__field_I5_J)).
% 181.68/124.51 thf(2236,plain,((! [TA: $tType]: ((ordere580206878836729694up_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)],[400])).
% 181.68/124.51 thf(986,axiom,((! [TA: $tType,TB: $tType]: (((finite_finite @ TB) & (finite_finite @ TA)) => (finite_finite @ (product_prod @ TB @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Finite__Set_Ofinite_398)).
% 181.68/124.51 thf(3923,plain,((! [TA: $tType,TB: $tType]: (((finite_finite @ TB) & (finite_finite @ TA)) => (finite_finite @ (product_prod @ TB @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[986])).
% 181.68/124.51 thf(503,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType]: (! [A:(product_prod @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)))))]: ~ (! [B:TF,C:TE,D:TD,E:TC,F:TB,G:TA]: (A != (product_Pair @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)))) @ B @ (product_Pair @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))) @ C @ (product_Pair @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)) @ D @ (product_Pair @ TC @ (product_prod @ TB @ TA) @ E @ (product_Pair @ TB @ TA @ F @ G)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_prod__cases6)).
% 181.68/124.51 thf(2555,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType]: (! [A:(product_prod @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)))))]: ~ (! [B:TF,C:TE,D:TD,E:TC,F:TB,G:TA]: ~ (A = (product_Pair @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)))) @ B @ (product_Pair @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))) @ C @ (product_Pair @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)) @ D @ (product_Pair @ TC @ (product_prod @ TB @ TA) @ E @ (product_Pair @ TB @ TA @ F @ G)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[503])).
% 181.68/124.51 thf(272,axiom,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ (heap_Time_return @ TA @ A) @ B @ C @ D @ E) => (~ ((D = A) => ((C = B) => (E != (one_one @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_effect__returnE)).
% 181.68/124.51 thf(1843,plain,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ (heap_Time_return @ TA @ A) @ B @ C @ D @ E) => (~ ((D = A) => ((C = B) => (~ (E = (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])).
% 181.68/124.51 thf(287,axiom,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (heap_Time_ureturn @ TA @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_success__ureturnI)).
% 181.68/124.51 thf(1886,plain,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (heap_Time_ureturn @ TA @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])).
% 181.68/124.51 thf(492,axiom,((! [TA: $tType,TB: $tType]: ((uminus @ TA) => (uminus @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus)).
% 181.68/124.51 thf(2530,plain,((! [TA: $tType,TB: $tType]: ((uminus @ TA) => (uminus @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[492])).
% 181.68/124.51 thf(706,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(nat > TA),C:(heap_ext @ product_unit)]: (heap_Time_success @ (array @ TA) @ (array_make @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_success__makeI)).
% 181.68/124.51 thf(3157,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(nat > TA),C:(heap_ext @ product_unit)]: (heap_Time_success @ (array @ TA) @ (array_make @ TA @ A @ (B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[706])).
% 181.68/124.51 thf(901,axiom,((! [A:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ~ (! [B:(heap_ext @ product_unit),C:(set @ nat)]: (A != (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5640_one__assn__raw_Ocases)).
% 181.68/124.51 thf(3756,plain,((! [A:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ~ (! [B:(heap_ext @ product_unit),C:(set @ nat)]: ~ (A = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[901])).
% 181.68/124.51 thf(148,axiom,((! [A:code_integer]: ((minus_minus @ code_integer @ A @ (zero_zero @ code_integer)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1276_minus__integer__code_I1_J)).
% 181.68/124.51 thf(1433,plain,((! [A:code_integer]: ((minus_minus @ code_integer @ A @ (zero_zero @ code_integer)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
% 181.68/124.51 thf(566,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ TB),B:assn,C:(heap_Time_Heap @ TA),D:(TA > assn),E:(TB > (heap_Time_Heap @ TA))]: (((A = (none @ TB)) => (hoare_hoare_triple @ TA @ B @ C @ D)) => ((! [F:TB]: ((A = (some @ TB @ F)) => (hoare_hoare_triple @ TA @ B @ (E @ F) @ D))) => (hoare_hoare_triple @ TA @ B @ (case_option @ (heap_Time_Heap @ TA) @ TB @ C @ E @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5664_case__option__rule)).
% 181.68/124.51 thf(2750,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ TB),B:assn,C:(heap_Time_Heap @ TA),D:(TA > assn),E:(TB > (heap_Time_Heap @ TA))]: (((A = (none @ TB)) => (hoare_hoare_triple @ TA @ B @ C @ (D))) => ((! [F:TB]: ((A = (some @ TB @ F)) => (hoare_hoare_triple @ TA @ B @ (E @ F) @ (D)))) => (hoare_hoare_triple @ TA @ B @ (case_option @ (heap_Time_Heap @ TA) @ TB @ C @ (E) @ A) @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[566])).
% 181.68/124.51 thf(958,axiom,((boolea8198339166811842893lgebra @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Boolean__Algebras_Oboolean__algebra_403)).
% 181.68/124.51 thf(3870,plain,((boolea8198339166811842893lgebra @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[958])).
% 181.68/124.51 thf(794,axiom,((! [TA: $tType]: (! [A:TA]: ((heap_Time_execute @ TA @ (heap_Time_return @ TA @ A)) = (comp @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ A @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_execute__return)).
% 181.68/124.51 thf(3406,plain,((! [TA: $tType]: (! [A:TA]: ((heap_Time_execute @ TA @ (heap_Time_return @ TA @ A)) = (comp @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ A @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[794])).
% 181.68/124.51 thf(1028,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (option @ TC))]: ((map_comp @ TC @ TB @ TA @ (^ [B:TC]: (none @ TB)) @ A) = (^ [B:TA]: (none @ TB)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_map__comp__empty_I2_J)).
% 181.68/124.51 thf(4033,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (option @ TC))]: ((map_comp @ TC @ TB @ TA @ (^ [B:TC]: (none @ TB)) @ A) = (^ [B:TA]: (none @ TB)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028])).
% 181.68/124.51 thf(716,axiom,((! [TA: $tType,TB: $tType]: (cl_HOL_Oequal @ (product_prod @ TB @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___HOL_Oequal_400)).
% 181.68/124.51 thf(3189,plain,((! [TA: $tType,TB: $tType]: (cl_HOL_Oequal @ (product_prod @ TB @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[716])).
% 181.68/124.51 thf(461,axiom,((cancel2418104881723323429up_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ocancel__ab__semigroup__add_531)).
% 181.68/124.51 thf(2424,plain,((cancel2418104881723323429up_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[461])).
% 181.68/124.51 thf(639,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: ((comp @ TA @ TB @ TC) = (^ [A:(TA > TB),B:(TC > TA),C:TC]: (A @ (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_comp__def)).
% 181.68/124.51 thf(2979,plain,((! [TA: $tType,TB: $tType,TC: $tType]: ((comp @ TA @ TB @ TC) = (^ [A:(TA > TB),B:(TC > TA),C:TC]: (A @ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[639])).
% 181.68/124.51 thf(582,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TB > $o)),B:(TA > (TB > $o))]: ((ord_less_eq @ (TA > (TB > $o)) @ A @ B) => (ord_less_eq @ (set @ (product_prod @ TA @ TB)) @ (collect @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ A)) @ (collect @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_Collect__case__prod__mono)).
% 181.68/124.51 thf(2799,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TB > $o)),B:(TA > (TB > $o))]: ((ord_less_eq @ (TA > (TB > $o)) @ (A) @ (B)) => (ord_less_eq @ (set @ (product_prod @ TA @ TB)) @ (collect @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ A)) @ (collect @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[582])).
% 181.68/124.51 thf(1031,axiom,((comple9053668089753744459l_ccpo @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Complete__Partial__Order_Occpo_404)).
% 181.68/124.51 thf(4038,plain,((comple9053668089753744459l_ccpo @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031])).
% 181.68/124.51 thf(585,axiom,((! [TA: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(option @ TA)]: ((partial_flat_ord @ (option @ TA) @ (none @ TA) @ A @ B) => ((partial_flat_ord @ (option @ TA) @ (none @ TA) @ B @ C) => (partial_flat_ord @ (option @ TA) @ (none @ TA) @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5973_option_Oleq__trans)).
% 181.68/124.51 thf(2804,plain,((! [TA: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(option @ TA)]: ((partial_flat_ord @ (option @ TA) @ (none @ TA) @ A @ B) => ((partial_flat_ord @ (option @ TA) @ (none @ TA) @ B @ C) => (partial_flat_ord @ (option @ TA) @ (none @ TA) @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[585])).
% 181.68/124.51 thf(634,axiom,((! [TA: $tType,TB: $tType]: ((complete_Sup @ TA) => (complete_Sup @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_OSup)).
% 181.68/124.51 thf(2965,plain,((! [TA: $tType,TB: $tType]: ((complete_Sup @ TA) => (complete_Sup @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[634])).
% 181.68/124.51 thf(844,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (TA > $o)),B:TB,C:TA]: ((A @ B @ C) => (product_case_prod @ TB @ TA @ $o @ A @ (product_Pair @ TB @ TA @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1122_case__prodI)).
% 181.68/124.51 thf(3588,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (TA > $o)),B:TB,C:TA]: ((A @ B @ C) => (product_case_prod @ TB @ TA @ $o @ (A) @ (product_Pair @ TB @ TA @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[844])).
% 181.68/124.51 thf(32,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/sandbox/benchmark/theBenchmark.p',fact_996_Suc__diff__eq__diff__pred)).
% 181.68/124.51 thf(1104,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)],[32])).
% 181.68/124.51 thf(78,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ (one_one @ nat) @ A) => ((suc @ (minus_minus @ nat @ B @ A)) = (minus_minus @ nat @ B @ (minus_minus @ nat @ A @ (one_one @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_Suc__diff)).
% 181.68/124.51 thf(1242,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ (one_one @ nat) @ A) => ((suc @ (minus_minus @ nat @ B @ A)) = (minus_minus @ nat @ B @ (minus_minus @ nat @ A @ (one_one @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
% 181.68/124.51 thf(835,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA]: ((! [C:TA]: ((A @ B) => ((A @ C) => (C = B)))) => (((eps_Opt @ TA @ A) = (some @ TA @ B)) = (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Eps__Opt__eq__Some)).
% 181.68/124.51 thf(3559,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA]: ((! [C:TA]: ((A @ B) => ((A @ C) => (C = B)))) => (((eps_Opt @ TA @ (A)) = (some @ TA @ B)) = (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[835])).
% 181.68/124.51 thf(726,axiom,((typerep2 @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Typerep_Otyperep_55)).
% 181.68/124.51 thf(3211,plain,((typerep2 @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[726])).
% 181.68/124.51 thf(451,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/sandbox/benchmark/theBenchmark.p',fact_556_Nat_Odiff__diff__right)).
% 181.68/124.51 thf(2392,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)],[451])).
% 181.68/124.51 thf(174,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:(TA > $o)]: ((! [C:TA]: ((A @ C) = (B @ C))) => ((collect @ TA @ A) = (collect @ TA @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__cong)).
% 181.68/124.51 thf(1521,plain,((! [TA: $tType]: (! [A:(TA > $o),B:(TA > $o)]: ((! [C:TA]: ((A @ C) = (B @ C))) => ((collect @ TA @ (A)) = (collect @ TA @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
% 181.68/124.51 thf(516,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/sandbox/benchmark/theBenchmark.p',fact_468_add__le__mono1)).
% 181.68/124.51 thf(2586,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)],[516])).
% 181.68/124.51 thf(640,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ (heap_Time_tap @ TA @ A) @ B @ C @ D @ E) => (~ ((C = B) => ((D = (A @ B)) => (E != (one_one @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_effect__tapE)).
% 181.68/124.51 thf(2982,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ (heap_Time_tap @ TA @ (A)) @ B @ C @ D @ E) => (~ ((C = B) => ((D = (A @ B)) => (~ (E = (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[640])).
% 181.68/124.51 thf(605,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF))))) > $o),B:(product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF)))))]: ((! [C:TA,D:TB,E:TC,F:TD,G:TE,H:TF]: (A @ (product_Pair @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF)))) @ C @ (product_Pair @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF))) @ D @ (product_Pair @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF)) @ E @ (product_Pair @ TD @ (product_prod @ TE @ TF) @ F @ (product_Pair @ TE @ TF @ G @ H))))))) => (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_prod__induct6)).
% 181.68/124.51 thf(2884,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF))))) > $o),B:(product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF)))))]: ((! [C:TA,D:TB,E:TC,F:TD,G:TE,H:TF]: (A @ (product_Pair @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF)))) @ C @ (product_Pair @ TB @ (product_prod @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF))) @ D @ (product_Pair @ TC @ (product_prod @ TD @ (product_prod @ TE @ TF)) @ E @ (product_Pair @ TD @ (product_prod @ TE @ TF) @ F @ (product_Pair @ TE @ TF @ G @ H))))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[605])).
% 181.68/124.51 thf(826,axiom,((! [TA: $tType,TB: $tType]: (((finite_finite @ TB) & (finite_finite @ TA)) => (finite_finite @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite)).
% 181.68/124.51 thf(3510,plain,((! [TA: $tType,TB: $tType]: (((finite_finite @ TB) & (finite_finite @ TA)) => (finite_finite @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[826])).
% 181.68/124.51 thf(188,axiom,((euclid3128863361964157862miring @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Euclidean__Division_Ounique__euclidean__semiring_515)).
% 181.68/124.51 thf(1564,plain,((euclid3128863361964157862miring @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
% 181.68/124.51 thf(629,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: ~ (time_fails @ nat @ (array_len @ TA @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4126_fails__array__len)).
% 181.68/124.51 thf(2954,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: ~ (time_fails @ nat @ (array_len @ TA @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[629])).
% 181.68/124.51 thf(327,axiom,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: (((minus_minus @ (set @ TA) @ A @ B) != A) = ((inf_inf @ (set @ TA) @ A @ B) != (bot_bot @ (set @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3053_disjoint__alt__simp2)).
% 181.68/124.51 thf(2011,plain,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: ((~ ((minus_minus @ (set @ TA) @ A @ B) = A)) = (~ ((inf_inf @ (set @ TA) @ A @ B) = (bot_bot @ (set @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])).
% 181.68/124.51 thf(951,axiom,((semiri3467727345109120633visors @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors_100)).
% 181.68/124.51 thf(3857,plain,((semiri3467727345109120633visors @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[951])).
% 181.68/124.51 thf(823,axiom,(((one_one @ nat) = (one_one @ nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_one__natural_Orsp)).
% 181.68/124.51 thf(3503,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[823])).
% 181.68/124.51 thf(478,axiom,((! [TA: $tType]: (! [A:TA,B:(TA > $o)]: ((member @ TA @ A @ (collect @ TA @ B)) = (B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_mem__Collect__eq)).
% 181.68/124.51 thf(2473,plain,((! [TA: $tType]: (! [A:TA,B:(TA > $o)]: ((member @ TA @ A @ (collect @ TA @ (B))) = (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])).
% 181.68/124.51 thf(836,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:nat,D:(array @ TA),E:nat]: ((A = B) => ((C = (array_length @ TA @ B @ D)) => ((E = (one_one @ nat)) => (heap_Time_effect @ nat @ (array_len @ TA @ D) @ B @ A @ C @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4149_effect__lengthI)).
% 181.68/124.51 thf(3567,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:nat,D:(array @ TA),E:nat]: ((A = B) => ((C = (array_length @ TA @ B @ D)) => ((E = (one_one @ nat)) => (heap_Time_effect @ nat @ (array_len @ TA @ D) @ B @ A @ C @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[836])).
% 181.68/124.51 thf(511,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA]: ~ (ord_less_eq @ (option @ TA) @ (some @ TA @ A) @ (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_less__eq__option__Some__None)).
% 181.68/124.51 thf(2574,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA]: ~ (ord_less_eq @ (option @ TA) @ (some @ TA @ A) @ (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[511])).
% 181.68/124.51 thf(101,axiom,(((one_one @ nat) = (suc @ (zero_zero @ nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_One__nat__def)).
% 181.68/124.51 thf(1306,plain,(((one_one @ nat) = (suc @ (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
% 181.68/124.51 thf(43,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/sandbox/benchmark/theBenchmark.p',fact_599_mult_Oassoc)).
% 181.68/124.51 thf(1153,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)],[43])).
% 181.68/124.51 thf(1011,axiom,((! [TA: $tType]: ((heap_Time_effect @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_execute @ TA @ A @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_effect__def)).
% 181.68/124.51 thf(3995,plain,((! [TA: $tType]: ((heap_Time_effect @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_execute @ TA @ A @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011])).
% 181.68/124.51 thf(295,axiom,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_add__less__le__mono)).
% 181.68/124.51 thf(1915,plain,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less @ TA @ A @ B) => ((ord_less_eq @ TA @ C @ D) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])).
% 181.68/124.51 thf(534,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > $o),B:(TC > (TA > TB)),C:(product_prod @ TC @ TA)]: ((A @ (product_case_prod @ TC @ TA @ TB @ B @ C)) => (~ (! [D:TC,E:TA]: ((C = (product_Pair @ TC @ TA @ D @ E)) => (~ (A @ (B @ D @ E)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1075_case__prodE2)).
% 181.68/124.51 thf(2641,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > $o),B:(TC > (TA > TB)),C:(product_prod @ TC @ TA)]: ((A @ (product_case_prod @ TC @ TA @ TB @ (B) @ C)) => (~ (! [D:TC,E:TA]: ((C = (product_Pair @ TC @ TA @ D @ E)) => (~ (A @ (B @ D @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[534])).
% 181.68/124.51 thf(919,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:(TA > (option @ TB))]: (((map_add @ TA @ TB @ A @ B) = (^ [C:TA]: (none @ TB))) = ((A = (^ [C:TA]: (none @ TB))) & (B = (^ [C:TA]: (none @ TB)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3394_map__add__eq__empty__iff)).
% 181.68/124.51 thf(3795,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:(TA > (option @ TB))]: (((map_add @ TA @ TB @ A @ B) = (^ [C:TA]: (none @ TB))) = (((A) = (^ [C:TA]: (none @ TB))) & ((B) = (^ [C:TA]: (none @ TB)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[919])).
% 181.68/124.51 thf(47,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ C) @ D)) => (? [E:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ D) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4984_relpow__Suc__D2)).
% 181.68/124.51 thf(1163,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ C) @ D)) => (? [E:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ D) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
% 181.68/124.51 thf(19,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (modulo_modulo @ nat @ B @ C)) = (((C = (zero_zero @ nat)) => (A @ B)) & ((C != (zero_zero @ nat)) => (! [D:nat,E:nat]: ((ord_less @ nat @ E @ C) => ((B = (plus_plus @ nat @ (times_times @ nat @ C @ D) @ E)) => (A @ E))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_897_split__mod)).
% 181.68/124.51 thf(1074,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (modulo_modulo @ nat @ B @ C)) = (((C = (zero_zero @ nat)) => (A @ B)) & ((~ (C = (zero_zero @ nat))) => (! [D:nat,E:nat]: ((ord_less @ nat @ E @ C) => ((B = (plus_plus @ nat @ (times_times @ nat @ C @ D) @ E)) => (A @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 181.68/124.51 thf(203,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: ((ord_less @ (option @ TA) @ (none @ TA) @ A) => (? [B:TA]: (A = (some @ TA @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_less__option__None__is__Some)).
% 181.68/124.51 thf(1604,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: ((ord_less @ (option @ TA) @ (none @ TA) @ A) => (? [B:TA]: (A = (some @ TA @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
% 181.68/124.51 thf(974,axiom,((zero @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_151)).
% 181.68/124.51 thf(3899,plain,((zero @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[974])).
% 181.68/124.51 thf(103,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA)),E:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ E) @ D) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ C) @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4983_relpow__Suc__I)).
% 181.68/124.51 thf(1311,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA)),E:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ E) @ D) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ C) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
% 181.68/124.51 thf(419,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA)]: (((none @ TB) = (map_option @ TA @ TB @ A @ B)) = (B = (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_None__eq__map__option__iff)).
% 181.68/124.51 thf(2307,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA)]: (((none @ TB) = (map_option @ TA @ TB @ (A) @ B)) = (B = (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])).
% 181.68/124.51 thf(537,axiom,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounded_lattice_top @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__top_63)).
% 181.68/124.51 thf(2660,plain,((! [TA: $tType,TB: $tType]: ((bounded_lattice @ TA) => (bounded_lattice_top @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[537])).
% 181.68/124.51 thf(253,axiom,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((minus_minus @ TA @ (minus_minus @ TA @ A @ B) @ C) = (minus_minus @ TA @ (minus_minus @ TA @ A @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_cancel__ab__semigroup__add__class_Odiff__right__commute)).
% 181.68/124.51 thf(1768,plain,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((minus_minus @ TA @ (minus_minus @ TA @ A @ B) @ C) = (minus_minus @ TA @ (minus_minus @ TA @ A @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])).
% 181.68/124.51 thf(448,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (TA > $o))]: ((? [B:TB,C:TA]: (A @ B @ C)) => ((! [B:TA,C:TA]: ((? [D:TB]: (A @ D @ B)) => ((? [D:TB]: (A @ D @ C)) => (B = C)))) => (A @ (fChoice @ TB @ (^ [B:TB]: ? [C:TA]: (A @ B @ C))) @ (the @ TA @ (^ [B:TA]: ? [C:TB]: (A @ C @ B))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4662_some__theI)).
% 181.68/124.51 thf(2382,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (TA > $o))]: ((? [B:TB,C:TA]: (A @ B @ C)) => ((! [B:TA,C:TA]: ((? [D:TB]: (A @ D @ B)) => ((? [D:TB]: (A @ D @ C)) => (B = C)))) => (A @ (fChoice @ TB @ (^ [B:TB]: ? [C:TA]: (A @ B @ C))) @ (the @ TA @ (^ [B:TA]: ? [C:TB]: (A @ C @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[448])).
% 181.68/124.51 thf(344,axiom,((! [TA: $tType]: (! [A:(option @ TA)]: ((map_option @ TA @ TA @ (^ [B:TA]: (B)) @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_option_Omap__ident)).
% 181.68/124.51 thf(2061,plain,((! [TA: $tType]: (! [A:(option @ TA)]: ((map_option @ TA @ TA @ (^ [B:TA]: (B)) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])).
% 181.68/124.51 thf(832,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(array @ TA)]: ((heap_Time_bind @ (array @ TA) @ (array @ TA) @ (array_upd @ TA @ A @ B @ C) @ (^ [D:(array @ TA)]: (heap_Time_ureturn @ (array @ TA) @ C))) = (array_upd @ TA @ A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4107_upd__ureturn)).
% 181.68/124.51 thf(3550,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(array @ TA)]: ((heap_Time_bind @ (array @ TA) @ (array @ TA) @ (array_upd @ TA @ A @ B @ C) @ (^ [D:(array @ TA)]: (heap_Time_ureturn @ (array @ TA) @ C))) = (array_upd @ TA @ A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[832])).
% 181.68/124.51 thf(572,axiom,((! [A:nat,B:nat]: (ord_less_eq @ nat @ A @ (plus_plus @ nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_le__add2)).
% 181.68/124.51 thf(2773,plain,((! [A:nat,B:nat]: (ord_less_eq @ nat @ A @ (plus_plus @ nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[572])).
% 181.68/124.51 thf(323,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((~ (ord_less @ TA @ (zero_zero @ TA) @ A)) = (A = (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_not__gr__zero)).
% 181.68/124.51 thf(2000,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)],[323])).
% 181.68/124.51 thf(541,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_len @ TA) = (^ [A:(array @ TA)]: (heap_Time_tap @ nat @ (^ [B:(heap_ext @ product_unit)]: (array_length @ TA @ B @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4145_len__def)).
% 181.68/124.51 thf(2673,plain,((! [TA: $tType]: ((heap @ TA) => ((array_len @ TA) = (^ [A:(array @ TA)]: (heap_Time_tap @ nat @ (^ [B:(heap_ext @ product_unit)]: (array_length @ TA @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[541])).
% 181.68/124.51 thf(517,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (TA > (heap_Time_Heap @ TB))),B:(TC > TC),C:((TA > (heap_Time_Heap @ TB)) > TC),D:TC,E:(TA > ((heap_ext @ product_unit) > ((heap_ext @ product_unit) > (TB > (nat > $o))))),F:TA,G:(heap_ext @ product_unit),H:(heap_ext @ product_unit),I:TB,J:nat]: ((! [K:TA]: (comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TB) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TB) @ (^ [L:(TA > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ L)) @ K)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (^ [K:(TA > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ K))))))) => ((! [K:(TA > (heap_Time_Heap @ TB))]: ((A @ (C @ K)) = K)) => ((! [K:TC,L:TA,M:(heap_ext @ product_unit),N:(heap_ext @ product_unit),O:TB,P:nat]: ((! [Q:TA,R:(heap_ext @ product_unit),S:(heap_ext @ product_unit),T:TB,U:nat]: ((heap_Time_effect @ TB @ (A @ K @ Q) @ R @ S @ T @ U) => (E @ Q @ R @ S @ T @ U))) => ((heap_Time_effect @ TB @ (A @ (B @ K) @ L) @ M @ N @ O @ P) => (E @ L @ M @ N @ O @ P)))) => ((heap_Time_effect @ TB @ (A @ D @ F) @ G @ H @ I @ J) => (E @ F @ G @ H @ I @ J))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5987_fixp__induct__heap)).
% 181.68/124.51 thf(2589,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (TA > (heap_Time_Heap @ TB))),B:(TC > TC),C:((TA > (heap_Time_Heap @ TB)) > TC),D:TC,E:(TA > ((heap_ext @ product_unit) > ((heap_ext @ product_unit) > (TB > (nat > $o))))),F:TA,G:(heap_ext @ product_unit),H:(heap_ext @ product_unit),I:TB,J:nat]: ((! [K:TA]: (comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TB) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TB) @ (^ [L:(TA > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ L)) @ K)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (^ [K:(TA > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ K))))))) => ((! [K:(TA > (heap_Time_Heap @ TB))]: ((A @ (C @ K)) = (K))) => ((! [K:TC,L:TA,M:(heap_ext @ product_unit),N:(heap_ext @ product_unit),O:TB,P:nat]: ((! [Q:TA,R:(heap_ext @ product_unit),S:(heap_ext @ product_unit),T:TB,U:nat]: ((heap_Time_effect @ TB @ (A @ K @ Q) @ R @ S @ T @ U) => (E @ Q @ R @ S @ T @ U))) => ((heap_Time_effect @ TB @ (A @ (B @ K) @ L) @ M @ N @ O @ P) => (E @ L @ M @ N @ O @ P)))) => ((heap_Time_effect @ TB @ (A @ D @ F) @ G @ H @ I @ J) => (E @ F @ G @ H @ I @ J))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[517])).
% 181.68/124.52 thf(552,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(TB > (heap_Time_Heap @ TA)),C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat]: ((heap_Time_effect @ TA @ (heap_Time_bind @ TB @ TA @ A @ B) @ C @ D @ E @ F) => (~ (! [G:(heap_ext @ product_unit),H:TB,I:nat]: ((heap_Time_effect @ TB @ A @ C @ G @ H @ I) => (! [J:nat]: ((heap_Time_effect @ TA @ (B @ H) @ G @ D @ E @ J) => (F != (plus_plus @ nat @ I @ J))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_effect__bindE)).
% 181.68/124.52 thf(2705,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(TB > (heap_Time_Heap @ TA)),C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat]: ((heap_Time_effect @ TA @ (heap_Time_bind @ TB @ TA @ A @ (B)) @ C @ D @ E @ F) => (~ (! [G:(heap_ext @ product_unit),H:TB,I:nat]: ((heap_Time_effect @ TB @ A @ C @ G @ H @ I) => (! [J:nat]: ((heap_Time_effect @ TA @ (B @ H) @ G @ D @ E @ J) => (~ (F = (plus_plus @ nat @ I @ J)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[552])).
% 181.68/124.52 thf(406,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TC > (option @ TB))),B:(TA > TA),C:((TC > (option @ TB)) > TA),D:TA,E:((TC > (option @ TB)) > $o)]: ((! [F:TC]: (comple7038119648293358887notone @ (TC > (option @ TB)) @ (option @ TB) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TB) @ (none @ TB)) @ (^ [G:(TC > (option @ TB))]: (A @ (B @ (C @ G)) @ F)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TC > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (^ [F:(TC > (option @ TB))]: (A @ (B @ (C @ F))))))) => ((! [F:(TC > (option @ TB))]: ((A @ (C @ F)) = F)) => ((comple1908693960933563346ssible @ (TC > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ E) => ((E @ (^ [F:TC]: (none @ TB))) => ((! [F:TA]: ((E @ (A @ F)) => (E @ (A @ (B @ F))))) => (E @ (A @ D))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5979_option_Ofixp__induct__uc)).
% 181.68/124.52 thf(2249,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TC > (option @ TB))),B:(TA > TA),C:((TC > (option @ TB)) > TA),D:TA,E:((TC > (option @ TB)) > $o)]: ((! [F:TC]: (comple7038119648293358887notone @ (TC > (option @ TB)) @ (option @ TB) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TB) @ (none @ TB)) @ (^ [G:(TC > (option @ TB))]: (A @ (B @ (C @ G)) @ F)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TC > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (^ [F:(TC > (option @ TB))]: (A @ (B @ (C @ F))))))) => ((! [F:(TC > (option @ TB))]: ((A @ (C @ F)) = (F))) => ((comple1908693960933563346ssible @ (TC > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (E)) => ((E @ (^ [F:TC]: (none @ TB))) => ((! [F:TA]: ((E @ (A @ F)) => (E @ (A @ (B @ F))))) => (E @ (A @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])).
% 181.68/124.52 thf(6,axiom,((ordere6658533253407199908up_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Oordered__ab__semigroup__add_449)).
% 181.68/124.52 thf(1042,plain,((ordere6658533253407199908up_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 181.68/124.52 thf(35,axiom,(((plus_plus @ nat @ (one_one @ nat)) = suc)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_plus__1__eq__Suc)).
% 181.68/124.52 thf(1123,plain,(((plus_plus @ nat @ (one_one @ nat)) = (suc))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 181.68/124.52 thf(166,axiom,((ordere580206878836729694up_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oordered__cancel__ab__semigroup__add_518)).
% 181.68/124.52 thf(1502,plain,((ordere580206878836729694up_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
% 181.68/124.52 thf(222,axiom,((! [A:(heap_ext @ product_unit)]: (in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ (bot_bot @ (set @ nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5684_in__range__empty)).
% 181.68/124.52 thf(1666,plain,((! [A:(heap_ext @ product_unit)]: (in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ (bot_bot @ (set @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
% 181.68/124.52 thf(849,axiom,((! [TA: $tType]: (! [A:nat,B:nat,C:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((heap_Time_timeFrame @ TA @ A @ (heap_Time_timeFrame @ TA @ B @ C)) = (heap_Time_timeFrame @ TA @ (plus_plus @ nat @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_timeFrame__assoc)).
% 181.68/124.52 thf(3610,plain,((! [TA: $tType]: (! [A:nat,B:nat,C:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((heap_Time_timeFrame @ TA @ A @ (heap_Time_timeFrame @ TA @ B @ C)) = (heap_Time_timeFrame @ TA @ (plus_plus @ nat @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[849])).
% 181.68/124.52 thf(931,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: (refine_Imp_refines @ TA @ A @ (heap_Time_Heap2 @ TA @ (^ [B:(heap_ext @ product_unit)]: (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2863_refines__empty)).
% 181.68/124.52 thf(3816,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: (refine_Imp_refines @ TA @ A @ (heap_Time_Heap2 @ TA @ (^ [B:(heap_ext @ product_unit)]: (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[931])).
% 181.68/124.52 thf(743,axiom,((cl_HOL_Oequal @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___HOL_Oequal_286)).
% 181.68/124.52 thf(3261,plain,((cl_HOL_Oequal @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[743])).
% 181.68/124.52 thf(71,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(TA > TA),B:(ref @ TA),C:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (ref_change @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_success__changeI)).
% 181.68/124.52 thf(1223,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(TA > TA),B:(ref @ TA),C:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (ref_change @ TA @ (A) @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
% 181.68/124.52 thf(937,axiom,((! [TA: $tType]: (! [A:TA]: ((the_default @ TA @ A @ (none @ TA)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_the__default_Osimps_I2_J)).
% 181.68/124.52 thf(3827,plain,((! [TA: $tType]: (! [A:TA]: ((the_default @ TA @ A @ (none @ TA)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[937])).
% 181.68/124.52 thf(463,axiom,((! [TA: $tType]: ((typerep2 @ TA) => (quickc3360725361186068524ustive @ (ref @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oref___Quickcheck__Exhaustive_Ofull__exhaustive_287)).
% 181.68/124.52 thf(2428,plain,((! [TA: $tType]: ((typerep2 @ TA) => (quickc3360725361186068524ustive @ (ref @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[463])).
% 181.68/124.52 thf(886,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA,C:TB,D:TA]: (((product_Pair @ TB @ TA @ A @ B) = (product_Pair @ TB @ TA @ C @ D)) = ((A = C) & (B = D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_prod_Oinject)).
% 181.68/124.52 thf(3711,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA,C:TB,D:TA]: (((product_Pair @ TB @ TA @ A @ B) = (product_Pair @ TB @ TA @ C @ D)) = ((A = C) & (B = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[886])).
% 181.68/124.52 thf(117,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/sandbox/benchmark/theBenchmark.p',fact_983_nat__induct__non__zero)).
% 181.68/124.52 thf(1343,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)],[117])).
% 181.68/124.52 thf(505,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (heap_Time_Heap @ TB))]: (comple1908693960933563346ssible @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (^ [B:(TA > (heap_Time_Heap @ TB))]: ! [C:TA]: (refine_Imp_refines @ TB @ (A @ C) @ (B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5988_refines__adm)).
% 181.68/124.52 thf(2560,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (heap_Time_Heap @ TB))]: (comple1908693960933563346ssible @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (^ [B:(TA > (heap_Time_Heap @ TB))]: ! [C:TA]: (refine_Imp_refines @ TB @ (A @ C) @ (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])).
% 181.68/124.52 thf(1006,axiom,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (heap_ext @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oheap_Oheap__ext___Quickcheck__Random_Orandom_424)).
% 181.68/124.52 thf(3972,plain,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (heap_ext @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006])).
% 181.68/124.52 thf(1009,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:TB,D:(heap_ext @ product_unit),E:nat,F:(TB > (heap_Time_Heap @ TA))]: (((heap_Time_execute @ TB @ A @ B) = (some @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))) => ((heap_Time_execute @ TA @ (heap_Time_bind @ TB @ TA @ A @ F) @ B) = (heap_Time_timeFrame @ TA @ E @ (heap_Time_execute @ TA @ (F @ C) @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_execute__bind_I1_J)).
% 181.68/124.52 thf(3989,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:TB,D:(heap_ext @ product_unit),E:nat,F:(TB > (heap_Time_Heap @ TA))]: (((heap_Time_execute @ TB @ A @ B) = (some @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))) => ((heap_Time_execute @ TA @ (heap_Time_bind @ TB @ TA @ A @ (F)) @ B) = (heap_Time_timeFrame @ TA @ E @ (heap_Time_execute @ TA @ (F @ C) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009])).
% 181.68/124.52 thf(737,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA]: ((the @ (product_prod @ TB @ TA) @ (product_case_prod @ TB @ TA @ $o @ (^ [C:TB,D:TA]: ((A = C) & (B = D))))) = (product_Pair @ TB @ TA @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3215_The__split__eq)).
% 181.68/124.52 thf(3239,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA]: ((the @ (product_prod @ TB @ TA) @ (product_case_prod @ TB @ TA @ $o @ (^ [C:TB,D:TA]: ((A = C) & (B = D))))) = (product_Pair @ TB @ TA @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[737])).
% 181.68/124.52 thf(670,axiom,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ $o @ (product_prod @ TB @ (set @ TA)))]: ~ (! [B:$o,C:TB,D:(set @ TA)]: (A != (product_Pair @ $o @ (product_prod @ TB @ (set @ TA)) @ B @ (product_Pair @ TB @ (set @ TA) @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5632_pure__assn__raw_Ocases)).
% 181.68/124.52 thf(3069,plain,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ $o @ (product_prod @ TB @ (set @ TA)))]: ~ (! [B:$o,C:TB,D:(set @ TA)]: ~ (A = (product_Pair @ $o @ (product_prod @ TB @ (set @ TA)) @ B @ (product_Pair @ TB @ (set @ TA) @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[670])).
% 181.68/124.52 thf(735,axiom,((heap_Time_wait = (^ [A:nat]: (heap_Time_Heap2 @ product_unit @ (^ [B:(heap_ext @ product_unit)]: (some @ (product_prod @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat) @ product_Unity @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3074_wait__def)).
% 181.68/124.52 thf(3233,plain,(((heap_Time_wait) = (^ [A:nat]: (heap_Time_Heap2 @ product_unit @ (^ [B:(heap_ext @ product_unit)]: (some @ (product_prod @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat) @ product_Unity @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[735])).
% 181.68/124.52 thf(964,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((! [C:TA,D:(product_prod @ (heap_ext @ product_unit) @ nat)]: ((heap_Time_execute @ TA @ A @ B) != (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ D)))) => ((heap_Time_execute @ TA @ A @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Heap__cases)).
% 181.68/124.52 thf(3884,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((! [C:TA,D:(product_prod @ (heap_ext @ product_unit) @ nat)]: ~ ((heap_Time_execute @ TA @ A @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ D)))) => ((heap_Time_execute @ TA @ A @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[964])).
% 181.68/124.52 thf(622,axiom,((! [TA: $tType]: (! [A:nat,B:TA,C:(heap_ext @ product_unit),D:nat]: ((heap_Time_timeFrame @ TA @ A @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ B @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ D)))) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ B @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ (plus_plus @ nat @ A @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_timeFrame_Osimps_I1_J)).
% 181.68/124.52 thf(2937,plain,((! [TA: $tType]: (! [A:nat,B:TA,C:(heap_ext @ product_unit),D:nat]: ((heap_Time_timeFrame @ TA @ A @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ B @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ D)))) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ B @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ (plus_plus @ nat @ A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[622])).
% 181.68/124.52 thf(705,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TA > (option @ TB))]: ((bind @ TA @ TB @ (some @ TA @ A) @ B) = (B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_bind_Obind__lunit)).
% 181.68/124.52 thf(3154,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TA > (option @ TB))]: ((bind @ TA @ TB @ (some @ TA @ A) @ (B)) = (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[705])).
% 181.68/124.52 thf(698,axiom,((! [TA: $tType]: ((finite_finite @ TA) => (countable @ (set @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Countable_Ocountable_255)).
% 181.68/124.52 thf(3134,plain,((! [TA: $tType]: ((finite_finite @ TA) => (countable @ (set @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[698])).
% 181.68/124.52 thf(368,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((intrel @ (product_Pair @ nat @ nat @ A @ B) @ (product_Pair @ nat @ nat @ C @ D)) = ((plus_plus @ nat @ A @ D) = (plus_plus @ nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2680_intrel__iff)).
% 181.68/124.52 thf(2132,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((intrel @ (product_Pair @ nat @ nat @ A @ B) @ (product_Pair @ nat @ nat @ C @ D)) = ((plus_plus @ nat @ A @ D) = (plus_plus @ nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])).
% 181.68/124.52 thf(459,axiom,((! [A:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:(product_prod @ (heap_ext @ product_unit) @ (set @ nat)),D:$o]: (((times_assn_raw @ A @ B @ C) = D) => (~ (! [E:(heap_ext @ product_unit),F:(set @ nat)]: ((C = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ E @ F)) => (D = (~ (? [G:(set @ nat),H:(set @ nat)]: ((F = (sup_sup @ (set @ nat) @ G @ H)) & ((inf_inf @ (set @ nat) @ G @ H) = (bot_bot @ (set @ nat))) & (A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ E @ G)) & (B @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ E @ H)))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5651_times__assn__raw_Oelims_I1_J)).
% 181.68/124.52 thf(2414,plain,((! [A:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:(product_prod @ (heap_ext @ product_unit) @ (set @ nat)),D:$o]: (((times_assn_raw @ (A) @ (B) @ C) = D) => (~ (! [E:(heap_ext @ product_unit),F:(set @ nat)]: ((C = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ E @ F)) => (D = (~ (? [G:(set @ nat),H:(set @ nat)]: ((F = (sup_sup @ (set @ nat) @ G @ H)) & ((inf_inf @ (set @ nat) @ G @ H) = (bot_bot @ (set @ nat))) & (A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ E @ G)) & (B @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ E @ H)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[459])).
% 181.68/124.52 thf(740,axiom,((! [TA: $tType]: (comple9053668089753744459l_ccpo @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Partial__Order_Occpo_246)).
% 181.68/124.52 thf(3250,plain,((! [TA: $tType]: (comple9053668089753744459l_ccpo @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[740])).
% 181.68/124.52 thf(491,axiom,(((ord_less_eq @ nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus @ nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_nat__le__iff__add)).
% 181.68/124.52 thf(2528,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)],[491])).
% 181.68/124.52 thf(871,axiom,((! [TA: $tType]: (((!) @ (option @ TA)) = (^ [A:((option @ TA) > $o)]: ((A @ (none @ TA)) & ! [B:TA]: (A @ (some @ TA @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_split__option__all)).
% 181.68/124.52 thf(3664,plain,((! [TA: $tType]: (((!) @ (option @ TA)) = (^ [A:((option @ TA) > $o)]: ((A @ (none @ TA)) & ! [B:TA]: (A @ (some @ TA @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[871])).
% 181.68/124.52 thf(724,axiom,((! [TA: $tType]: ((semilattice_sup @ TA) => (semilattice_sup @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Lattices_Osemilattice__sup_318)).
% 181.68/124.52 thf(3207,plain,((! [TA: $tType]: ((semilattice_sup @ TA) => (semilattice_sup @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[724])).
% 181.68/124.52 thf(452,axiom,((semidom_modulo @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Osemidom__modulo_549)).
% 181.68/124.52 thf(2396,plain,((semidom_modulo @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[452])).
% 181.68/124.52 thf(877,axiom,((! [TA: $tType,TB: $tType]: (((countable @ TB) & (countable @ TA)) => (countable @ (product_prod @ TB @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Countable_Ocountable_397)).
% 181.68/124.52 thf(3682,plain,((! [TA: $tType,TB: $tType]: (((countable @ TB) & (countable @ TA)) => (countable @ (product_prod @ TB @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[877])).
% 181.68/124.52 thf(1023,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((heap_Time_execute @ TA @ (heap_Time_heap @ TA @ A)) = (comp @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_execute__heap)).
% 181.68/124.52 thf(4021,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((heap_Time_execute @ TA @ (heap_Time_heap @ TA @ A)) = (comp @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023])).
% 181.68/124.52 thf(910,axiom,((ordere8940638589300402666id_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_94)).
% 181.68/124.52 thf(3778,plain,((ordere8940638589300402666id_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[910])).
% 181.68/124.52 thf(328,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/sandbox/benchmark/theBenchmark.p',fact_652_Nat_Ole__diff__conv2)).
% 181.68/124.52 thf(2015,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)],[328])).
% 181.68/124.52 thf(967,axiom,((! [TA: $tType]: (is_none @ TA @ (none @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5559_is__none__code_I1_J)).
% 181.68/124.52 thf(3889,plain,((! [TA: $tType]: (is_none @ TA @ (none @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[967])).
% 181.68/124.52 thf(286,axiom,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: (((minus_minus @ (set @ TA) @ A @ B) = A) = ((inf_inf @ (set @ TA) @ A @ B) = (bot_bot @ (set @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3054_disjoint__alt__simp1)).
% 181.68/124.52 thf(1883,plain,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: (((minus_minus @ (set @ TA) @ A @ B) = A) = ((inf_inf @ (set @ TA) @ A @ B) = (bot_bot @ (set @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])).
% 181.68/124.52 thf(187,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/sandbox/benchmark/theBenchmark.p',fact_655_Nat_Ole__imp__diff__is__add)).
% 181.68/124.52 thf(1560,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)],[187])).
% 181.68/124.52 thf(753,axiom,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (plus_plus @ TA @ A @ B)) = (ord_less_eq @ TA @ (zero_zero @ TA) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_le__add__same__cancel1)).
% 181.68/124.52 thf(3282,plain,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ (plus_plus @ TA @ A @ B)) = (ord_less_eq @ TA @ (zero_zero @ TA) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[753])).
% 181.68/124.52 thf(465,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: ~ (ord_less @ (option @ TA) @ A @ (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_less__option__None)).
% 181.68/124.52 thf(2433,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: ~ (ord_less @ (option @ TA) @ A @ (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])).
% 181.68/124.52 thf(428,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA),B:TB,C:TA]: (((fun_upd @ TB @ TA @ A @ B @ C) = A) = ((A @ B) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2733_fun__upd__idem__iff)).
% 181.68/124.52 thf(2332,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA),B:TB,C:TA]: (((fun_upd @ TB @ TA @ A @ B @ C) = (A)) = ((A @ B) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])).
% 181.68/124.52 thf(385,axiom,((one @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oone_570)).
% 181.68/124.52 thf(2200,plain,((one @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])).
% 181.68/124.52 thf(426,axiom,((! [A:(product_prod @ (code_natural > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:(code_natural > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_natural,D:code_natural]: (A != (product_Pair @ (code_natural > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural) @ B @ (product_Pair @ code_natural @ code_natural @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4217_exhaustive__natural_H_Ocases)).
% 181.68/124.52 thf(2327,plain,((! [A:(product_prod @ (code_natural > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:(code_natural > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_natural,D:code_natural]: ~ (A = (product_Pair @ (code_natural > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural) @ (B) @ (product_Pair @ code_natural @ code_natural @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[426])).
% 181.68/124.52 thf(654,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(heap_ext @ product_unit)]: (heap_Time_success @ (array @ TA) @ (array_new @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_success__newI)).
% 181.68/124.52 thf(3028,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(heap_ext @ product_unit)]: (heap_Time_success @ (array @ TA) @ (array_new @ TA @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[654])).
% 181.68/124.52 thf(563,axiom,((! [TA: $tType]: ((heap @ TA) => (typerep2 @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Heap_Oheap___Typerep_Otyperep)).
% 181.68/124.52 thf(2741,plain,((! [TA: $tType]: ((heap @ TA) => (typerep2 @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[563])).
% 181.68/124.52 thf(872,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: ((comp @ TA @ TB @ TC) = (^ [A:(TA > TB),B:(TC > TA),C:TC]: (A @ (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_comp__apply)).
% 181.68/124.52 thf(3667,plain,((! [TA: $tType,TB: $tType,TC: $tType]: ((comp @ TA @ TB @ TC) = (^ [A:(TA > TB),B:(TC > TA),C:TC]: (A @ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[872])).
% 181.68/124.52 thf(656,axiom,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (set @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Typerep_Otyperep_48)).
% 181.68/124.52 thf(3033,plain,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (set @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[656])).
% 181.68/124.52 thf(748,axiom,((! [TA: $tType]: (partia7178651479351089652itions @ (option @ TA) @ (partial_flat_ord @ (option @ TA) @ (none @ TA)) @ (partial_flat_lub @ (option @ TA) @ (none @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5983_option_Opartial__function__definitions__axioms)).
% 181.68/124.52 thf(3271,plain,((! [TA: $tType]: (partia7178651479351089652itions @ (option @ TA) @ (partial_flat_ord @ (option @ TA) @ (none @ TA)) @ (partial_flat_lub @ (option @ TA) @ (none @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[748])).
% 181.68/124.52 thf(710,axiom,((! [TA: $tType]: (bounded_lattice_top @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__top_49)).
% 181.68/124.52 thf(3166,plain,((! [TA: $tType]: (bounded_lattice_top @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[710])).
% 181.68/124.52 thf(999,axiom,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA)]: ((combine_options @ TA @ A @ (none @ TA) @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_combine__options__simps_I1_J)).
% 181.68/124.52 thf(3958,plain,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA)]: ((combine_options @ TA @ (A) @ (none @ TA) @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[999])).
% 181.68/124.52 thf(717,axiom,((! [TA: $tType]: (uminus @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ouminus_260)).
% 181.68/124.52 thf(3191,plain,((! [TA: $tType]: (uminus @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[717])).
% 181.68/124.52 thf(303,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TA > TB)]: ((comp @ (list @ TB) @ (list @ TC) @ (list @ TA) @ (map @ TB @ TC @ A) @ (map @ TA @ TB @ B)) = (map @ TA @ TC @ (comp @ TB @ TC @ TA @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3480_map__comp__map)).
% 181.68/124.52 thf(1938,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TA > TB)]: ((comp @ (list @ TB) @ (list @ TC) @ (list @ TA) @ (map @ TB @ TC @ A) @ (map @ TA @ TB @ B)) = (map @ TA @ TC @ (comp @ TB @ TC @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])).
% 181.68/124.52 thf(601,axiom,((! [TA: $tType]: (cl_HOL_Oequal @ (list @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___HOL_Oequal_296)).
% 181.68/124.52 thf(2873,plain,((! [TA: $tType]: (cl_HOL_Oequal @ (list @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[601])).
% 181.68/124.52 thf(1,conjecture,(((heap_Time_execute @ (array @ a) @ (array_of_list @ a @ xs) @ h) != (none @ (product_prod @ (array @ a) @ (product_prod @ (heap_ext @ product_unit) @ nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 181.68/124.52 thf(2,negated_conjecture,((~ ((heap_Time_execute @ (array @ a) @ (array_of_list @ a @ xs) @ h) != (none @ (product_prod @ (array @ a) @ (product_prod @ (heap_ext @ product_unit) @ nat)))))),inference(neg_conjecture,[status(cth)],[1])).
% 181.68/124.52 thf(1032,plain,((~ (~ ((heap_Time_execute @ (array @ a) @ (array_of_list @ a @ xs) @ h) = (none @ (product_prod @ (array @ a) @ (product_prod @ (heap_ext @ product_unit) @ nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 181.68/124.52 thf(747,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/sandbox/benchmark/theBenchmark.p',fact_452_add__left__mono)).
% 181.68/124.52 thf(3269,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)],[747])).
% 181.68/124.52 thf(540,axiom,((! [TA: $tType]: (! [A:TA,B:TA]: ((the_default @ TA @ A @ (some @ TA @ B)) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_the__default_Osimps_I1_J)).
% 181.68/124.52 thf(2670,plain,((! [TA: $tType]: (! [A:TA,B:TA]: ((the_default @ TA @ A @ (some @ TA @ B)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[540])).
% 181.68/124.52 thf(927,axiom,((cancel_semigroup_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_108)).
% 181.68/124.52 thf(3810,plain,((cancel_semigroup_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[927])).
% 181.68/124.52 thf(679,axiom,((! [TA: $tType]: (partia7178651479351089652itions @ (heap_Time_Heap @ TA) @ (heap_Time_Heap_ord @ TA) @ (heap_Time_Heap_lub @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5515_heap__interpretation)).
% 181.68/124.52 thf(3090,plain,((! [TA: $tType]: (partia7178651479351089652itions @ (heap_Time_Heap @ TA) @ (heap_Time_Heap_ord @ TA) @ (heap_Time_Heap_lub @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[679])).
% 181.68/124.52 thf(508,axiom,((! [A:nat]: ((plus_plus @ nat @ (zero_zero @ nat) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_plus__nat_Oadd__0)).
% 181.68/124.52 thf(2565,plain,((! [A:nat]: ((plus_plus @ nat @ (zero_zero @ nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])).
% 181.68/124.52 thf(720,axiom,((bounded_lattice_top @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__top_45)).
% 181.68/124.52 thf(3198,plain,((bounded_lattice_top @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[720])).
% 181.68/124.52 thf(897,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(array @ TA),C:nat,D:(TA > TA)]: ((ord_less_eq @ nat @ (array_length @ TA @ A @ B) @ C) => ((heap_Time_execute @ (array @ TA) @ (array_map_entry @ TA @ C @ D @ B) @ A) = (none @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4079_execute__map__entry_I2_J)).
% 181.68/124.52 thf(3750,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(array @ TA),C:nat,D:(TA > TA)]: ((ord_less_eq @ nat @ (array_length @ TA @ A @ B) @ C) => ((heap_Time_execute @ (array @ TA) @ (array_map_entry @ TA @ C @ (D) @ B) @ A) = (none @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[897])).
% 181.68/124.52 thf(776,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:(TA > TA)]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => (heap_Time_success @ (array @ TA) @ (array_map_entry @ TA @ A @ D @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4082_success__map__entryI)).
% 181.68/124.52 thf(3349,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:(TA > TA)]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => (heap_Time_success @ (array @ TA) @ (array_map_entry @ TA @ A @ (D) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[776])).
% 181.68/124.52 thf(834,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:nat,C:(heap_ext @ product_unit)]: ((time_fails @ TA @ (array_nth @ TA @ A @ B) @ C) = (~ (ord_less @ nat @ B @ (array_length @ TA @ C @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4072_fails__array__nth)).
% 181.68/124.52 thf(3556,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:nat,C:(heap_ext @ product_unit)]: ((time_fails @ TA @ (array_nth @ TA @ A @ B) @ C) = (~ (ord_less @ nat @ B @ (array_length @ TA @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[834])).
% 181.68/124.52 thf(288,axiom,((linord4140545234300271783up_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Olinordered__ab__semigroup__add_525)).
% 181.68/124.52 thf(1888,plain,((linord4140545234300271783up_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])).
% 181.68/124.52 thf(961,axiom,((! [TA: $tType]: ((time_time @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: (case_option @ nat @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (zero_zero @ nat) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ nat @ (^ [C:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ nat @ (^ [D:(heap_ext @ product_unit),E:nat]: (E))))) @ (heap_Time_execute @ TA @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1751_time__def)).
% 181.68/124.52 thf(3877,plain,((! [TA: $tType]: ((time_time @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: (case_option @ nat @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (zero_zero @ nat) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ nat @ (^ [C:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ nat @ (^ [D:(heap_ext @ product_unit),E:nat]: (E))))) @ (heap_Time_execute @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[961])).
% 181.68/124.52 thf(830,axiom,((! [TA: $tType]: ((typerep2 @ TA) => (quickc3360725361186068524ustive @ (array @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oarray___Quickcheck__Exhaustive_Ofull__exhaustive_297)).
% 181.68/124.52 thf(3546,plain,((! [TA: $tType]: ((typerep2 @ TA) => (quickc3360725361186068524ustive @ (array @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[830])).
% 181.68/124.52 thf(702,axiom,((! [TA: $tType]: ((heap_Time_heap @ TA) = (^ [A:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: (heap_Time_Heap2 @ TA @ (comp @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_heap__def)).
% 181.68/124.52 thf(3144,plain,((! [TA: $tType]: ((heap_Time_heap @ TA) = (^ [A:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: (heap_Time_Heap2 @ TA @ (comp @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[702])).
% 181.68/124.52 thf(45,axiom,((quickc3360725361186068524ustive @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Quickcheck__Exhaustive_Ofull__exhaustive_439)).
% 181.68/124.52 thf(1159,plain,((quickc3360725361186068524ustive @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
% 181.68/124.52 thf(432,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/sandbox/benchmark/theBenchmark.p',fact_183_add__strict__mono)).
% 181.68/124.52 thf(2344,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)],[432])).
% 181.68/124.52 thf(421,axiom,((comm_s4317794764714335236cancel @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1__cancel_533)).
% 181.68/124.52 thf(2313,plain,((comm_s4317794764714335236cancel @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[421])).
% 181.68/124.52 thf(37,axiom,((suc = (^ [A:nat]: (plus_plus @ nat @ A @ (one_one @ nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_Suc__eq__plus1)).
% 181.68/124.52 thf(1128,plain,(((suc) = (^ [A:nat]: (plus_plus @ nat @ A @ (one_one @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
% 181.68/124.52 thf(571,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat]: ((A @ B) => ((C = D) => ((E = B) => ((F = (one_one @ nat)) => (heap_Time_effect @ TA @ (heap_Time_assert @ TA @ A @ B) @ D @ C @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_effect__assertI)).
% 181.68/124.52 thf(2769,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat]: ((A @ B) => ((C = D) => ((E = B) => ((F = (one_one @ nat)) => (heap_Time_effect @ TA @ (heap_Time_assert @ TA @ (A) @ B) @ D @ C @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[571])).
% 181.68/124.52 thf(1025,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ TA @ (heap_Time_tap @ TA @ A) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (A @ B) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_execute__tap)).
% 181.68/124.52 thf(4027,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ TA @ (heap_Time_tap @ TA @ (A)) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (A @ B) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025])).
% 181.68/124.52 thf(889,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > (TC > (TA > $o))),B:(product_prod @ TB @ TC),C:TA]: ((product_case_prod @ TB @ TC @ (TA > $o) @ A @ B @ C) => (~ (! [D:TB,E:TC]: ((B = (product_Pair @ TB @ TC @ D @ E)) => (~ (A @ D @ E @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_case__prodE_H)).
% 181.68/124.52 thf(3731,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > (TC > (TA > $o))),B:(product_prod @ TB @ TC),C:TA]: ((product_case_prod @ TB @ TC @ (TA > $o) @ (A) @ B @ C) => (~ (! [D:TB,E:TC]: ((B = (product_Pair @ TB @ TC @ D @ E)) => (~ (A @ D @ E @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[889])).
% 181.68/124.52 thf(1004,axiom,((complete_Sup @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Complete__Lattices_OSup_123)).
% 181.68/124.52 thf(3968,plain,((complete_Sup @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004])).
% 181.68/124.52 thf(913,axiom,((semiri1453513574482234551roduct @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_82)).
% 181.68/124.52 thf(3782,plain,((semiri1453513574482234551roduct @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[913])).
% 181.68/124.52 thf(316,axiom,((! [A:nat,B:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_diff__add__inverse2)).
% 181.68/124.52 thf(1983,plain,((! [A:nat,B:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])).
% 181.68/124.52 thf(583,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:(TA > $o)]: ((ord_less_eq @ (TA > $o) @ A @ B) => (ord_less_eq @ ((option @ TA) > $o) @ (pred_option @ TA @ A) @ (pred_option @ TA @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5056_option_Opred__mono)).
% 181.68/124.52 thf(2801,plain,((! [TA: $tType]: (! [A:(TA > $o),B:(TA > $o)]: ((ord_less_eq @ (TA > $o) @ (A) @ (B)) => (ord_less_eq @ ((option @ TA) > $o) @ (pred_option @ TA @ A) @ (pred_option @ TA @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[583])).
% 181.68/124.52 thf(953,axiom,((power @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Power_Opower_149)).
% 181.68/124.52 thf(3862,plain,((power @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[953])).
% 181.68/124.52 thf(609,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/sandbox/benchmark/theBenchmark.p',fact_519_add__strict__increasing)).
% 181.68/124.52 thf(2895,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)],[609])).
% 181.68/124.52 thf(548,axiom,((! [TA: $tType,TB: $tType]: (((quickc3360725361186068524ustive @ TB) & (quickc3360725361186068524ustive @ TA)) => (quickc3360725361186068524ustive @ (product_prod @ TB @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Quickcheck__Exhaustive_Ofull__exhaustive_394)).
% 181.68/124.52 thf(2694,plain,((! [TA: $tType,TB: $tType]: (((quickc3360725361186068524ustive @ TB) & (quickc3360725361186068524ustive @ TA)) => (quickc3360725361186068524ustive @ (product_prod @ TB @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[548])).
% 181.68/124.52 thf(485,axiom,((! [TA: $tType]: (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:TA]: ((A = B) => (heap_Time_effect @ TA @ (heap_Time_ureturn @ TA @ C) @ A @ B @ C @ (zero_zero @ nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_effect__ureturnI)).
% 181.68/124.52 thf(2509,plain,((! [TA: $tType]: (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:TA]: ((A = B) => (heap_Time_effect @ TA @ (heap_Time_ureturn @ TA @ C) @ A @ B @ C @ (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[485])).
% 181.68/124.52 thf(789,axiom,((! [TA: $tType,TB: $tType]: (! [A:((product_prod @ TA @ TB) > $o),B:(product_prod @ TA @ TB)]: ((! [C:TA,D:TB]: (A @ (product_Pair @ TA @ TB @ C @ D))) => (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_prod__cases)).
% 181.68/124.52 thf(3386,plain,((! [TA: $tType,TB: $tType]: (! [A:((product_prod @ TA @ TB) > $o),B:(product_prod @ TA @ TB)]: ((! [C:TA,D:TB]: (A @ (product_Pair @ TA @ TB @ C @ D))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[789])).
% 181.68/124.52 thf(859,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:(heap_ext @ product_unit),E:TA,F:nat]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => ((D = (array_update @ TA @ C @ A @ E @ B)) => ((F = (one_one @ nat)) => (heap_Time_effect @ (array @ TA) @ (array_upd @ TA @ A @ E @ C) @ B @ D @ C @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4106_effect__updI)).
% 181.68/124.52 thf(3632,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:(heap_ext @ product_unit),E:TA,F:nat]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => ((D = (array_update @ TA @ C @ A @ E @ B)) => ((F = (one_one @ nat)) => (heap_Time_effect @ (array @ TA) @ (array_upd @ TA @ A @ E @ C) @ B @ D @ C @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[859])).
% 181.68/124.52 thf(674,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TB > TA)]: ((case_option @ TA @ TB @ A @ B @ (none @ TB)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_option_Osimps_I4_J)).
% 181.68/124.52 thf(3078,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TB > TA)]: ((case_option @ TA @ TB @ A @ (B) @ (none @ TB)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[674])).
% 181.68/124.52 thf(994,axiom,((canoni5634975068530333245id_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add)).
% 181.68/124.52 thf(3941,plain,((canoni5634975068530333245id_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[994])).
% 181.68/124.52 thf(533,axiom,((! [A:nat,B:nat]: (((plus_plus @ nat @ A @ B) = (zero_zero @ nat)) = ((A = (zero_zero @ nat)) & (B = (zero_zero @ nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_add__is__0)).
% 181.68/124.52 thf(2638,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)],[533])).
% 181.68/124.52 thf(409,axiom,((! [TA: $tType]: (! [A:(nat > (TA > TA)),B:nat,C:nat,D:TA,E:((nat > (TA > TA)) > (nat > (nat > (TA > $o))))]: ((accp @ (product_prod @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA))) @ (set_fo1817059534552279752at_rel @ TA) @ (product_Pair @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA)) @ A @ (product_Pair @ nat @ (product_prod @ nat @ TA) @ B @ (product_Pair @ nat @ TA @ C @ D)))) => ((! [F:(nat > (TA > TA)),G:nat,H:nat,I:TA]: ((accp @ (product_prod @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA))) @ (set_fo1817059534552279752at_rel @ TA) @ (product_Pair @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA)) @ F @ (product_Pair @ nat @ (product_prod @ nat @ TA) @ G @ (product_Pair @ nat @ TA @ H @ I)))) => (((~ (ord_less @ nat @ H @ G)) => (E @ F @ (plus_plus @ nat @ G @ (one_one @ nat)) @ H @ (F @ G @ I))) => (E @ F @ G @ H @ I)))) => (E @ A @ B @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_fold__atLeastAtMost__nat_Opinduct)).
% 181.68/124.52 thf(2268,plain,((! [TA: $tType]: (! [A:(nat > (TA > TA)),B:nat,C:nat,D:TA,E:((nat > (TA > TA)) > (nat > (nat > (TA > $o))))]: ((accp @ (product_prod @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA))) @ (set_fo1817059534552279752at_rel @ TA) @ (product_Pair @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA)) @ (A) @ (product_Pair @ nat @ (product_prod @ nat @ TA) @ B @ (product_Pair @ nat @ TA @ C @ D)))) => ((! [F:(nat > (TA > TA)),G:nat,H:nat,I:TA]: ((accp @ (product_prod @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA))) @ (set_fo1817059534552279752at_rel @ TA) @ (product_Pair @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA)) @ (F) @ (product_Pair @ nat @ (product_prod @ nat @ TA) @ G @ (product_Pair @ nat @ TA @ H @ I)))) => (((~ (ord_less @ nat @ H @ G)) => (E @ (F) @ (plus_plus @ nat @ G @ (one_one @ nat)) @ H @ (F @ G @ I))) => (E @ (F) @ G @ H @ I)))) => (E @ (A) @ B @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[409])).
% 181.68/124.52 thf(685,axiom,((! [TA: $tType]: ((cancel_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: (((plus_plus @ TA @ A @ B) = (plus_plus @ TA @ C @ B)) = (A = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_add__right__cancel)).
% 181.68/124.52 thf(3105,plain,((! [TA: $tType]: ((cancel_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: (((plus_plus @ TA @ A @ B) = (plus_plus @ TA @ C @ B)) = (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[685])).
% 181.68/124.52 thf(817,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > $o),B:(TA > $o),C:(TA > (heap_Time_Heap @ TB)),D:(TA > (heap_Time_Heap @ TB)),E:TA]: ((A = B) => ((! [F:TA]: ((B @ F) => ((C @ F) = (D @ F)))) => ((heap_Time_bind @ TA @ TB @ (heap_Time_assert @ TA @ A @ E) @ C) = (heap_Time_bind @ TA @ TB @ (heap_Time_assert @ TA @ B @ E) @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_assert__cong)).
% 181.68/124.52 thf(3467,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > $o),B:(TA > $o),C:(TA > (heap_Time_Heap @ TB)),D:(TA > (heap_Time_Heap @ TB)),E:TA]: (((A) = (B)) => ((! [F:TA]: ((B @ F) => ((C @ F) = (D @ F)))) => ((heap_Time_bind @ TA @ TB @ (heap_Time_assert @ TA @ (A) @ E) @ (C)) = (heap_Time_bind @ TA @ TB @ (heap_Time_assert @ TA @ (B) @ E) @ (D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[817])).
% 181.68/124.52 thf(883,axiom,((quickcheck_random @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Quickcheck__Random_Orandom_110)).
% 181.68/124.52 thf(3699,plain,((quickcheck_random @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[883])).
% 181.68/124.52 thf(417,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/sandbox/benchmark/theBenchmark.p',fact_555_Nat_Oadd__diff__assoc2)).
% 181.68/124.52 thf(2300,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)],[417])).
% 181.68/124.52 thf(251,axiom,((! [TA: $tType]: ((sup @ TA) => (! [A:TA,B:TA]: ((sup_sup @ (option @ TA) @ (some @ TA @ A) @ (some @ TA @ B)) = (some @ TA @ (sup_sup @ TA @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2679_sup__Some)).
% 181.68/124.52 thf(1762,plain,((! [TA: $tType]: ((sup @ TA) => (! [A:TA,B:TA]: ((sup_sup @ (option @ TA) @ (some @ TA @ A) @ (some @ TA @ B)) = (some @ TA @ (sup_sup @ TA @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])).
% 181.68/124.52 thf(359,axiom,((! [TA: $tType]: (! [A:$o,B:TA,C:TA]: (((A) => ((heap_Time_return @ TA @ B) = (heap_Time_return @ TA @ (if @ TA @ A @ B @ C)))) & ((~ (A)) => ((heap_Time_return @ TA @ C) = (heap_Time_return @ TA @ (if @ TA @ A @ B @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_fold__if__return)).
% 181.68/124.52 thf(2100,plain,((! [TA: $tType]: (! [A:$o,B:TA,C:TA]: (((A) => ((heap_Time_return @ TA @ B) = (heap_Time_return @ TA @ (if @ TA @ A @ B @ C)))) & ((~ (A)) => ((heap_Time_return @ TA @ C) = (heap_Time_return @ TA @ (if @ TA @ A @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[359])).
% 181.68/124.52 thf(273,axiom,((! [TA: $tType]: (! [A:nat,B:nat,C:nat,D:(nat > TA)]: ((ord_less @ nat @ A @ (minus_minus @ nat @ B @ C)) => ((nth @ TA @ (map @ nat @ TA @ D @ (upt @ C @ B)) @ A) = (D @ (plus_plus @ nat @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3585_nth__map__upt)).
% 181.68/124.52 thf(1851,plain,((! [TA: $tType]: (! [A:nat,B:nat,C:nat,D:(nat > TA)]: ((ord_less @ nat @ A @ (minus_minus @ nat @ B @ C)) => ((nth @ TA @ (map @ nat @ TA @ (D) @ (upt @ C @ B)) @ A) = (D @ (plus_plus @ nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])).
% 181.68/124.52 thf(255,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:(TA > (TA > $o)),C:TA,D:(TA > $o)]: ((ord_less_eq @ (TA > $o) @ A @ (accp @ TA @ B)) => ((! [E:TA,F:TA]: ((A @ E) => ((B @ F @ E) => (A @ F)))) => ((A @ C) => ((! [E:TA]: ((A @ E) => ((! [F:TA]: ((B @ F @ E) => (D @ F))) => (D @ E)))) => (D @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_accp__subset__induct)).
% 181.68/124.52 thf(1772,plain,((! [TA: $tType]: (! [A:(TA > $o),B:(TA > (TA > $o)),C:TA,D:(TA > $o)]: ((ord_less_eq @ (TA > $o) @ (A) @ (accp @ TA @ B)) => ((! [E:TA,F:TA]: ((A @ E) => ((B @ F @ E) => (A @ F)))) => ((A @ C) => ((! [E:TA]: ((A @ E) => ((! [F:TA]: ((B @ F @ E) => (D @ F))) => (D @ E)))) => (D @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])).
% 181.68/124.52 thf(84,axiom,((! [TA: $tType]: ((semiri1453513574482234551roduct @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((A != B) & (C != D)) = ((plus_plus @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)) != (plus_plus @ TA @ (times_times @ TA @ A @ D) @ (times_times @ TA @ B @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_crossproduct__noteq)).
% 181.68/124.52 thf(1259,plain,((! [TA: $tType]: ((semiri1453513574482234551roduct @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((~ (A = B) & ~ (C = D)) = (~ ((plus_plus @ TA @ (times_times @ TA @ A @ C) @ (times_times @ TA @ B @ D)) = (plus_plus @ TA @ (times_times @ TA @ A @ D) @ (times_times @ TA @ B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
% 181.68/124.52 thf(641,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TB),B:(TA > TD),C:TA,D:(TC > TB),E:(TA > TC)]: (((A @ (B @ C)) = (D @ (E @ C))) => ((comp @ TD @ TB @ TA @ A @ B @ C) = (comp @ TC @ TB @ TA @ D @ E @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_comp__apply__eq)).
% 181.68/124.52 thf(2990,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TB),B:(TA > TD),C:TA,D:(TC > TB),E:(TA > TC)]: (((A @ (B @ C)) = (D @ (E @ C))) => ((comp @ TD @ TB @ TA @ (A) @ (B) @ C) = (comp @ TC @ TB @ TA @ (D) @ (E) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[641])).
% 181.68/124.52 thf(179,axiom,((! [TA: $tType]: (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:TA]: ((A = B) => (heap_Time_effect @ TA @ (heap_Time_return @ TA @ C) @ A @ B @ C @ (one_one @ nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_effect__returnI)).
% 181.68/124.52 thf(1534,plain,((! [TA: $tType]: (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:TA]: ((A = B) => (heap_Time_effect @ TA @ (heap_Time_return @ TA @ C) @ A @ B @ C @ (one_one @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
% 181.68/124.52 thf(307,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => (ord_less_eq @ TA @ C @ (minus_minus @ TA @ (plus_plus @ TA @ B @ C) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_le__add__diff)).
% 181.68/124.52 thf(1953,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => (ord_less_eq @ TA @ C @ (minus_minus @ TA @ (plus_plus @ TA @ B @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])).
% 181.68/124.52 thf(126,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TB > (option @ TA))]: ((member @ TB @ A @ (dom @ TB @ TA @ B)) = ((B @ A) != (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3323_domIff)).
% 181.68/124.52 thf(1375,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TB > (option @ TA))]: ((member @ TB @ A @ (dom @ TB @ TA @ (B))) = (~ ((B @ A) = (none @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
% 181.68/124.52 thf(637,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))))]: ~ (! [B:TE,C:TD,D:TC,E:TB,F:TA]: (A != (product_Pair @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))) @ B @ (product_Pair @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)) @ C @ (product_Pair @ TC @ (product_prod @ TB @ TA) @ D @ (product_Pair @ TB @ TA @ E @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_prod__cases5)).
% 181.68/124.52 thf(2973,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))))]: ~ (! [B:TE,C:TD,D:TC,E:TB,F:TA]: ~ (A = (product_Pair @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))) @ B @ (product_Pair @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)) @ C @ (product_Pair @ TC @ (product_prod @ TB @ TA) @ D @ (product_Pair @ TB @ TA @ E @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[637])).
% 181.68/124.52 thf(787,axiom,((! [TA: $tType]: ((ab_semigroup_add @ TA) => ((plus_plus @ TA) = (^ [A:TA,B:TA]: (plus_plus @ TA @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_ab__semigroup__add__class_Oadd_Ocommute)).
% 181.68/124.52 thf(3381,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)],[787])).
% 181.68/124.52 thf(14,axiom,((ordere1937475149494474687imp_le @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Oordered__ab__semigroup__monoid__add__imp__le_430)).
% 181.68/124.52 thf(1064,plain,((ordere1937475149494474687imp_le @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 181.68/124.52 thf(181,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ A @ C)) = (ord_less @ nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_nat__add__left__cancel__less)).
% 181.68/124.52 thf(1540,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)],[181])).
% 181.68/124.52 thf(1001,axiom,((strict9044650504122735259up_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_88)).
% 181.68/124.52 thf(3963,plain,((strict9044650504122735259up_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001])).
% 181.68/124.52 thf(558,axiom,((finite_finite @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_279)).
% 181.68/124.52 thf(2724,plain,((finite_finite @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[558])).
% 181.68/124.52 thf(238,axiom,((! [TA: $tType]: (! [A:(product_prod @ ((product_prod @ code_natural @ code_natural) > (product_prod @ (product_prod @ TA @ (product_unit > code_term)) @ (product_prod @ code_natural @ code_natural))) @ (product_prod @ code_natural @ (product_prod @ code_natural @ code_natural)))]: ~ (! [B:((product_prod @ code_natural @ code_natural) > (product_prod @ (product_prod @ TA @ (product_unit > code_term)) @ (product_prod @ code_natural @ code_natural))),C:code_natural,D:(product_prod @ code_natural @ code_natural)]: (A != (product_Pair @ ((product_prod @ code_natural @ code_natural) > (product_prod @ (product_prod @ TA @ (product_unit > code_term)) @ (product_prod @ code_natural @ code_natural))) @ (product_prod @ code_natural @ (product_prod @ code_natural @ code_natural)) @ B @ (product_Pair @ code_natural @ (product_prod @ code_natural @ code_natural) @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4220_iter_Ocases)).
% 181.68/124.52 thf(1719,plain,((! [TA: $tType]: (! [A:(product_prod @ ((product_prod @ code_natural @ code_natural) > (product_prod @ (product_prod @ TA @ (product_unit > code_term)) @ (product_prod @ code_natural @ code_natural))) @ (product_prod @ code_natural @ (product_prod @ code_natural @ code_natural)))]: ~ (! [B:((product_prod @ code_natural @ code_natural) > (product_prod @ (product_prod @ TA @ (product_unit > code_term)) @ (product_prod @ code_natural @ code_natural))),C:code_natural,D:(product_prod @ code_natural @ code_natural)]: ~ (A = (product_Pair @ ((product_prod @ code_natural @ code_natural) > (product_prod @ (product_prod @ TA @ (product_unit > code_term)) @ (product_prod @ code_natural @ code_natural))) @ (product_prod @ code_natural @ (product_prod @ code_natural @ code_natural)) @ (B) @ (product_Pair @ code_natural @ (product_prod @ code_natural @ code_natural) @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
% 181.68/124.52 thf(865,axiom,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA),C:(option @ TA),D:(option @ TA)]: ((! [E:TA,F:TA,G:TA]: ((A @ (A @ E @ F) @ G) = (A @ E @ (A @ F @ G)))) => ((combine_options @ TA @ A @ (combine_options @ TA @ A @ B @ C) @ D) = (combine_options @ TA @ A @ B @ (combine_options @ TA @ A @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_combine__options__assoc)).
% 181.68/124.52 thf(3650,plain,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA),C:(option @ TA),D:(option @ TA)]: ((! [E:TA,F:TA,G:TA]: ((A @ (A @ E @ F) @ G) = (A @ E @ (A @ F @ G)))) => ((combine_options @ TA @ (A) @ (combine_options @ TA @ (A) @ B @ C) @ D) = (combine_options @ TA @ (A) @ B @ (combine_options @ TA @ (A) @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[865])).
% 181.68/124.52 thf(1020,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit)]: ((A @ B) => ((heap_Time_execute @ TA @ (heap_Time_assert @ TA @ A @ B) @ C) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ B @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ (one_one @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_execute__assert_I1_J)).
% 181.68/124.52 thf(4012,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit)]: ((A @ B) => ((heap_Time_execute @ TA @ (heap_Time_assert @ TA @ (A) @ B) @ C) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ B @ (product_Pair @ (heap_ext @ product_unit) @ nat @ C @ (one_one @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020])).
% 181.68/124.52 thf(666,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > $o),B:(heap_ext @ product_unit),C:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((A @ B) => (heap_Time_success @ TA @ (heap_Time_guard @ TA @ A @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_success__guardI)).
% 181.68/124.52 thf(3060,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > $o),B:(heap_ext @ product_unit),C:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((A @ B) => (heap_Time_success @ TA @ (heap_Time_guard @ TA @ (A) @ (C)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[666])).
% 181.68/124.52 thf(677,axiom,((quickcheck_random @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Quickcheck__Random_Orandom_268)).
% 181.68/124.52 thf(3087,plain,((quickcheck_random @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[677])).
% 181.68/124.52 thf(650,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA]: ((pred_option @ TA @ A @ (some @ TA @ B)) = (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5055_option_Opred__inject_I2_J)).
% 181.68/124.52 thf(3018,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA]: ((pred_option @ TA @ (A) @ (some @ TA @ B)) = (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[650])).
% 181.68/124.52 thf(119,axiom,((comm_s4317794764714335236cancel @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Ocomm__semiring__1__cancel_457)).
% 181.68/124.52 thf(1361,plain,((comm_s4317794764714335236cancel @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
% 181.68/124.52 thf(985,axiom,((ordere6658533253407199908up_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_101)).
% 181.68/124.52 thf(3922,plain,((ordere6658533253407199908up_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[985])).
% 181.68/124.52 thf(53,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/sandbox/benchmark/theBenchmark.p',fact_998_add__eq__if)).
% 181.68/124.52 thf(1182,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)],[53])).
% 181.68/124.52 thf(887,axiom,((! [TA: $tType]: (! [A:(option @ TA)]: ((A != (none @ TA)) = (? [B:TA]: (A = (some @ TA @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_not__None__eq)).
% 181.68/124.52 thf(3714,plain,((! [TA: $tType]: (! [A:(option @ TA)]: ((~ (A = (none @ TA))) = (? [B:TA]: (A = (some @ TA @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[887])).
% 181.68/124.52 thf(847,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 @ (plus_plus @ TA @ A @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_add_Oright__commute)).
% 181.68/124.52 thf(3596,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 @ (plus_plus @ TA @ A @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[847])).
% 181.68/124.52 thf(352,axiom,((preorder @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_277)).
% 181.68/124.52 thf(2080,plain,((preorder @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])).
% 181.68/124.52 thf(141,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ A) => ((modulo_modulo @ nat @ (suc @ (times_times @ nat @ A @ B)) @ A) = (one_one @ nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_Suc__times__mod__eq)).
% 181.68/124.52 thf(1414,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (suc @ (zero_zero @ nat)) @ A) => ((modulo_modulo @ nat @ (suc @ (times_times @ nat @ A @ B)) @ A) = (one_one @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
% 181.68/124.52 thf(524,axiom,((! [TA: $tType]: (((?) @ (option @ TA)) = (^ [A:((option @ TA) > $o)]: ((A @ (none @ TA)) | ? [B:TA]: (A @ (some @ TA @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_split__option__ex)).
% 181.68/124.52 thf(2613,plain,((! [TA: $tType]: (((?) @ (option @ TA)) = (^ [A:((option @ TA) > $o)]: ((A @ (none @ TA)) | ? [B:TA]: (A @ (some @ TA @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[524])).
% 181.68/124.52 thf(862,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA,C:TB,D:TA]: (((product_Pair @ TB @ TA @ A @ B) = (product_Pair @ TB @ TA @ C @ D)) = ((A = C) & (B = D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_old_Oprod_Oinject)).
% 181.68/124.52 thf(3643,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA,C:TB,D:TA]: (((product_Pair @ TB @ TA @ A @ B) = (product_Pair @ TB @ TA @ C @ D)) = ((A = C) & (B = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[862])).
% 181.68/124.52 thf(289,axiom,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:(TA > (TA > $o))]: ((ord_less_eq @ (TA > (TA > $o)) @ A @ B) => (ord_less_eq @ (TA > $o) @ (accp @ TA @ B) @ (accp @ TA @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_accp__subset)).
% 181.68/124.52 thf(1889,plain,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:(TA > (TA > $o))]: ((ord_less_eq @ (TA > (TA > $o)) @ (A) @ (B)) => (ord_less_eq @ (TA > $o) @ (accp @ TA @ B) @ (accp @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])).
% 181.68/124.52 thf(535,axiom,((! [TA: $tType]: ((quickc3360725361186068524ustive @ TA) => (quickc3360725361186068524ustive @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Quickcheck__Exhaustive_Ofull__exhaustive_314)).
% 181.68/124.52 thf(2649,plain,((! [TA: $tType]: ((quickc3360725361186068524ustive @ TA) => (quickc3360725361186068524ustive @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[535])).
% 181.68/124.52 thf(838,axiom,((boolea8198339166811842893lgebra @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Boolean__Algebras_Oboolean__algebra_266)).
% 181.68/124.52 thf(3573,plain,((boolea8198339166811842893lgebra @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[838])).
% 181.68/124.52 thf(992,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_success @ TA @ A @ B) => (~ (! [C:TA,D:(product_prod @ (heap_ext @ product_unit) @ nat)]: ((heap_Time_execute @ TA @ A @ B) != (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_successE)).
% 181.68/124.52 thf(3935,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_success @ TA @ A @ B) => (~ (! [C:TA,D:(product_prod @ (heap_ext @ product_unit) @ nat)]: ~ ((heap_Time_execute @ TA @ A @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[992])).
% 181.68/124.52 thf(472,axiom,((! [TA: $tType]: (! [A:nat,B:(set @ (product_prod @ TA @ TA))]: ((compow @ (TA > (TA > $o)) @ A @ (^ [C:TA,D:TA]: (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ B))) = (^ [C:TA,D:TA]: (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ (compow @ (set @ (product_prod @ TA @ TA)) @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4989_relpowp__relpow__eq)).
% 181.68/124.52 thf(2460,plain,((! [TA: $tType]: (! [A:nat,B:(set @ (product_prod @ TA @ TA))]: ((compow @ (TA > (TA > $o)) @ A @ (^ [C:TA,D:TA]: (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ B))) = (^ [C:TA,D:TA]: (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ (compow @ (set @ (product_prod @ TA @ TA)) @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])).
% 181.68/124.52 thf(164,axiom,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA)),B:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ B) @ (init_seg_of @ TA)) => ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ B @ A) @ (init_seg_of @ TA)) => (A = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4358_antisym__init__seg__of)).
% 181.68/124.52 thf(1493,plain,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA)),B:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ B) @ (init_seg_of @ TA)) => ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ B @ A) @ (init_seg_of @ TA)) => (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
% 181.68/124.52 thf(46,axiom,((! [A:code_integer]: ((times_times @ code_integer @ (zero_zero @ code_integer) @ A) = (zero_zero @ code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1275_times__integer__code_I2_J)).
% 181.68/124.52 thf(1160,plain,((! [A:code_integer]: ((times_times @ code_integer @ (zero_zero @ code_integer) @ A) = (zero_zero @ code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
% 181.68/124.52 thf(909,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ((heap_Time_Heap2 @ TA @ (heap_Time_execute @ TA @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Heap__execute)).
% 181.68/124.52 thf(3775,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ((heap_Time_Heap2 @ TA @ (heap_Time_execute @ TA @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[909])).
% 181.68/124.52 thf(701,axiom,((! [TA: $tType,TB: $tType]: (! [A:((TA > (option @ TB)) > (TA > (option @ TB)))]: ((! [B:TA]: (comple7038119648293358887notone @ (TA > (option @ TB)) @ (option @ TB) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TB) @ (none @ TB)) @ (^ [C:(TA > (option @ TB))]: (A @ C @ B)))) => ((comple187402453842119260l_fixp @ (TA > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ A) = (A @ (comple187402453842119260l_fixp @ (TA > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5982_option_Omono__body__fixp)).
% 181.68/124.52 thf(3141,plain,((! [TA: $tType,TB: $tType]: (! [A:((TA > (option @ TB)) > (TA > (option @ TB)))]: ((! [B:TA]: (comple7038119648293358887notone @ (TA > (option @ TB)) @ (option @ TB) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TB) @ (none @ TB)) @ (^ [C:(TA > (option @ TB))]: (A @ C @ B)))) => ((comple187402453842119260l_fixp @ (TA > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (A)) = (A @ (comple187402453842119260l_fixp @ (TA > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[701])).
% 181.68/124.52 thf(96,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TB > (option @ TA))]: ((member @ TB @ A @ (dom @ TB @ TA @ B)) => (? [C:TA]: ((B @ A) = (some @ TA @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3322_domD)).
% 181.68/124.52 thf(1292,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TB > (option @ TA))]: ((member @ TB @ A @ (dom @ TB @ TA @ (B))) => (? [C:TA]: ((B @ A) = (some @ TA @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
% 181.68/124.52 thf(855,axiom,((complete_Inf @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Lattices_OInf_273)).
% 181.68/124.52 thf(3622,plain,((complete_Inf @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[855])).
% 181.68/124.52 thf(144,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/sandbox/benchmark/theBenchmark.p',fact_657_add__mult__distrib2)).
% 181.68/124.52 thf(1424,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)],[144])).
% 181.68/124.52 thf(806,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: (((map_add @ TB @ TA @ A @ B @ C) = (some @ TA @ D)) = (((B @ C) = (some @ TA @ D)) | (((B @ C) = (none @ TA)) & ((A @ C) = (some @ TA @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3408_map__add__Some__iff)).
% 181.68/124.52 thf(3441,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: (((map_add @ TB @ TA @ (A) @ (B) @ C) = (some @ TA @ D)) = (((B @ C) = (some @ TA @ D)) | (((B @ C) = (none @ TA)) & ((A @ C) = (some @ TA @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[806])).
% 181.68/124.52 thf(423,axiom,((! [A:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:(heap_ext @ product_unit),D:(set @ nat)]: ((times_assn_raw @ A @ B @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ D)) = (? [E:(set @ nat),F:(set @ nat)]: ((D = (sup_sup @ (set @ nat) @ E @ F)) & ((inf_inf @ (set @ nat) @ E @ F) = (bot_bot @ (set @ nat))) & (A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ E)) & (B @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5648_times__assn__raw_Osimps)).
% 181.68/124.52 thf(2317,plain,((! [A:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:(heap_ext @ product_unit),D:(set @ nat)]: ((times_assn_raw @ (A) @ (B) @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ D)) = (? [E:(set @ nat),F:(set @ nat)]: ((D = (sup_sup @ (set @ nat) @ E @ F)) & ((inf_inf @ (set @ nat) @ E @ F) = (bot_bot @ (set @ nat))) & (A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ E)) & (B @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[423])).
% 181.68/124.52 thf(757,axiom,((! [A:nat,B:nat]: (ord_less_eq @ nat @ A @ (plus_plus @ nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_le__add1)).
% 181.68/124.52 thf(3294,plain,((! [A:nat,B:nat]: (ord_less_eq @ nat @ A @ (plus_plus @ nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[757])).
% 181.68/124.52 thf(738,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: (heap_Time_Heap_ord @ TA @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_heap_Oleq__refl)).
% 181.68/124.52 thf(3242,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: (heap_Time_Heap_ord @ TA @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[738])).
% 181.68/124.52 thf(267,axiom,(((sup_sup @ product_unit) = (^ [A:product_unit,B:product_unit]: (product_Unity)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3038_sup__unit__def)).
% 181.68/124.52 thf(1825,plain,(((sup_sup @ product_unit) = (^ [A:product_unit,B:product_unit]: (product_Unity)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])).
% 181.68/124.52 thf(868,axiom,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ A @ B) @ B) = (ord_less_eq @ TA @ A @ (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_add__le__same__cancel2)).
% 181.68/124.52 thf(3656,plain,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ A @ B) @ B) = (ord_less_eq @ TA @ A @ (zero_zero @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[868])).
% 181.68/124.52 thf(596,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:(TA > (option @ TB))]: ((! [C:TA,D:TB]: (((A @ C) = (some @ TB @ D)) => ((B @ C) = (some @ TB @ D)))) => (map_le @ TA @ TB @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3404_map__leI)).
% 181.68/124.52 thf(2845,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:(TA > (option @ TB))]: ((! [C:TA,D:TB]: (((A @ C) = (some @ TB @ D)) => ((B @ C) = (some @ TB @ D)))) => (map_le @ TA @ TB @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[596])).
% 181.68/124.52 thf(893,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(list @ TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ (array @ TA) @ (array_of_list @ TA @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_success__of__listI)).
% 181.68/124.52 thf(3743,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(list @ TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ (array @ TA) @ (array_of_list @ TA @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[893])).
% 181.68/124.52 thf(731,axiom,((! [TA: $tType,TB: $tType]: ((map_option @ TA @ TB) = (^ [A:(TA > TB)]: (case_option @ (option @ TB) @ TA @ (none @ TB) @ (^ [B:TA]: (some @ TB @ (A @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_map__option__case)).
% 181.68/124.52 thf(3222,plain,((! [TA: $tType,TB: $tType]: ((map_option @ TA @ TB) = (^ [A:(TA > TB)]: (case_option @ (option @ TB) @ TA @ (none @ TB) @ (^ [B:TA]: (some @ TB @ (A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[731])).
% 181.68/124.52 thf(305,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((plus_plus @ TA @ (minus_minus @ TA @ B @ A) @ C) = (minus_minus @ TA @ (plus_plus @ TA @ B @ C) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2)).
% 181.68/124.52 thf(1947,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((plus_plus @ TA @ (minus_minus @ TA @ B @ A) @ C) = (minus_minus @ TA @ (plus_plus @ TA @ B @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])).
% 181.68/124.52 thf(588,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TC @ (product_prod @ TB @ TA))]: ~ (! [B:TC,C:TB,D:TA]: (A != (product_Pair @ TC @ (product_prod @ TB @ TA) @ B @ (product_Pair @ TB @ TA @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_prod__cases3)).
% 181.68/124.52 thf(2813,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TC @ (product_prod @ TB @ TA))]: ~ (! [B:TC,C:TB,D:TA]: ~ (A = (product_Pair @ TC @ (product_prod @ TB @ TA) @ B @ (product_Pair @ TB @ TA @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[588])).
% 181.68/124.52 thf(689,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TB,B:(TA > TC)]: ((comp @ TC @ TB @ TA @ (^ [C:TC]: (A)) @ B) = (^ [C:TA]: (A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_K__record__comp)).
% 181.68/124.52 thf(3115,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TB,B:(TA > TC)]: ((comp @ TC @ TB @ TA @ (^ [C:TC]: (A)) @ B) = (^ [C:TA]: (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[689])).
% 181.68/124.52 thf(668,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(list @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ (array @ TA) @ (array_of_list @ TA @ A) @ B) = (some @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [C:(array @ TA),D:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ (plus_plus @ nat @ (one_one @ nat) @ (size_size @ (list @ TA) @ A))))) @ (array_alloc @ TA @ A @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3530_execute__of__list)).
% 181.68/124.52 thf(3064,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(list @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ (array @ TA) @ (array_of_list @ TA @ A) @ B) = (some @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [C:(array @ TA),D:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ (plus_plus @ nat @ (one_one @ nat) @ (size_size @ (list @ TA) @ A))))) @ (array_alloc @ TA @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[668])).
% 181.68/124.52 thf(983,axiom,((ordere1170586879665033532d_diff @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff)).
% 181.68/124.52 thf(3920,plain,((ordere1170586879665033532d_diff @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[983])).
% 181.68/124.52 thf(728,axiom,((! [TA: $tType]: (order_top @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_253)).
% 181.68/124.52 thf(3215,plain,((! [TA: $tType]: (order_top @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[728])).
% 181.68/124.52 thf(196,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (plus_plus @ nat @ A @ B) @ C) => (ord_less @ nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_add__lessD1)).
% 181.68/124.52 thf(1588,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)],[196])).
% 181.68/124.52 thf(30,axiom,((! [TA: $tType]: (! [A:(TA > nat),B:TA,C:TA,D:(set @ (product_prod @ TA @ TA))]: ((ord_less @ nat @ (A @ B) @ (A @ C)) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ C) @ (mlex_prod @ TA @ A @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_mlex__less)).
% 181.68/124.52 thf(1099,plain,((! [TA: $tType]: (! [A:(TA > nat),B:TA,C:TA,D:(set @ (product_prod @ TA @ TA))]: ((ord_less @ nat @ (A @ B) @ (A @ C)) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ C) @ (mlex_prod @ TA @ (A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 181.68/124.52 thf(42,axiom,((! [A:nat,B:nat]: ((times_times @ nat @ A @ (suc @ B)) = (plus_plus @ nat @ A @ (times_times @ nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_mult__Suc__right)).
% 181.68/124.52 thf(1150,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)],[42])).
% 181.68/124.52 thf(159,axiom,((! [A:code_integer]: ((plus_plus @ code_integer @ (zero_zero @ code_integer) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1277_plus__integer__code_I2_J)).
% 181.68/124.52 thf(1478,plain,((! [A:code_integer]: ((plus_plus @ code_integer @ (zero_zero @ code_integer) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
% 181.68/124.52 thf(694,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(heap_ext @ product_unit)]: ~ (time_fails @ (array @ TA) @ (array_new @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_fails__array__new)).
% 181.68/124.52 thf(3126,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(heap_ext @ product_unit)]: ~ (time_fails @ (array @ TA) @ (array_new @ TA @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[694])).
% 181.68/124.52 thf(828,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TC > TD),B:(TB > TC),C:(TA > TB)]: ((comp @ TB @ TD @ TA @ (comp @ TC @ TD @ TB @ A @ B) @ C) = (comp @ TC @ TD @ TA @ A @ (comp @ TB @ TC @ TA @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_comp__assoc)).
% 181.68/124.52 thf(3541,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TC > TD),B:(TB > TC),C:(TA > TB)]: ((comp @ TB @ TD @ TA @ (comp @ TC @ TD @ TB @ A @ B) @ C) = (comp @ TC @ TD @ TA @ A @ (comp @ TB @ TC @ TA @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[828])).
% 181.68/124.52 thf(151,axiom,((! [TA: $tType,TB: $tType]: ((preorder @ TB) => (! [A:(TA > (option @ TB)),B:(TA > (option @ TB))]: ((ord_less_eq @ (TA > (option @ TB)) @ A @ B) => (ord_less_eq @ (set @ TA) @ (dom @ TA @ TB @ A) @ (dom @ TA @ TB @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3361_le__map__dom__mono)).
% 181.68/124.52 thf(1451,plain,((! [TA: $tType,TB: $tType]: ((preorder @ TB) => (! [A:(TA > (option @ TB)),B:(TA > (option @ TB))]: ((ord_less_eq @ (TA > (option @ TB)) @ (A) @ (B)) => (ord_less_eq @ (set @ TA) @ (dom @ TA @ TB @ (A)) @ (dom @ TA @ TB @ (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
% 181.68/124.52 thf(418,axiom,((! [A:(heap_ext @ product_unit),B:(set @ nat),C:(set @ nat)]: ((in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ (sup_sup @ (set @ nat) @ B @ C))) = ((in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ B)) & (in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5685_in__range__dist__union)).
% 181.68/124.52 thf(2304,plain,((! [A:(heap_ext @ product_unit),B:(set @ nat),C:(set @ nat)]: ((in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ (sup_sup @ (set @ nat) @ B @ C))) = ((in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ B)) & (in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[418])).
% 181.68/124.52 thf(177,axiom,((zero_less_one @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Ozero__less__one_553)).
% 181.68/124.52 thf(1530,plain,((zero_less_one @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])).
% 181.68/124.52 thf(129,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/sandbox/benchmark/theBenchmark.p',fact_610_nat__less__add__iff1)).
% 181.68/124.52 thf(1382,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)],[129])).
% 181.68/124.52 thf(86,axiom,((! [A:assn,B:(heap_ext @ product_unit),C:(heap_ext @ product_unit)]: ((rep_assn @ A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ B @ (bot_bot @ (set @ nat)))) = (rep_assn @ A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ (bot_bot @ (set @ nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5644_mod__h__bot__indep)).
% 181.68/124.52 thf(1266,plain,((! [A:assn,B:(heap_ext @ product_unit),C:(heap_ext @ product_unit)]: ((rep_assn @ A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ B @ (bot_bot @ (set @ nat)))) = (rep_assn @ A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ (bot_bot @ (set @ nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
% 181.68/124.52 thf(778,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: (((map_add @ TB @ TA @ A @ B @ C) = (some @ TA @ D)) => (((B @ C) = (some @ TA @ D)) | (((B @ C) = (none @ TA)) & ((A @ C) = (some @ TA @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3409_map__add__SomeD)).
% 181.68/124.52 thf(3354,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: (((map_add @ TB @ TA @ (A) @ (B) @ C) = (some @ TA @ D)) => (((B @ C) = (some @ TA @ D)) | (((B @ C) = (none @ TA)) & ((A @ C) = (some @ TA @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[778])).
% 181.68/124.52 thf(611,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: ((map_comp @ TA @ TB @ TC) = (^ [A:(TA > (option @ TB)),B:(TC > (option @ TA)),C:TC]: (case_option @ (option @ TB) @ TA @ (none @ TB) @ A @ (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_map__comp__def)).
% 181.68/124.52 thf(2900,plain,((! [TA: $tType,TB: $tType,TC: $tType]: ((map_comp @ TA @ TB @ TC) = (^ [A:(TA > (option @ TB)),B:(TC > (option @ TA)),C:TC]: (case_option @ (option @ TB) @ TA @ (none @ TB) @ A @ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[611])).
% 181.68/124.52 thf(223,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(list @ TA),C:(list @ TA),D:nat]: (((map @ TA @ TB @ A @ B) = (map @ TA @ TB @ A @ C)) => ((A @ (nth @ TA @ B @ D)) = (A @ (nth @ TA @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3575_map__eq__nth__eq)).
% 181.68/124.52 thf(1668,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(list @ TA),C:(list @ TA),D:nat]: (((map @ TA @ TB @ (A) @ B) = (map @ TA @ TB @ (A) @ C)) => ((A @ (nth @ TA @ B @ D)) = (A @ (nth @ TA @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
% 181.68/124.52 thf(313,axiom,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: ((ord_less @ (set @ TA) @ (minus_minus @ (set @ TA) @ A @ B) @ A) = ((inf_inf @ (set @ TA) @ A @ B) != (bot_bot @ (set @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3070_disjoint__alt__simp3)).
% 181.68/124.52 thf(1974,plain,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: ((ord_less @ (set @ TA) @ (minus_minus @ (set @ TA) @ A @ B) @ A) = (~ ((inf_inf @ (set @ TA) @ A @ B) = (bot_bot @ (set @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])).
% 181.68/124.52 thf(597,axiom,((! [TA: $tType,TB: $tType]: ((order_top @ TA) => (order_top @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top)).
% 181.68/124.52 thf(2851,plain,((! [TA: $tType,TB: $tType]: ((order_top @ TA) => (order_top @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[597])).
% 181.68/124.52 thf(403,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((A != (zero_zero @ TA)) => (ord_less @ TA @ (zero_zero @ TA) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_gr__zeroI)).
% 181.68/124.52 thf(2243,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)],[403])).
% 181.68/124.52 thf(514,axiom,((! [TA: $tType]: ((heap @ TA) => (heap @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Heap_Oheap_333)).
% 181.68/124.52 thf(2581,plain,((! [TA: $tType]: ((heap @ TA) => (heap @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[514])).
% 181.68/124.52 thf(474,axiom,((quickc658316121487927005ustive @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Quickcheck__Exhaustive_Oexhaustive_527)).
% 181.68/124.52 thf(2465,plain,((quickc658316121487927005ustive @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[474])).
% 181.68/124.52 thf(933,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(array @ TA),C:nat,D:TA]: ((ord_less_eq @ nat @ (array_length @ TA @ A @ B) @ C) => ((heap_Time_execute @ (array @ TA) @ (array_upd @ TA @ C @ D @ B) @ A) = (none @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4105_execute__upd_I2_J)).
% 181.68/124.52 thf(3819,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(array @ TA),C:nat,D:TA]: ((ord_less_eq @ nat @ (array_length @ TA @ A @ B) @ C) => ((heap_Time_execute @ (array @ TA) @ (array_upd @ TA @ C @ D @ B) @ A) = (none @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[933])).
% 181.68/124.52 thf(790,axiom,((cl_HOL_Oequal @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___HOL_Oequal_423)).
% 181.68/124.52 thf(3390,plain,((cl_HOL_Oequal @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[790])).
% 181.68/124.52 thf(902,axiom,((euclid3725896446679973847miring @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Euclidean__Division_Oeuclidean__semiring_95)).
% 181.68/124.52 thf(3760,plain,((euclid3725896446679973847miring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[902])).
% 181.68/124.52 thf(795,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (option @ TA)),B:TC,C:TA,D:(TA > (option @ TB))]: (((A @ B) = (some @ TA @ C)) => ((map_comp @ TA @ TB @ TC @ D @ A @ B) = (D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_map__comp__simps_I2_J)).
% 181.68/124.52 thf(3409,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (option @ TA)),B:TC,C:TA,D:(TA > (option @ TB))]: (((A @ B) = (some @ TA @ C)) => ((map_comp @ TA @ TB @ TC @ (D) @ (A) @ B) = (D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[795])).
% 181.68/124.52 thf(570,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:TA,B:(heap_ext @ product_unit)]: ((heap_Time_execute @ (ref @ TA) @ (ref_ref @ TA @ A) @ B) = (some @ (product_prod @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_case_prod @ (ref @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [C:(ref @ TA),D:(heap_ext @ product_unit)]: (product_Pair @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ (one_one @ nat)))) @ (ref_alloc @ TA @ A @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5721_execute__ref)).
% 181.68/124.52 thf(2766,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:TA,B:(heap_ext @ product_unit)]: ((heap_Time_execute @ (ref @ TA) @ (ref_ref @ TA @ A) @ B) = (some @ (product_prod @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_case_prod @ (ref @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [C:(ref @ TA),D:(heap_ext @ product_unit)]: (product_Pair @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ (one_one @ nat)))) @ (ref_alloc @ TA @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[570])).
% 181.68/124.52 thf(340,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:TB]: (((A @ B) = (some @ TB @ C)) => ((fun_upd @ TA @ (option @ TB) @ A @ B @ (some @ TB @ C)) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2735_map__upd__triv)).
% 181.68/124.52 thf(2052,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:TB]: (((A @ B) = (some @ TB @ C)) => ((fun_upd @ TA @ (option @ TB) @ A @ B @ (some @ TB @ C)) = (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])).
% 181.68/124.52 thf(481,axiom,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less @ TA @ A @ B) & (C = D)) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_add__mono__thms__linordered__field_I1_J)).
% 181.68/124.52 thf(2482,plain,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less @ TA @ A @ B) & (C = D)) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])).
% 181.68/124.52 thf(80,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/sandbox/benchmark/theBenchmark.p',fact_611_nat__less__add__iff2)).
% 181.68/124.52 thf(1246,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)],[80])).
% 181.68/124.52 thf(722,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA)]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => (heap_Time_success @ TA @ (array_nth @ TA @ C @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4071_success__nthI)).
% 181.68/124.52 thf(3201,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA)]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => (heap_Time_success @ TA @ (array_nth @ TA @ C @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[722])).
% 181.68/124.52 thf(132,axiom,((! [A:nat,B:nat]: ((A = (times_times @ nat @ A @ B)) => ((B = (one_one @ nat)) | (A = (zero_zero @ nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_mult__eq__self__implies__10)).
% 181.68/124.52 thf(1393,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)],[132])).
% 181.68/124.52 thf(703,axiom,((! [TA: $tType]: ((heap_Time_ureturn @ TA) = (^ [A:TA]: (heap_Time_heap @ TA @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ A @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (zero_zero @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_ureturn__def)).
% 181.68/124.52 thf(3147,plain,((! [TA: $tType]: ((heap_Time_ureturn @ TA) = (^ [A:TA]: (heap_Time_heap @ TA @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ A @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (zero_zero @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[703])).
% 181.68/124.52 thf(900,axiom,((bounded_lattice_top @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Obounded__lattice__top)).
% 181.68/124.52 thf(3755,plain,((bounded_lattice_top @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[900])).
% 181.68/124.52 thf(922,axiom,((semiring_modulo @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__modulo_119)).
% 181.68/124.52 thf(3802,plain,((semiring_modulo @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[922])).
% 181.68/124.52 thf(732,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA]: ((fChoice @ (product_prod @ TB @ TA) @ (product_case_prod @ TB @ TA @ $o @ (^ [C:TB,D:TA]: ((A = C) & (B = D))))) = (product_Pair @ TB @ TA @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4649_Eps__case__prod__eq)).
% 181.68/124.52 thf(3225,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA]: ((fChoice @ (product_prod @ TB @ TA) @ (product_case_prod @ TB @ TA @ $o @ (^ [C:TB,D:TA]: ((A = C) & (B = D))))) = (product_Pair @ TB @ TA @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[732])).
% 181.68/124.52 thf(230,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:nat,D:TA,E:(heap_ext @ product_unit)]: (((product_Pair @ (array @ TA) @ (heap_ext @ product_unit) @ A @ B) = (array_alloc @ TA @ (replicate @ TA @ C @ D) @ E)) => (heap_Time_effect @ (array @ TA) @ (array_new @ TA @ C @ D) @ E @ B @ A @ (plus_plus @ nat @ C @ (one_one @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3559_effect__newI)).
% 181.68/124.52 thf(1695,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:nat,D:TA,E:(heap_ext @ product_unit)]: (((product_Pair @ (array @ TA) @ (heap_ext @ product_unit) @ A @ B) = (array_alloc @ TA @ (replicate @ TA @ C @ D) @ E)) => (heap_Time_effect @ (array @ TA) @ (array_new @ TA @ C @ D) @ E @ B @ A @ (plus_plus @ nat @ C @ (one_one @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
% 181.68/124.52 thf(846,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ TD))) > $o),B:(product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ TD)))]: ((! [C:TA,D:TB,E:TC,F:TD]: (A @ (product_Pair @ TA @ (product_prod @ TB @ (product_prod @ TC @ TD)) @ C @ (product_Pair @ TB @ (product_prod @ TC @ TD) @ D @ (product_Pair @ TC @ TD @ E @ F))))) => (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_prod__induct4)).
% 181.68/124.52 thf(3592,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ TD))) > $o),B:(product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ TD)))]: ((! [C:TA,D:TB,E:TC,F:TD]: (A @ (product_Pair @ TA @ (product_prod @ TB @ (product_prod @ TC @ TD)) @ C @ (product_Pair @ TB @ (product_prod @ TC @ TD) @ D @ (product_Pair @ TC @ TD @ E @ F))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[846])).
% 181.68/124.52 thf(57,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/sandbox/benchmark/theBenchmark.p',fact_592_nat__diff__add__eq1)).
% 181.68/124.52 thf(1187,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)],[57])).
% 181.68/124.52 thf(48,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/sandbox/benchmark/theBenchmark.p',fact_588_nat__eq__add__iff1)).
% 181.68/124.52 thf(1167,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)],[48])).
% 181.68/124.52 thf(643,axiom,((! [TA: $tType]: ((quickc3360725361186068524ustive @ TA) => (quickc3360725361186068524ustive @ (set @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Quickcheck__Exhaustive_Ofull__exhaustive_242)).
% 181.68/124.52 thf(2995,plain,((! [TA: $tType]: ((quickc3360725361186068524ustive @ TA) => (quickc3360725361186068524ustive @ (set @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[643])).
% 181.68/124.52 thf(943,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: ((heap_Time_execute @ TA @ (heap_Time_Heap2 @ TA @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_execute_Osimps)).
% 181.68/124.52 thf(3841,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: ((heap_Time_execute @ TA @ (heap_Time_Heap2 @ TA @ A)) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[943])).
% 181.68/124.52 thf(242,axiom,(((top_top @ product_unit) = product_Unity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3034_top__unit__def)).
% 181.68/124.52 thf(1732,plain,(((top_top @ product_unit) = product_Unity)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
% 181.68/124.52 thf(925,axiom,(((default_default @ product_unit) = product_Unity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3112_default__unit__def)).
% 181.68/124.52 thf(3807,plain,(((default_default @ product_unit) = product_Unity)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[925])).
% 181.68/124.52 thf(936,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(array @ TA),C:nat,D:TA]: ((ord_less_eq @ nat @ (array_length @ TA @ A @ B) @ C) => ((heap_Time_execute @ TA @ (array_swap @ TA @ C @ D @ B) @ A) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4102_execute__swap_I2_J)).
% 181.68/124.52 thf(3824,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(array @ TA),C:nat,D:TA]: ((ord_less_eq @ nat @ (array_length @ TA @ A @ B) @ C) => ((heap_Time_execute @ TA @ (array_swap @ TA @ C @ D @ B) @ A) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[936])).
% 181.68/124.52 thf(275,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TC @ TB),B:assn,C:(TC > (TB > (heap_Time_Heap @ TA))),D:(TA > assn)]: ((! [E:TC,F:TB]: ((A = (product_Pair @ TC @ TB @ E @ F)) => (hoare_hoare_triple @ TA @ B @ (C @ E @ F) @ D))) => (hoare_hoare_triple @ TA @ B @ (product_case_prod @ TC @ TB @ (heap_Time_Heap @ TA) @ C @ A) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5662_case__prod__rule)).
% 181.68/124.52 thf(1857,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TC @ TB),B:assn,C:(TC > (TB > (heap_Time_Heap @ TA))),D:(TA > assn)]: ((! [E:TC,F:TB]: ((A = (product_Pair @ TC @ TB @ E @ F)) => (hoare_hoare_triple @ TA @ B @ (C @ E @ F) @ (D)))) => (hoare_hoare_triple @ TA @ B @ (product_case_prod @ TC @ TB @ (heap_Time_Heap @ TA) @ (C) @ A) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])).
% 181.68/124.52 thf(320,axiom,((! [TA: $tType]: (! [A:nat,B:nat,C:(list @ TA)]: ((rotate @ TA @ A @ (rotate @ TA @ B @ C)) = (rotate @ TA @ (plus_plus @ nat @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4013_rotate__rotate)).
% 181.68/124.52 thf(1991,plain,((! [TA: $tType]: (! [A:nat,B:nat,C:(list @ TA)]: ((rotate @ TA @ A @ (rotate @ TA @ B @ C)) = (rotate @ TA @ (plus_plus @ nat @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])).
% 181.68/124.52 thf(107,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((A = B) => ((ord_less @ nat @ C @ D) => (ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ E) @ C) @ (plus_plus @ nat @ (times_times @ nat @ B @ E) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_mlex__snd__decrI)).
% 181.68/124.52 thf(1318,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((A = B) => ((ord_less @ nat @ C @ D) => (ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ E) @ C) @ (plus_plus @ nat @ (times_times @ nat @ B @ E) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
% 181.68/124.52 thf(62,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:(TA > nat),D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (mlex_prod @ TA @ C @ D)) = ((ord_less @ nat @ (C @ A) @ (C @ B)) | (((C @ A) = (C @ B)) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_mlex__iff)).
% 181.68/124.52 thf(1202,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:(TA > nat),D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (mlex_prod @ TA @ (C) @ D)) = ((ord_less @ nat @ (C @ A) @ (C @ B)) | (((C @ A) = (C @ B)) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
% 181.68/124.52 thf(388,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > TB),B:(TC > (option @ TA)),C:TC,D:TA]: ((comp @ (option @ TA) @ (option @ TB) @ TC @ (map_option @ TA @ TB @ A) @ (fun_upd @ TC @ (option @ TA) @ B @ C @ (some @ TA @ D))) = (fun_upd @ TC @ (option @ TB) @ (comp @ (option @ TA) @ (option @ TB) @ TC @ (map_option @ TA @ TB @ A) @ B) @ C @ (some @ TB @ (A @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2726_map__option__o__map__upd)).
% 181.68/124.52 thf(2203,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > TB),B:(TC > (option @ TA)),C:TC,D:TA]: ((comp @ (option @ TA) @ (option @ TB) @ TC @ (map_option @ TA @ TB @ A) @ (fun_upd @ TC @ (option @ TA) @ B @ C @ (some @ TA @ D))) = (fun_upd @ TC @ (option @ TB) @ (comp @ (option @ TA) @ (option @ TB) @ TC @ (map_option @ TA @ TB @ A) @ B) @ C @ (some @ TB @ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])).
% 181.68/124.52 thf(551,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:TA]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => ((heap_Time_execute @ (array @ TA) @ (array_upd @ TA @ A @ D @ C) @ B) = (some @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ (array_update @ TA @ C @ A @ D @ B) @ (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4103_execute__upd_I1_J)).
% 181.68/124.52 thf(2702,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:TA]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => ((heap_Time_execute @ (array @ TA) @ (array_upd @ TA @ A @ D @ C) @ B) = (some @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ (array_update @ TA @ C @ A @ D @ B) @ (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[551])).
% 181.68/124.52 thf(500,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/sandbox/benchmark/theBenchmark.p',fact_455_le__iff__add)).
% 181.68/124.52 thf(2546,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)],[500])).
% 181.68/124.52 thf(338,axiom,((! [TA: $tType]: (! [A:$o,B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat,G:(heap_Time_Heap @ TA)]: (((A) => (heap_Time_effect @ TA @ B @ C @ D @ E @ F)) => (((~ (A)) => (heap_Time_effect @ TA @ G @ C @ D @ E @ F)) => (heap_Time_effect @ TA @ (if @ (heap_Time_Heap @ TA) @ A @ B @ G) @ C @ D @ E @ F)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_effect__ifI)).
% 181.68/124.52 thf(2043,plain,((! [TA: $tType]: (! [A:$o,B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat,G:(heap_Time_Heap @ TA)]: (((A) => (heap_Time_effect @ TA @ B @ C @ D @ E @ F)) => (((~ (A)) => (heap_Time_effect @ TA @ G @ C @ D @ E @ F)) => (heap_Time_effect @ TA @ (if @ (heap_Time_Heap @ TA) @ A @ B @ G) @ C @ D @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])).
% 181.68/124.52 thf(752,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TA > TB),C:TA]: ((rec_option @ TB @ TA @ A @ B @ (some @ TA @ C)) = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_option_Osimps_I7_J)).
% 181.68/124.52 thf(3279,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TA > TB),C:TA]: ((rec_option @ TB @ TA @ A @ (B) @ (some @ TA @ C)) = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[752])).
% 181.68/124.52 thf(633,axiom,((! [TA: $tType,TB: $tType]: (((quickcheck_random @ TB) & (quickcheck_random @ TA)) => (quickcheck_random @ (product_prod @ TB @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_396)).
% 181.68/124.52 thf(2963,plain,((! [TA: $tType,TB: $tType]: (((quickcheck_random @ TB) & (quickcheck_random @ TA)) => (quickcheck_random @ (product_prod @ TB @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[633])).
% 181.68/124.52 thf(768,axiom,((! [TA: $tType]: ((heap_Time_Heap_lub @ TA @ (bot_bot @ (set @ (heap_Time_Heap @ TA)))) = (heap_Time_Heap2 @ TA @ (^ [A:(heap_ext @ product_unit)]: (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4849_Heap__lub__empty)).
% 181.68/124.52 thf(3321,plain,((! [TA: $tType]: ((heap_Time_Heap_lub @ TA @ (bot_bot @ (set @ (heap_Time_Heap @ TA)))) = (heap_Time_Heap2 @ TA @ (^ [A:(heap_ext @ product_unit)]: (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[768])).
% 181.68/124.52 thf(3,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo @ nat @ A @ B) = (modulo_modulo @ nat @ C @ B)) = (? [D:nat,E:nat]: ((plus_plus @ nat @ A @ (times_times @ nat @ B @ D)) = (plus_plus @ nat @ C @ (times_times @ nat @ B @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_nat__mod__eq__iff)).
% 181.68/124.52 thf(1035,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo @ nat @ A @ B) = (modulo_modulo @ nat @ C @ B)) = (? [D:nat,E:nat]: ((plus_plus @ nat @ A @ (times_times @ nat @ B @ D)) = (plus_plus @ nat @ C @ (times_times @ nat @ B @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 181.68/124.52 thf(457,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:nat,C:(array @ TA),D:TA,E:TA,F:(heap_ext @ product_unit)]: ((A != B) => ((array_update @ TA @ C @ A @ D @ (array_update @ TA @ C @ B @ E @ F)) = (array_update @ TA @ C @ B @ E @ (array_update @ TA @ C @ A @ D @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4094_update__swap__neqIndex)).
% 181.68/124.52 thf(2408,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:nat,C:(array @ TA),D:TA,E:TA,F:(heap_ext @ product_unit)]: ((~ (A = B)) => ((array_update @ TA @ C @ A @ D @ (array_update @ TA @ C @ B @ E @ F)) = (array_update @ TA @ C @ B @ E @ (array_update @ TA @ C @ A @ D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])).
% 181.68/124.52 thf(221,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(option @ TA),C:(TA > (option @ TB))]: ((map_option @ TB @ TC @ A @ (bind @ TA @ TB @ B @ C)) = (bind @ TA @ TC @ B @ (comp @ (option @ TB) @ (option @ TC) @ TA @ (map_option @ TB @ TC @ A) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_map__option__bind)).
% 181.68/124.52 thf(1663,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(option @ TA),C:(TA > (option @ TB))]: ((map_option @ TB @ TC @ (A) @ (bind @ TA @ TB @ B @ (C))) = (bind @ TA @ TC @ B @ (comp @ (option @ TB) @ (option @ TC) @ TA @ (map_option @ TB @ TC @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
% 181.68/124.52 thf(172,axiom,((! [A:nat,B:(heap_ext @ product_unit)]: ~ (time_fails @ product_unit @ (heap_Time_wait @ A) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_fails__wait)).
% 181.68/124.52 thf(1515,plain,((! [A:nat,B:(heap_ext @ product_unit)]: ~ (time_fails @ product_unit @ (heap_Time_wait @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
% 181.68/124.52 thf(1029,axiom,((inf @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Oinf_421)).
% 181.68/124.52 thf(4036,plain,((inf @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029])).
% 181.68/124.52 thf(538,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (TA > $o)),B:(product_prod @ TB @ TA)]: ((product_case_prod @ TB @ TA @ $o @ A @ B) => (~ (! [C:TB,D:TA]: ((B = (product_Pair @ TB @ TA @ C @ D)) => (~ (A @ C @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_case__prodE)).
% 181.68/124.52 thf(2662,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (TA > $o)),B:(product_prod @ TB @ TA)]: ((product_case_prod @ TB @ TA @ $o @ (A) @ B) => (~ (! [C:TB,D:TA]: ((B = (product_Pair @ TB @ TA @ C @ D)) => (~ (A @ C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[538])).
% 181.68/124.52 thf(55,axiom,((cl_HOL_Oequal @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___HOL_Oequal_511)).
% 181.68/124.52 thf(1185,plain,((cl_HOL_Oequal @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
% 181.68/124.52 thf(399,axiom,((comm_semiring_0 @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__0_547)).
% 181.68/124.52 thf(2235,plain,((comm_semiring_0 @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])).
% 181.68/124.52 thf(696,axiom,((! [TA: $tType]: ((bounded_lattice_top @ TA) => (bounded_lattice_top @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Lattices_Obounded__lattice__top_29)).
% 181.68/124.52 thf(3130,plain,((! [TA: $tType]: ((bounded_lattice_top @ TA) => (bounded_lattice_top @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[696])).
% 181.68/124.52 thf(381,axiom,((! [TA: $tType]: (! [A:nat,B:(TA > (nat > $o))]: ((! [C:nat]: ((ord_less @ nat @ C @ A) => (? [D:TA]: (B @ D @ C)))) => (~ (! [C:(list @ TA)]: (((size_size @ (list @ TA) @ C) = A) => (~ (! [D:nat]: ((ord_less @ nat @ D @ A) => (B @ (nth @ TA @ C @ D) @ D))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3578_obtain__list__from__elements)).
% 181.68/124.52 thf(2176,plain,((! [TA: $tType]: (! [A:nat,B:(TA > (nat > $o))]: ((! [C:nat]: ((ord_less @ nat @ C @ A) => (? [D:TA]: (B @ D @ C)))) => (~ (! [C:(list @ TA)]: (((size_size @ (list @ TA) @ C) = A) => (~ (! [D:nat]: ((ord_less @ nat @ D @ A) => (B @ (nth @ TA @ C @ D) @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])).
% 181.68/124.52 thf(613,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/sandbox/benchmark/theBenchmark.p',fact_305_Euclid__induct)).
% 181.68/124.52 thf(2904,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)],[613])).
% 181.68/124.52 thf(231,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_make @ TA) = (^ [A:nat,B:(nat > TA)]: (heap_Time_heap @ (array @ TA) @ (^ [C:(heap_ext @ product_unit)]: (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [D:(array @ TA),E:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ (one_one @ nat))))) @ (array_alloc @ TA @ (map @ nat @ TA @ B @ (upt @ (zero_zero @ nat) @ A)) @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3542_Array__Time_Omake__def)).
% 181.68/124.52 thf(1698,plain,((! [TA: $tType]: ((heap @ TA) => ((array_make @ TA) = (^ [A:nat,B:(nat > TA)]: (heap_Time_heap @ (array @ TA) @ (^ [C:(heap_ext @ product_unit)]: (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [D:(array @ TA),E:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ (one_one @ nat))))) @ (array_alloc @ TA @ (map @ nat @ TA @ B @ (upt @ (zero_zero @ nat) @ A)) @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])).
% 181.68/124.52 thf(68,axiom,((comm_semiring @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Ocomm__semiring_481)).
% 181.68/124.52 thf(1219,plain,((comm_semiring @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
% 181.68/124.52 thf(89,axiom,((! [A:nat]: ((minus_minus @ nat @ (suc @ A) @ (one_one @ nat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_diff__Suc__1)).
% 181.68/124.52 thf(1273,plain,((! [A:nat]: ((minus_minus @ nat @ (suc @ A) @ (one_one @ nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
% 181.68/124.52 thf(246,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TA > TB)]: ((comp @ (option @ TB) @ (option @ TC) @ (option @ TA) @ (map_option @ TB @ TC @ A) @ (map_option @ TA @ TB @ B)) = (map_option @ TA @ TC @ (comp @ TB @ TC @ TA @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_map__option_Ocomp)).
% 181.68/124.52 thf(1747,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TA > TB)]: ((comp @ (option @ TB) @ (option @ TC) @ (option @ TA) @ (map_option @ TB @ TC @ A) @ (map_option @ TA @ TB @ B)) = (map_option @ TA @ TC @ (comp @ TB @ TC @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])).
% 181.68/124.52 thf(744,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(TA > (option @ TB))]: ((A = B) => ((bind @ TA @ TB @ A @ C) = (bind @ TA @ TB @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_bind__option__cong__code)).
% 181.68/124.52 thf(3262,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(TA > (option @ TB))]: ((A = B) => ((bind @ TA @ TB @ A @ (C)) = (bind @ TA @ TB @ B @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[744])).
% 181.68/124.52 thf(519,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:(list @ TA),D:(heap_ext @ product_unit)]: (((product_Pair @ (array @ TA) @ (heap_ext @ product_unit) @ A @ B) = (array_alloc @ TA @ C @ D)) => (heap_Time_effect @ (array @ TA) @ (array_of_list @ TA @ C) @ D @ B @ A @ (plus_plus @ nat @ (one_one @ nat) @ (size_size @ (list @ TA) @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3539_effect__of__listI)).
% 181.68/124.52 thf(2602,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:(list @ TA),D:(heap_ext @ product_unit)]: (((product_Pair @ (array @ TA) @ (heap_ext @ product_unit) @ A @ B) = (array_alloc @ TA @ C @ D)) => (heap_Time_effect @ (array @ TA) @ (array_of_list @ TA @ C) @ D @ B @ A @ (plus_plus @ nat @ (one_one @ nat) @ (size_size @ (list @ TA) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])).
% 181.68/124.52 thf(918,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: ((map_add @ TA @ TB @ (^ [B:TA]: (none @ TB)) @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3396_empty__map__add)).
% 181.68/124.52 thf(3792,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: ((map_add @ TA @ TB @ (^ [B:TA]: (none @ TB)) @ A) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[918])).
% 181.68/124.52 thf(774,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TA),B:(TA > (heap_Time_Heap @ TB)),C:(heap_ext @ product_unit)]: ((time_fails @ TB @ (heap_Time_bind @ TA @ TB @ A @ B) @ C) = ((~ (time_fails @ TA @ A @ C)) => (time_fails @ TB @ (B @ (time_the_res @ TA @ A @ C)) @ (time_the_heap @ TA @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_fails__bind)).
% 181.68/124.52 thf(3343,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TA),B:(TA > (heap_Time_Heap @ TB)),C:(heap_ext @ product_unit)]: ((time_fails @ TB @ (heap_Time_bind @ TA @ TB @ A @ (B)) @ C) = ((~ (time_fails @ TA @ A @ C)) => (time_fails @ TB @ (B @ (time_the_res @ TA @ A @ C)) @ (time_the_heap @ TA @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[774])).
% 181.68/124.52 thf(40,axiom,((dvd @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Odvd_510)).
% 181.68/124.52 thf(1146,plain,((dvd @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
% 181.68/124.52 thf(413,axiom,((! [TA: $tType]: ((pred_option @ TA @ (^ [A:TA]: (($true)))) = (^ [A:(option @ TA)]: (($true)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5058_option_Opred__True)).
% 181.68/124.52 thf(2292,plain,((! [TA: $tType]: ((pred_option @ TA @ (^ [A:TA]: (($true)))) = (^ [A:(option @ TA)]: (($true)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])).
% 181.68/124.52 thf(959,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(array @ TA),C:nat]: ((ord_less_eq @ nat @ (array_length @ TA @ A @ B) @ C) => ((heap_Time_execute @ TA @ (array_nth @ TA @ B @ C) @ A) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4073_execute__nth_I2_J)).
% 181.68/124.52 thf(3871,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(array @ TA),C:nat]: ((ord_less_eq @ nat @ (array_length @ TA @ A @ B) @ C) => ((heap_Time_execute @ TA @ (array_nth @ TA @ B @ C) @ A) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[959])).
% 181.68/124.52 thf(334,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:TB]: ((fun_upd @ TA @ (option @ TB) @ A @ B @ (some @ TB @ C)) != (^ [D:TA]: (none @ TB)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2741_map__upd__nonempty)).
% 181.68/124.52 thf(2033,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:TB]: ~ ((fun_upd @ TA @ (option @ TB) @ A @ B @ (some @ TB @ C)) = (^ [D:TA]: (none @ TB)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])).
% 181.68/124.52 thf(891,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/sandbox/benchmark/theBenchmark.p',fact_467_trans__le__add1)).
% 181.68/124.52 thf(3738,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)],[891])).
% 181.68/124.52 thf(332,axiom,((! [TA: $tType,TB: $tType]: ((preorder @ TA) => (preorder @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder)).
% 181.68/124.52 thf(2028,plain,((! [TA: $tType,TB: $tType]: ((preorder @ TA) => (preorder @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])).
% 181.68/124.52 thf(99,axiom,((! [A:nat,B:nat]: ((times_times @ nat @ (suc @ A) @ B) = (plus_plus @ nat @ B @ (times_times @ nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_mult__Suc)).
% 181.68/124.52 thf(1301,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)],[99])).
% 181.68/124.52 thf(966,axiom,((zero_less_one @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__less__one_129)).
% 181.68/124.52 thf(3888,plain,((zero_less_one @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[966])).
% 181.68/124.52 thf(941,axiom,((semiring @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring_145)).
% 181.68/124.52 thf(3839,plain,((semiring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[941])).
% 181.68/124.52 thf(489,axiom,((countable @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Countable_Ocountable_133)).
% 181.68/124.52 thf(2524,plain,((countable @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[489])).
% 181.68/124.52 thf(446,axiom,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((minus_minus @ TA @ (plus_plus @ TA @ A @ B) @ (plus_plus @ TA @ C @ B)) = (minus_minus @ TA @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_add__diff__cancel__right)).
% 181.68/124.52 thf(2376,plain,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA,C:TA]: ((minus_minus @ TA @ (plus_plus @ TA @ A @ B) @ (plus_plus @ TA @ C @ B)) = (minus_minus @ TA @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[446])).
% 181.68/124.52 thf(560,axiom,((! [TA: $tType]: (! [A:$o,B:(TA > $o),C:(option @ TA)]: ((case_option @ $o @ TA @ A @ B @ C) => (((C = (none @ TA)) => (~ (A))) => (~ (! [D:TA]: ((C = (some @ TA @ D)) => (~ (B @ D)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_case__optionE)).
% 181.68/124.52 thf(2727,plain,((! [TA: $tType]: (! [A:$o,B:(TA > $o),C:(option @ TA)]: ((case_option @ $o @ TA @ A @ (B) @ C) => (((C = (none @ TA)) => (~ (A))) => (~ (! [D:TA]: ((C = (some @ TA @ D)) => (~ (B @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[560])).
% 181.68/124.52 thf(906,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ TB)]: ((bind @ TB @ TA @ A @ (^ [B:TB]: (none @ TA))) = (none @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_bind__rzero)).
% 181.68/124.52 thf(3768,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ TB)]: ((bind @ TB @ TA @ A @ (^ [B:TB]: (none @ TA))) = (none @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[906])).
% 181.68/124.52 thf(824,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: ((map_le @ TB @ TA @ A @ B) => (((A @ C) = (some @ TA @ D)) => ((B @ C) = (some @ TA @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3405_map__leD)).
% 181.68/124.52 thf(3504,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: ((map_le @ TB @ TA @ (A) @ (B)) => (((A @ C) = (some @ TA @ D)) => ((B @ C) = (some @ TA @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[824])).
% 181.68/124.52 thf(131,axiom,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus @ nat @ B @ C)) => ((suc @ A) = (plus_plus @ nat @ B @ (suc @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_nat__arith_Osuc1)).
% 181.68/124.52 thf(1389,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)],[131])).
% 181.68/124.52 thf(928,axiom,((semilattice_sup @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Osemilattice__sup_406)).
% 181.68/124.52 thf(3811,plain,((semilattice_sup @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[928])).
% 181.68/124.52 thf(36,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ D) => (ord_less_eq @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ E) @ C) @ (plus_plus @ nat @ (times_times @ nat @ B @ E) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_mlex__leI)).
% 181.68/124.52 thf(1125,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ C @ D) => (ord_less_eq @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ E) @ C) @ (plus_plus @ nat @ (times_times @ nat @ B @ E) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
% 181.68/124.52 thf(490,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: ((product_case_prod @ TA @ TB @ (TC > TD)) = (^ [A:(TA > (TB > (TC > TD))),B:(product_prod @ TA @ TB),C:TC]: (product_case_prod @ TA @ TB @ TD @ (^ [D:TA,E:TB]: (A @ D @ E @ C)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_nested__case__prod__simp)).
% 181.68/124.52 thf(2525,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: ((product_case_prod @ TA @ TB @ (TC > TD)) = (^ [A:(TA > (TB > (TC > TD))),B:(product_prod @ TA @ TB),C:TC]: (product_case_prod @ TA @ TB @ TD @ (^ [D:TA,E:TB]: (A @ D @ E @ C)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[490])).
% 181.68/124.52 thf(208,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:TB,C:TA,D:TB,E:TA]: (((fun_upd @ TB @ (option @ TA) @ A @ B @ (some @ TA @ C) @ D) = (some @ TA @ E)) = (((D = B) & (C = E)) | ((D != B) & ((A @ D) = (some @ TA @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2734_map__upd__Some__unfold)).
% 181.68/124.52 thf(1620,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:TB,C:TA,D:TB,E:TA]: (((fun_upd @ TB @ (option @ TA) @ (A) @ B @ (some @ TA @ C) @ D) = (some @ TA @ E)) = (((D = B) & (C = E)) | (~ (D = B) & ((A @ D) = (some @ TA @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
% 181.68/124.52 thf(1027,axiom,((complete_Inf @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Complete__Lattices_OInf_410)).
% 181.68/124.52 thf(4032,plain,((complete_Inf @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027])).
% 181.68/124.52 thf(975,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: (map_le @ TA @ TB @ (^ [B:TA]: (none @ TB)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3407_map__le__empty)).
% 181.68/124.52 thf(3900,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: (map_le @ TA @ TB @ (^ [B:TA]: (none @ TB)) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[975])).
% 181.68/124.52 thf(586,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TB > TD),C:(TB > TC),D:(TA > TB)]: (((comp @ TD @ TC @ TB @ A @ B) = C) => ((comp @ TD @ TC @ TA @ A @ (comp @ TB @ TD @ TA @ B @ D)) = (comp @ TB @ TC @ TA @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_rewriteL__comp__comp)).
% 181.68/124.52 thf(2806,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TB > TD),C:(TB > TC),D:(TA > TB)]: (((comp @ TD @ TC @ TB @ A @ B) = (C)) => ((comp @ TD @ TC @ TA @ A @ (comp @ TB @ TD @ TA @ B @ D)) = (comp @ TB @ TC @ TA @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[586])).
% 181.68/124.52 thf(555,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (option @ TC)),B:(TB > (option @ TA)),C:TB,D:TC]: (((map_comp @ TA @ TC @ TB @ A @ B @ C) = (some @ TC @ D)) = (? [E:TA]: (((B @ C) = (some @ TA @ E)) & ((A @ E) = (some @ TC @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_map__comp__Some__iff)).
% 181.68/124.52 thf(2716,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (option @ TC)),B:(TB > (option @ TA)),C:TB,D:TC]: (((map_comp @ TA @ TC @ TB @ (A) @ (B) @ C) = (some @ TC @ D)) = (? [E:TA]: (((B @ C) = (some @ TA @ E)) & ((A @ E) = (some @ TC @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[555])).
% 181.68/124.52 thf(957,axiom,((! [TA: $tType]: (cl_HOL_Oequal @ (array @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oarray___HOL_Oequal_301)).
% 181.68/124.52 thf(3868,plain,((! [TA: $tType]: (cl_HOL_Oequal @ (array @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[957])).
% 181.68/124.52 thf(83,axiom,((! [TA: $tType]: (! [A:nat,B:nat,C:(list @ TA)]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ B @ (size_size @ (list @ TA) @ C)) => ((size_size @ (list @ TA) @ (slice @ TA @ A @ B @ C)) = (minus_minus @ nat @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3534_slice__len)).
% 181.68/124.52 thf(1256,plain,((! [TA: $tType]: (! [A:nat,B:nat,C:(list @ TA)]: ((ord_less_eq @ nat @ A @ B) => ((ord_less_eq @ nat @ B @ (size_size @ (list @ TA) @ C)) => ((size_size @ (list @ TA) @ (slice @ TA @ A @ B @ C)) = (minus_minus @ nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
% 181.68/124.52 thf(892,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: (pred_option @ TA @ A @ (none @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5057_option_Opred__inject_I1_J)).
% 181.68/124.52 thf(3741,plain,((! [TA: $tType]: (! [A:(TA > $o)]: (pred_option @ TA @ (A) @ (none @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[892])).
% 181.68/124.52 thf(270,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ (ref_lookup @ TA @ A) @ B @ C @ D @ E) => (~ ((C = B) => ((D = (ref_get @ TA @ B @ A)) => (E != (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_effect__lookupE)).
% 181.68/124.52 thf(1833,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ (ref_lookup @ TA @ A) @ B @ C @ D @ E) => (~ ((C = B) => ((D = (ref_get @ TA @ B @ A)) => (~ (E = (one_one @ nat))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])).
% 181.68/124.52 thf(636,axiom,((! [TA: $tType]: ((inf @ TA) => ((inf_inf @ (option @ TA)) = (^ [A:(option @ TA),B:(option @ TA)]: (case_option @ (option @ TA) @ TA @ (none @ TA) @ (^ [C:TA]: (case_option @ (option @ TA) @ TA @ (none @ TA) @ (^ [D:TA]: (some @ TA @ (inf_inf @ TA @ C @ D))) @ B)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3050_inf__option__def)).
% 181.68/124.52 thf(2970,plain,((! [TA: $tType]: ((inf @ TA) => ((inf_inf @ (option @ TA)) = (^ [A:(option @ TA),B:(option @ TA)]: (case_option @ (option @ TA) @ TA @ (none @ TA) @ (^ [C:TA]: (case_option @ (option @ TA) @ TA @ (none @ TA) @ (^ [D:TA]: (some @ TA @ (inf_inf @ TA @ C @ D))) @ B)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[636])).
% 181.68/124.52 thf(767,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > ((heap_ext @ product_unit) > ((heap_ext @ product_unit) > (TB > (nat > $o)))))]: (comple1908693960933563346ssible @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (^ [B:(TA > (heap_Time_Heap @ TB))]: ! [C:TA,D:(heap_ext @ product_unit),E:(heap_ext @ product_unit),F:TB,G:nat]: ((heap_Time_effect @ TB @ (B @ C) @ D @ E @ F @ G) => (A @ C @ D @ E @ F @ G))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5992_admissible__heap)).
% 181.68/124.52 thf(3319,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > ((heap_ext @ product_unit) > ((heap_ext @ product_unit) > (TB > (nat > $o)))))]: (comple1908693960933563346ssible @ (TA > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (^ [B:(TA > (heap_Time_Heap @ TB))]: ! [C:TA,D:(heap_ext @ product_unit),E:(heap_ext @ product_unit),F:TB,G:nat]: ((heap_Time_effect @ TB @ (B @ C) @ D @ E @ F @ G) => (A @ C @ D @ E @ F @ G))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[767])).
% 181.68/124.52 thf(860,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/sandbox/benchmark/theBenchmark.p',fact_448_add__mono__thms__linordered__semiring_I3_J)).
% 181.68/124.52 thf(3636,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)],[860])).
% 181.68/124.52 thf(987,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB]: (((map_add @ TB @ TA @ A @ B @ C) = (none @ TA)) = (((B @ C) = (none @ TA)) & ((A @ C) = (none @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3395_map__add__None)).
% 181.68/124.52 thf(3925,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB]: (((map_add @ TB @ TA @ (A) @ (B) @ C) = (none @ TA)) = (((B @ C) = (none @ TA)) & ((A @ C) = (none @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[987])).
% 181.68/124.52 thf(217,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(list @ TA)]: ((map @ TC @ TB @ A @ (map @ TA @ TC @ B @ C)) = (map @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3482_List_Omap_Ocompositionality)).
% 181.68/124.52 thf(1652,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(list @ TA)]: ((map @ TC @ TB @ (A) @ (map @ TA @ TC @ (B) @ C)) = (map @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])).
% 181.68/124.52 thf(890,axiom,((! [TA: $tType]: (complete_Inf @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Lattices_OInf_252)).
% 181.68/124.52 thf(3736,plain,((! [TA: $tType]: (complete_Inf @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[890])).
% 181.68/124.52 thf(675,axiom,((! [TA: $tType]: ((heap @ TA) => ((ref_update @ TA) = (^ [A:(ref @ TA),B:TA]: (heap_Time_heap @ product_unit @ (^ [C:(heap_ext @ product_unit)]: (product_Pair @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat) @ product_Unity @ (product_Pair @ (heap_ext @ product_unit) @ nat @ (ref_set @ TA @ A @ B @ C) @ (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2988_Ref__Time_Oupdate__def)).
% 181.68/124.52 thf(3081,plain,((! [TA: $tType]: ((heap @ TA) => ((ref_update @ TA) = (^ [A:(ref @ TA),B:TA]: (heap_Time_heap @ product_unit @ (^ [C:(heap_ext @ product_unit)]: (product_Pair @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat) @ product_Unity @ (product_Pair @ (heap_ext @ product_unit) @ nat @ (ref_set @ TA @ A @ B @ C) @ (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[675])).
% 181.68/124.52 thf(300,axiom,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less @ TA @ C @ D) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_add__le__less__mono)).
% 181.68/124.52 thf(1929,plain,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: ((ord_less_eq @ 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)],[300])).
% 181.68/124.52 thf(745,axiom,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (heap_ext @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oheap_Oheap__ext___Typerep_Otyperep_8)).
% 181.68/124.52 thf(3266,plain,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (heap_ext @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[745])).
% 181.68/124.52 thf(509,axiom,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: ((ord_less_eq @ (TA > (TB > $o)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) = (ord_less_eq @ (set @ (product_prod @ TA @ TB)) @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_pred__subset__eq2)).
% 181.68/124.52 thf(2568,plain,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: ((ord_less_eq @ (TA > (TB > $o)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) = (ord_less_eq @ (set @ (product_prod @ TA @ TB)) @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])).
% 181.68/124.52 thf(136,axiom,((! [A:nat,B:nat]: ((plus_plus @ nat @ (suc @ A) @ B) = (suc @ (plus_plus @ nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_945_add__Suc)).
% 181.68/124.52 thf(1403,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)],[136])).
% 181.68/124.52 thf(813,axiom,((! [TA: $tType,TB: $tType]: (((quickc658316121487927005ustive @ TA) & (cl_HOL_Oequal @ TB) & (quickc658316121487927005ustive @ TB)) => (! [A:(product_prod @ ((TB > TA) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:((TB > TA) > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_natural,D:code_natural]: (A != (product_Pair @ ((TB > TA) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural) @ B @ (product_Pair @ code_natural @ code_natural @ C @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4218_exhaustive__fun_H_Ocases)).
% 181.68/124.52 thf(3458,plain,((! [TA: $tType,TB: $tType]: (((quickc658316121487927005ustive @ TA) & (cl_HOL_Oequal @ TB) & (quickc658316121487927005ustive @ TB)) => (! [A:(product_prod @ ((TB > TA) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:((TB > TA) > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_natural,D:code_natural]: ~ (A = (product_Pair @ ((TB > TA) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural) @ (B) @ (product_Pair @ code_natural @ code_natural @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[813])).
% 181.68/124.52 thf(258,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:TA]: ((fun_upd @ TA @ TB @ A @ B @ (A @ B)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2718_fun__upd__triv)).
% 181.68/124.52 thf(1795,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:TA]: ((fun_upd @ TA @ TB @ A @ B @ (A @ B)) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])).
% 181.68/124.52 thf(232,axiom,((! [A:nat,B:nat]: ((minus_minus @ nat @ A @ (plus_plus @ nat @ A @ B)) = (zero_zero @ nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_diff__add__0)).
% 181.68/124.52 thf(1701,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)],[232])).
% 181.68/124.52 thf(845,axiom,((! [TA: $tType]: ((heap @ TA) => (countable @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Heap_Oheap___Countable_Ocountable)).
% 181.68/124.52 thf(3590,plain,((! [TA: $tType]: ((heap @ TA) => (countable @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[845])).
% 181.68/124.52 thf(594,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TB,C:(TB > (heap_Time_Heap @ TA)),D:(heap_ext @ product_unit)]: ((A = B) => ((heap_Time_success @ TA @ (C @ A) @ D) => (heap_Time_success @ TA @ (C @ B) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_success__LetI)).
% 181.68/124.52 thf(2827,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TB,C:(TB > (heap_Time_Heap @ TA)),D:(heap_ext @ product_unit)]: ((A = B) => ((heap_Time_success @ TA @ (C @ A) @ D) => (heap_Time_success @ TA @ (C @ B) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[594])).
% 181.68/124.52 thf(848,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (TB > (option @ TA))),B:(TC > TC),C:((TB > (option @ TA)) > TC),D:TC,E:(TB > (TA > $o)),F:TB,G:TA]: ((! [H:TB]: (comple7038119648293358887notone @ (TB > (option @ TA)) @ (option @ TA) @ (partial_fun_ord @ (option @ TA) @ (option @ TA) @ TB @ (partial_flat_ord @ (option @ TA) @ (none @ TA))) @ (partial_flat_ord @ (option @ TA) @ (none @ TA)) @ (^ [I:(TB > (option @ TA))]: (A @ (B @ (C @ I)) @ H)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TB > (option @ TA)) @ (partial_fun_lub @ (option @ TA) @ (option @ TA) @ TB @ (partial_flat_lub @ (option @ TA) @ (none @ TA))) @ (partial_fun_ord @ (option @ TA) @ (option @ TA) @ TB @ (partial_flat_ord @ (option @ TA) @ (none @ TA))) @ (^ [H:(TB > (option @ TA))]: (A @ (B @ (C @ H))))))) => ((! [H:(TB > (option @ TA))]: ((A @ (C @ H)) = H)) => ((! [H:TC,I:TB,J:TA]: ((! [K:TB,L:TA]: (((A @ H @ K) = (some @ TA @ L)) => (E @ K @ L))) => (((A @ (B @ H) @ I) = (some @ TA @ J)) => (E @ I @ J)))) => (((A @ D @ F) = (some @ TA @ G)) => (E @ F @ G))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5980_fixp__induct__option)).
% 181.68/124.52 thf(3599,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (TB > (option @ TA))),B:(TC > TC),C:((TB > (option @ TA)) > TC),D:TC,E:(TB > (TA > $o)),F:TB,G:TA]: ((! [H:TB]: (comple7038119648293358887notone @ (TB > (option @ TA)) @ (option @ TA) @ (partial_fun_ord @ (option @ TA) @ (option @ TA) @ TB @ (partial_flat_ord @ (option @ TA) @ (none @ TA))) @ (partial_flat_ord @ (option @ TA) @ (none @ TA)) @ (^ [I:(TB > (option @ TA))]: (A @ (B @ (C @ I)) @ H)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TB > (option @ TA)) @ (partial_fun_lub @ (option @ TA) @ (option @ TA) @ TB @ (partial_flat_lub @ (option @ TA) @ (none @ TA))) @ (partial_fun_ord @ (option @ TA) @ (option @ TA) @ TB @ (partial_flat_ord @ (option @ TA) @ (none @ TA))) @ (^ [H:(TB > (option @ TA))]: (A @ (B @ (C @ H))))))) => ((! [H:(TB > (option @ TA))]: ((A @ (C @ H)) = (H))) => ((! [H:TC,I:TB,J:TA]: ((! [K:TB,L:TA]: (((A @ H @ K) = (some @ TA @ L)) => (E @ K @ L))) => (((A @ (B @ H) @ I) = (some @ TA @ J)) => (E @ I @ J)))) => (((A @ D @ F) = (some @ TA @ G)) => (E @ F @ G))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[848])).
% 181.68/124.52 thf(167,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((minus_minus @ TA @ (plus_plus @ TA @ B @ C) @ A) = (plus_plus @ TA @ (minus_minus @ TA @ B @ A) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2)).
% 181.68/124.52 thf(1503,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((minus_minus @ TA @ (plus_plus @ TA @ B @ C) @ A) = (plus_plus @ TA @ (minus_minus @ TA @ B @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
% 181.68/124.52 thf(425,axiom,((ab_semigroup_mult @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__mult_538)).
% 181.68/124.52 thf(2326,plain,((ab_semigroup_mult @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])).
% 181.68/124.52 thf(234,axiom,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: ((inf_inf @ (TA > (TB > $o)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) = (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ (inf_inf @ (set @ (product_prod @ TA @ TB)) @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3124_inf__Int__eq2)).
% 181.68/124.52 thf(1707,plain,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: ((inf_inf @ (TA > (TB > $o)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A)) @ (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) = (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ (inf_inf @ (set @ (product_prod @ TA @ TB)) @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])).
% 181.68/124.52 thf(863,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:((TA > (heap_Time_Heap @ TB)) > (heap_Time_Heap @ TD)),B:(TD > ((TA > (heap_Time_Heap @ TB)) > (heap_Time_Heap @ TC)))]: ((comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TD) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TD) @ A) => ((! [C:TD]: (comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TC) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TC) @ (B @ C))) => (comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TC) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TC) @ (^ [C:(TA > (heap_Time_Heap @ TB))]: (heap_Time_bind @ TD @ TC @ (A @ C) @ (^ [D:TD]: (B @ D @ C)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5986_Heap__Time__Monad_Obind__mono)).
% 181.68/124.52 thf(3646,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:((TA > (heap_Time_Heap @ TB)) > (heap_Time_Heap @ TD)),B:(TD > ((TA > (heap_Time_Heap @ TB)) > (heap_Time_Heap @ TC)))]: ((comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TD) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TD) @ (A)) => ((! [C:TD]: (comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TC) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TC) @ (B @ C))) => (comple7038119648293358887notone @ (TA > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TC) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TA @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TC) @ (^ [C:(TA > (heap_Time_Heap @ TB))]: (heap_Time_bind @ TD @ TC @ (A @ C) @ (^ [D:TD]: (B @ D @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[863])).
% 181.68/124.52 thf(12,axiom,((! [TA: $tType]: (! [A:(list @ TA)]: ((slice @ TA @ (zero_zero @ nat) @ (size_size @ (list @ TA) @ A) @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3535_slice__complete)).
% 181.68/124.52 thf(1058,plain,((! [TA: $tType]: (! [A:(list @ TA)]: ((slice @ TA @ (zero_zero @ nat) @ (size_size @ (list @ TA) @ A) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 181.68/124.52 thf(884,axiom,((! [A:$o,B:(heap_ext @ product_unit)]: ((time_fails @ product_unit @ (refine_Imp_assert @ A) @ B) = (~ (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_fails__assert_H)).
% 181.68/124.52 thf(3700,plain,((! [A:$o,B:(heap_ext @ product_unit)]: ((time_fails @ product_unit @ (refine_Imp_assert @ A) @ B) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[884])).
% 181.68/124.52 thf(292,axiom,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA,C:(TA > $o)]: ((accp @ TA @ A @ B) => ((! [D:TA]: ((accp @ TA @ A @ D) => ((! [E:TA]: ((A @ E @ D) => (C @ E))) => (C @ D)))) => (C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_accp__induct)).
% 181.68/124.52 thf(1897,plain,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA,C:(TA > $o)]: ((accp @ TA @ (A) @ B) => ((! [D:TA]: ((accp @ TA @ (A) @ D) => ((! [E:TA]: ((A @ E @ D) => (C @ E))) => (C @ D)))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])).
% 181.68/124.52 thf(462,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/sandbox/benchmark/theBenchmark.p',fact_648_diff__cancel2)).
% 181.68/124.52 thf(2425,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)],[462])).
% 181.68/124.52 thf(158,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) => (((C = (zero_zero @ nat)) => (A != B)) => (~ (! [E:TA,F:nat]: ((C = (suc @ F)) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ D) => (~ (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ F @ D)))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4990_relpow__E2)).
% 181.68/124.52 thf(1464,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) => (((C = (zero_zero @ nat)) => (~ (A = B))) => (~ (! [E:TA,F:nat]: ((C = (suc @ F)) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ D) => (~ (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ F @ D)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
% 181.68/124.52 thf(760,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_upd @ TA) = (^ [A:nat,B:TA,C:(array @ TA)]: (heap_Time_guard @ (array @ TA) @ (^ [D:(heap_ext @ product_unit)]: (ord_less @ nat @ A @ (array_length @ TA @ D @ C))) @ (^ [D:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ (array_update @ TA @ C @ A @ B @ D) @ (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4104_upd__def)).
% 181.68/124.52 thf(3302,plain,((! [TA: $tType]: ((heap @ TA) => ((array_upd @ TA) = (^ [A:nat,B:TA,C:(array @ TA)]: (heap_Time_guard @ (array @ TA) @ (^ [D:(heap_ext @ product_unit)]: (ord_less @ nat @ A @ (array_length @ TA @ D @ C))) @ (^ [D:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ (array_update @ TA @ C @ A @ B @ D) @ (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[760])).
% 181.68/124.52 thf(146,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/sandbox/benchmark/theBenchmark.p',fact_929_diff__Suc__diff__eq1)).
% 181.68/124.52 thf(1428,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)],[146])).
% 181.68/124.52 thf(377,axiom,((semigroup_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_552)).
% 181.68/124.52 thf(2161,plain,((semigroup_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])).
% 181.68/124.52 thf(690,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_success @ TA @ A @ B) => (~ (! [C:TA,D:(heap_ext @ product_unit),E:nat]: ~ (heap_Time_effect @ TA @ A @ B @ D @ C @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_success__effectE)).
% 181.68/124.52 thf(3118,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_success @ TA @ A @ B) => (~ (! [C:TA,D:(heap_ext @ product_unit),E:nat]: ~ (heap_Time_effect @ TA @ A @ B @ D @ C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[690])).
% 181.68/124.52 thf(394,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ (option @ TA) @ (some @ TA @ A) @ (some @ TA @ B)) = (ord_less_eq @ TA @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_less__eq__option__Some)).
% 181.68/124.52 thf(2220,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ (option @ TA) @ (some @ TA @ A) @ (some @ TA @ B)) = (ord_less_eq @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])).
% 181.68/124.52 thf(1002,axiom,((inf @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Oinf_148)).
% 181.68/124.52 thf(3964,plain,((inf @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002])).
% 181.68/124.52 thf(773,axiom,((! [TA: $tType]: ((heap_Time_guard @ TA) = (^ [A:((heap_ext @ product_unit) > $o),B:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: (heap_Time_Heap2 @ TA @ (^ [C:(heap_ext @ product_unit)]: (if @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (A @ C) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (B @ C)) @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_guard__def)).
% 181.68/124.52 thf(3340,plain,((! [TA: $tType]: ((heap_Time_guard @ TA) = (^ [A:((heap_ext @ product_unit) > $o),B:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: (heap_Time_Heap2 @ TA @ (^ [C:(heap_ext @ product_unit)]: (if @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (A @ C) @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (B @ C)) @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[773])).
% 181.68/124.52 thf(77,axiom,((! [A:nat,B:nat]: (((suc @ (zero_zero @ nat)) = (plus_plus @ nat @ A @ B)) = (((A = (suc @ (zero_zero @ nat))) & (B = (zero_zero @ nat))) | ((A = (zero_zero @ nat)) & (B = (suc @ (zero_zero @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_one__is__add)).
% 181.68/124.52 thf(1239,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)],[77])).
% 181.68/124.52 thf(322,axiom,((! [TA: $tType]: (! [A:(set @ TA)]: ((A != (bot_bot @ (set @ TA))) => (~ (! [B:TA]: ~ (member @ TA @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2114_set__notEmptyE)).
% 181.68/124.52 thf(1997,plain,((! [TA: $tType]: (! [A:(set @ TA)]: ((~ (A = (bot_bot @ (set @ TA)))) => (~ (! [B:TA]: ~ (member @ TA @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])).
% 181.68/124.52 thf(567,axiom,((enum @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Enum_Oenum_43)).
% 181.68/124.52 thf(2759,plain,((enum @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[567])).
% 181.68/124.52 thf(804,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA]: (map_le @ TA @ TB @ (fun_upd @ TA @ (option @ TB) @ A @ B @ (none @ TB)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3412_upd__None__map__le)).
% 181.68/124.52 thf(3436,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA]: (map_le @ TA @ TB @ (fun_upd @ TA @ (option @ TB) @ A @ B @ (none @ TB)) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[804])).
% 181.68/124.52 thf(914,axiom,((! [TA: $tType,TB: $tType]: (((enum @ TB) & (enum @ TA)) => (enum @ (product_prod @ TB @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Enum_Oenum_12)).
% 181.68/124.52 thf(3783,plain,((! [TA: $tType,TB: $tType]: (((enum @ TB) & (enum @ TA)) => (enum @ (product_prod @ TB @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[914])).
% 181.68/124.52 thf(341,axiom,((typerep2 @ code_term)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Evaluation_Oterm___Typerep_Otyperep_6)).
% 181.68/124.52 thf(2055,plain,((typerep2 @ code_term)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])).
% 181.68/124.52 thf(26,axiom,((suc = (plus_plus @ nat @ (one_one @ nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_Suc__eq__plus1__left)).
% 181.68/124.52 thf(1092,plain,(((suc) = (plus_plus @ nat @ (one_one @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 181.68/124.52 thf(379,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ~ (ord_less @ TA @ A @ (zero_zero @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_not__less__zero)).
% 181.68/124.52 thf(2166,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ~ (ord_less @ TA @ A @ (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])).
% 181.68/124.52 thf(252,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA),B:TB,C:TA]: ((fun_upd @ TB @ TA @ A @ B @ C @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2730_fun__upd__same)).
% 181.68/124.52 thf(1765,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA),B:TB,C:TA]: ((fun_upd @ TB @ TA @ (A) @ B @ C @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])).
% 181.68/124.52 thf(25,axiom,((! [A:nat,B:nat]: (ord_less @ nat @ A @ (suc @ (plus_plus @ nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_less__add__Suc1)).
% 181.68/124.52 thf(1090,plain,((! [A:nat,B:nat]: (ord_less @ nat @ A @ (suc @ (plus_plus @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 181.68/124.52 thf(373,axiom,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((A = B) & (ord_less @ TA @ C @ D)) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_add__mono__thms__linordered__field_I2_J)).
% 181.68/124.52 thf(2148,plain,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D: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)],[373])).
% 181.68/124.52 thf(438,axiom,(((bot_bot @ product_unit) = product_Unity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3036_bot__unit__def)).
% 181.68/124.52 thf(2358,plain,(((bot_bot @ product_unit) = product_Unity)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])).
% 181.68/124.52 thf(488,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TA,C:(TA > TB),D:TB]: ((A != B) => ((fun_upd @ TA @ TB @ C @ B @ D @ A) = (C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2731_fun__upd__other)).
% 181.68/124.52 thf(2521,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TA,C:(TA > TB),D:TB]: ((~ (A = B)) => ((fun_upd @ TA @ TB @ (C) @ B @ D @ A) = (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[488])).
% 181.68/124.52 thf(930,axiom,((euclid3128863361964157862miring @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Euclidean__Division_Ounique__euclidean__semiring_85)).
% 181.68/124.52 thf(3815,plain,((euclid3128863361964157862miring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[930])).
% 181.68/124.52 thf(291,axiom,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: (((^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A)) = (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_pred__equals__eq2)).
% 181.68/124.52 thf(1894,plain,((! [TA: $tType,TB: $tType]: (! [A:(set @ (product_prod @ TA @ TB)),B:(set @ (product_prod @ TA @ TB))]: (((^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ A)) = (^ [C:TA,D:TB]: (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ C @ D) @ B))) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])).
% 181.68/124.52 thf(262,axiom,((! [TA: $tType]: (! [A:(list @ TA),B:nat,C:nat,D:(nat > TA)]: (((size_size @ (list @ TA) @ A) = (minus_minus @ nat @ B @ C)) => ((! [E:nat]: ((ord_less @ nat @ E @ (size_size @ (list @ TA) @ A)) => ((nth @ TA @ A @ E) = (D @ (plus_plus @ nat @ C @ E))))) => ((map @ nat @ TA @ D @ (upt @ C @ B)) = A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3589_map__upt__eqI)).
% 181.68/124.52 thf(1806,plain,((! [TA: $tType]: (! [A:(list @ TA),B:nat,C:nat,D:(nat > TA)]: (((size_size @ (list @ TA) @ A) = (minus_minus @ nat @ B @ C)) => ((! [E:nat]: ((ord_less @ nat @ E @ (size_size @ (list @ TA) @ A)) => ((nth @ TA @ A @ E) = (D @ (plus_plus @ nat @ C @ E))))) => ((map @ nat @ TA @ (D) @ (upt @ C @ B)) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])).
% 181.68/124.52 thf(175,axiom,((! [A:nat,B:nat]: ~ (ord_less @ nat @ (plus_plus @ nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_not__add__less1)).
% 181.68/124.52 thf(1524,plain,((! [A:nat,B:nat]: ~ (ord_less @ nat @ (plus_plus @ nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
% 181.68/124.52 thf(358,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/sandbox/benchmark/theBenchmark.p',fact_716_nat__diff__split__asm)).
% 181.68/124.52 thf(2097,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)],[358])).
% 181.68/124.52 thf(404,axiom,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TA @ TB)]: (product_case_prod @ TA @ TB @ $o @ (^ [B:TA,C:TB]: (($true))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1253_prod_Odisc__eq__case)).
% 181.68/124.52 thf(2246,plain,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TA @ TB)]: (product_case_prod @ TA @ TB @ $o @ (^ [B:TA,C:TB]: (($true))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])).
% 181.68/124.52 thf(239,axiom,((! [A:nat,B:(nat > $o)]: (((! [C:nat]: ((ord_less @ nat @ C @ A) => (~ (B @ C)))) => (B @ A)) => (? [C:nat]: ((ord_less_eq @ nat @ C @ A) & (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_exists__leI)).
% 181.68/124.52 thf(1722,plain,((! [A:nat,B:(nat > $o)]: (((! [C:nat]: ((ord_less @ nat @ C @ A) => (~ (B @ C)))) => (B @ A)) => (? [C:nat]: ((ord_less_eq @ nat @ C @ A) & (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
% 181.68/124.52 thf(7,axiom,((ab_semigroup_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Oab__semigroup__add_467)).
% 181.68/124.52 thf(1043,plain,((ab_semigroup_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 181.68/124.52 thf(700,axiom,((! [A:product_unit]: (A = product_Unity))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3033_old_Ounit_Oexhaust)).
% 181.68/124.52 thf(3138,plain,((! [A:product_unit]: (A = product_Unity))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[700])).
% 181.68/124.52 thf(788,axiom,((! [TA: $tType]: ((cl_HOL_Oequal @ TA) => (cl_HOL_Oequal @ (set @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___HOL_Oequal_263)).
% 181.68/124.52 thf(3384,plain,((! [TA: $tType]: ((cl_HOL_Oequal @ TA) => (cl_HOL_Oequal @ (set @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[788])).
% 181.68/124.52 thf(150,axiom,((! [A:(nat > $o),B:nat]: ((A @ (zero_zero @ nat)) => ((! [C:nat]: ((! [D:nat]: ((ord_less_eq @ nat @ D @ C) => (A @ D))) => (A @ (suc @ C)))) => (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_nat__compl__induct)).
% 181.68/124.52 thf(1439,plain,((! [A:(nat > $o),B:nat]: ((A @ (zero_zero @ nat)) => ((! [C:nat]: ((! [D:nat]: ((ord_less_eq @ nat @ D @ C) => (A @ D))) => (A @ (suc @ C)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
% 181.68/124.52 thf(311,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (plus_plus @ nat @ A @ B) @ C) => ((nth @ nat @ (upt @ A @ C) @ B) = (plus_plus @ nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3569_nth__upt)).
% 181.68/124.52 thf(1969,plain,((! [A:nat,B:nat,C:nat]: ((ord_less @ nat @ (plus_plus @ nat @ A @ B) @ C) => ((nth @ nat @ (upt @ A @ C) @ B) = (plus_plus @ nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])).
% 181.68/124.52 thf(346,axiom,((ab_semigroup_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_542)).
% 181.68/124.52 thf(2065,plain,((ab_semigroup_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])).
% 181.68/124.52 thf(59,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ C @ D) => ((ord_less @ nat @ E @ D) => (ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ D) @ C) @ (plus_plus @ nat @ (times_times @ nat @ B @ D) @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_mlex__fst__decrI)).
% 181.68/124.52 thf(1194,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less @ nat @ A @ B) => ((ord_less @ nat @ C @ D) => ((ord_less @ nat @ E @ D) => (ord_less @ nat @ (plus_plus @ nat @ (times_times @ nat @ A @ D) @ C) @ (plus_plus @ nat @ (times_times @ nat @ B @ D) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
% 181.68/124.52 thf(433,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: (ord_less_eq @ (option @ TA) @ (none @ TA) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_less__eq__option__None__code)).
% 181.68/124.52 thf(2346,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: (ord_less_eq @ (option @ TA) @ (none @ TA) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[433])).
% 181.68/124.52 thf(65,axiom,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((suc @ (minus_minus @ nat @ A @ (one_one @ nat))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_Suc__diff__1)).
% 181.68/124.52 thf(1209,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)],[65])).
% 181.68/124.52 thf(557,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:TB,C:TA,D:(TB > (option @ TA))]: (((A @ B) = (some @ TA @ C)) => ((map_add @ TB @ TA @ D @ A @ B) = (some @ TA @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3393_map__add__find__right)).
% 181.68/124.52 thf(2721,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:TB,C:TA,D:(TB > (option @ TA))]: (((A @ B) = (some @ TA @ C)) => ((map_add @ TB @ TA @ (D) @ (A) @ B) = (some @ TA @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[557])).
% 181.68/124.52 thf(496,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/sandbox/benchmark/theBenchmark.p',fact_520_add__strict__increasing2)).
% 181.68/124.52 thf(2538,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)],[496])).
% 181.68/124.52 thf(138,axiom,((semiring_numeral @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Num_Osemiring__numeral_478)).
% 181.68/124.52 thf(1408,plain,((semiring_numeral @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
% 181.68/124.52 thf(354,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA),B:TB,C:TA,D:(TB > TA),E:TA]: (((fun_upd @ TB @ TA @ A @ B @ C) = (fun_upd @ TB @ TA @ D @ B @ E)) => (C = E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2728_fun__upd__eqD)).
% 181.68/124.52 thf(2084,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA),B:TB,C:TA,D:(TB > TA),E:TA]: (((fun_upd @ TB @ TA @ A @ B @ C) = (fun_upd @ TB @ TA @ D @ B @ E)) => (C = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])).
% 181.68/124.52 thf(528,axiom,((! [TA: $tType]: (! [A:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((heap_Time_timeFrame @ TA @ (zero_zero @ nat) @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_timeFrame__zero)).
% 181.68/124.52 thf(2624,plain,((! [TA: $tType]: (! [A:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((heap_Time_timeFrame @ TA @ (zero_zero @ nat) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[528])).
% 181.68/124.52 thf(658,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_new @ TA) = (^ [A:nat,B:TA]: (heap_Time_heap @ (array @ TA) @ (^ [C:(heap_ext @ product_unit)]: (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [D:(array @ TA),E:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ (one_one @ nat))))) @ (array_alloc @ TA @ (replicate @ TA @ A @ B) @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3543_new__def)).
% 181.68/124.52 thf(3038,plain,((! [TA: $tType]: ((heap @ TA) => ((array_new @ TA) = (^ [A:nat,B:TA]: (heap_Time_heap @ (array @ TA) @ (^ [C:(heap_ext @ product_unit)]: (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [D:(array @ TA),E:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ (one_one @ nat))))) @ (array_alloc @ TA @ (replicate @ TA @ A @ B) @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[658])).
% 181.68/124.52 thf(460,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA]: (ord_less @ (option @ TA) @ (none @ TA) @ (some @ TA @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_less__option__None__Some)).
% 181.68/124.52 thf(2422,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:TA]: (ord_less @ (option @ TA) @ (none @ TA) @ (some @ TA @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[460])).
% 181.68/124.52 thf(911,axiom,((semidom_modulo @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__modulo_125)).
% 181.68/124.52 thf(3779,plain,((semidom_modulo @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[911])).
% 181.68/124.52 thf(9,axiom,((! [TA: $tType]: ((semiri1453513574482234551roduct @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((A != (zero_zero @ TA)) => (((B = C) & (D != E)) => ((plus_plus @ TA @ B @ (times_times @ TA @ A @ D)) != (plus_plus @ TA @ C @ (times_times @ TA @ A @ E))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_add__scale__eq__noteq)).
% 181.68/124.52 thf(1048,plain,((! [TA: $tType]: ((semiri1453513574482234551roduct @ TA) => (! [A:TA,B:TA,C:TA,D:TA,E:TA]: ((~ (A = (zero_zero @ TA))) => (((B = C) & ~ (D = E)) => (~ ((plus_plus @ TA @ B @ (times_times @ TA @ A @ D)) = (plus_plus @ TA @ C @ (times_times @ TA @ A @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 181.68/124.52 thf(254,axiom,((semiring_modulo @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Osemiring__modulo_545)).
% 181.68/124.52 thf(1771,plain,((semiring_modulo @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])).
% 181.68/124.52 thf(625,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:TA,C:(heap_ext @ product_unit)]: ((heap_Time_execute @ product_unit @ (ref_update @ TA @ A @ B) @ C) = (some @ (product_prod @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat) @ product_Unity @ (product_Pair @ (heap_ext @ product_unit) @ nat @ (ref_set @ TA @ A @ B @ C) @ (one_one @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3105_execute__update)).
% 181.68/124.52 thf(2945,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:TA,C:(heap_ext @ product_unit)]: ((heap_Time_execute @ product_unit @ (ref_update @ TA @ A @ B) @ C) = (some @ (product_prod @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat) @ product_Unity @ (product_Pair @ (heap_ext @ product_unit) @ nat @ (ref_set @ TA @ A @ B @ C) @ (one_one @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[625])).
% 181.68/124.52 thf(812,axiom,((! [TA: $tType]: ((sup @ TA) => (sup @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Lattices_Osup_331)).
% 181.68/124.52 thf(3456,plain,((! [TA: $tType]: ((sup @ TA) => (sup @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[812])).
% 181.68/124.52 thf(283,axiom,((! [TA: $tType,TB: $tType]: ((fun_upd @ TA @ TB) = (^ [A:(TA > TB),B:TA,C:TB,D:TA]: (if @ TB @ (D = B) @ C @ (A @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2719_fun__upd__apply)).
% 181.68/124.52 thf(1877,plain,((! [TA: $tType,TB: $tType]: ((fun_upd @ TA @ TB) = (^ [A:(TA > TB),B:TA,C:TB,D:TA]: (if @ TB @ (D = B) @ C @ (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])).
% 181.68/124.52 thf(361,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA)]: ((is_none @ TB @ (map_option @ TA @ TB @ A @ B)) = (is_none @ TA @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5560_is__none__map__option)).
% 181.68/124.52 thf(2111,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA)]: ((is_none @ TB @ (map_option @ TA @ TB @ (A) @ B)) = (is_none @ TA @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])).
% 181.68/124.52 thf(276,axiom,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA]: ((! [C:TA]: ((A @ C @ B) => (accp @ TA @ A @ C))) => (accp @ TA @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_accpI)).
% 181.68/124.52 thf(1862,plain,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA]: ((! [C:TA]: ((A @ C @ B) => (accp @ TA @ (A) @ C))) => (accp @ TA @ (A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])).
% 181.68/124.52 thf(851,axiom,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (heap_Time_Heap @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap__Time__Monad_OHeap___Quickcheck__Random_Orandom_573)).
% 181.68/124.52 thf(3614,plain,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (heap_Time_Heap @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[851])).
% 181.68/124.52 thf(810,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit)]: ((refine_Imp_refines @ TA @ A @ B) => ((time_fails @ TA @ A @ C) => (time_fails @ TA @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2851_fails__refines)).
% 181.68/124.52 thf(3451,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit)]: ((refine_Imp_refines @ TA @ A @ B) => ((time_fails @ TA @ A @ C) => (time_fails @ TA @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[810])).
% 181.68/124.52 thf(842,axiom,((! [TA: $tType]: ((typerep2 @ TA) => (quickcheck_random @ (array @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oarray___Quickcheck__Random_Orandom_298)).
% 181.68/124.52 thf(3583,plain,((! [TA: $tType]: ((typerep2 @ TA) => (quickcheck_random @ (array @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[842])).
% 181.68/124.52 thf(502,axiom,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (list @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Typerep_Otyperep_39)).
% 181.68/124.52 thf(2553,plain,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (list @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])).
% 181.68/124.52 thf(614,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:((product_prod @ TA @ TB) > TC)]: ((product_case_prod @ TA @ TB @ TC @ (^ [B:TA,C:TB]: (A @ (product_Pair @ TA @ TB @ B @ C)))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1074_case__prod__eta)).
% 181.68/124.52 thf(2911,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:((product_prod @ TA @ TB) > TC)]: ((product_case_prod @ TA @ TB @ TC @ (^ [B:TA,C:TB]: (A @ (product_Pair @ TA @ TB @ B @ C)))) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[614])).
% 181.68/124.52 thf(730,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ (list @ TA) @ (array_freeze @ TA @ A) @ B) = (some @ (product_prod @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (array_get @ TA @ B @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (plus_plus @ nat @ (one_one @ nat) @ (array_length @ TA @ B @ A)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4080_execute__freeze)).
% 181.68/124.52 thf(3219,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ (list @ TA) @ (array_freeze @ TA @ A) @ B) = (some @ (product_prod @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (array_get @ TA @ B @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (plus_plus @ nat @ (one_one @ nat) @ (array_length @ TA @ B @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[730])).
% 181.68/124.52 thf(593,axiom,((! [TA: $tType]: (! [A:(option @ TA),B:(option @ TA)]: ((partial_flat_ord @ (option @ TA) @ (none @ TA) @ A @ B) => ((partial_flat_ord @ (option @ TA) @ (none @ TA) @ B @ A) => (A = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5972_option_Oleq__antisym)).
% 181.68/124.52 thf(2824,plain,((! [TA: $tType]: (! [A:(option @ TA),B:(option @ TA)]: ((partial_flat_ord @ (option @ TA) @ (none @ TA) @ A @ B) => ((partial_flat_ord @ (option @ TA) @ (none @ TA) @ B @ A) => (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[593])).
% 181.68/124.52 thf(330,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (ref_lookup @ TA @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_success__lookupI)).
% 181.68/124.52 thf(2025,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (ref_lookup @ TA @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])).
% 181.68/124.52 thf(531,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((ord_less_eq @ TA @ A @ (zero_zero @ TA)) = (A = (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_le__zero__eq)).
% 181.68/124.52 thf(2632,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)],[531])).
% 181.68/124.52 thf(115,axiom,((cancel_semigroup_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Ocancel__semigroup__add_461)).
% 181.68/124.52 thf(1339,plain,((cancel_semigroup_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
% 181.68/124.52 thf(520,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (option @ TC)),B:(TB > (option @ TA)),C:TB]: (((map_comp @ TA @ TC @ TB @ A @ B @ C) = (none @ TC)) = (((B @ C) = (none @ TA)) | ? [D:TA]: (((B @ C) = (some @ TA @ D)) & ((A @ D) = (none @ TC)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_map__comp__None__iff)).
% 181.68/124.52 thf(2605,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (option @ TC)),B:(TB > (option @ TA)),C:TB]: (((map_comp @ TA @ TC @ TB @ (A) @ (B) @ C) = (none @ TC)) = (((B @ C) = (none @ TA)) | ? [D:TA]: (((B @ C) = (some @ TA @ D)) & ((A @ D) = (none @ TC)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[520])).
% 181.68/124.52 thf(653,axiom,((bounded_lattice @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice_271)).
% 181.68/124.52 thf(3027,plain,((bounded_lattice @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[653])).
% 181.68/124.52 thf(664,axiom,((! [TA: $tType,TB: $tType]: (! [A:((option @ TB) > $o),B:(option @ TA),C:(TA > (option @ TB))]: ((A @ (bind @ TA @ TB @ B @ C)) = (~ (((B = (none @ TA)) & ~ (A @ (none @ TB))) | ? [D:TA]: ((B = (some @ TA @ D)) & ~ (A @ (C @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_bind__split__asm)).
% 181.68/124.52 thf(3055,plain,((! [TA: $tType,TB: $tType]: (! [A:((option @ TB) > $o),B:(option @ TA),C:(TA > (option @ TB))]: ((A @ (bind @ TA @ TB @ B @ (C))) = (~ (((B = (none @ TA)) & ~ (A @ (none @ TB))) | ? [D:TA]: ((B = (some @ TA @ D)) & ~ (A @ (C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[664])).
% 181.68/124.52 thf(1017,axiom,((comm_s4317794764714335236cancel @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1__cancel_105)).
% 181.68/124.52 thf(4009,plain,((comm_s4317794764714335236cancel @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017])).
% 181.68/124.52 thf(422,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((minus_minus @ TA @ (plus_plus @ TA @ C @ B) @ A) = (plus_plus @ TA @ C @ (minus_minus @ TA @ B @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc)).
% 181.68/124.52 thf(2314,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((minus_minus @ TA @ (plus_plus @ TA @ C @ B) @ A) = (plus_plus @ TA @ C @ (minus_minus @ TA @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])).
% 181.68/124.52 thf(367,axiom,((! [TA: $tType]: ((eps_Opt @ TA) = (^ [A:(TA > $o)]: (if @ (option @ TA) @ (? [B:TA]: (A @ B)) @ (some @ TA @ (fChoice @ TA @ A)) @ (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4646_Eps__Opt__def)).
% 181.68/124.52 thf(2129,plain,((! [TA: $tType]: ((eps_Opt @ TA) = (^ [A:(TA > $o)]: (if @ (option @ TA) @ (? [B:TA]: (A @ B)) @ (some @ TA @ (fChoice @ TA @ A)) @ (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])).
% 181.68/124.52 thf(266,axiom,((! [A:(product_prod @ ((product_prod @ code_natural @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:((product_prod @ code_natural @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_natural,D:code_natural]: (A != (product_Pair @ ((product_prod @ code_natural @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural) @ B @ (product_Pair @ code_natural @ code_natural @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4215_full__exhaustive__natural_H_Ocases)).
% 181.68/124.52 thf(1821,plain,((! [A:(product_prod @ ((product_prod @ code_natural @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:((product_prod @ code_natural @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_natural,D:code_natural]: ~ (A = (product_Pair @ ((product_prod @ code_natural @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural) @ (B) @ (product_Pair @ code_natural @ code_natural @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])).
% 181.68/124.52 thf(241,axiom,((ordere1937475149494474687imp_le @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__monoid__add__imp__le_514)).
% 181.68/124.52 thf(1731,plain,((ordere1937475149494474687imp_le @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
% 181.68/124.52 thf(498,axiom,((! [TA: $tType,TB: $tType]: ((complete_Inf @ TA) => (complete_Inf @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_OInf)).
% 181.68/124.52 thf(2542,plain,((! [TA: $tType,TB: $tType]: ((complete_Inf @ TA) => (complete_Inf @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])).
% 181.68/124.52 thf(156,axiom,((! [TA: $tType]: (! [A:nat,B:(TA > TA)]: ((compow @ (TA > TA) @ (suc @ A) @ B) = (comp @ TA @ TA @ TA @ (compow @ (TA > TA) @ A @ B) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4903_funpow__Suc__right)).
% 181.68/124.52 thf(1460,plain,((! [TA: $tType]: (! [A:nat,B:(TA > TA)]: ((compow @ (TA > TA) @ (suc @ A) @ B) = (comp @ TA @ TA @ TA @ (compow @ (TA > TA) @ A @ B) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
% 181.68/124.52 thf(704,axiom,((! [TA: $tType]: (! [A:(option @ TA),B:TA]: ((A = (some @ TA @ B)) => (A != (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_option_OdiscI)).
% 181.68/124.52 thf(3150,plain,((! [TA: $tType]: (! [A:(option @ TA),B:TA]: ((A = (some @ TA @ B)) => (~ (A = (none @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[704])).
% 181.68/124.52 thf(13,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: (((dom @ TA @ TB @ A) = (bot_bot @ (set @ TA))) = (A = (^ [B:TA]: (none @ TB))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3311_dom__eq__empty__conv)).
% 181.68/124.52 thf(1061,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: (((dom @ TA @ TB @ (A)) = (bot_bot @ (set @ TA))) = ((A) = (^ [B:TA]: (none @ TB))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 181.68/124.52 thf(49,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/sandbox/benchmark/theBenchmark.p',fact_661_mult__eq__if)).
% 181.68/124.52 thf(1171,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)],[49])).
% 181.68/124.52 thf(350,axiom,((! [TA: $tType]: ((preorder @ TA) => (preorder @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Orderings_Opreorder_326)).
% 181.68/124.52 thf(2075,plain,((! [TA: $tType]: ((preorder @ TA) => (preorder @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])).
% 181.68/124.52 thf(391,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > TB),B:(TC > TA),C:TC,D:TA]: ((comp @ TA @ TB @ TC @ A @ (fun_upd @ TC @ TA @ B @ C @ D)) = (fun_upd @ TC @ TB @ (comp @ TA @ TB @ TC @ A @ B) @ C @ (A @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2740_fun__upd__comp)).
% 181.68/124.52 thf(2212,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > TB),B:(TC > TA),C:TC,D:TA]: ((comp @ TA @ TB @ TC @ A @ (fun_upd @ TC @ TA @ B @ C @ D)) = (fun_upd @ TC @ TB @ (comp @ TA @ TB @ TC @ A @ B) @ C @ (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[391])).
% 181.68/124.52 thf(16,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/sandbox/benchmark/theBenchmark.p',fact_591_nat__le__add__iff2)).
% 181.68/124.52 thf(1066,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)],[16])).
% 181.68/124.52 thf(687,axiom,((! [TA: $tType,TB: $tType]: (((enum @ TB) & (enum @ TA)) => (enum @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Enum_Oenum_61)).
% 181.68/124.52 thf(3110,plain,((! [TA: $tType,TB: $tType]: (((enum @ TB) & (enum @ TA)) => (enum @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[687])).
% 181.68/124.52 thf(879,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TA,C:(TA > (heap_Time_Heap @ TB)),D:(heap_ext @ product_unit),E:(heap_ext @ product_unit),F:TB,G:nat]: ((A = B) => ((heap_Time_effect @ TB @ (C @ A) @ D @ E @ F @ G) => (heap_Time_effect @ TB @ (C @ B) @ D @ E @ F @ G)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_effect__LetI)).
% 181.68/124.52 thf(3687,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TA,C:(TA > (heap_Time_Heap @ TB)),D:(heap_ext @ product_unit),E:(heap_ext @ product_unit),F:TB,G:nat]: ((A = B) => ((heap_Time_effect @ TB @ (C @ A) @ D @ E @ F @ G) => (heap_Time_effect @ TB @ (C @ B) @ D @ E @ F @ G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[879])).
% 181.68/124.52 thf(51,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less_eq @ nat @ A @ B) => (ord_less @ nat @ (minus_minus @ nat @ A @ (suc @ (zero_zero @ nat))) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_nz__le__conv__less)).
% 181.68/124.52 thf(1176,plain,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => ((ord_less_eq @ nat @ A @ B) => (ord_less @ nat @ (minus_minus @ nat @ A @ (suc @ (zero_zero @ nat))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
% 181.68/124.52 thf(620,axiom,((! [TA: $tType,TB: $tType]: (! [A:(list @ char),B:(TB > (heap_Time_Heap @ TA))]: ((heap_Time_bind @ TB @ TA @ (heap_Time_raise @ TB @ A) @ B) = (heap_Time_raise @ TA @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_raise__bind)).
% 181.68/124.52 thf(2931,plain,((! [TA: $tType,TB: $tType]: (! [A:(list @ char),B:(TB > (heap_Time_Heap @ TA))]: ((heap_Time_bind @ TB @ TA @ (heap_Time_raise @ TB @ A) @ (B)) = (heap_Time_raise @ TA @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[620])).
% 181.68/124.52 thf(581,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))),B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (heap_Time_heap @ TA @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_success__heapI)).
% 181.68/124.52 thf(2797,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))),B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (heap_Time_heap @ TA @ (A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[581])).
% 181.68/124.52 thf(495,axiom,((! [TA: $tType]: (! [A:TA]: ((eps_Opt @ TA @ (^ [B:TA]: (B = A))) = (some @ TA @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_some__opt__eq__trivial)).
% 181.68/124.52 thf(2535,plain,((! [TA: $tType]: (! [A:TA]: ((eps_Opt @ TA @ (^ [B:TA]: (B = A))) = (some @ TA @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[495])).
% 181.68/124.52 thf(165,axiom,((! [TA: $tType,TB: $tType]: (! [A:$o,B:(heap_Time_Heap @ TA),C:(heap_Time_Heap @ TA),D:(TA > (heap_Time_Heap @ TB))]: (((A) => ((heap_Time_bind @ TA @ TB @ (if @ (heap_Time_Heap @ TA) @ A @ B @ C) @ D) = (heap_Time_bind @ TA @ TB @ B @ D))) & ((~ (A)) => ((heap_Time_bind @ TA @ TB @ (if @ (heap_Time_Heap @ TA) @ A @ B @ C) @ D) = (heap_Time_bind @ TA @ TB @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_distrib__if__bind)).
% 181.68/124.52 thf(1496,plain,((! [TA: $tType,TB: $tType]: (! [A:$o,B:(heap_Time_Heap @ TA),C:(heap_Time_Heap @ TA),D:(TA > (heap_Time_Heap @ TB))]: (((A) => ((heap_Time_bind @ TA @ TB @ (if @ (heap_Time_Heap @ TA) @ A @ B @ C) @ (D)) = (heap_Time_bind @ TA @ TB @ B @ (D)))) & ((~ (A)) => ((heap_Time_bind @ TA @ TB @ (if @ (heap_Time_Heap @ TA) @ A @ B @ C) @ (D)) = (heap_Time_bind @ TA @ TB @ C @ (D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
% 181.68/124.52 thf(827,axiom,((! [TA: $tType]: (! [A:nat,B:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))),C:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: (((heap_Time_timeFrame @ TA @ A @ B) = C) => ((accp @ (product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ (heap_T5500966940807335491me_rel @ TA) @ (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A @ B)) => ((! [D:TA,E:(heap_ext @ product_unit),F:nat]: ((B = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ F)))) => ((C = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ F))))) => (~ (accp @ (product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ (heap_T5500966940807335491me_rel @ TA) @ (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ F))))))))) => (~ ((B = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => ((C = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => (~ (accp @ (product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ (heap_T5500966940807335491me_rel @ TA) @ (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_timeFrame_Opelims)).
% 181.68/124.52 thf(3512,plain,((! [TA: $tType]: (! [A:nat,B:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))),C:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: (((heap_Time_timeFrame @ TA @ A @ B) = C) => ((accp @ (product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ (heap_T5500966940807335491me_rel @ TA) @ (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A @ B)) => ((! [D:TA,E:(heap_ext @ product_unit),F:nat]: ((B = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ F)))) => ((C = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ F))))) => (~ (accp @ (product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ (heap_T5500966940807335491me_rel @ TA) @ (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A @ (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ F))))))))) => (~ ((B = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => ((C = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => (~ (accp @ (product_prod @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ (heap_T5500966940807335491me_rel @ TA) @ (product_Pair @ nat @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ A @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[827])).
% 181.68/124.52 thf(645,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TA @ TB),B:(TA > (TB > TC)),C:(TA > (TB > TC)),D:(product_prod @ TA @ TB)]: ((! [E:TA,F:TB]: (((product_Pair @ TA @ TB @ E @ F) = A) => ((B @ E @ F) = (C @ E @ F)))) => ((D = A) => ((product_case_prod @ TA @ TB @ TC @ B @ D) = (product_case_prod @ TA @ TB @ TC @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_split__cong)).
% 181.68/124.52 thf(2999,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(product_prod @ TA @ TB),B:(TA > (TB > TC)),C:(TA > (TB > TC)),D:(product_prod @ TA @ TB)]: ((! [E:TA,F:TB]: (((product_Pair @ TA @ TB @ E @ F) = A) => ((B @ E @ F) = (C @ E @ F)))) => ((D = A) => ((product_case_prod @ TA @ TB @ TC @ (B) @ D) = (product_case_prod @ TA @ TB @ TC @ (C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[645])).
% 181.68/124.52 thf(978,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA)]: ((! [C:(heap_ext @ product_unit)]: (((heap_Time_execute @ TA @ A @ C) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) | ((heap_Time_execute @ TA @ A @ C) = (heap_Time_execute @ TA @ B @ C)))) => (heap_Time_Heap_ord @ TA @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Heap__ordI)).
% 181.68/124.52 thf(3908,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA)]: ((! [C:(heap_ext @ product_unit)]: (((heap_Time_execute @ TA @ A @ C) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) | ((heap_Time_execute @ TA @ A @ C) = (heap_Time_execute @ TA @ B @ C)))) => (heap_Time_Heap_ord @ TA @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[978])).
% 181.68/124.52 thf(271,axiom,((! [TA: $tType]: (typerep2 @ (ref @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oref___Typerep_Otyperep_41)).
% 181.68/124.52 thf(1841,plain,((! [TA: $tType]: (typerep2 @ (ref @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])).
% 181.68/124.52 thf(133,axiom,((! [A:nat]: ((times_times @ nat @ A @ (one_one @ nat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_nat__mult__1__right)).
% 181.68/124.52 thf(1396,plain,((! [A:nat]: ((times_times @ nat @ A @ (one_one @ nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
% 181.68/124.52 thf(299,axiom,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (plus_plus @ TA @ A @ B) @ A) = (ord_less @ TA @ B @ (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__less__same__cancel1)).
% 181.68/124.52 thf(1926,plain,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ (plus_plus @ TA @ A @ B) @ A) = (ord_less @ TA @ B @ (zero_zero @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])).
% 181.68/124.52 thf(441,axiom,((power @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Power_Opower_566)).
% 181.68/124.52 thf(2365,plain,((power @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])).
% 181.68/124.52 thf(559,axiom,((! [TA: $tType]: (semilattice_inf @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_249)).
% 181.68/124.52 thf(2725,plain,((! [TA: $tType]: (semilattice_inf @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[559])).
% 181.68/124.52 thf(199,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/sandbox/benchmark/theBenchmark.p',fact_696_less__diff__conv)).
% 181.68/124.52 thf(1594,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)],[199])).
% 181.68/124.52 thf(800,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > TB),B:(TA > TB),C:(TB > TC)]: ((A = B) => ((comp @ TB @ TC @ TA @ C @ A) = (comp @ TB @ TC @ TA @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_comp__cong__right)).
% 181.68/124.52 thf(3423,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > TB),B:(TA > TB),C:(TB > TC)]: (((A) = (B)) => ((comp @ TB @ TC @ TA @ C @ A) = (comp @ TB @ TC @ TA @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[800])).
% 181.68/124.52 thf(8,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/sandbox/benchmark/theBenchmark.p',fact_928_diff__Suc__diff__eq2)).
% 181.68/124.52 thf(1044,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)],[8])).
% 181.68/124.52 thf(79,axiom,((semiring @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Osemiring_500)).
% 181.68/124.52 thf(1245,plain,((semiring @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
% 181.68/124.52 thf(707,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/sandbox/benchmark/theBenchmark.p',fact_454_add__right__mono)).
% 181.68/124.52 thf(3159,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)],[707])).
% 181.68/124.52 thf(345,axiom,((plus @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oplus_569)).
% 181.68/124.52 thf(2064,plain,((plus @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])).
% 181.68/124.52 thf(443,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA)]: (((map_option @ TA @ TB @ A @ B) = (none @ TB)) = (B = (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_option_Omap__disc__iff)).
% 181.68/124.52 thf(2369,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA)]: (((map_option @ TA @ TB @ (A) @ B) = (none @ TB)) = (B = (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[443])).
% 181.68/124.52 thf(874,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TB,B:(TC > TB),C:(TA > TC)]: ((comp @ (option @ TC) @ TB @ (option @ TA) @ (rec_option @ TB @ TC @ A @ B) @ (map_option @ TA @ TC @ C)) = (rec_option @ TB @ TA @ A @ (^ [D:TA]: (B @ (C @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_option_Orec__o__map)).
% 181.68/124.52 thf(3674,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TB,B:(TC > TB),C:(TA > TC)]: ((comp @ (option @ TC) @ TB @ (option @ TA) @ (rec_option @ TB @ TC @ A @ B) @ (map_option @ TA @ TC @ C)) = (rec_option @ TB @ TA @ A @ (^ [D:TA]: (B @ (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[874])).
% 181.68/124.52 thf(780,axiom,((! [A:(set @ nat),B:(set @ nat),C:(heap_ext @ product_unit)]: ((ord_less_eq @ (set @ nat) @ A @ B) => ((in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ B)) => (in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5690_in__range__subset)).
% 181.68/124.52 thf(3363,plain,((! [A:(set @ nat),B:(set @ nat),C:(heap_ext @ product_unit)]: ((ord_less_eq @ (set @ nat) @ A @ B) => ((in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ B)) => (in_range @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[780])).
% 181.68/124.52 thf(763,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA]: (((eps_Opt @ TA @ A) = (some @ TA @ B)) => (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Eps__Opt__eq__Some__implies)).
% 181.68/124.52 thf(3310,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA]: (((eps_Opt @ TA @ (A)) = (some @ TA @ B)) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[763])).
% 181.68/124.52 thf(635,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ nat @ (array_len @ TA @ A) @ B) = (some @ (product_prod @ nat @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ nat @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (array_length @ TA @ B @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4112_execute__len)).
% 181.68/124.52 thf(2967,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: ((heap_Time_execute @ nat @ (array_len @ TA @ A) @ B) = (some @ (product_prod @ nat @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ nat @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (array_length @ TA @ B @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[635])).
% 181.68/124.52 thf(81,axiom,((! [A:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ A) => (A = (suc @ (minus_minus @ nat @ A @ (one_one @ nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_Suc__pred_H)).
% 181.68/124.52 thf(1250,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)],[81])).
% 181.68/124.52 thf(348,axiom,((! [TA: $tType]: (! [A:TA,B:(set @ (product_prod @ TA @ TA))]: (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ A) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (zero_zero @ nat) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4981_relpow__0__I)).
% 181.68/124.52 thf(2069,plain,((! [TA: $tType]: (! [A:TA,B:(set @ (product_prod @ TA @ TA))]: (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ A) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (zero_zero @ nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])).
% 181.68/124.52 thf(599,axiom,((! [TA: $tType]: ((enum @ TA) => (enum @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Enum_Oenum_27)).
% 181.68/124.52 thf(2867,plain,((! [TA: $tType]: ((enum @ TA) => (enum @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[599])).
% 181.68/124.52 thf(807,axiom,((! [TA: $tType]: (! [A:TA]: ~ (is_none @ TA @ (some @ TA @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5567_is__none__simps_I2_J)).
% 181.68/124.52 thf(3444,plain,((! [TA: $tType]: (! [A:TA]: ~ (is_none @ TA @ (some @ TA @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[807])).
% 181.68/124.52 thf(628,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: ((map_le @ TB @ TA @ A @ B) => (map_le @ TB @ TA @ (fun_upd @ TB @ (option @ TA) @ A @ C @ (none @ TA)) @ (fun_upd @ TB @ (option @ TA) @ B @ C @ (some @ TA @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3419_map__le__imp__upd__le)).
% 181.68/124.52 thf(2952,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: ((map_le @ TB @ TA @ (A) @ (B)) => (map_le @ TB @ TA @ (fun_upd @ TB @ (option @ TA) @ A @ C @ (none @ TA)) @ (fun_upd @ TB @ (option @ TA) @ B @ C @ (some @ TA @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[628])).
% 181.68/124.52 thf(64,axiom,((comm_semiring_0 @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Ocomm__semiring__0_474)).
% 181.68/124.52 thf(1208,plain,((comm_semiring_0 @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
% 181.68/124.52 thf(477,axiom,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit)]: ~ (time_fails @ TA @ (heap_Time_return @ TA @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_fails__return)).
% 181.68/124.52 thf(2471,plain,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit)]: ~ (time_fails @ TA @ (heap_Time_return @ TA @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])).
% 181.68/124.52 thf(336,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TB > (heap_Time_Heap @ TA))]: ((heap_Time_bind @ TB @ TA @ (heap_Time_return @ TB @ A) @ B) = (heap_Time_bind @ product_unit @ TA @ (heap_Time_wait @ (one_one @ nat)) @ (^ [C:product_unit]: (B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_return__bind)).
% 181.68/124.52 thf(2037,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TB > (heap_Time_Heap @ TA))]: ((heap_Time_bind @ TB @ TA @ (heap_Time_return @ TB @ A) @ (B)) = (heap_Time_bind @ product_unit @ TA @ (heap_Time_wait @ (one_one @ nat)) @ (^ [C:product_unit]: (B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])).
% 181.68/124.52 thf(603,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (TA > $o)),B:TB,C:TA]: ((product_case_prod @ TB @ TA @ $o @ A @ (product_Pair @ TB @ TA @ B @ C)) => (A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1169_case__prodD)).
% 181.68/124.52 thf(2878,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (TA > $o)),B:TB,C:TA]: ((product_case_prod @ TB @ TA @ $o @ (A) @ (product_Pair @ TB @ TA @ B @ C)) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[603])).
% 181.68/124.52 thf(170,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA]: ((fun_upd @ TA @ (option @ TB) @ (^ [B:TA]: (none @ TB)) @ A @ (none @ TB)) = (^ [B:TA]: (none @ TB)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2721_empty__upd__none)).
% 181.68/124.52 thf(1509,plain,((! [TA: $tType,TB: $tType]: (! [A:TA]: ((fun_upd @ TA @ (option @ TB) @ (^ [B:TA]: (none @ TB)) @ A @ (none @ TB)) = (^ [B:TA]: (none @ TB)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
% 181.68/124.52 thf(507,axiom,((order_bot @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_275)).
% 181.68/124.52 thf(2564,plain,((order_bot @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])).
% 181.68/124.52 thf(756,axiom,((! [TA: $tType]: (order_bot @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_254)).
% 181.68/124.52 thf(3292,plain,((! [TA: $tType]: (order_bot @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[756])).
% 181.68/124.52 thf(837,axiom,((! [TA: $tType,TB: $tType]: ((order_bot @ TA) => (order_bot @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot)).
% 181.68/124.52 thf(3571,plain,((! [TA: $tType,TB: $tType]: ((order_bot @ TA) => (order_bot @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[837])).
% 181.68/124.52 thf(947,axiom,((order_top @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__top_411)).
% 181.68/124.52 thf(3849,plain,((order_top @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[947])).
% 181.68/124.52 thf(140,axiom,((quickcheck_random @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Quickcheck__Random_Orandom_463)).
% 181.68/124.52 thf(1413,plain,((quickcheck_random @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
% 181.68/124.52 thf(963,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit)]: ((heap_Time_Heap_ord @ TA @ A @ B) => (((heap_Time_execute @ TA @ A @ C) != (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => ((heap_Time_execute @ TA @ A @ C) = (heap_Time_execute @ TA @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Heap__ordE)).
% 181.68/124.52 thf(3881,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit)]: ((heap_Time_Heap_ord @ TA @ A @ B) => ((~ ((heap_Time_execute @ TA @ A @ C) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))) => ((heap_Time_execute @ TA @ A @ C) = (heap_Time_execute @ TA @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[963])).
% 181.68/124.52 thf(210,axiom,((! [A:nat,B:nat]: ((ord_less @ nat @ (zero_zero @ nat) @ (plus_plus @ nat @ A @ B)) = ((ord_less @ nat @ (zero_zero @ nat) @ A) | (ord_less @ nat @ (zero_zero @ nat) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_add__gr__0)).
% 181.68/124.52 thf(1626,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)],[210])).
% 181.68/124.52 thf(647,axiom,((! [TA: $tType,TB: $tType]: ((map_option @ TA @ TB) = (^ [A:(TA > TB),B:(option @ TA)]: (bind @ TA @ TB @ B @ (comp @ TB @ (option @ TB) @ TA @ (some @ TB) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_map__conv__bind__option)).
% 181.68/124.52 thf(3009,plain,((! [TA: $tType,TB: $tType]: ((map_option @ TA @ TB) = (^ [A:(TA > TB),B:(option @ TA)]: (bind @ TA @ TB @ B @ (comp @ TB @ (option @ TB) @ TA @ (some @ TB) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[647])).
% 181.68/124.52 thf(615,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TB > TC)),B:((product_prod @ TA @ TB) > TC)]: ((! [C:TA,D:TB]: ((A @ C @ D) = (B @ (product_Pair @ TA @ TB @ C @ D)))) => ((product_case_prod @ TA @ TB @ TC @ A) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1073_cond__case__prod__eta)).
% 181.68/124.52 thf(2914,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TB > TC)),B:((product_prod @ TA @ TB) > TC)]: ((! [C:TA,D:TB]: ((A @ C @ D) = (B @ (product_Pair @ TA @ TB @ C @ D)))) => ((product_case_prod @ TA @ TB @ TC @ A) = (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[615])).
% 181.68/124.52 thf(589,axiom,((! [TA: $tType]: (! [A:(option @ TA)]: (partial_flat_ord @ (option @ TA) @ (none @ TA) @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5974_option_Oleq__refl)).
% 181.68/124.52 thf(2816,plain,((! [TA: $tType]: (! [A:(option @ TA)]: (partial_flat_ord @ (option @ TA) @ (none @ TA) @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[589])).
% 181.68/124.52 thf(100,axiom,((! [TA: $tType]: (! [A:(TA > nat),B:TA,C:TA,D:(set @ (product_prod @ TA @ TA))]: ((ord_less_eq @ nat @ (A @ B) @ (A @ C)) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ C) @ D) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ C) @ (mlex_prod @ TA @ A @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_mlex__leq)).
% 181.68/124.52 thf(1304,plain,((! [TA: $tType]: (! [A:(TA > nat),B:TA,C:TA,D:(set @ (product_prod @ TA @ TA))]: ((ord_less_eq @ nat @ (A @ B) @ (A @ C)) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ C) @ D) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ C) @ (mlex_prod @ TA @ (A) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])).
% 181.68/124.52 thf(281,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA)]: (((map_option @ TA @ TB @ A @ B) = (none @ TB)) = (B = (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_map__option__is__None)).
% 181.68/124.52 thf(1873,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:(option @ TA)]: (((map_option @ TA @ TB @ (A) @ B) = (none @ TB)) = (B = (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])).
% 181.68/124.52 thf(718,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => (heap_Time_success @ TA @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_effect__success)).
% 181.68/124.52 thf(3193,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => (heap_Time_success @ TA @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[718])).
% 181.68/124.52 thf(801,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_freeze @ TA) = (^ [A:(array @ TA)]: (heap_Time_heap @ (list @ TA) @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (array_get @ TA @ B @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (plus_plus @ nat @ (one_one @ nat) @ (array_length @ TA @ B @ A))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4078_freeze__def)).
% 181.68/124.52 thf(3427,plain,((! [TA: $tType]: ((heap @ TA) => ((array_freeze @ TA) = (^ [A:(array @ TA)]: (heap_Time_heap @ (list @ TA) @ (^ [B:(heap_ext @ product_unit)]: (product_Pair @ (list @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (array_get @ TA @ B @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (plus_plus @ nat @ (one_one @ nat) @ (array_length @ TA @ B @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[801])).
% 181.68/124.52 thf(708,axiom,((! [TA: $tType]: ((inf @ TA) => (inf @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Lattices_Oinf_332)).
% 181.68/124.52 thf(3161,plain,((! [TA: $tType]: ((inf @ TA) => (inf @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[708])).
% 181.68/124.52 thf(294,axiom,((! [A:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ((times_assn_raw @ A @ B @ C) => (~ (! [D:(heap_ext @ product_unit),E:(set @ nat)]: ((C = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E)) => (~ (? [F:(set @ nat),G:(set @ nat)]: ((E = (sup_sup @ (set @ nat) @ F @ G)) & ((inf_inf @ (set @ nat) @ F @ G) = (bot_bot @ (set @ nat))) & (A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ F)) & (B @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ G))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5650_times__assn__raw_Oelims_I2_J)).
% 181.68/124.52 thf(1905,plain,((! [A:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ((times_assn_raw @ (A) @ (B) @ C) => (~ (! [D:(heap_ext @ product_unit),E:(set @ nat)]: ((C = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E)) => (~ (? [F:(set @ nat),G:(set @ nat)]: ((E = (sup_sup @ (set @ nat) @ F @ G)) & ((inf_inf @ (set @ nat) @ F @ G) = (bot_bot @ (set @ nat))) & (A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ F)) & (B @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ G))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])).
% 181.68/124.52 thf(22,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ C) @ D)) => (~ (! [E:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ D) => (~ (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4985_relpow__Suc__E2)).
% 181.68/124.52 thf(1081,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ C) @ D)) => (~ (! [E:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ D) => (~ (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 181.68/124.52 thf(618,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/sandbox/benchmark/theBenchmark.p',fact_451_add__mono)).
% 181.68/124.52 thf(2927,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)],[618])).
% 181.68/124.52 thf(1008,axiom,((! [TA: $tType]: (! [A:nat,B:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))),C:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: (((heap_Time_timeFrame @ TA @ A @ B) = C) => ((! [D:TA,E:(heap_ext @ product_unit),F:nat]: ((B = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ F)))) => (C != (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ F))))))) => (~ ((B = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => (C != (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_timeFrame_Oelims)).
% 181.68/124.52 thf(3975,plain,((! [TA: $tType]: (! [A:nat,B:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))),C:(option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: (((heap_Time_timeFrame @ TA @ A @ B) = C) => ((! [D:TA,E:(heap_ext @ product_unit),F:nat]: ((B = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ F)))) => (~ (C = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ F)))))))) => (~ ((B = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => (~ (C = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008])).
% 181.68/124.52 thf(545,axiom,((! [TA: $tType]: (! [A:nat,B:nat]: ((rotate @ TA @ (plus_plus @ nat @ A @ B)) = (comp @ (list @ TA) @ (list @ TA) @ (list @ TA) @ (rotate @ TA @ A) @ (rotate @ TA @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4014_rotate__add)).
% 181.68/124.52 thf(2684,plain,((! [TA: $tType]: (! [A:nat,B:nat]: ((rotate @ TA @ (plus_plus @ nat @ A @ B)) = (comp @ (list @ TA) @ (list @ TA) @ (list @ TA) @ (rotate @ TA @ A) @ (rotate @ TA @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[545])).
% 181.68/124.52 thf(387,axiom,((typerep2 @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Typerep_Otyperep_2)).
% 181.68/124.52 thf(2202,plain,((typerep2 @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])).
% 181.68/124.52 thf(984,axiom,((comm_monoid_diff @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff)).
% 181.68/124.52 thf(3921,plain,((comm_monoid_diff @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[984])).
% 181.68/124.52 thf(116,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo @ nat @ (suc @ (plus_plus @ nat @ A @ (times_times @ nat @ B @ C))) @ C) = (modulo_modulo @ nat @ (suc @ A) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_Suc__mod__mult__self1)).
% 181.68/124.52 thf(1340,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo @ nat @ (suc @ (plus_plus @ nat @ A @ (times_times @ nat @ B @ C))) @ C) = (modulo_modulo @ nat @ (suc @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
% 181.68/124.52 thf(751,axiom,((intrel @ (product_Pair @ nat @ nat @ (one_one @ nat) @ (zero_zero @ nat)) @ (product_Pair @ nat @ nat @ (one_one @ nat) @ (zero_zero @ nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2696_one__int_Orsp)).
% 181.68/124.52 thf(3278,plain,((intrel @ (product_Pair @ nat @ nat @ (one_one @ nat) @ (zero_zero @ nat)) @ (product_Pair @ nat @ nat @ (one_one @ nat) @ (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[751])).
% 181.68/124.52 thf(309,axiom,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ code_natural @ (product_prod @ (TA > (TB > (product_prod @ TA @ TB))) @ TA))]: ~ (! [B:code_natural,C:(TA > (TB > (product_prod @ TA @ TB))),D:TA]: (A != (product_Pair @ code_natural @ (product_prod @ (TA > (TB > (product_prod @ TA @ TB))) @ TA) @ B @ (product_Pair @ (TA > (TB > (product_prod @ TA @ TB))) @ TA @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4298_iterate_Ocases)).
% 181.68/124.52 thf(1958,plain,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ code_natural @ (product_prod @ (TA > (TB > (product_prod @ TA @ TB))) @ TA))]: ~ (! [B:code_natural,C:(TA > (TB > (product_prod @ TA @ TB))),D:TA]: ~ (A = (product_Pair @ code_natural @ (product_prod @ (TA > (TB > (product_prod @ TA @ TB))) @ TA) @ B @ (product_Pair @ (TA > (TB > (product_prod @ TA @ TB))) @ TA @ (C) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])).
% 181.68/124.52 thf(624,axiom,((! [TA: $tType]: (! [A:(option @ TA)]: ((A != (none @ TA)) => (~ (! [B:TA]: (A != (some @ TA @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_option_Oexhaust)).
% 181.68/124.52 thf(2942,plain,((! [TA: $tType]: (! [A:(option @ TA)]: ((~ (A = (none @ TA))) => (~ (! [B:TA]: ~ (A = (some @ TA @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[624])).
% 181.68/124.52 thf(486,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(option @ TA)]: ((map_option @ TC @ TB @ A @ (map_option @ TA @ TC @ B @ C)) = (map_option @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_option_Omap__comp)).
% 181.68/124.52 thf(2513,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(option @ TA)]: ((map_option @ TC @ TB @ (A) @ (map_option @ TA @ TC @ (B) @ C)) = (map_option @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])).
% 181.68/124.52 thf(184,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/sandbox/benchmark/theBenchmark.p',fact_199_add__less__mono)).
% 181.68/124.52 thf(1547,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)],[184])).
% 181.68/124.52 thf(785,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TD > TB),B:(TE > TD),C:TE,D:(TC > TB),E:(TA > TC),F:TA]: (((A @ (B @ C)) = (D @ (E @ F))) => ((comp @ TD @ TB @ TE @ A @ B @ C) = (comp @ TC @ TB @ TA @ D @ E @ F)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_comp__cong)).
% 181.68/124.52 thf(3376,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TD > TB),B:(TE > TD),C:TE,D:(TC > TB),E:(TA > TC),F:TA]: (((A @ (B @ C)) = (D @ (E @ F))) => ((comp @ TD @ TB @ TE @ (A) @ (B) @ C) = (comp @ TC @ TB @ TA @ (D) @ (E) @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[785])).
% 181.68/124.52 thf(310,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(TA > TB),D:(TA > TB)]: ((A = B) => ((! [E:TA]: ((B = (some @ TA @ E)) => ((C @ E) = (D @ E)))) => ((map_option @ TA @ TB @ C @ A) = (map_option @ TA @ TB @ D @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_map__option__cong)).
% 181.68/124.52 thf(1961,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(TA > TB),D:(TA > TB)]: ((A = B) => ((! [E:TA]: ((B = (some @ TA @ E)) => ((C @ E) = (D @ E)))) => ((map_option @ TA @ TB @ (C) @ A) = (map_option @ TA @ TB @ (D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])).
% 181.68/124.52 thf(384,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:TA,B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:(ref @ TA),E:nat]: ((heap_Time_effect @ (ref @ TA) @ (ref_ref @ TA @ A) @ B @ C @ D @ E) => (~ (((ref_get @ TA @ C @ D) = A) => ((ref_present @ TA @ C @ D) => ((~ (ref_present @ TA @ B @ D)) => (E != (one_one @ nat))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5722_effect__refE)).
% 181.68/124.52 thf(2192,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:TA,B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:(ref @ TA),E:nat]: ((heap_Time_effect @ (ref @ TA) @ (ref_ref @ TA @ A) @ B @ C @ D @ E) => (~ (((ref_get @ TA @ C @ D) = A) => ((ref_present @ TA @ C @ D) => ((~ (ref_present @ TA @ B @ D)) => (~ (E = (one_one @ nat)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])).
% 181.68/124.52 thf(899,axiom,((dvd @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Odvd_154)).
% 181.68/124.52 thf(3754,plain,((dvd @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[899])).
% 181.68/124.52 thf(304,axiom,((! [A:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ((~ (times_assn_raw @ A @ B @ C)) => (~ (! [D:(heap_ext @ product_unit),E:(set @ nat)]: ((C = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E)) => (? [F:(set @ nat),G:(set @ nat)]: ((E = (sup_sup @ (set @ nat) @ F @ G)) & ((inf_inf @ (set @ nat) @ F @ G) = (bot_bot @ (set @ nat))) & (A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ F)) & (B @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ G)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5649_times__assn__raw_Oelims_I3_J)).
% 181.68/124.52 thf(1941,plain,((! [A:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),B:((product_prod @ (heap_ext @ product_unit) @ (set @ nat)) > $o),C:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ((~ (times_assn_raw @ (A) @ (B) @ C)) => (~ (! [D:(heap_ext @ product_unit),E:(set @ nat)]: ((C = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E)) => (? [F:(set @ nat),G:(set @ nat)]: ((E = (sup_sup @ (set @ nat) @ F @ G)) & ((inf_inf @ (set @ nat) @ F @ G) = (bot_bot @ (set @ nat))) & (A @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ F)) & (B @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ G)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])).
% 181.68/124.52 thf(998,axiom,((! [A:$o,B:(heap_ext @ product_unit)]: (((A) => ((heap_Time_execute @ product_unit @ (refine_Imp_assert @ A) @ B) = (some @ (product_prod @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat) @ product_Unity @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (zero_zero @ nat)))))) & ((~ (A)) => ((heap_Time_execute @ product_unit @ (refine_Imp_assert @ A) @ B) = (none @ (product_prod @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3090_execute__assert_H)).
% 181.68/124.52 thf(3949,plain,((! [A:$o,B:(heap_ext @ product_unit)]: (((A) => ((heap_Time_execute @ product_unit @ (refine_Imp_assert @ A) @ B) = (some @ (product_prod @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat) @ product_Unity @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (zero_zero @ nat)))))) & ((~ (A)) => ((heap_Time_execute @ product_unit @ (refine_Imp_assert @ A) @ B) = (none @ (product_prod @ product_unit @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[998])).
% 181.68/124.52 thf(733,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ~ (! [B:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: (A != (heap_Time_Heap2 @ TA @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Heap_Oexhaust)).
% 181.68/124.52 thf(3228,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ~ (! [B:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: ~ (A = (heap_Time_Heap2 @ TA @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[733])).
% 181.68/124.52 thf(178,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:nat,C:(array @ TA),D:TA,E:(heap_ext @ product_unit)]: ((A != B) => ((nth @ TA @ (array_get @ TA @ (array_update @ TA @ C @ B @ D @ E) @ C) @ A) = (nth @ TA @ (array_get @ TA @ E @ C) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4091_get__update__elem__neqIndex)).
% 181.68/124.52 thf(1531,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:nat,C:(array @ TA),D:TA,E:(heap_ext @ product_unit)]: ((~ (A = B)) => ((nth @ TA @ (array_get @ TA @ (array_update @ TA @ C @ B @ D @ E) @ C) @ A) = (nth @ TA @ (array_get @ TA @ E @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
% 181.68/124.52 thf(161,axiom,(((ord_less @ nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (suc @ (plus_plus @ nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_less__iff__Suc__add)).
% 181.68/124.52 thf(1484,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)],[161])).
% 181.68/124.52 thf(595,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/sandbox/benchmark/theBenchmark.p',fact_594_bounded__Max__nat)).
% 181.68/124.52 thf(2831,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)],[595])).
% 181.68/124.52 thf(259,axiom,((! [TA: $tType]: ((zero_less_one @ TA) => (ord_less @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_zero__less__one)).
% 181.68/124.52 thf(1798,plain,((! [TA: $tType]: ((zero_less_one @ TA) => (ord_less @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])).
% 181.68/124.52 thf(416,axiom,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: (ord_less_eq @ (option @ TA) @ (none @ TA) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_less__eq__option__None)).
% 181.68/124.52 thf(2298,plain,((! [TA: $tType]: ((preorder @ TA) => (! [A:(option @ TA)]: (ord_less_eq @ (option @ TA) @ (none @ TA) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])).
% 181.68/124.52 thf(791,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:nat,E:nat]: ((heap_Time_effect @ nat @ (array_len @ TA @ A) @ B @ C @ D @ E) => (~ ((D = (array_length @ TA @ C @ A)) => ((C = B) => (E != (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4148_effect__lengthE)).
% 181.68/124.52 thf(3391,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:nat,E:nat]: ((heap_Time_effect @ nat @ (array_len @ TA @ A) @ B @ C @ D @ E) => (~ ((D = (array_length @ TA @ C @ A)) => ((C = B) => (~ (E = (one_one @ nat))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[791])).
% 181.68/124.52 thf(861,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/sandbox/benchmark/theBenchmark.p',fact_231_add__eq__0__iff__both__eq__0)).
% 181.68/124.52 thf(3640,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)],[861])).
% 181.68/124.52 thf(765,axiom,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (set @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Quickcheck__Random_Orandom_247)).
% 181.68/124.52 thf(3315,plain,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (set @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[765])).
% 181.68/124.52 thf(201,axiom,((! [TA: $tType,TB: $tType]: (! [A:nat,B:(TA > TA)]: ((compow @ ((TB > TA) > (TB > TA)) @ A @ (comp @ TA @ TA @ TB @ B)) = (comp @ TA @ TA @ TB @ (compow @ (TA > TA) @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4901_comp__funpow)).
% 181.68/124.52 thf(1598,plain,((! [TA: $tType,TB: $tType]: (! [A:nat,B:(TA > TA)]: ((compow @ ((TB > TA) > (TB > TA)) @ A @ (comp @ TA @ TA @ TB @ B)) = (comp @ TA @ TA @ TB @ (compow @ (TA > TA) @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
% 181.68/124.52 thf(453,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: ((A @ (fChoice @ TA @ A)) = (? [B:TA]: (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fChoice_1_1_T)).
% 181.68/124.52 thf(2397,plain,((! [TA: $tType]: (! [A:(TA > $o)]: ((A @ (fChoice @ TA @ (A))) = (? [B:TA]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[453])).
% 181.68/124.52 thf(825,axiom,((! [TA: $tType,TB: $tType]: (! [A:((option @ TB) > $o),B:(option @ TA),C:(TA > (option @ TB))]: ((A @ (bind @ TA @ TB @ B @ C)) = (((B = (none @ TA)) => (A @ (none @ TB))) & ! [D:TA]: ((B = (some @ TA @ D)) => (A @ (C @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_bind__split)).
% 181.68/124.52 thf(3507,plain,((! [TA: $tType,TB: $tType]: (! [A:((option @ TB) > $o),B:(option @ TA),C:(TA > (option @ TB))]: ((A @ (bind @ TA @ TB @ B @ (C))) = (((B = (none @ TA)) => (A @ (none @ TB))) & ! [D:TA]: ((B = (some @ TA @ D)) => (A @ (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[825])).
% 181.68/124.52 thf(17,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/sandbox/benchmark/theBenchmark.p',fact_641_combine__common__factor)).
% 181.68/124.52 thf(1070,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)],[17])).
% 181.68/124.52 thf(688,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/sandbox/benchmark/theBenchmark.p',fact_466_trans__le__add2)).
% 181.68/124.52 thf(3112,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)],[688])).
% 181.68/124.52 thf(445,axiom,((ordere6658533253407199908up_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_529)).
% 181.68/124.52 thf(2375,plain,((ordere6658533253407199908up_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[445])).
% 181.68/124.52 thf(44,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:TB]: (((A @ B) = (some @ TB @ C)) => (member @ TA @ B @ (dom @ TA @ TB @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3321_domI)).
% 181.68/124.52 thf(1156,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:TB]: (((A @ B) = (some @ TB @ C)) => (member @ TA @ B @ (dom @ TA @ TB @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
% 181.68/124.52 thf(72,axiom,((! [A:nat,B:nat]: (((times_times @ nat @ A @ B) = (one_one @ nat)) = ((A = (one_one @ nat)) & (B = (one_one @ nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_nat__mult__eq__1__iff)).
% 181.68/124.52 thf(1225,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)],[72])).
% 181.68/124.52 thf(245,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ A @ B) => (((minus_minus @ TA @ B @ A) = C) = (B = (plus_plus @ TA @ C @ A))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add)).
% 181.68/124.52 thf(1743,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA,C:TA]: ((ord_less_eq @ TA @ A @ B) => ((ord_less_eq @ TA @ A @ B) => (((minus_minus @ TA @ B @ A) = C) = (B = (plus_plus @ TA @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
% 181.68/124.52 thf(135,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/sandbox/benchmark/theBenchmark.p',fact_972_diff__Suc__eq__diff__pred)).
% 181.68/124.52 thf(1400,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)],[135])).
% 181.68/124.52 thf(939,axiom,((! [TA: $tType]: ((heap_Time_Heap_lub @ TA) = (partial_img_lub @ (heap_Time_Heap @ TA) @ ((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ ((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ (heap_Time_Heap @ TA) @ (heap_Time_execute @ TA) @ (heap_Time_Heap2 @ TA) @ (partial_fun_lub @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (partial_flat_lub @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5968_Heap__lub__def)).
% 181.68/124.52 thf(3833,plain,((! [TA: $tType]: ((heap_Time_Heap_lub @ TA) = (partial_img_lub @ (heap_Time_Heap @ TA) @ ((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ ((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) @ (heap_Time_Heap @ TA) @ (heap_Time_execute @ TA) @ (heap_Time_Heap2 @ TA) @ (partial_fun_lub @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (heap_ext @ product_unit) @ (partial_flat_lub @ (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[939])).
% 181.68/124.52 thf(869,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))),B:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: (((heap_Time_Heap2 @ TA @ A) = (heap_Time_Heap2 @ TA @ B)) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Heap_Oinject)).
% 181.68/124.52 thf(3659,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))),B:((heap_ext @ product_unit) > (option @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))]: (((heap_Time_Heap2 @ TA @ (A)) = (heap_Time_Heap2 @ TA @ (B))) = ((A) = (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[869])).
% 181.68/124.52 thf(592,axiom,((! [A:nat,B:nat]: (((plus_plus @ nat @ A @ B) = A) => (B = (zero_zero @ nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_add__eq__self__zero)).
% 181.68/124.52 thf(2821,plain,((! [A:nat,B:nat]: (((plus_plus @ nat @ A @ B) = A) => (B = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[592])).
% 181.68/124.52 thf(725,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ (list @ TA) @ (array_freeze @ TA @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4081_success__freezeI)).
% 181.68/124.52 thf(3209,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ (list @ TA) @ (array_freeze @ TA @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[725])).
% 181.68/124.52 thf(248,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (zero_zero @ nat) @ C)) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4980_relpow__0__E)).
% 181.68/124.52 thf(1753,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (zero_zero @ nat) @ C)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])).
% 181.68/124.52 thf(916,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (option @ TB))]: ((map_comp @ TC @ TB @ TA @ A @ (^ [B:TA]: (none @ TC))) = (^ [B:TA]: (none @ TB)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_map__comp__empty_I1_J)).
% 181.68/124.53 thf(3786,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (option @ TB))]: ((map_comp @ TC @ TB @ TA @ A @ (^ [B:TA]: (none @ TC))) = (^ [B:TA]: (none @ TB)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[916])).
% 181.68/124.53 thf(665,axiom,((! [TA: $tType,TB: $tType]: ((boolea8198339166811842893lgebra @ TA) => (boolea8198339166811842893lgebra @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Boolean__Algebras_Oboolean__algebra)).
% 181.68/124.53 thf(3058,plain,((! [TA: $tType,TB: $tType]: ((boolea8198339166811842893lgebra @ TA) => (boolea8198339166811842893lgebra @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[665])).
% 181.68/124.53 thf(29,axiom,((strict9044650504122735259up_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Ostrict__ordered__ab__semigroup__add_435)).
% 181.68/124.53 thf(1098,plain,((strict9044650504122735259up_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 181.68/124.53 thf(606,axiom,((quickc3360725361186068524ustive @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Quickcheck__Exhaustive_Ofull__exhaustive_92)).
% 181.68/124.53 thf(2888,plain,((quickc3360725361186068524ustive @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[606])).
% 181.68/124.53 thf(565,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TA > TD),C:(TB > TC),D:(TA > TB),E:TA]: (((comp @ TD @ TC @ TA @ A @ B) = (comp @ TB @ TC @ TA @ C @ D)) => ((A @ (B @ E)) = (C @ (D @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_comp__eq__dest)).
% 181.68/124.53 thf(2747,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TA > TD),C:(TB > TC),D:(TA > TB),E:TA]: (((comp @ TD @ TC @ TA @ A @ B) = (comp @ TB @ TC @ TA @ C @ D)) => ((A @ (B @ E)) = (C @ (D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[565])).
% 181.68/124.53 thf(356,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ((heap_Time_bind @ TA @ TA @ A @ (heap_Time_ureturn @ TA)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_bind__ureturn)).
% 181.68/124.53 thf(2092,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ((heap_Time_bind @ TA @ TA @ A @ (heap_Time_ureturn @ TA)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])).
% 181.68/124.53 thf(56,axiom,((zero_less_one @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Ozero__less__one_480)).
% 181.68/124.53 thf(1186,plain,((zero_less_one @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
% 181.68/124.53 thf(4,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/sandbox/benchmark/theBenchmark.p',fact_597_ab__semigroup__mult__class_Omult_Oleft__commute)).
% 181.68/124.53 thf(1038,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)],[4])).
% 181.68/124.53 thf(256,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit),C:TA,D:(heap_ext @ product_unit),E:nat]: (((product_Pair @ (ref @ TA) @ (heap_ext @ product_unit) @ A @ B) = (ref_alloc @ TA @ C @ D)) => ((E = (one_one @ nat)) => (heap_Time_effect @ (ref @ TA) @ (ref_ref @ TA @ C) @ D @ B @ A @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5719_effect__refI)).
% 181.68/124.53 thf(1785,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit),C:TA,D:(heap_ext @ product_unit),E:nat]: (((product_Pair @ (ref @ TA) @ (heap_ext @ product_unit) @ A @ B) = (ref_alloc @ TA @ C @ D)) => ((E = (one_one @ nat)) => (heap_Time_effect @ (ref @ TA) @ (ref_ref @ TA @ C) @ D @ B @ A @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])).
% 181.68/124.53 thf(818,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(heap_Time_Heap @ TB),D:(heap_Time_Heap @ TB),E:(TA > (heap_Time_Heap @ TB)),F:(TA > (heap_Time_Heap @ TB))]: ((A = B) => ((refine_Imp_refines @ TB @ C @ D) => ((! [G:TA]: (refine_Imp_refines @ TB @ (E @ G) @ (F @ G))) => (refine_Imp_refines @ TB @ (case_option @ (heap_Time_Heap @ TB) @ TA @ C @ E @ A) @ (case_option @ (heap_Time_Heap @ TB) @ TA @ D @ F @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2866_refines__option)).
% 181.68/124.53 thf(3475,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(heap_Time_Heap @ TB),D:(heap_Time_Heap @ TB),E:(TA > (heap_Time_Heap @ TB)),F:(TA > (heap_Time_Heap @ TB))]: ((A = B) => ((refine_Imp_refines @ TB @ C @ D) => ((! [G:TA]: (refine_Imp_refines @ TB @ (E @ G) @ (F @ G))) => (refine_Imp_refines @ TB @ (case_option @ (heap_Time_Heap @ TB) @ TA @ C @ (E) @ A) @ (case_option @ (heap_Time_Heap @ TB) @ TA @ D @ (F) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[818])).
% 181.68/124.53 thf(829,axiom,((! [TA: $tType]: (boolea8198339166811842893lgebra @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Boolean__Algebras_Oboolean__algebra_245)).
% 181.68/124.53 thf(3544,plain,((! [TA: $tType]: (boolea8198339166811842893lgebra @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[829])).
% 181.68/124.53 thf(23,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo @ nat @ A @ B) = (modulo_modulo @ nat @ C @ B)) => ((ord_less_eq @ nat @ C @ A) => (? [D:nat]: (A = (plus_plus @ nat @ C @ (times_times @ nat @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_nat__mod__eq__lemma)).
% 181.68/124.53 thf(1085,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo @ nat @ A @ B) = (modulo_modulo @ nat @ C @ B)) => ((ord_less_eq @ nat @ C @ A) => (? [D:nat]: (A = (plus_plus @ nat @ C @ (times_times @ nat @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 181.68/124.53 thf(114,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo @ nat @ (suc @ (plus_plus @ nat @ A @ (times_times @ nat @ B @ C))) @ B) = (modulo_modulo @ nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_Suc__mod__mult__self2)).
% 181.68/124.53 thf(1336,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo @ nat @ (suc @ (plus_plus @ nat @ A @ (times_times @ nat @ B @ C))) @ B) = (modulo_modulo @ nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
% 181.68/124.53 thf(69,axiom,((semiring_modulo @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Osemiring__modulo_470)).
% 181.68/124.53 thf(1220,plain,((semiring_modulo @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
% 181.68/124.53 thf(436,axiom,((! [TA: $tType]: (! [A:(list @ TA),B:nat]: ((ord_less_eq @ nat @ (size_size @ (list @ TA) @ A) @ (one_one @ nat)) => ((rotate @ TA @ B @ A) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4012_rotate__length01)).
% 181.68/124.53 thf(2354,plain,((! [TA: $tType]: (! [A:(list @ TA),B:nat]: ((ord_less_eq @ nat @ (size_size @ (list @ TA) @ A) @ (one_one @ nat)) => ((rotate @ TA @ B @ A) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[436])).
% 181.68/124.53 thf(318,axiom,((zero @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ozero_568)).
% 181.68/124.53 thf(1987,plain,((zero @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])).
% 181.68/124.53 thf(237,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_of_list @ TA) = (^ [A:(list @ TA)]: (array_make @ TA @ (size_size @ (list @ TA) @ A) @ (nth @ TA @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3584_array__of__list__make)).
% 181.68/124.53 thf(1716,plain,((! [TA: $tType]: ((heap @ TA) => ((array_of_list @ TA) = (^ [A:(list @ TA)]: (array_make @ TA @ (size_size @ (list @ TA) @ A) @ (nth @ TA @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
% 181.68/124.53 thf(471,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/sandbox/benchmark/theBenchmark.p',fact_278_canonically__ordered__monoid__add__class_OlessE)).
% 181.68/124.53 thf(2454,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)],[471])).
% 181.68/124.53 thf(761,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(product_prod @ (ref @ TA) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))))]: ~ (! [B:(ref @ TA),C:TA,D:(heap_ext @ product_unit),E:(set @ nat)]: (A != (product_Pair @ (ref @ TA) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))) @ B @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat)) @ C @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5638_sngr__assn__raw_Ocases)).
% 181.68/124.53 thf(3305,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(product_prod @ (ref @ TA) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))))]: ~ (! [B:(ref @ TA),C:TA,D:(heap_ext @ product_unit),E:(set @ nat)]: ~ (A = (product_Pair @ (ref @ TA) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat))) @ B @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ (set @ nat)) @ C @ (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ D @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[761])).
% 181.68/124.53 thf(147,axiom,((semidom_divide @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Osemidom__divide_477)).
% 181.68/124.53 thf(1432,plain,((semidom_divide @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
% 181.68/124.53 thf(932,axiom,((enum @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Enum_Oenum)).
% 181.68/124.53 thf(3818,plain,((enum @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[932])).
% 181.68/124.53 thf(880,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TA > (TB > TD)),C:(product_prod @ TA @ TB)]: ((A @ (product_case_prod @ TA @ TB @ TD @ B @ C)) = (product_case_prod @ TA @ TB @ TC @ (^ [D:TA,E:TB]: (A @ (B @ D @ E))) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_prod_Ocase__distrib)).
% 181.68/124.53 thf(3691,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TA > (TB > TD)),C:(product_prod @ TA @ TB)]: ((A @ (product_case_prod @ TA @ TB @ TD @ (B) @ C)) = (product_case_prod @ TA @ TB @ TC @ (^ [D:TA,E:TB]: (A @ (B @ D @ E))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[880])).
% 181.68/124.53 thf(213,axiom,((! [TA: $tType,TB: $tType]: ((preorder @ TB) => (! [A:(TA > (option @ TB)),B:(TA > (option @ TB)),C:(TA > (option @ TB)),D:(TA > (option @ TB))]: ((ord_less_eq @ (TA > (option @ TB)) @ A @ B) => ((ord_less_eq @ (TA > (option @ TB)) @ C @ D) => (((inf_inf @ (set @ TA) @ (dom @ TA @ TB @ B) @ (dom @ TA @ TB @ D)) = (bot_bot @ (set @ TA))) => (ord_less_eq @ (TA > (option @ TB)) @ (map_add @ TA @ TB @ A @ C) @ (map_add @ TA @ TB @ B @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3420_map__add__distinct__le)).
% 181.68/124.53 thf(1637,plain,((! [TA: $tType,TB: $tType]: ((preorder @ TB) => (! [A:(TA > (option @ TB)),B:(TA > (option @ TB)),C:(TA > (option @ TB)),D:(TA > (option @ TB))]: ((ord_less_eq @ (TA > (option @ TB)) @ (A) @ (B)) => ((ord_less_eq @ (TA > (option @ TB)) @ (C) @ (D)) => (((inf_inf @ (set @ TA) @ (dom @ TA @ TB @ (B)) @ (dom @ TA @ TB @ (D))) = (bot_bot @ (set @ TA))) => (ord_less_eq @ (TA > (option @ TB)) @ (map_add @ TA @ TB @ A @ C) @ (map_add @ TA @ TB @ B @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
% 181.68/124.53 thf(749,axiom,((! [TA: $tType]: (inf @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oinf_262)).
% 181.68/124.53 thf(3273,plain,((! [TA: $tType]: (inf @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[749])).
% 181.68/124.53 thf(867,axiom,((comple9053668089753744459l_ccpo @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Partial__Order_Occpo_267)).
% 181.68/124.53 thf(3655,plain,((comple9053668089753744459l_ccpo @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[867])).
% 181.68/124.53 thf(85,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo @ nat @ A @ B) = (modulo_modulo @ nat @ C @ B)) => ((ord_less_eq @ nat @ A @ C) => (~ (! [D:nat]: (C != (plus_plus @ nat @ A @ (times_times @ nat @ B @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_mod__eq__nat2E)).
% 181.68/124.53 thf(1262,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo @ nat @ A @ B) = (modulo_modulo @ nat @ C @ B)) => ((ord_less_eq @ nat @ A @ C) => (~ (! [D:nat]: ~ (C = (plus_plus @ nat @ A @ (times_times @ nat @ B @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
% 181.68/124.53 thf(76,axiom,((! [A:nat,B:nat]: (((suc @ A) = B) => (A = (minus_minus @ nat @ B @ (suc @ (zero_zero @ nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_966_Suc__to__right)).
% 181.68/124.53 thf(1235,plain,((! [A:nat,B:nat]: (((suc @ A) = B) => (A = (minus_minus @ nat @ B @ (suc @ (zero_zero @ nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
% 181.68/124.53 thf(935,axiom,((cancel2418104881723323429up_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_103)).
% 181.68/124.53 thf(3823,plain,((cancel2418104881723323429up_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[935])).
% 181.68/124.53 thf(430,axiom,((! [TA: $tType]: (! [A:nat,B:nat,C:(list @ TA),D:nat]: ((ord_less @ nat @ A @ B) => ((ord_less_eq @ nat @ B @ (size_size @ (list @ TA) @ C)) => ((ord_less @ nat @ D @ (minus_minus @ nat @ B @ A)) => ((nth @ TA @ (slice @ TA @ A @ B @ C) @ D) = (nth @ TA @ C @ (plus_plus @ nat @ A @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3590_slice__nth)).
% 181.68/124.53 thf(2337,plain,((! [TA: $tType]: (! [A:nat,B:nat,C:(list @ TA),D:nat]: ((ord_less @ nat @ A @ B) => ((ord_less_eq @ nat @ B @ (size_size @ (list @ TA) @ C)) => ((ord_less @ nat @ D @ (minus_minus @ nat @ B @ A)) => ((nth @ TA @ (slice @ TA @ A @ B @ C) @ D) = (nth @ TA @ C @ (plus_plus @ nat @ A @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])).
% 181.68/124.53 thf(921,axiom,((plus @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oplus_152)).
% 181.68/124.53 thf(3801,plain,((plus @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[921])).
% 181.68/124.53 thf(315,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_new @ TA) = (^ [A:nat,B:TA]: (array_make @ TA @ A @ (^ [C:nat]: (B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_array__make)).
% 181.68/124.53 thf(1980,plain,((! [TA: $tType]: ((heap @ TA) => ((array_new @ TA) = (^ [A:nat,B:TA]: (array_make @ TA @ A @ (^ [C:nat]: (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])).
% 181.68/124.53 thf(106,axiom,((linord4140545234300271783up_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Olinordered__ab__semigroup__add_444)).
% 181.68/124.53 thf(1317,plain,((linord4140545234300271783up_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
% 181.68/124.53 thf(269,axiom,((! [A:nat,B:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_diff__add__inverse)).
% 181.68/124.53 thf(1830,plain,((! [A:nat,B:nat]: ((minus_minus @ nat @ (plus_plus @ nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])).
% 181.68/124.53 thf(180,axiom,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (heap_Time_return @ TA @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_success__returnI)).
% 181.68/124.53 thf(1538,plain,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (heap_Time_return @ TA @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])).
% 181.68/124.53 thf(482,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:nat,C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat]: ((heap_Time_effect @ TA @ (array_nth @ TA @ A @ B) @ C @ D @ E @ F) => (~ ((ord_less @ nat @ B @ (array_length @ TA @ C @ A)) => ((E = (nth @ TA @ (array_get @ TA @ C @ A) @ B)) => ((D = C) => (F != (one_one @ nat))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4075_effect__nthE)).
% 181.68/124.53 thf(2486,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:nat,C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat]: ((heap_Time_effect @ TA @ (array_nth @ TA @ A @ B) @ C @ D @ E @ F) => (~ ((ord_less @ nat @ B @ (array_length @ TA @ C @ A)) => ((E = (nth @ TA @ (array_get @ TA @ C @ A) @ B)) => ((D = C) => (~ (F = (one_one @ nat)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[482])).
% 181.68/124.53 thf(945,axiom,((no_top @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top_141)).
% 181.68/124.53 thf(3847,plain,((no_top @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[945])).
% 181.68/124.53 thf(612,axiom,((quickc3360725361186068524ustive @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Quickcheck__Exhaustive_Ofull__exhaustive_264)).
% 181.68/124.53 thf(2903,plain,((quickc3360725361186068524ustive @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[612])).
% 181.68/124.53 thf(856,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (plus_plus @ nat @ A @ B) @ (plus_plus @ nat @ A @ C)) = (ord_less_eq @ nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_nat__add__left__cancel__le)).
% 181.68/124.53 thf(3623,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)],[856])).
% 181.68/124.53 thf(796,axiom,((! [TA: $tType]: ((order_top @ TA) => (order_top @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Orderings_Oorder__top_323)).
% 181.68/124.53 thf(3412,plain,((! [TA: $tType]: ((order_top @ TA) => (order_top @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[796])).
% 181.68/124.53 thf(38,axiom,((~ (ord_less @ code_integer @ (zero_zero @ code_integer) @ (zero_zero @ code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1352_less__integer__code_I1_J)).
% 181.68/124.53 thf(1130,plain,((~ (ord_less @ code_integer @ (zero_zero @ code_integer) @ (zero_zero @ code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
% 181.68/124.53 thf(193,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TA > TB)]: ((comp @ (list @ TB) @ (list @ TC) @ (list @ TA) @ (map @ TB @ TC @ A) @ (map @ TA @ TB @ B)) = (map @ TA @ TC @ (comp @ TB @ TC @ TA @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3484_List_Omap_Ocomp)).
% 181.68/124.53 thf(1579,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:(TA > TB)]: ((comp @ (list @ TB) @ (list @ TC) @ (list @ TA) @ (map @ TB @ TC @ A) @ (map @ TA @ TB @ B)) = (map @ TA @ TC @ (comp @ TB @ TC @ TA @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
% 181.68/124.53 thf(659,axiom,((! [TA: $tType,TB: $tType]: (! [A:$o,B:(TA > (TB > $o))]: ((product_case_prod @ TA @ TB @ $o @ (^ [C:TA,D:TB]: ((A) & (B @ C @ D)))) = (^ [C:(product_prod @ TA @ TB)]: ((A) & (product_case_prod @ TA @ TB @ $o @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1252_split__part)).
% 181.68/124.53 thf(3041,plain,((! [TA: $tType,TB: $tType]: (! [A:$o,B:(TA > (TB > $o))]: ((product_case_prod @ TA @ TB @ $o @ (^ [C:TA,D:TB]: ((A) & (B @ C @ D)))) = (^ [C:(product_prod @ TA @ TB)]: ((A) & (product_case_prod @ TA @ TB @ $o @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[659])).
% 181.68/124.53 thf(949,axiom,((zero_neq_one @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__neq__one_134)).
% 181.68/124.53 thf(3853,plain,((zero_neq_one @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[949])).
% 181.68/124.53 thf(626,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > $o)),B:(option @ TB)]: (comple7038119648293358887notone @ TA @ (option @ TB) @ A @ (partial_flat_ord @ (option @ TB) @ (none @ TB)) @ (^ [C:TA]: (B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5978_option_Oconst__mono)).
% 181.68/124.53 thf(2948,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > $o)),B:(option @ TB)]: (comple7038119648293358887notone @ TA @ (option @ TB) @ (A) @ (partial_flat_ord @ (option @ TB) @ (none @ TB)) @ (^ [C:TA]: (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[626])).
% 181.68/124.53 thf(458,axiom,((! [TA: $tType]: ((mlex_prod @ TA) = (^ [A:(TA > nat),B:(set @ (product_prod @ TA @ TA))]: (collect @ (product_prod @ TA @ TA) @ (product_case_prod @ TA @ TA @ $o @ (^ [C:TA,D:TA]: ((ord_less @ nat @ (A @ C) @ (A @ D)) | ((ord_less_eq @ nat @ (A @ C) @ (A @ D)) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1248_mlex__eq)).
% 181.68/124.53 thf(2411,plain,((! [TA: $tType]: ((mlex_prod @ TA) = (^ [A:(TA > nat),B:(set @ (product_prod @ TA @ TA))]: (collect @ (product_prod @ TA @ TA) @ (product_case_prod @ TA @ TA @ $o @ (^ [C:TA,D:TA]: ((ord_less @ nat @ (A @ C) @ (A @ D)) | ((ord_less_eq @ nat @ (A @ C) @ (A @ D)) & (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ C @ D) @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[458])).
% 181.68/124.53 thf(182,axiom,((! [TA: $tType]: (preorder @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_256)).
% 181.68/124.53 thf(1543,plain,((! [TA: $tType]: (preorder @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
% 181.68/124.53 thf(504,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (heap_Time_tap @ TA @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_success__tapI)).
% 181.68/124.53 thf(2558,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ TA @ (heap_Time_tap @ TA @ (A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[504])).
% 181.68/124.53 thf(693,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:((TA > (option @ TB)) > (option @ TD)),B:(TD > ((TA > (option @ TB)) > (option @ TC)))]: ((comple7038119648293358887notone @ (TA > (option @ TB)) @ (option @ TD) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TD) @ (none @ TD)) @ A) => ((! [C:TD]: (comple7038119648293358887notone @ (TA > (option @ TB)) @ (option @ TC) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TC) @ (none @ TC)) @ (B @ C))) => (comple7038119648293358887notone @ (TA > (option @ TB)) @ (option @ TC) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TC) @ (none @ TC)) @ (^ [C:(TA > (option @ TB))]: (bind @ TD @ TC @ (A @ C) @ (^ [D:TD]: (B @ D @ C)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5977_Partial__Function_Obind__mono)).
% 181.68/124.53 thf(3124,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:((TA > (option @ TB)) > (option @ TD)),B:(TD > ((TA > (option @ TB)) > (option @ TC)))]: ((comple7038119648293358887notone @ (TA > (option @ TB)) @ (option @ TD) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TD) @ (none @ TD)) @ (A)) => ((! [C:TD]: (comple7038119648293358887notone @ (TA > (option @ TB)) @ (option @ TC) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TC) @ (none @ TC)) @ (B @ C))) => (comple7038119648293358887notone @ (TA > (option @ TB)) @ (option @ TC) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TA @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TC) @ (none @ TC)) @ (^ [C:(TA > (option @ TB))]: (bind @ TD @ TC @ (A @ C) @ (^ [D:TD]: (B @ D @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[693])).
% 181.68/124.53 thf(447,axiom,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (plus_plus @ TA @ A @ B)) = (ord_less @ TA @ (zero_zero @ TA) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_less__add__same__cancel1)).
% 181.68/124.53 thf(2379,plain,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (plus_plus @ TA @ A @ B)) = (ord_less @ TA @ (zero_zero @ TA) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[447])).
% 181.68/124.53 thf(513,axiom,((! [TA: $tType]: ((zero_less_one @ TA) => (ord_less_eq @ TA @ (zero_zero @ TA) @ (one_one @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_zero__less__one__class_Ozero__le__one)).
% 181.68/124.53 thf(2579,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)],[513])).
% 181.68/124.53 thf(145,axiom,((strict7427464778891057005id_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Ostrict__ordered__comm__monoid__add_440)).
% 181.68/124.53 thf(1427,plain,((strict7427464778891057005id_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
% 181.68/124.53 thf(652,axiom,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ A @ B) @ A) = (ord_less_eq @ TA @ B @ (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_add__le__same__cancel1)).
% 181.68/124.53 thf(3024,plain,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ (plus_plus @ TA @ A @ B) @ A) = (ord_less_eq @ TA @ B @ (zero_zero @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[652])).
% 181.68/124.53 thf(1000,axiom,((! [TA: $tType]: (typerep2 @ (array @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oarray___Typerep_Otyperep_37)).
% 181.68/124.53 thf(3961,plain,((! [TA: $tType]: (typerep2 @ (array @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000])).
% 181.68/124.53 thf(781,axiom,((semilattice_sup @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_269)).
% 181.68/124.53 thf(3366,plain,((semilattice_sup @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[781])).
% 181.68/124.53 thf(646,axiom,((! [TA: $tType]: ((bounded_lattice_top @ TA) => (bounded_lattice @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Lattices_Obounded__lattice_320)).
% 181.68/124.53 thf(3007,plain,((! [TA: $tType]: ((bounded_lattice_top @ TA) => (bounded_lattice @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[646])).
% 181.68/124.53 thf(207,axiom,((! [A:nat,B:nat]: ((~ (ord_less @ nat @ A @ B)) => ((plus_plus @ nat @ B @ (minus_minus @ nat @ A @ B)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_add__diff__inverse__nat)).
% 181.68/124.53 thf(1617,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)],[207])).
% 181.68/124.53 thf(342,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: ((ord_less @ TA @ (zero_zero @ TA) @ A) = (A != (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_zero__less__iff__neq__zero)).
% 181.68/124.53 thf(2056,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)],[342])).
% 181.68/124.53 thf(118,axiom,((! [TA: $tType]: ((semiri1453513574482234551roduct @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((plus_plus @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ D)) = (plus_plus @ TA @ (times_times @ TA @ A @ D) @ (times_times @ TA @ C @ B))) = ((A = C) | (B = D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_crossproduct__eq)).
% 181.68/124.53 thf(1358,plain,((! [TA: $tType]: ((semiri1453513574482234551roduct @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((plus_plus @ TA @ (times_times @ TA @ A @ B) @ (times_times @ TA @ C @ D)) = (plus_plus @ TA @ (times_times @ TA @ A @ D) @ (times_times @ TA @ C @ B))) = ((A = C) | (B = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
% 181.68/124.53 thf(70,axiom,((! [A:nat,B:nat]: (ord_less @ nat @ A @ (suc @ (plus_plus @ nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_963_less__add__Suc2)).
% 181.68/124.53 thf(1221,plain,((! [A:nat,B:nat]: (ord_less @ nat @ A @ (suc @ (plus_plus @ nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
% 181.68/124.53 thf(93,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: ((A != (^ [B:TA]: (none @ TB))) => (~ (! [B:TA]: ~ (member @ TA @ B @ (dom @ TA @ TB @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3324_nempty__dom)).
% 181.68/124.53 thf(1284,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: ((~ ((A) = (^ [B:TA]: (none @ TB)))) => (~ (! [B:TA]: ~ (member @ TA @ B @ (dom @ TA @ TB @ (A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
% 181.68/124.53 thf(411,axiom,((! [A:(product_prod @ (heap_ext @ product_unit) @ (set @ nat)),B:$o]: (((in_range @ A) = B) => (~ (! [C:(heap_ext @ product_unit),D:(set @ nat)]: ((A = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ D)) => (B = (~ (! [E:nat]: ((member @ nat @ E @ D) => (ord_less @ nat @ E @ (lim @ product_unit @ C)))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5693_in__range_Oelims_I1_J)).
% 181.68/124.53 thf(2279,plain,((! [A:(product_prod @ (heap_ext @ product_unit) @ (set @ nat)),B:$o]: (((in_range @ A) = B) => (~ (! [C:(heap_ext @ product_unit),D:(set @ nat)]: ((A = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ C @ D)) => (B = (~ (! [E:nat]: ((member @ nat @ E @ D) => (ord_less @ nat @ E @ (lim @ product_unit @ C)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[411])).
% 181.68/124.53 thf(437,axiom,((intrel @ (product_Pair @ nat @ nat @ (zero_zero @ nat) @ (zero_zero @ nat)) @ (product_Pair @ nat @ nat @ (zero_zero @ nat) @ (zero_zero @ nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2690_zero__int_Orsp)).
% 181.68/124.53 thf(2357,plain,((intrel @ (product_Pair @ nat @ nat @ (zero_zero @ nat) @ (zero_zero @ nat)) @ (product_Pair @ nat @ nat @ (zero_zero @ nat) @ (zero_zero @ nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[437])).
% 181.68/124.53 thf(308,axiom,((! [TA: $tType]: ((inf @ TA) => (! [A:TA,B:TA]: ((inf_inf @ (option @ TA) @ (some @ TA @ A) @ (some @ TA @ B)) = (some @ TA @ (inf_inf @ TA @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2994_inf__Some)).
% 181.68/124.53 thf(1955,plain,((! [TA: $tType]: ((inf @ TA) => (! [A:TA,B:TA]: ((inf_inf @ (option @ TA) @ (some @ TA @ A) @ (some @ TA @ B)) = (some @ TA @ (inf_inf @ TA @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])).
% 181.68/124.53 thf(372,axiom,((! [TA: $tType]: (! [A:nat,B:nat,C:(TA > TA)]: ((compow @ (TA > TA) @ (plus_plus @ nat @ A @ B) @ C) = (comp @ TA @ TA @ TA @ (compow @ (TA > TA) @ A @ C) @ (compow @ (TA > TA) @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4904_funpow__add)).
% 181.68/124.53 thf(2145,plain,((! [TA: $tType]: (! [A:nat,B:nat,C:(TA > TA)]: ((compow @ (TA > TA) @ (plus_plus @ nat @ A @ B) @ C) = (comp @ TA @ TA @ TA @ (compow @ (TA > TA) @ A @ C) @ (compow @ (TA > TA) @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])).
% 181.68/124.53 thf(312,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TC,B:(TB > (TA > (set @ TC))),C:TB,D:TA]: ((member @ TC @ A @ (B @ C @ D)) => (member @ TC @ A @ (product_case_prod @ TB @ TA @ (set @ TC) @ B @ (product_Pair @ TB @ TA @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_mem__case__prodI)).
% 181.68/124.53 thf(1972,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TC,B:(TB > (TA > (set @ TC))),C:TB,D:TA]: ((member @ TC @ A @ (B @ C @ D)) => (member @ TC @ A @ (product_case_prod @ TB @ TA @ (set @ TC) @ (B) @ (product_Pair @ TB @ TA @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])).
% 181.68/124.53 thf(424,axiom,((! [A:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ((~ (in_range @ A)) => (~ (! [B:(heap_ext @ product_unit),C:(set @ nat)]: ((A = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ B @ C)) => (! [D:nat]: ((member @ nat @ D @ C) => (ord_less @ nat @ D @ (lim @ product_unit @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5691_in__range_Oelims_I3_J)).
% 181.68/124.53 thf(2320,plain,((! [A:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ((~ (in_range @ A)) => (~ (! [B:(heap_ext @ product_unit),C:(set @ nat)]: ((A = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ B @ C)) => (! [D:nat]: ((member @ nat @ D @ C) => (ord_less @ nat @ D @ (lim @ product_unit @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])).
% 181.68/124.53 thf(10,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo @ nat @ (suc @ (plus_plus @ nat @ (times_times @ nat @ A @ B) @ C)) @ A) = (modulo_modulo @ nat @ (suc @ C) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_Suc__mod__mult__self4)).
% 181.68/124.53 thf(1052,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo @ nat @ (suc @ (plus_plus @ nat @ (times_times @ nat @ A @ B) @ C)) @ A) = (modulo_modulo @ nat @ (suc @ C) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 181.68/124.53 thf(553,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: ((product_scomp @ TA @ TB @ TC @ TD) = (^ [A:(TA > (product_prod @ TB @ TC)),B:(TB > (TC > TD)),C:TA]: (product_case_prod @ TB @ TC @ TD @ B @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4279_scomp__def)).
% 181.68/124.53 thf(2711,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: ((product_scomp @ TA @ TB @ TC @ TD) = (^ [A:(TA > (product_prod @ TB @ TC)),B:(TB > (TC > TD)),C:TA]: (product_case_prod @ TB @ TC @ TD @ B @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[553])).
% 181.68/124.53 thf(168,axiom,((cancel_semigroup_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_535)).
% 181.68/124.53 thf(1506,plain,((cancel_semigroup_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])).
% 181.68/124.53 thf(195,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ((size_size @ (heap_Time_Heap @ TA) @ A) != (zero_zero @ nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1026_Heap_Osize__neq)).
% 181.68/124.53 thf(1585,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA)]: ~ ((size_size @ (heap_Time_Heap @ TA) @ A) = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
% 181.68/124.53 thf(27,axiom,((! [A:nat,B:nat]: (((ord_less @ nat @ A @ B) & (ord_less_eq @ nat @ B @ (suc @ A))) = (B = (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_nat__in__between__eq_I1_J)).
% 181.68/124.53 thf(1094,plain,((! [A:nat,B:nat]: (((ord_less @ nat @ A @ B) & (ord_less_eq @ nat @ B @ (suc @ A))) = (B = (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
% 181.68/124.53 thf(996,axiom,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA)]: ((combine_options @ TA @ A @ B @ (none @ TA)) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_combine__options__simps_I2_J)).
% 181.68/124.53 thf(3943,plain,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA)]: ((combine_options @ TA @ (A) @ B @ (none @ TA)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[996])).
% 181.68/124.53 thf(333,axiom,((! [TA: $tType]: ((accp @ TA) = (^ [A:(TA > (TA > $o)),B:TA]: ? [C:TA]: ((B = C) & ! [D:TA]: ((A @ D @ C) => (accp @ TA @ A @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_accp_Osimps)).
% 181.68/124.53 thf(2030,plain,((! [TA: $tType]: ((accp @ TA) = (^ [A:(TA > (TA > $o)),B:TA]: ? [C:TA]: ((B = C) & ! [D:TA]: ((A @ D @ C) => (accp @ TA @ A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])).
% 181.68/124.53 thf(125,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TA > (option @ TB))]: ((~ (member @ TA @ A @ (dom @ TA @ TB @ B))) => ((fun_upd @ TA @ (option @ TB) @ B @ A @ (none @ TB)) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3312_fun__upd__None__if__notin__dom)).
% 181.68/124.53 thf(1372,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TA > (option @ TB))]: ((~ (member @ TA @ A @ (dom @ TA @ TB @ (B)))) => ((fun_upd @ TA @ (option @ TB) @ B @ A @ (none @ TB)) = (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
% 181.68/124.53 thf(742,axiom,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TA @ TB),B:(TA > (TB > $o))]: ((! [C:TA,D:TB]: ((A = (product_Pair @ TA @ TB @ C @ D)) => (B @ C @ D))) => (product_case_prod @ TA @ TB @ $o @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_case__prodI2)).
% 181.68/124.53 thf(3256,plain,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TA @ TB),B:(TA > (TB > $o))]: ((! [C:TA,D:TB]: ((A = (product_Pair @ TA @ TB @ C @ D)) => (B @ C @ D))) => (product_case_prod @ TA @ TB @ $o @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[742])).
% 181.68/124.53 thf(608,axiom,((! [TA: $tType]: (! [A:(product_unit > TA)]: ((^ [B:product_unit]: (A @ product_Unity)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2993_unit__abs__eta__conv)).
% 181.68/124.53 thf(2892,plain,((! [TA: $tType]: (! [A:(product_unit > TA)]: ((^ [B:product_unit]: (A @ product_Unity)) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[608])).
% 181.68/124.53 thf(88,axiom,((euclid3725896446679973847miring @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Euclidean__Division_Oeuclidean__semiring_442)).
% 181.68/124.53 thf(1272,plain,((euclid3725896446679973847miring @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
% 181.68/124.53 thf(979,axiom,((quickc658316121487927005ustive @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Quickcheck__Exhaustive_Oexhaustive_99)).
% 181.68/124.53 thf(3914,plain,((quickc658316121487927005ustive @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[979])).
% 181.68/124.53 thf(878,axiom,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA))]: ((compow @ (set @ (product_prod @ TA @ TA)) @ (one_one @ nat) @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4977_relpow__1)).
% 181.68/124.53 thf(3684,plain,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA))]: ((compow @ (set @ (product_prod @ TA @ TA)) @ (one_one @ nat) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[878])).
% 181.68/124.53 thf(755,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ TE)))) > $o),B:(product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ TE))))]: ((! [C:TA,D:TB,E:TC,F:TD,G:TE]: (A @ (product_Pair @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ TE))) @ C @ (product_Pair @ TB @ (product_prod @ TC @ (product_prod @ TD @ TE)) @ D @ (product_Pair @ TC @ (product_prod @ TD @ TE) @ E @ (product_Pair @ TD @ TE @ F @ G)))))) => (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_prod__induct5)).
% 181.68/124.53 thf(3288,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ TE)))) > $o),B:(product_prod @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ TE))))]: ((! [C:TA,D:TB,E:TC,F:TD,G:TE]: (A @ (product_Pair @ TA @ (product_prod @ TB @ (product_prod @ TC @ (product_prod @ TD @ TE))) @ C @ (product_Pair @ TB @ (product_prod @ TC @ (product_prod @ TD @ TE)) @ D @ (product_Pair @ TC @ (product_prod @ TD @ TE) @ E @ (product_Pair @ TD @ TE @ F @ G)))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[755])).
% 181.68/124.53 thf(143,axiom,((! [TA: $tType]: ((ab_semigroup_mult @ TA) => ((times_times @ TA) = (^ [A:TA,B:TA]: (times_times @ TA @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_ab__semigroup__mult__class_Omult_Ocommute)).
% 181.68/124.53 thf(1421,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)],[143])).
% 181.68/124.53 thf(854,axiom,((! [TA: $tType]: (cl_HOL_Oequal @ (heap_Time_Heap @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap__Time__Monad_OHeap___HOL_Oequal_574)).
% 181.68/124.53 thf(3620,plain,((! [TA: $tType]: (cl_HOL_Oequal @ (heap_Time_Heap @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[854])).
% 181.68/124.53 thf(216,axiom,((! [TA: $tType]: ((inf @ TA) => (! [A:(option @ TA)]: ((inf_inf @ (option @ TA) @ A @ (none @ TA)) = (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3117_inf__None__2)).
% 181.68/124.53 thf(1649,plain,((! [TA: $tType]: ((inf @ TA) => (! [A:(option @ TA)]: ((inf_inf @ (option @ TA) @ A @ (none @ TA)) = (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
% 181.68/124.53 thf(480,axiom,((! [A:nat,B:nat,C:nat]: ((map @ nat @ nat @ (^ [D:nat]: (plus_plus @ nat @ D @ A)) @ (upt @ B @ C)) = (upt @ (plus_plus @ nat @ B @ A) @ (plus_plus @ nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3552_map__add__upt_H)).
% 181.68/124.53 thf(2479,plain,((! [A:nat,B:nat,C:nat]: ((map @ nat @ nat @ (^ [D:nat]: (plus_plus @ nat @ D @ A)) @ (upt @ B @ C)) = (upt @ (plus_plus @ nat @ B @ A) @ (plus_plus @ nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[480])).
% 181.68/124.53 thf(831,axiom,((! [TA: $tType]: (cl_HOL_Oequal @ (heap_ext @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oheap_Oheap__ext___HOL_Oequal_425)).
% 181.68/124.53 thf(3548,plain,((! [TA: $tType]: (cl_HOL_Oequal @ (heap_ext @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[831])).
% 181.68/124.53 thf(392,axiom,((dvd @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Odvd_571)).
% 181.68/124.53 thf(2215,plain,((dvd @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[392])).
% 181.68/124.53 thf(617,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(TA > (option @ TB)),D:(TA > (option @ TB))]: ((A = B) => ((! [E:TA]: ((B = (some @ TA @ E)) => ((C @ E) = (D @ E)))) => ((bind @ TA @ TB @ A @ C) = (bind @ TA @ TB @ B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_Option_Obind__cong)).
% 181.68/124.53 thf(2919,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(TA > (option @ TB)),D:(TA > (option @ TB))]: ((A = B) => ((! [E:TA]: ((B = (some @ TA @ E)) => ((C @ E) = (D @ E)))) => ((bind @ TA @ TB @ A @ (C)) = (bind @ TA @ TB @ B @ (D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[617])).
% 181.68/124.53 thf(33,axiom,((! [A:(nat > $o),B:nat]: ((A @ (zero_zero @ nat)) => ((! [C:nat]: ((! [D:nat]: ((ord_less_eq @ nat @ D @ C) => (A @ D))) => (A @ (suc @ C)))) => (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_955_nat__compl__induct_H)).
% 181.68/124.53 thf(1108,plain,((! [A:(nat > $o),B:nat]: ((A @ (zero_zero @ nat)) => ((! [C:nat]: ((! [D:nat]: ((ord_less_eq @ nat @ D @ C) => (A @ D))) => (A @ (suc @ C)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 181.68/124.53 thf(602,axiom,((! [TA: $tType]: ((one @ TA) => (! [A:TA]: (((one_one @ TA) = A) = (A = (one_one @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_one__reorient)).
% 181.68/124.53 thf(2875,plain,((! [TA: $tType]: ((one @ TA) => (! [A:TA]: (((one_one @ TA) = A) = (A = (one_one @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[602])).
% 181.68/124.53 thf(711,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB)]: ((comp @ TB @ TB @ TA @ (^ [B:TB]: (B)) @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_fun_Omap__ident)).
% 181.68/124.53 thf(3168,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB)]: ((comp @ TB @ TB @ TA @ (^ [B:TB]: (B)) @ A) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[711])).
% 181.68/124.53 thf(466,axiom,((! [TA: $tType]: (! [A:(TA > (TA > $o))]: ((compow @ (TA > (TA > $o)) @ (one_one @ nat) @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4899_relpowp__1)).
% 181.68/124.53 thf(2435,plain,((! [TA: $tType]: (! [A:(TA > (TA > $o))]: ((compow @ (TA > (TA > $o)) @ (one_one @ nat) @ A) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[466])).
% 181.68/124.53 thf(568,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(nat > TA),C:(heap_ext @ product_unit)]: ((heap_Time_execute @ (array @ TA) @ (array_make @ TA @ A @ B) @ C) = (some @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [D:(array @ TA),E:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ (one_one @ nat))))) @ (array_alloc @ TA @ (map @ nat @ TA @ B @ (upt @ (zero_zero @ nat) @ A)) @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3540_execute__make)).
% 181.68/124.53 thf(2760,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(nat > TA),C:(heap_ext @ product_unit)]: ((heap_Time_execute @ (array @ TA) @ (array_make @ TA @ A @ (B)) @ C) = (some @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [D:(array @ TA),E:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ (one_one @ nat))))) @ (array_alloc @ TA @ (map @ nat @ TA @ (B) @ (upt @ (zero_zero @ nat) @ A)) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[568])).
% 181.68/124.53 thf(803,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType]: (! [A:(product_prod @ TG @ (product_prod @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))))))]: ~ (! [B:TG,C:TF,D:TE,E:TD,F:TC,G:TB,H:TA]: (A != (product_Pair @ TG @ (product_prod @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))))) @ B @ (product_Pair @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)))) @ C @ (product_Pair @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))) @ D @ (product_Pair @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)) @ E @ (product_Pair @ TC @ (product_prod @ TB @ TA) @ F @ (product_Pair @ TB @ TA @ G @ H))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_prod__cases7)).
% 181.68/124.53 thf(3433,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType]: (! [A:(product_prod @ TG @ (product_prod @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))))))]: ~ (! [B:TG,C:TF,D:TE,E:TD,F:TC,G:TB,H:TA]: ~ (A = (product_Pair @ TG @ (product_prod @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))))) @ B @ (product_Pair @ TF @ (product_prod @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)))) @ C @ (product_Pair @ TE @ (product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA))) @ D @ (product_Pair @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)) @ E @ (product_Pair @ TC @ (product_prod @ TB @ TA) @ F @ (product_Pair @ TB @ TA @ G @ H))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[803])).
% 181.68/124.53 thf(997,axiom,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > $o),B:(heap_ext @ product_unit),C:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((A @ B) => ((heap_Time_execute @ TA @ (heap_Time_guard @ TA @ A @ C) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_execute__guard_I2_J)).
% 181.68/124.53 thf(3946,plain,((! [TA: $tType]: (! [A:((heap_ext @ product_unit) > $o),B:(heap_ext @ product_unit),C:((heap_ext @ product_unit) > (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))]: ((A @ B) => ((heap_Time_execute @ TA @ (heap_Time_guard @ TA @ (A) @ (C)) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[997])).
% 181.68/124.53 thf(155,axiom,((power @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Power_Opower_504)).
% 181.68/124.53 thf(1459,plain,((power @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
% 181.68/124.53 thf(680,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:(list @ TA),D:(array @ TA),E:nat]: ((A = B) => ((C = (array_get @ TA @ B @ D)) => ((E = (array_length @ TA @ B @ D)) => (heap_Time_effect @ (list @ TA) @ (array_freeze @ TA @ D) @ B @ A @ C @ (plus_plus @ nat @ E @ (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4084_effect__freezeI)).
% 181.68/124.53 thf(3092,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:(list @ TA),D:(array @ TA),E:nat]: ((A = B) => ((C = (array_get @ TA @ B @ D)) => ((E = (array_length @ TA @ B @ D)) => (heap_Time_effect @ (list @ TA) @ (array_freeze @ TA @ D) @ B @ A @ C @ (plus_plus @ nat @ E @ (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[680])).
% 181.68/124.53 thf(590,axiom,((inf @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oinf_284)).
% 181.68/124.53 thf(2818,plain,((inf @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[590])).
% 181.68/124.53 thf(669,axiom,((! [TA: $tType]: ((countable @ TA) => (countable @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Countable_Ocountable_325)).
% 181.68/124.53 thf(3067,plain,((! [TA: $tType]: ((countable @ TA) => (countable @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[669])).
% 181.68/124.53 thf(549,axiom,((! [A:nat]: ((plus_plus @ nat @ A @ (zero_zero @ nat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Nat_Oadd__0__right)).
% 181.68/124.53 thf(2696,plain,((! [A:nat]: ((plus_plus @ nat @ A @ (zero_zero @ nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[549])).
% 181.68/124.53 thf(186,axiom,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA,C:(TA > $o)]: ((accp @ TA @ A @ B) => ((! [D:TA]: ((accp @ TA @ A @ D) => ((! [E:TA]: ((A @ E @ D) => (C @ E))) => (C @ D)))) => (C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_accp__induct__rule)).
% 181.68/124.53 thf(1553,plain,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA,C:(TA > $o)]: ((accp @ TA @ (A) @ B) => ((! [D:TA]: ((accp @ TA @ (A) @ D) => ((! [E:TA]: ((A @ E @ D) => (C @ E))) => (C @ D)))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])).
% 181.68/124.53 thf(712,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TC > (heap_Time_Heap @ TB))),B:(TA > TA),C:((TC > (heap_Time_Heap @ TB)) > TA),D:TA]: ((! [E:TC]: (comple7038119648293358887notone @ (TC > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TB) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TB) @ (^ [F:(TC > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ F)) @ E)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TC > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ (^ [E:(TC > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ E))))))) => ((! [E:TA]: ((C @ (A @ E)) = E)) => (D = (B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5991_heap_Ofixp__rule__uc)).
% 181.68/124.53 thf(3171,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TC > (heap_Time_Heap @ TB))),B:(TA > TA),C:((TC > (heap_Time_Heap @ TB)) > TA),D:TA]: ((! [E:TC]: (comple7038119648293358887notone @ (TC > (heap_Time_Heap @ TB)) @ (heap_Time_Heap @ TB) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ (heap_Time_Heap_ord @ TB) @ (^ [F:(TC > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ F)) @ E)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TC > (heap_Time_Heap @ TB)) @ (partial_fun_lub @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_lub @ TB)) @ (partial_fun_ord @ (heap_Time_Heap @ TB) @ (heap_Time_Heap @ TB) @ TC @ (heap_Time_Heap_ord @ TB)) @ (^ [E:(TC > (heap_Time_Heap @ TB))]: (A @ (B @ (C @ E))))))) => ((! [E:TA]: ((C @ (A @ E)) = E)) => (D = (B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[712])).
% 181.68/124.53 thf(632,axiom,((! [TA: $tType,TB: $tType]: ((fChoice @ (product_prod @ TA @ TB)) = (^ [A:((product_prod @ TA @ TB) > $o)]: (fChoice @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ (^ [B:TA,C:TB]: (A @ (product_Pair @ TA @ TB @ B @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4656_split__paired__Eps)).
% 181.68/124.53 thf(2960,plain,((! [TA: $tType,TB: $tType]: ((fChoice @ (product_prod @ TA @ TB)) = (^ [A:((product_prod @ TA @ TB) > $o)]: (fChoice @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ (^ [B:TA,C:TB]: (A @ (product_Pair @ TA @ TB @ B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[632])).
% 181.68/124.53 thf(420,axiom,((! [A:nat,B:nat]: ((map @ nat @ nat @ (^ [C:nat]: (plus_plus @ nat @ C @ A)) @ (upt @ (zero_zero @ nat) @ B)) = (upt @ A @ (plus_plus @ nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3554_map__add__upt)).
% 181.68/124.53 thf(2310,plain,((! [A:nat,B:nat]: ((map @ nat @ nat @ (^ [C:nat]: (plus_plus @ nat @ C @ A)) @ (upt @ (zero_zero @ nat) @ B)) = (upt @ A @ (plus_plus @ nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[420])).
% 181.68/124.53 thf(960,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA)]: ((! [C:(heap_ext @ product_unit)]: ((heap_Time_execute @ TA @ A @ C) = (heap_Time_execute @ TA @ B @ C))) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Heap__eqI)).
% 181.68/124.53 thf(3874,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA)]: ((! [C:(heap_ext @ product_unit)]: ((heap_Time_execute @ TA @ A @ C) = (heap_Time_execute @ TA @ B @ C))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[960])).
% 181.68/124.53 thf(522,axiom,((order_top @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_274)).
% 181.68/124.53 thf(2611,plain,((order_top @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[522])).
% 181.68/124.53 thf(988,axiom,((! [TA: $tType,TB: $tType]: (((quickc658316121487927005ustive @ TB) & (quickc658316121487927005ustive @ TA)) => (quickc658316121487927005ustive @ (product_prod @ TB @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Quickcheck__Exhaustive_Oexhaustive_395)).
% 181.68/124.53 thf(3928,plain,((! [TA: $tType,TB: $tType]: (((quickc658316121487927005ustive @ TB) & (quickc658316121487927005ustive @ TA)) => (quickc658316121487927005ustive @ (product_prod @ TB @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[988])).
% 181.68/124.53 thf(67,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/sandbox/benchmark/theBenchmark.p',fact_656_add__mult__distrib)).
% 181.68/124.53 thf(1216,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)],[67])).
% 181.68/124.53 thf(390,axiom,((! [TA: $tType]: ((power @ TA) => ((power_power @ TA) = (^ [A:TA,B:nat]: (if @ TA @ (B = (zero_zero @ nat)) @ (one_one @ TA) @ (times_times @ TA @ A @ (power_power @ TA @ A @ (minus_minus @ nat @ B @ (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_power__eq__if)).
% 181.68/124.53 thf(2209,plain,((! [TA: $tType]: ((power @ TA) => ((power_power @ TA) = (^ [A:TA,B:nat]: (if @ TA @ (B = (zero_zero @ nat)) @ (one_one @ TA) @ (times_times @ TA @ A @ (power_power @ TA @ A @ (minus_minus @ nat @ B @ (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])).
% 181.68/124.53 thf(564,axiom,((! [TA: $tType]: (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:TA,D:((heap_ext @ product_unit) > TA)]: ((A = B) => ((C = (D @ B)) => (heap_Time_effect @ TA @ (heap_Time_tap @ TA @ D) @ B @ A @ C @ (one_one @ nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_effect__tapI)).
% 181.68/124.53 thf(2743,plain,((! [TA: $tType]: (! [A:(heap_ext @ product_unit),B:(heap_ext @ product_unit),C:TA,D:((heap_ext @ product_unit) > TA)]: ((A = B) => ((C = (D @ B)) => (heap_Time_effect @ TA @ (heap_Time_tap @ TA @ (D)) @ B @ A @ C @ (one_one @ nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[564])).
% 181.68/124.53 thf(644,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:TA]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => (heap_Time_success @ TA @ (array_swap @ TA @ A @ D @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4101_success__swapI)).
% 181.68/124.53 thf(2997,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:TA]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => (heap_Time_success @ TA @ (array_swap @ TA @ A @ D @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[644])).
% 181.68/124.53 thf(383,axiom,((! [TA: $tType]: (! [A:(code_natural > TA),B:code_natural,C:code_natural,D:((code_natural > TA) > (code_natural > (code_natural > $o)))]: ((accp @ (product_prod @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural)) @ (iterate_upto_rel @ TA) @ (product_Pair @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural) @ A @ (product_Pair @ code_natural @ code_natural @ B @ C))) => ((! [E:(code_natural > TA),F:code_natural,G:code_natural]: ((accp @ (product_prod @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural)) @ (iterate_upto_rel @ TA) @ (product_Pair @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural) @ E @ (product_Pair @ code_natural @ code_natural @ F @ G))) => ((! [H:product_unit]: ((~ (ord_less @ code_natural @ G @ F)) => (D @ E @ (plus_plus @ code_natural @ F @ (one_one @ code_natural)) @ G))) => (D @ E @ F @ G)))) => (D @ A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4272_Predicate_Oiterate__upto_Opinduct)).
% 181.68/124.53 thf(2187,plain,((! [TA: $tType]: (! [A:(code_natural > TA),B:code_natural,C:code_natural,D:((code_natural > TA) > (code_natural > (code_natural > $o)))]: ((accp @ (product_prod @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural)) @ (iterate_upto_rel @ TA) @ (product_Pair @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural) @ (A) @ (product_Pair @ code_natural @ code_natural @ B @ C))) => ((! [E:(code_natural > TA),F:code_natural,G:code_natural]: ((accp @ (product_prod @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural)) @ (iterate_upto_rel @ TA) @ (product_Pair @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural) @ (E) @ (product_Pair @ code_natural @ code_natural @ F @ G))) => (((~ (ord_less @ code_natural @ G @ F)) => (D @ (E) @ (plus_plus @ code_natural @ F @ (one_one @ code_natural)) @ G)) => (D @ (E) @ F @ G)))) => (D @ (A) @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])).
% 181.68/124.53 thf(775,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)))]: ~ (! [B:TD,C:TC,D:TB,E:TA]: (A != (product_Pair @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)) @ B @ (product_Pair @ TC @ (product_prod @ TB @ TA) @ C @ (product_Pair @ TB @ TA @ D @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_prod__cases4)).
% 181.68/124.53 thf(3346,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(product_prod @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)))]: ~ (! [B:TD,C:TC,D:TB,E:TA]: ~ (A = (product_Pair @ TD @ (product_prod @ TC @ (product_prod @ TB @ TA)) @ B @ (product_Pair @ TC @ (product_prod @ TB @ TA) @ C @ (product_Pair @ TB @ TA @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[775])).
% 181.68/124.53 thf(396,axiom,((comm_semiring @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring_554)).
% 181.68/124.53 thf(2226,plain,((comm_semiring @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])).
% 181.68/124.53 thf(152,axiom,((zero @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Ozero_506)).
% 181.68/124.53 thf(1453,plain,((zero @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
% 181.68/124.53 thf(277,axiom,((strict7427464778891057005id_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__comm__monoid__add_522)).
% 181.68/124.53 thf(1866,plain,((strict7427464778891057005id_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])).
% 181.68/124.53 thf(349,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:(heap_ext @ product_unit),E:TA,F:nat]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => ((D = B) => ((E = (nth @ TA @ (array_get @ TA @ B @ C) @ A)) => ((F = (one_one @ nat)) => (heap_Time_effect @ TA @ (array_nth @ TA @ C @ A) @ B @ D @ E @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4076_effect__nthI)).
% 181.68/124.53 thf(2071,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA),D:(heap_ext @ product_unit),E:TA,F:nat]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => ((D = B) => ((E = (nth @ TA @ (array_get @ TA @ B @ C) @ A)) => ((F = (one_one @ nat)) => (heap_Time_effect @ TA @ (array_nth @ TA @ C @ A) @ B @ D @ E @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])).
% 181.68/124.53 thf(573,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TA,B:(TA > (TC > TB))]: ((product_scomp @ TC @ TA @ TC @ TB @ (product_Pair @ TA @ TC @ A) @ B) = (B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4278_Pair__scomp)).
% 181.68/124.53 thf(2775,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TA,B:(TA > (TC > TB))]: ((product_scomp @ TC @ TA @ TC @ TB @ (product_Pair @ TA @ TC @ A) @ B) = (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[573])).
% 181.68/124.53 thf(243,axiom,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA]: ((minus_minus @ TA @ (plus_plus @ TA @ A @ B) @ B) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_add__diff__cancel__right_H)).
% 181.68/124.53 thf(1734,plain,((! [TA: $tType]: ((cancel2418104881723323429up_add @ TA) => (! [A:TA,B:TA]: ((minus_minus @ TA @ (plus_plus @ TA @ A @ B) @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])).
% 181.68/124.53 thf(579,axiom,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:TA,C:TA]: ((combine_options @ TA @ A @ (some @ TA @ B) @ (some @ TA @ C)) = (some @ TA @ (A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_combine__options__simps_I3_J)).
% 181.68/124.53 thf(2792,plain,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:TA,C:TA]: ((combine_options @ TA @ (A) @ (some @ TA @ B) @ (some @ TA @ C)) = (some @ TA @ (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[579])).
% 181.68/124.53 thf(215,axiom,((! [TA: $tType]: (! [A:(set @ TA)]: ((collect @ TA @ (^ [B:TA]: (member @ TA @ B @ A))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__mem__eq)).
% 181.68/124.53 thf(1646,plain,((! [TA: $tType]: (! [A:(set @ TA)]: ((collect @ TA @ (^ [B:TA]: (member @ TA @ B @ A))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])).
% 181.68/124.53 thf(109,axiom,((zero_neq_one @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Ozero__neq__one_484)).
% 181.68/124.53 thf(1326,plain,((zero_neq_one @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
% 181.68/124.53 thf(955,axiom,((linord4140545234300271783up_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Olinordered__ab__semigroup__add_96)).
% 181.68/124.53 thf(3864,plain,((linord4140545234300271783up_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[955])).
% 181.68/124.53 thf(410,axiom,((! [TA: $tType]: (! [A:$o,B:(heap_Time_Heap @ TA),C:(heap_Time_Heap @ TA),D:(heap_ext @ product_unit),E:(heap_ext @ product_unit),F:TA,G:nat]: ((heap_Time_effect @ TA @ (if @ (heap_Time_Heap @ TA) @ A @ B @ C) @ D @ E @ F @ G) => (((A) => (~ (heap_Time_effect @ TA @ B @ D @ E @ F @ G))) => (~ ((~ (A)) => (~ (heap_Time_effect @ TA @ C @ D @ E @ F @ G))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_effect__ifE)).
% 181.68/124.53 thf(2273,plain,((! [TA: $tType]: (! [A:$o,B:(heap_Time_Heap @ TA),C:(heap_Time_Heap @ TA),D:(heap_ext @ product_unit),E:(heap_ext @ product_unit),F:TA,G:nat]: ((heap_Time_effect @ TA @ (if @ (heap_Time_Heap @ TA) @ A @ B @ C) @ D @ E @ F @ G) => (((A) => (~ (heap_Time_effect @ TA @ B @ D @ E @ F @ G))) => (~ ((~ (A)) => (~ (heap_Time_effect @ TA @ C @ D @ E @ F @ G))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[410])).
% 181.68/124.53 thf(450,axiom,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA),C:(set @ TA)]: ((minus_minus @ (set @ TA) @ (minus_minus @ (set @ TA) @ A @ B) @ C) = (minus_minus @ (set @ TA) @ A @ (sup_sup @ (set @ TA) @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2685_set__diff__diff__left)).
% 181.68/124.53 thf(2389,plain,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA),C:(set @ TA)]: ((minus_minus @ (set @ TA) @ (minus_minus @ (set @ TA) @ A @ B) @ C) = (minus_minus @ (set @ TA) @ A @ (sup_sup @ (set @ TA) @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[450])).
% 181.68/124.53 thf(598,axiom,((! [TA: $tType,TB: $tType]: (! [A:$o,B:(TA > $o),C:(option @ TA),D:(TB > $o),E:TB,F:(TA > TB)]: ((case_option @ $o @ TA @ A @ B @ C) => (((A) => (D @ E)) => ((! [G:TA]: ((B @ G) => (D @ (F @ G)))) => (D @ (case_option @ TB @ TA @ E @ F @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_disjE__realizer2)).
% 181.68/124.53 thf(2853,plain,((! [TA: $tType,TB: $tType]: (! [A:$o,B:(TA > $o),C:(option @ TA),D:(TB > $o),E:TB,F:(TA > TB)]: ((case_option @ $o @ TA @ A @ (B) @ C) => (((A) => (D @ E)) => ((! [G:TA]: ((B @ G) => (D @ (F @ G)))) => (D @ (case_option @ TB @ TA @ E @ (F) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[598])).
% 181.68/124.53 thf(369,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA)]: ((map_option @ TB @ TA @ A @ (none @ TB)) = (none @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_option_Osimps_I8_J)).
% 181.68/124.53 thf(2135,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA)]: ((map_option @ TB @ TA @ (A) @ (none @ TB)) = (none @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])).
% 181.68/124.53 thf(493,axiom,(((zero_zero @ nat) = (zero_zero @ nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_zero__natural_Orsp)).
% 181.68/124.53 thf(2532,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])).
% 181.68/124.53 thf(160,axiom,((! [A:nat,B:nat]: ((plus_plus @ nat @ A @ (suc @ B)) = (suc @ (plus_plus @ nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_add__Suc__right)).
% 181.68/124.53 thf(1481,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)],[160])).
% 181.68/124.53 thf(31,axiom,((! [A:nat]: ((compow @ (nat > nat) @ A @ suc) = (plus_plus @ nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4900_Suc__funpow)).
% 181.68/124.53 thf(1101,plain,((! [A:nat]: ((compow @ (nat > nat) @ A @ suc) = (plus_plus @ nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 181.68/124.53 thf(211,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/sandbox/benchmark/theBenchmark.p',fact_653_Nat_Odiff__add__assoc)).
% 181.68/124.53 thf(1629,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)],[211])).
% 181.68/124.53 thf(895,axiom,((ab_semigroup_add @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_116)).
% 181.68/124.53 thf(3748,plain,((ab_semigroup_add @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[895])).
% 181.68/124.53 thf(274,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(option @ TA)]: ((map_option @ TC @ TB @ A @ (map_option @ TA @ TC @ B @ C)) = (map_option @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_map__option_Ocompositionality)).
% 181.68/124.53 thf(1854,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(option @ TA)]: ((map_option @ TC @ TB @ (A) @ (map_option @ TA @ TC @ (B) @ C)) = (map_option @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])).
% 181.68/124.53 thf(822,axiom,((intrel = (product_case_prod @ nat @ nat @ ((product_prod @ nat @ nat) > $o) @ (^ [A:nat,B:nat]: (product_case_prod @ nat @ nat @ $o @ (^ [C:nat,D:nat]: ((plus_plus @ nat @ A @ D) = (plus_plus @ nat @ C @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2702_intrel__def)).
% 181.68/124.53 thf(3501,plain,(((intrel) = (product_case_prod @ nat @ nat @ ((product_prod @ nat @ nat) > $o) @ (^ [A:nat,B:nat]: (product_case_prod @ nat @ nat @ $o @ (^ [C:nat,D:nat]: ((plus_plus @ nat @ A @ D) = (plus_plus @ nat @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[822])).
% 181.68/124.53 thf(1018,axiom,((semilattice_sup @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__sup_111)).
% 181.68/124.53 thf(4010,plain,((semilattice_sup @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018])).
% 181.68/124.53 thf(699,axiom,((! [TA: $tType]: ((quickc3360725361186068524ustive @ TA) => (quickc3360725361186068524ustive @ (list @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Quickcheck__Exhaustive_Ofull__exhaustive_292)).
% 181.68/124.53 thf(3136,plain,((! [TA: $tType]: ((quickc3360725361186068524ustive @ TA) => (quickc3360725361186068524ustive @ (list @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[699])).
% 181.68/124.53 thf(741,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ TC)) > $o),B:(product_prod @ TA @ (product_prod @ TB @ TC))]: ((! [C:TA,D:TB,E:TC]: (A @ (product_Pair @ TA @ (product_prod @ TB @ TC) @ C @ (product_Pair @ TB @ TC @ D @ E)))) => (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_prod__induct3)).
% 181.68/124.53 thf(3252,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:((product_prod @ TA @ (product_prod @ TB @ TC)) > $o),B:(product_prod @ TA @ (product_prod @ TB @ TC))]: ((! [C:TA,D:TB,E:TC]: (A @ (product_Pair @ TA @ (product_prod @ TB @ TC) @ C @ (product_Pair @ TB @ TC @ D @ E)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[741])).
% 181.68/124.53 thf(90,axiom,((! [TA: $tType,TB: $tType]: ((dom @ TA @ TB) = (^ [A:(TA > (option @ TB))]: (collect @ TA @ (^ [B:TA]: ((A @ B) != (none @ TB)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3340_dom__def)).
% 181.68/124.53 thf(1276,plain,((! [TA: $tType,TB: $tType]: ((dom @ TA @ TB) = (^ [A:(TA > (option @ TB))]: (collect @ TA @ (^ [B:TA]: ~ ((A @ B) = (none @ TB)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
% 181.68/124.53 thf(197,axiom,((preorder @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Opreorder_414)).
% 181.68/124.53 thf(1590,plain,((preorder @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
% 181.68/124.53 thf(850,axiom,((uminus @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_282)).
% 181.68/124.53 thf(3613,plain,((uminus @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[850])).
% 181.68/124.53 thf(82,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/sandbox/benchmark/theBenchmark.p',fact_639_distrib__left)).
% 181.68/124.53 thf(1253,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)],[82])).
% 181.68/124.53 thf(225,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(ref @ TA),C:TA,D:(heap_ext @ product_unit),E:nat,F:product_unit]: ((A = (ref_set @ TA @ B @ C @ D)) => ((E = (one_one @ nat)) => (heap_Time_effect @ product_unit @ (ref_update @ TA @ B @ C) @ D @ A @ F @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1484_effect__updateI)).
% 181.68/124.53 thf(1674,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(heap_ext @ product_unit),B:(ref @ TA),C:TA,D:(heap_ext @ product_unit),E:nat,F:product_unit]: ((A = (ref_set @ TA @ B @ C @ D)) => ((E = (one_one @ nat)) => (heap_Time_effect @ product_unit @ (ref_update @ TA @ B @ C) @ D @ A @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
% 181.68/124.53 thf(917,axiom,((! [TA: $tType]: (! [A:(product_prod @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA)))]: ~ (! [B:(nat > (TA > TA)),C:nat,D:nat,E:TA]: (A != (product_Pair @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA)) @ B @ (product_Pair @ nat @ (product_prod @ nat @ TA) @ C @ (product_Pair @ nat @ TA @ D @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_fold__atLeastAtMost__nat_Ocases)).
% 181.68/124.53 thf(3789,plain,((! [TA: $tType]: (! [A:(product_prod @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA)))]: ~ (! [B:(nat > (TA > TA)),C:nat,D:nat,E:TA]: ~ (A = (product_Pair @ (nat > (TA > TA)) @ (product_prod @ nat @ (product_prod @ nat @ TA)) @ (B) @ (product_Pair @ nat @ (product_prod @ nat @ TA) @ C @ (product_Pair @ nat @ TA @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[917])).
% 181.68/124.53 thf(521,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(array @ TA),D:(heap_ext @ product_unit)]: ((time_fails @ (array @ TA) @ (array_upd @ TA @ A @ B @ C) @ D) = (~ (ord_less @ nat @ A @ (array_length @ TA @ D @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4109_fails__array__upd)).
% 181.68/124.53 thf(2608,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(array @ TA),D:(heap_ext @ product_unit)]: ((time_fails @ (array @ TA) @ (array_upd @ TA @ A @ B @ C) @ D) = (~ (ord_less @ nat @ A @ (array_length @ TA @ D @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[521])).
% 181.68/124.53 thf(736,axiom,((! [A:(product_prod @ nat @ nat)]: ~ (! [B:nat,C:nat]: (A != (product_Pair @ nat @ nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2381_prod__decode__aux_Ocases)).
% 181.68/124.53 thf(3235,plain,((! [A:(product_prod @ nat @ nat)]: ~ (! [B:nat,C:nat]: ~ (A = (product_Pair @ nat @ nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[736])).
% 181.68/124.53 thf(870,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(TA > (heap_Time_Heap @ TB)),D:(TA > (heap_Time_Heap @ TB))]: ((refine_Imp_refines @ TA @ A @ B) => ((! [E:TA]: (refine_Imp_refines @ TB @ (C @ E) @ (D @ E))) => (refine_Imp_refines @ TB @ (heap_Time_bind @ TA @ TB @ A @ C) @ (heap_Time_bind @ TA @ TB @ B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2864_refines__bind)).
% 181.68/124.53 thf(3662,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA),C:(TA > (heap_Time_Heap @ TB)),D:(TA > (heap_Time_Heap @ TB))]: ((refine_Imp_refines @ TA @ A @ B) => ((! [E:TA]: (refine_Imp_refines @ TB @ (C @ E) @ (D @ E))) => (refine_Imp_refines @ TB @ (heap_Time_bind @ TA @ TB @ A @ (C)) @ (heap_Time_bind @ TA @ TB @ B @ (D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[870])).
% 181.68/124.53 thf(912,axiom,((! [TA: $tType]: (countable @ (array @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oarray___Countable_Ocountable_299)).
% 181.68/124.53 thf(3780,plain,((! [TA: $tType]: (countable @ (array @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[912])).
% 181.68/124.53 thf(621,axiom,((! [TA: $tType,TB: $tType]: ((heap_Time_bind @ TA @ TB) = (^ [A:(heap_Time_Heap @ TA),B:(TA > (heap_Time_Heap @ TB))]: (heap_Time_Heap2 @ TB @ (^ [C:(heap_ext @ product_unit)]: (case_option @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (none @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [D:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [E:(heap_ext @ product_unit),F:nat]: (heap_Time_timeFrame @ TB @ F @ (heap_Time_execute @ TB @ (B @ D) @ E)))))) @ (heap_Time_execute @ TA @ A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_Heap__Time__Monad_Obind__def)).
% 181.68/124.53 thf(2934,plain,((! [TA: $tType,TB: $tType]: ((heap_Time_bind @ TA @ TB) = (^ [A:(heap_Time_Heap @ TA),B:(TA > (heap_Time_Heap @ TB))]: (heap_Time_Heap2 @ TB @ (^ [C:(heap_ext @ product_unit)]: (case_option @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (none @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [D:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [E:(heap_ext @ product_unit),F:nat]: (heap_Time_timeFrame @ TB @ F @ (heap_Time_execute @ TB @ (B @ D) @ E)))))) @ (heap_Time_execute @ TA @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[621])).
% 181.68/124.53 thf(374,axiom,((! [TA: $tType,TB: $tType]: (! [A:(list @ TB),B:(list @ TA),C:(set @ (product_prod @ TB @ TA))]: ((member @ (product_prod @ (list @ TB) @ (list @ TA)) @ (product_Pair @ (list @ TB) @ (list @ TA) @ A @ B) @ (listrel @ TB @ TA @ C)) = (((size_size @ (list @ TB) @ A) = (size_size @ (list @ TA) @ B)) & ! [D:nat]: ((ord_less @ nat @ D @ (size_size @ (list @ TB) @ A)) => (member @ (product_prod @ TB @ TA) @ (product_Pair @ TB @ TA @ (nth @ TB @ A @ D) @ (nth @ TA @ B @ D)) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4029_listrel__iff__nth)).
% 181.68/124.53 thf(2152,plain,((! [TA: $tType,TB: $tType]: (! [A:(list @ TB),B:(list @ TA),C:(set @ (product_prod @ TB @ TA))]: ((member @ (product_prod @ (list @ TB) @ (list @ TA)) @ (product_Pair @ (list @ TB) @ (list @ TA) @ A @ B) @ (listrel @ TB @ TA @ C)) = (((size_size @ (list @ TB) @ A) = (size_size @ (list @ TA) @ B)) & ! [D:nat]: ((ord_less @ nat @ D @ (size_size @ (list @ TB) @ A)) => (member @ (product_prod @ TB @ TA) @ (product_Pair @ TB @ TA @ (nth @ TB @ A @ D) @ (nth @ TA @ B @ D)) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])).
% 181.68/124.53 thf(469,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(TA > TB),D:(TA > TB)]: ((A = B) => ((pred_option @ TA @ (^ [E:TA]: ((C @ E) = (D @ E))) @ B) => ((map_option @ TA @ TB @ C @ A) = (map_option @ TA @ TB @ D @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5061_option_Omap__cong__pred)).
% 181.68/124.53 thf(2447,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(option @ TA),C:(TA > TB),D:(TA > TB)]: ((A = B) => ((pred_option @ TA @ (^ [E:TA]: ((C @ E) = (D @ E))) @ B) => ((map_option @ TA @ TB @ (C) @ A) = (map_option @ TA @ TB @ (D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])).
% 181.68/124.53 thf(630,axiom,((heap @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Heap_Oheap_285)).
% 181.68/124.53 thf(2956,plain,((heap @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[630])).
% 181.68/124.53 thf(769,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:(list @ TA),E:nat]: ((heap_Time_effect @ (list @ TA) @ (array_freeze @ TA @ A) @ B @ C @ D @ E) => (~ ((C = B) => ((D = (array_get @ TA @ B @ A)) => (E != (plus_plus @ nat @ (array_length @ TA @ B @ A) @ (one_one @ nat))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4083_effect__freezeE)).
% 181.68/124.53 thf(3324,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:(list @ TA),E:nat]: ((heap_Time_effect @ (list @ TA) @ (array_freeze @ TA @ A) @ B @ C @ D @ E) => (~ ((C = B) => ((D = (array_get @ TA @ B @ A)) => (~ (E = (plus_plus @ nat @ (array_length @ TA @ B @ A) @ (one_one @ nat)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[769])).
% 181.68/124.53 thf(204,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit),C:TA,D:(heap_ext @ product_unit)]: (((product_Pair @ (ref @ TA) @ (heap_ext @ product_unit) @ A @ B) = (ref_alloc @ TA @ C @ D)) => (ref_present @ TA @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5724_next__present)).
% 181.68/124.53 thf(1607,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit),C:TA,D:(heap_ext @ product_unit)]: (((product_Pair @ (ref @ TA) @ (heap_ext @ product_unit) @ A @ B) = (ref_alloc @ TA @ C @ D)) => (ref_present @ TA @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
% 181.68/124.53 thf(777,axiom,((! [TA: $tType]: ((cancel_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: (((plus_plus @ TA @ A @ B) = (plus_plus @ TA @ A @ C)) = (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_add__left__cancel)).
% 181.68/124.53 thf(3351,plain,((! [TA: $tType]: ((cancel_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: (((plus_plus @ TA @ A @ B) = (plus_plus @ TA @ A @ C)) = (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[777])).
% 181.68/124.53 thf(364,axiom,((! [TA: $tType]: (! [A:TA,B:TA]: ((if @ TA @ ($true) @ A @ B) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T)).
% 181.68/124.53 thf(2120,plain,((! [TA: $tType]: (! [A:TA,B:TA]: ((if @ TA @ ($true) @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])).
% 181.68/124.53 thf(357,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/sandbox/benchmark/theBenchmark.p',fact_277_pos__add__strict)).
% 181.68/124.53 thf(2095,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)],[357])).
% 181.68/124.53 thf(562,axiom,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: (ord_less_eq @ TA @ (zero_zero @ TA) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_zero__le)).
% 181.68/124.53 thf(2739,plain,((! [TA: $tType]: ((canoni5634975068530333245id_add @ TA) => (! [A:TA]: (ord_less_eq @ TA @ (zero_zero @ TA) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[562])).
% 181.68/124.53 thf(321,axiom,((! [TA: $tType]: (! [A:(product_prod @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:(code_natural > TA),C:code_natural,D:code_natural]: (A != (product_Pair @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural) @ B @ (product_Pair @ code_natural @ code_natural @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4219_Lazy__Sequence_Oiterate__upto_Ocases)).
% 181.68/124.53 thf(1994,plain,((! [TA: $tType]: (! [A:(product_prod @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:(code_natural > TA),C:code_natural,D:code_natural]: ~ (A = (product_Pair @ (code_natural > TA) @ (product_prod @ code_natural @ code_natural) @ (B) @ (product_Pair @ code_natural @ code_natural @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])).
% 181.68/124.53 thf(329,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA,C:(set @ (product_prod @ TB @ TA)),D:(TB > (TA > $o))]: ((member @ (product_prod @ TB @ TA) @ (product_Pair @ TB @ TA @ A @ B) @ C) => (((member @ (product_prod @ TB @ TA) @ (product_Pair @ TB @ TA @ A @ B) @ C) => (D @ A @ B)) => (? [E:TB,F:TA]: ((member @ (product_prod @ TB @ TA) @ (product_Pair @ TB @ TA @ E @ F) @ C) & (D @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_bex2I)).
% 181.68/124.53 thf(2019,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA,C:(set @ (product_prod @ TB @ TA)),D:(TB > (TA > $o))]: ((member @ (product_prod @ TB @ TA) @ (product_Pair @ TB @ TA @ A @ B) @ C) => (((member @ (product_prod @ TB @ TA) @ (product_Pair @ TB @ TA @ A @ B) @ C) => (D @ A @ B)) => (? [E:TB,F:TA]: ((member @ (product_prod @ TB @ TA) @ (product_Pair @ TB @ TA @ E @ F) @ C) & (D @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])).
% 181.68/124.53 thf(799,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (product_prod @ TB @ TC))]: ((product_scomp @ TA @ TB @ TC @ (product_prod @ TB @ TC) @ A @ (product_Pair @ TB @ TC)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4277_scomp__Pair)).
% 181.68/124.53 thf(3420,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (product_prod @ TB @ TC))]: ((product_scomp @ TA @ TB @ TC @ (product_prod @ TB @ TC) @ A @ (product_Pair @ TB @ TC)) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[799])).
% 181.68/124.53 thf(228,axiom,((! [TA: $tType,TB: $tType]: ((fun_upd @ TA @ TB) = (^ [A:(TA > TB),B:TA,C:TB,D:TA]: (if @ TB @ (D = B) @ C @ (A @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2727_fun__upd__def)).
% 181.68/124.53 thf(1689,plain,((! [TA: $tType,TB: $tType]: ((fun_upd @ TA @ TB) = (^ [A:(TA > TB),B:TA,C:TB,D:TA]: (if @ TB @ (D = B) @ C @ (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
% 181.68/124.53 thf(353,axiom,((! [TA: $tType]: ((sup @ TA) => (! [A:(option @ TA)]: ((sup_sup @ (option @ TA) @ (none @ TA) @ A) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2722_sup__None__1)).
% 181.68/124.53 thf(2081,plain,((! [TA: $tType]: ((sup @ TA) => (! [A:(option @ TA)]: ((sup_sup @ (option @ TA) @ (none @ TA) @ A) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])).
% 181.68/124.53 thf(881,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TC > (option @ TB))),B:(TA > TA),C:((TC > (option @ TB)) > TA),D:TA]: ((! [E:TC]: (comple7038119648293358887notone @ (TC > (option @ TB)) @ (option @ TB) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TB) @ (none @ TB)) @ (^ [F:(TC > (option @ TB))]: (A @ (B @ (C @ F)) @ E)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TC > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (^ [E:(TC > (option @ TB))]: (A @ (B @ (C @ E))))))) => ((! [E:TA]: ((C @ (A @ E)) = E)) => (D = (B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5981_option_Ofixp__rule__uc)).
% 181.68/124.53 thf(3694,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TC > (option @ TB))),B:(TA > TA),C:((TC > (option @ TB)) > TA),D:TA]: ((! [E:TC]: (comple7038119648293358887notone @ (TC > (option @ TB)) @ (option @ TB) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (partial_flat_ord @ (option @ TB) @ (none @ TB)) @ (^ [F:(TC > (option @ TB))]: (A @ (B @ (C @ F)) @ E)))) => ((D = (C @ (comple187402453842119260l_fixp @ (TC > (option @ TB)) @ (partial_fun_lub @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_lub @ (option @ TB) @ (none @ TB))) @ (partial_fun_ord @ (option @ TB) @ (option @ TB) @ TC @ (partial_flat_ord @ (option @ TB) @ (none @ TB))) @ (^ [E:(TC > (option @ TB))]: (A @ (B @ (C @ E))))))) => ((! [E:TA]: ((C @ (A @ E)) = E)) => (D = (B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[881])).
% 181.68/124.53 thf(577,axiom,((sup @ $o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osup_283)).
% 181.68/124.53 thf(2786,plain,((sup @ $o)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[577])).
% 181.68/124.53 thf(944,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:TB,D:(heap_ext @ product_unit),E:nat,F:(TB > (heap_Time_Heap @ TA)),G:TA,H:(heap_ext @ product_unit),I:nat]: (((heap_Time_execute @ TB @ A @ B) = (some @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))) => (((heap_Time_execute @ TA @ (F @ C) @ D) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ G @ (product_Pair @ (heap_ext @ product_unit) @ nat @ H @ I)))) => ((heap_Time_execute @ TA @ (heap_Time_bind @ TB @ TA @ A @ F) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ G @ (product_Pair @ (heap_ext @ product_unit) @ nat @ H @ (plus_plus @ nat @ E @ I)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_execute__bind__eq__SomeI)).
% 181.68/124.53 thf(3844,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:TB,D:(heap_ext @ product_unit),E:nat,F:(TB > (heap_Time_Heap @ TA)),G:TA,H:(heap_ext @ product_unit),I:nat]: (((heap_Time_execute @ TB @ A @ B) = (some @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))) => (((heap_Time_execute @ TA @ (F @ C) @ D) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ G @ (product_Pair @ (heap_ext @ product_unit) @ nat @ H @ I)))) => ((heap_Time_execute @ TA @ (heap_Time_bind @ TB @ TA @ A @ (F)) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ G @ (product_Pair @ (heap_ext @ product_unit) @ nat @ H @ (plus_plus @ nat @ E @ I)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[944])).
% 181.68/124.53 thf(843,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TA > TD),C:(TB > TC),D:(TA > TB)]: (((comp @ TD @ TC @ TA @ A @ B) = (comp @ TB @ TC @ TA @ C @ D)) => (! [E:TA]: ((A @ (B @ E)) = (C @ (D @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_comp__eq__elim)).
% 181.68/124.53 thf(3585,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:(TD > TC),B:(TA > TD),C:(TB > TC),D:(TA > TB)]: (((comp @ TD @ TC @ TA @ A @ B) = (comp @ TB @ TC @ TA @ C @ D)) => (! [E:TA]: ((A @ (B @ E)) = (C @ (D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[843])).
% 181.68/124.53 thf(802,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:TB,C:(TA > TB),D:(option @ TA)]: ((A @ (case_option @ TB @ TA @ B @ C @ D)) = (case_option @ TC @ TA @ (A @ B) @ (^ [E:TA]: (A @ (C @ E))) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_option_Ocase__distrib)).
% 181.68/124.53 thf(3430,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TB > TC),B:TB,C:(TA > TB),D:(option @ TA)]: ((A @ (case_option @ TB @ TA @ B @ (C) @ D)) = (case_option @ TC @ TA @ (A @ B) @ (^ [E:TA]: (A @ (C @ E))) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[802])).
% 181.68/124.53 thf(102,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/sandbox/benchmark/theBenchmark.p',fact_638_comm__semiring__class_Odistrib)).
% 181.68/124.53 thf(1308,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)],[102])).
% 181.68/124.53 thf(971,axiom,((ab_semigroup_mult @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult_113)).
% 181.68/124.53 thf(3896,plain,((ab_semigroup_mult @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[971])).
% 181.68/124.53 thf(512,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/sandbox/benchmark/theBenchmark.p',fact_230_zero__eq__add__iff__both__eq__0)).
% 181.68/124.53 thf(2576,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)],[512])).
% 181.68/124.53 thf(347,axiom,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: ((ord_less_eq @ (set @ TA) @ A @ B) => ((minus_minus @ (set @ TA) @ A @ B) = (bot_bot @ (set @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2123_subset__minus__empty)).
% 181.68/124.53 thf(2066,plain,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: ((ord_less_eq @ (set @ TA) @ A @ B) => ((minus_minus @ (set @ TA) @ A @ B) = (bot_bot @ (set @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])).
% 181.68/124.53 thf(20,axiom,((semigroup_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Osemigroup__add_479)).
% 181.68/124.53 thf(1077,plain,((semigroup_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 181.68/124.53 thf(875,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TA > TB),C:TA]: ((case_option @ TB @ TA @ A @ B @ (some @ TA @ C)) = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_option_Osimps_I5_J)).
% 181.68/124.53 thf(3677,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:(TA > TB),C:TA]: ((case_option @ TB @ TA @ A @ (B) @ (some @ TA @ C)) = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[875])).
% 181.68/124.53 thf(378,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/sandbox/benchmark/theBenchmark.p',fact_554_Nat_Oadd__diff__assoc)).
% 181.68/124.53 thf(2162,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)],[378])).
% 181.68/124.53 thf(543,axiom,((! [TA: $tType]: (complete_Sup @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Lattices_OSup_251)).
% 181.68/124.53 thf(2680,plain,((! [TA: $tType]: (complete_Sup @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[543])).
% 181.68/124.53 thf(66,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/sandbox/benchmark/theBenchmark.p',fact_590_nat__le__add__iff1)).
% 181.68/124.53 thf(1212,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)],[66])).
% 181.68/124.53 thf(398,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TB,B:(TC > (TA > (set @ TB))),C:(product_prod @ TC @ TA)]: ((member @ TB @ A @ (product_case_prod @ TC @ TA @ (set @ TB) @ B @ C)) => (~ (! [D:TC,E:TA]: ((C = (product_Pair @ TC @ TA @ D @ E)) => (~ (member @ TB @ A @ (B @ D @ E)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_mem__case__prodE)).
% 181.68/124.53 thf(2230,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:TB,B:(TC > (TA > (set @ TB))),C:(product_prod @ TC @ TA)]: ((member @ TB @ A @ (product_case_prod @ TC @ TA @ (set @ TB) @ (B) @ C)) => (~ (! [D:TC,E:TA]: ((C = (product_Pair @ TC @ TA @ D @ E)) => (~ (member @ TB @ A @ (B @ D @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[398])).
% 181.68/124.53 thf(335,axiom,((quickc3360725361186068524ustive @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Quickcheck__Exhaustive_Ofull__exhaustive_521)).
% 181.68/124.53 thf(2036,plain,((quickc3360725361186068524ustive @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])).
% 181.68/124.53 thf(616,axiom,((! [TA: $tType]: ((finite_finite @ TA) => (finite_finite @ (set @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_257)).
% 181.68/124.53 thf(2917,plain,((! [TA: $tType]: ((finite_finite @ TA) => (finite_finite @ (set @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[616])).
% 181.68/124.53 thf(903,axiom,((sup @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Osup_420)).
% 181.68/124.53 thf(3761,plain,((sup @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[903])).
% 181.68/124.53 thf(365,axiom,((! [TA: $tType]: ((heap @ TA) => ((array_length @ TA) = (^ [A:(heap_ext @ product_unit),B:(array @ TA)]: (size_size @ (list @ TA) @ (array_get @ TA @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4074_length__def)).
% 181.68/124.53 thf(2123,plain,((! [TA: $tType]: ((heap @ TA) => ((array_length @ TA) = (^ [A:(heap_ext @ product_unit),B:(array @ TA)]: (size_size @ (list @ TA) @ (array_get @ TA @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])).
% 181.68/124.53 thf(412,axiom,((! [A:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ((in_range @ A) => (~ (! [B:(heap_ext @ product_unit),C:(set @ nat)]: ((A = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ B @ C)) => (~ (! [D:nat]: ((member @ nat @ D @ C) => (ord_less @ nat @ D @ (lim @ product_unit @ B))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5692_in__range_Oelims_I2_J)).
% 181.68/124.53 thf(2287,plain,((! [A:(product_prod @ (heap_ext @ product_unit) @ (set @ nat))]: ((in_range @ A) => (~ (! [B:(heap_ext @ product_unit),C:(set @ nat)]: ((A = (product_Pair @ (heap_ext @ product_unit) @ (set @ nat) @ B @ C)) => (~ (! [D:nat]: ((member @ nat @ D @ C) => (ord_less @ nat @ D @ (lim @ product_unit @ B))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])).
% 181.68/124.53 thf(171,axiom,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (plus_plus @ TA @ B @ A)) = (ord_less @ TA @ (zero_zero @ TA) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_less__add__same__cancel2)).
% 181.68/124.53 thf(1512,plain,((! [TA: $tType]: ((ordere1937475149494474687imp_le @ TA) => (! [A:TA,B:TA]: ((ord_less @ TA @ A @ (plus_plus @ TA @ B @ A)) = (ord_less @ TA @ (zero_zero @ TA) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
% 181.68/124.53 thf(375,axiom,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA),C:(set @ TA),D:(set @ TA)]: ((ord_less_eq @ (set @ TA) @ A @ B) => ((ord_less_eq @ (set @ TA) @ C @ D) => (((inf_inf @ (set @ TA) @ B @ D) = (bot_bot @ (set @ TA))) => ((inf_inf @ (set @ TA) @ A @ C) = (bot_bot @ (set @ TA))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3052_disjoint__mono)).
% 181.68/124.53 thf(2155,plain,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA),C:(set @ TA),D:(set @ TA)]: ((ord_less_eq @ (set @ TA) @ A @ B) => ((ord_less_eq @ (set @ TA) @ C @ D) => (((inf_inf @ (set @ TA) @ B @ D) = (bot_bot @ (set @ TA))) => ((inf_inf @ (set @ TA) @ A @ C) = (bot_bot @ (set @ TA))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])).
% 181.68/124.53 thf(28,axiom,((cancel2418104881723323429up_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Ocancel__ab__semigroup__add_453)).
% 181.68/124.53 thf(1097,plain,((cancel2418104881723323429up_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 181.68/124.53 thf(74,axiom,((! [A:nat,B:nat]: (((ord_less_eq @ nat @ A @ B) & (ord_less @ nat @ B @ (suc @ A))) = (B = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_nat__in__between__eq_I2_J)).
% 181.68/124.53 thf(1229,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)],[74])).
% 181.68/124.53 thf(969,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit)]: ((~ (A @ B)) => ((heap_Time_execute @ TA @ (heap_Time_assert @ TA @ A @ B) @ C) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_execute__assert_I2_J)).
% 181.68/124.53 thf(3892,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit)]: ((~ (A @ B)) => ((heap_Time_execute @ TA @ (heap_Time_assert @ TA @ (A) @ B) @ C) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[969])).
% 181.68/124.53 thf(683,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat,F:(heap_ext @ product_unit),G:TA,H:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => ((heap_Time_effect @ TA @ A @ B @ F @ G @ H) => (E = H)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_effect__deterministic_I3_J)).
% 181.68/124.53 thf(3100,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat,F:(heap_ext @ product_unit),G:TA,H:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => ((heap_Time_effect @ TA @ A @ B @ F @ G @ H) => (E = H)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[683])).
% 181.68/124.53 thf(282,axiom,((cl_HOL_Oequal @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___HOL_Oequal_572)).
% 181.68/124.53 thf(1876,plain,((cl_HOL_Oequal @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])).
% 181.68/124.53 thf(697,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ nat @ (array_len @ TA @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4125_success__lenI)).
% 181.68/124.53 thf(3132,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(array @ TA),B:(heap_ext @ product_unit)]: (heap_Time_success @ nat @ (array_len @ TA @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[697])).
% 181.68/124.53 thf(1010,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TB > TA)]: ((rec_option @ TA @ TB @ A @ B @ (none @ TB)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_option_Osimps_I6_J)).
% 181.68/124.53 thf(3992,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(TB > TA)]: ((rec_option @ TA @ TB @ A @ (B) @ (none @ TB)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010])).
% 181.68/124.53 thf(324,axiom,((! [TA: $tType]: (! [A:TA,B:(set @ TA)]: ((member @ TA @ A @ B) => (B != (bot_bot @ (set @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2115_memb__imp__not__empty)).
% 181.68/124.53 thf(2003,plain,((! [TA: $tType]: (! [A:TA,B:(set @ TA)]: ((member @ TA @ A @ B) => (~ (B = (bot_bot @ (set @ TA)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])).
% 181.68/124.53 thf(371,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:TA]: ((map_option @ TA @ TB @ A @ (some @ TA @ B)) = (some @ TB @ (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_option_Osimps_I9_J)).
% 181.68/124.53 thf(2142,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > TB),B:TA]: ((map_option @ TA @ TB @ (A) @ (some @ TA @ B)) = (some @ TB @ (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[371])).
% 181.68/124.53 thf(786,axiom,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (heap_Time_Heap @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap__Time__Monad_OHeap___Typerep_Otyperep)).
% 181.68/124.53 thf(3379,plain,((! [TA: $tType]: ((typerep2 @ TA) => (typerep2 @ (heap_Time_Heap @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[786])).
% 181.68/124.53 thf(226,axiom,((! [TA: $tType]: ((inf @ TA) => (! [A:(option @ TA)]: ((inf_inf @ (option @ TA) @ (none @ TA) @ A) = (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3118_inf__None__1)).
% 181.68/124.53 thf(1678,plain,((! [TA: $tType]: ((inf @ TA) => (! [A:(option @ TA)]: ((inf_inf @ (option @ TA) @ (none @ TA) @ A) = (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
% 181.68/124.53 thf(915,axiom,((heap @ a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0)).
% 181.68/124.53 thf(3785,plain,((heap @ a)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[915])).
% 181.68/124.53 thf(956,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:(TA > (option @ TB))]: (((A @ B) = (none @ TB)) => ((map_add @ TA @ TB @ C @ A @ B) = (C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3402_map__add__find__left)).
% 181.68/124.53 thf(3865,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:(TA > (option @ TB))]: (((A @ B) = (none @ TB)) => ((map_add @ TA @ TB @ (C) @ (A) @ B) = (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[956])).
% 181.68/124.53 thf(556,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/sandbox/benchmark/theBenchmark.p',fact_471_add__leD2)).
% 181.68/124.53 thf(2719,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)],[556])).
% 181.68/124.53 thf(784,axiom,((! [TA: $tType]: ((heap @ TA) => ((ref_ref @ TA) = (^ [A:TA]: (heap_Time_heap @ (ref @ TA) @ (^ [B:(heap_ext @ product_unit)]: (product_case_prod @ (ref @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [C:(ref @ TA),D:(heap_ext @ product_unit)]: (product_Pair @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ (one_one @ nat)))) @ (ref_alloc @ TA @ A @ B))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5720_ref__def)).
% 181.68/124.53 thf(3373,plain,((! [TA: $tType]: ((heap @ TA) => ((ref_ref @ TA) = (^ [A:TA]: (heap_Time_heap @ (ref @ TA) @ (^ [B:(heap_ext @ product_unit)]: (product_case_prod @ (ref @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [C:(ref @ TA),D:(heap_ext @ product_unit)]: (product_Pair @ (ref @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ (one_one @ nat)))) @ (ref_alloc @ TA @ A @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[784])).
% 181.68/124.53 thf(816,axiom,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TA @ TB)]: ((product_case_prod @ TA @ TB @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB) @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1070_case__prod__Pair__iden)).
% 181.68/124.53 thf(3464,plain,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TA @ TB)]: ((product_case_prod @ TA @ TB @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[816])).
% 181.68/124.53 thf(561,axiom,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TB @ TA)]: ~ (! [B:TB,C:TA]: (A != (product_Pair @ TB @ TA @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_old_Oprod_Oexhaust)).
% 181.68/124.53 thf(2736,plain,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TB @ TA)]: ~ (! [B:TB,C:TA]: ~ (A = (product_Pair @ TB @ TA @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[561])).
% 181.68/124.53 thf(317,axiom,((zero_neq_one @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_556)).
% 181.68/124.53 thf(1986,plain,((zero_neq_one @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])).
% 181.68/124.53 thf(176,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/sandbox/benchmark/theBenchmark.p',fact_715_nat__diff__split)).
% 181.68/124.53 thf(1527,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)],[176])).
% 181.68/124.53 thf(772,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(heap_ext @ product_unit)]: ((heap_Time_execute @ (array @ TA) @ (array_new @ TA @ A @ B) @ C) = (some @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [D:(array @ TA),E:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ (one_one @ nat))))) @ (array_alloc @ TA @ (replicate @ TA @ A @ B) @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3541_execute__new)).
% 181.68/124.53 thf(3337,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:TA,C:(heap_ext @ product_unit)]: ((heap_Time_execute @ (array @ TA) @ (array_new @ TA @ A @ B) @ C) = (some @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_case_prod @ (array @ TA) @ (heap_ext @ product_unit) @ (product_prod @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (^ [D:(array @ TA),E:(heap_ext @ product_unit)]: (product_Pair @ (array @ TA) @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ (plus_plus @ nat @ A @ (one_one @ nat))))) @ (array_alloc @ TA @ (replicate @ TA @ A @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[772])).
% 181.68/124.53 thf(723,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/sandbox/benchmark/theBenchmark.p',fact_475_add__leE)).
% 181.68/124.53 thf(3203,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)],[723])).
% 181.68/124.53 thf(667,axiom,((! [TA: $tType,TB: $tType]: (((typerep2 @ TB) & (typerep2 @ TA)) => (typerep2 @ (product_prod @ TB @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Typerep_Otyperep_13)).
% 181.68/124.53 thf(3062,plain,((! [TA: $tType,TB: $tType]: (((typerep2 @ TB) & (typerep2 @ TA)) => (typerep2 @ (product_prod @ TB @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[667])).
% 181.68/124.53 thf(934,axiom,((quickc3360725361186068524ustive @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Quickcheck__Exhaustive_Ofull__exhaustive_401)).
% 181.68/124.53 thf(3822,plain,((quickc3360725361186068524ustive @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[934])).
% 181.68/124.53 thf(649,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat,F:(heap_ext @ product_unit),G:TA,H:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => ((heap_Time_effect @ TA @ A @ B @ F @ G @ H) => (D = G)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_effect__deterministic_I1_J)).
% 181.68/124.53 thf(3015,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat,F:(heap_ext @ product_unit),G:TA,H:nat]: ((heap_Time_effect @ TA @ A @ B @ C @ D @ E) => ((heap_Time_effect @ TA @ A @ B @ F @ G @ H) => (D = G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[649])).
% 181.68/124.53 thf(149,axiom,((! [TA: $tType]: (! [A:TA]: ((size_size @ (option @ TA) @ (some @ TA @ A)) = (suc @ (zero_zero @ nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1030_option_Osize_I4_J)).
% 181.68/124.53 thf(1436,plain,((! [TA: $tType]: (! [A:TA]: ((size_size @ (option @ TA) @ (some @ TA @ A)) = (suc @ (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
% 181.68/124.53 thf(219,axiom,((! [TA: $tType]: (! [A:nat,B:(list @ TA),C:nat]: ((ord_less @ nat @ A @ (size_size @ (list @ TA) @ B)) => ((nth @ TA @ (rotate @ TA @ C @ B) @ A) = (nth @ TA @ B @ (modulo_modulo @ nat @ (plus_plus @ nat @ C @ A) @ (size_size @ (list @ TA) @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4007_nth__rotate)).
% 181.68/124.53 thf(1657,plain,((! [TA: $tType]: (! [A:nat,B:(list @ TA),C:nat]: ((ord_less @ nat @ A @ (size_size @ (list @ TA) @ B)) => ((nth @ TA @ (rotate @ TA @ C @ B) @ A) = (nth @ TA @ B @ (modulo_modulo @ nat @ (plus_plus @ nat @ C @ A) @ (size_size @ (list @ TA) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
% 181.68/124.53 thf(948,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: (((eps_Opt @ TA @ A) = (none @ TA)) = (~ (? [B:TA]: (A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2811_Eps__Opt__eq__None)).
% 181.68/124.53 thf(3850,plain,((! [TA: $tType]: (! [A:(TA > $o)]: (((eps_Opt @ TA @ (A)) = (none @ TA)) = (~ (? [B:TA]: (A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[948])).
% 181.68/124.53 thf(819,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq @ nat @ (plus_plus @ nat @ A @ B) @ C) => (ord_less_eq @ nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_add__leD1)).
% 181.68/124.53 thf(3479,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)],[819])).
% 181.68/124.53 thf(257,axiom,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: ((! [C:TA]: ((member @ TA @ C @ A) => (~ (member @ TA @ C @ B)))) => ((inf_inf @ (set @ TA) @ A @ B) = (bot_bot @ (set @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3041_disjointI)).
% 181.68/124.53 thf(1789,plain,((! [TA: $tType]: (! [A:(set @ TA),B:(set @ TA)]: ((! [C:TA]: ((member @ TA @ C @ A) => (~ (member @ TA @ C @ B)))) => ((inf_inf @ (set @ TA) @ A @ B) = (bot_bot @ (set @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])).
% 181.68/124.53 thf(442,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ B) => ((plus_plus @ TA @ A @ (minus_minus @ TA @ B @ A)) = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse)).
% 181.68/124.53 thf(2366,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ B) => ((plus_plus @ TA @ A @ (minus_minus @ TA @ B @ A)) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[442])).
% 181.68/124.53 thf(337,axiom,((! [TA: $tType,TB: $tType]: ((heap @ TB) => (! [A:(ref @ TB),B:(heap_Time_Heap @ TA)]: ((heap_Time_bind @ TB @ TA @ (ref_lookup @ TB @ A) @ (^ [C:TB]: (B))) = (heap_Time_bind @ product_unit @ TA @ (heap_Time_wait @ (one_one @ nat)) @ (^ [C:product_unit]: (B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_lookup__chain)).
% 181.68/124.53 thf(2040,plain,((! [TA: $tType,TB: $tType]: ((heap @ TB) => (! [A:(ref @ TB),B:(heap_Time_Heap @ TA)]: ((heap_Time_bind @ TB @ TA @ (ref_lookup @ TB @ A) @ (^ [C:TB]: (B))) = (heap_Time_bind @ product_unit @ TA @ (heap_Time_wait @ (one_one @ nat)) @ (^ [C:product_unit]: (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])).
% 181.68/124.53 thf(431,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TB,C:(set @ (product_prod @ TA @ TB)),D:TB]: ((member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ A @ B) @ C) => ((D = B) => (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ A @ D) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_ssubst__Pair__rhs)).
% 181.68/124.53 thf(2340,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TB,C:(set @ (product_prod @ TA @ TB)),D:TB]: ((member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ A @ B) @ C) => ((D = B) => (member @ (product_prod @ TA @ TB) @ (product_Pair @ TA @ TB @ A @ D) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])).
% 181.68/124.53 thf(205,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:TB,C:TA,D:(TB > (option @ TA)),E:TA]: (((fun_upd @ TB @ (option @ TA) @ A @ B @ (some @ TA @ C)) = (fun_upd @ TB @ (option @ TA) @ D @ B @ (some @ TA @ E))) => (C = E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2736_map__upd__eqD1)).
% 181.68/124.53 thf(1610,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:TB,C:TA,D:(TB > (option @ TA)),E:TA]: (((fun_upd @ TB @ (option @ TA) @ A @ B @ (some @ TA @ C)) = (fun_upd @ TB @ (option @ TA) @ D @ B @ (some @ TA @ E))) => (C = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
% 181.68/124.53 thf(536,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat]: ((heap_Time_effect @ TA @ (heap_Time_assert @ TA @ A @ B) @ C @ D @ E @ F) => (~ ((A @ B) => ((E = B) => ((D = C) => (F != (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_effect__assertE)).
% 181.68/124.53 thf(2651,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:(heap_ext @ product_unit),D:(heap_ext @ product_unit),E:TA,F:nat]: ((heap_Time_effect @ TA @ (heap_Time_assert @ TA @ (A) @ B) @ C @ D @ E @ F) => (~ ((A @ B) => ((E = B) => ((D = C) => (~ (F = (one_one @ nat))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[536])).
% 181.68/124.53 thf(576,axiom,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(TA > (option @ TB)),C:TB]: (((bind @ TA @ TB @ A @ B) = (some @ TB @ C)) = (? [D:TA]: ((A = (some @ TA @ D)) & ((B @ D) = (some @ TB @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_bind__eq__Some__conv)).
% 181.68/124.53 thf(2783,plain,((! [TA: $tType,TB: $tType]: (! [A:(option @ TA),B:(TA > (option @ TB)),C:TB]: (((bind @ TA @ TB @ A @ (B)) = (some @ TB @ C)) = (? [D:TA]: ((A = (some @ TA @ D)) & ((B @ D) = (some @ TB @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[576])).
% 181.68/124.53 thf(501,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(TA > TB),D:TA]: (((comp @ TC @ TB @ TA @ A @ B) = C) => ((A @ (B @ D)) = (C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_comp__eq__dest__lhs)).
% 181.68/124.53 thf(2549,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(TA > TB),D:TA]: (((comp @ TC @ TB @ TA @ A @ B) = (C)) => ((A @ (B @ D)) = (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])).
% 181.68/124.53 thf(972,axiom,((finite_finite @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Finite__Set_Ofinite_416)).
% 181.68/124.53 thf(3897,plain,((finite_finite @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[972])).
% 181.68/124.53 thf(386,axiom,((preorder @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_135)).
% 181.68/124.53 thf(2201,plain,((preorder @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])).
% 181.68/124.53 thf(121,axiom,((! [A:code_integer]: ((times_times @ code_integer @ A @ (zero_zero @ code_integer)) = (zero_zero @ code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1274_times__integer__code_I1_J)).
% 181.68/124.53 thf(1363,plain,((! [A:code_integer]: ((times_times @ code_integer @ A @ (zero_zero @ code_integer)) = (zero_zero @ code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
% 181.68/124.53 thf(105,axiom,((! [A:code_integer]: ((plus_plus @ code_integer @ A @ (zero_zero @ code_integer)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1278_plus__integer__code_I1_J)).
% 181.68/124.53 thf(1314,plain,((! [A:code_integer]: ((plus_plus @ code_integer @ A @ (zero_zero @ code_integer)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
% 181.68/124.53 thf(714,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (TA > TB)),B:TC,C:TA]: ((product_case_prod @ TC @ TA @ TB @ A @ (product_Pair @ TC @ TA @ B @ C)) = (A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1040_case__prod__conv)).
% 181.68/124.53 thf(3177,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (TA > TB)),B:TC,C:TA]: ((product_case_prod @ TC @ TA @ TB @ (A) @ (product_Pair @ TC @ TA @ B @ C)) = (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[714])).
% 181.68/124.53 thf(924,axiom,((! [TA: $tType]: (! [A:nat]: ((heap_Time_timeFrame @ TA @ A @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_timeFrame_Osimps_I2_J)).
% 181.68/124.53 thf(3804,plain,((! [TA: $tType]: (! [A:nat]: ((heap_Time_timeFrame @ TA @ A @ (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[924])).
% 181.68/124.53 thf(113,axiom,((semiri3467727345109120633visors @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Osemiring__no__zero__divisors_448)).
% 181.68/124.53 thf(1335,plain,((semiri3467727345109120633visors @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
% 181.68/124.53 thf(1024,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (option @ TB)),B:TC,C:(TB > (option @ TA))]: (((A @ B) = (none @ TB)) => ((map_comp @ TB @ TA @ TC @ C @ A @ B) = (none @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_map__comp__simps_I1_J)).
% 181.68/124.53 thf(4024,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > (option @ TB)),B:TC,C:(TB > (option @ TA))]: (((A @ B) = (none @ TB)) => ((map_comp @ TB @ TA @ TC @ (C) @ (A) @ B) = (none @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024])).
% 181.68/124.53 thf(95,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ C) @ D)) => (~ (! [E:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) => (~ (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4982_relpow__Suc__E)).
% 181.68/124.53 thf(1288,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ C) @ D)) => (~ (! [E:TA]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ E) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) => (~ (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ E @ B) @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])).
% 181.68/124.53 thf(235,axiom,((! [TA: $tType]: (! [A:(set @ TA)]: ((A != (bot_bot @ (set @ TA))) => (member @ TA @ (fChoice @ TA @ (^ [B:TA]: (member @ TA @ B @ A))) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4651_some__elem)).
% 181.68/124.53 thf(1710,plain,((! [TA: $tType]: (! [A:(set @ TA)]: ((~ (A = (bot_bot @ (set @ TA)))) => (member @ TA @ (fChoice @ TA @ (^ [B:TA]: (member @ TA @ B @ A))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])).
% 181.68/124.53 thf(60,axiom,((! [TA: $tType]: ((semidom_modulo @ TA) => (! [A:TA]: ((modulo_modulo @ TA @ A @ (one_one @ TA)) = (zero_zero @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_mod__by__1)).
% 181.68/124.53 thf(1197,plain,((! [TA: $tType]: ((semidom_modulo @ TA) => (! [A:TA]: ((modulo_modulo @ TA @ A @ (one_one @ TA)) = (zero_zero @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
% 181.68/124.53 thf(554,axiom,((! [TA: $tType]: (bounded_lattice @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_250)).
% 181.68/124.53 thf(2714,plain,((! [TA: $tType]: (bounded_lattice @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[554])).
% 181.68/124.53 thf(290,axiom,((! [TA: $tType]: (! [A:nat,B:nat,C:TA]: ((enumerate @ TA @ A @ (replicate @ TA @ B @ C)) = (map @ nat @ (product_prod @ nat @ TA) @ (^ [D:nat]: (product_Pair @ nat @ TA @ D @ C)) @ (upt @ A @ (plus_plus @ nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3564_enumerate__replicate__eq)).
% 181.68/124.53 thf(1891,plain,((! [TA: $tType]: (! [A:nat,B:nat,C:TA]: ((enumerate @ TA @ A @ (replicate @ TA @ B @ C)) = (map @ nat @ (product_prod @ nat @ TA) @ (^ [D:nat]: (product_Pair @ nat @ TA @ D @ C)) @ (upt @ A @ (plus_plus @ nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])).
% 181.68/124.53 thf(655,axiom,((! [TA: $tType]: ((semiri1453513574482234551roduct @ TA) => (! [A:TA,B:TA]: ((A = (plus_plus @ TA @ A @ B)) = (B = (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_add__0__iff)).
% 181.68/124.53 thf(3030,plain,((! [TA: $tType]: ((semiri1453513574482234551roduct @ TA) => (! [A:TA,B:TA]: ((A = (plus_plus @ TA @ A @ B)) = (B = (zero_zero @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[655])).
% 181.68/124.53 thf(905,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:(TB > (heap_Time_Heap @ TA))]: (((heap_Time_execute @ TB @ A @ B) = (none @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => ((heap_Time_execute @ TA @ (heap_Time_bind @ TB @ TA @ A @ C) @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_execute__bind_I2_J)).
% 181.68/124.53 thf(3765,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TB),B:(heap_ext @ product_unit),C:(TB > (heap_Time_Heap @ TA))]: (((heap_Time_execute @ TB @ A @ B) = (none @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat)))) => ((heap_Time_execute @ TA @ (heap_Time_bind @ TB @ TA @ A @ (C)) @ B) = (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[905])).
% 181.68/124.53 thf(395,axiom,((! [TA: $tType]: ((sup @ TA) => (! [A:(option @ TA)]: ((sup_sup @ (option @ TA) @ A @ (none @ TA)) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2723_sup__None__2)).
% 181.68/124.53 thf(2223,plain,((! [TA: $tType]: ((sup @ TA) => (! [A:(option @ TA)]: ((sup_sup @ (option @ TA) @ A @ (none @ TA)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])).
% 181.68/124.53 thf(580,axiom,((! [TA: $tType]: ((semilattice_inf @ TA) => (semilattice_inf @ (option @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Lattices_Osemilattice__inf_319)).
% 181.68/124.53 thf(2795,plain,((! [TA: $tType]: ((semilattice_inf @ TA) => (semilattice_inf @ (option @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[580])).
% 181.68/124.53 thf(526,axiom,((! [TA: $tType]: (! [A:(product_prod @ (TA > (TA > $o)) @ (list @ TA))]: ~ (! [B:(TA > (TA > $o)),C:(list @ TA)]: (A != (product_Pair @ (TA > (TA > $o)) @ (list @ TA) @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3574_mergesort__by__rel_Ocases)).
% 181.68/124.53 thf(2619,plain,((! [TA: $tType]: (! [A:(product_prod @ (TA > (TA > $o)) @ (list @ TA))]: ~ (! [B:(TA > (TA > $o)),C:(list @ TA)]: ~ (A = (product_Pair @ (TA > (TA > $o)) @ (list @ TA) @ (B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[526])).
% 181.68/124.53 thf(15,axiom,((semidom_modulo @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Rings_Osemidom__modulo_476)).
% 181.68/124.53 thf(1065,plain,((semidom_modulo @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 181.68/124.53 thf(435,axiom,((strict9044650504122735259up_add @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__ab__semigroup__add_517)).
% 181.68/124.53 thf(2353,plain,((strict9044650504122735259up_add @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[435])).
% 181.68/124.53 thf(739,axiom,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA,C:TB,D:TA]: (((product_Pair @ TB @ TA @ A @ B) = (product_Pair @ TB @ TA @ C @ D)) => (~ ((A = C) => (B != D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Pair__inject)).
% 181.68/124.53 thf(3244,plain,((! [TA: $tType,TB: $tType]: (! [A:TB,B:TA,C:TB,D:TA]: (((product_Pair @ TB @ TA @ A @ B) = (product_Pair @ TB @ TA @ C @ D)) => (~ ((A = C) => (~ (B = D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[739])).
% 181.68/124.53 thf(402,axiom,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA]: ((accp @ TA @ A @ B) => (! [C:TA]: ((A @ C @ B) => (accp @ TA @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_accp_Ocases)).
% 181.68/124.53 thf(2241,plain,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA]: ((accp @ TA @ (A) @ B) => (! [C:TA]: ((A @ C @ B) => (accp @ TA @ (A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])).
% 181.68/124.53 thf(587,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA)]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => ((heap_Time_execute @ TA @ (array_nth @ TA @ C @ A) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (nth @ TA @ (array_get @ TA @ B @ C) @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4068_execute__nth_I1_J)).
% 181.68/124.53 thf(2810,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:nat,B:(heap_ext @ product_unit),C:(array @ TA)]: ((ord_less @ nat @ A @ (array_length @ TA @ B @ C)) => ((heap_Time_execute @ TA @ (array_nth @ TA @ C @ A) @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (nth @ TA @ (array_get @ TA @ B @ C) @ A) @ (product_Pair @ (heap_ext @ product_unit) @ nat @ B @ (one_one @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[587])).
% 181.68/124.53 thf(464,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) = (? [E:(nat > TA)]: (((E @ (zero_zero @ nat)) = A) & ((E @ C) = B) & ! [F:nat]: ((ord_less @ nat @ F @ C) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ (E @ F) @ (E @ (suc @ F))) @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4975_relpow__fun__conv)).
% 181.68/124.53 thf(2430,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:nat,D:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ (compow @ (set @ (product_prod @ TA @ TA)) @ C @ D)) = (? [E:(nat > TA)]: (((E @ (zero_zero @ nat)) = A) & ((E @ C) = B) & ! [F:nat]: ((ord_less @ nat @ F @ C) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ (E @ F) @ (E @ (suc @ F))) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[464])).
% 181.68/124.53 thf(584,axiom,((cl_HOL_Oequal @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___HOL_Oequal_156)).
% 181.68/124.53 thf(2803,plain,((cl_HOL_Oequal @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[584])).
% 181.68/124.53 thf(518,axiom,((! [TA: $tType,TB: $tType]: (((typerep2 @ TB) & (typerep2 @ TA)) => (typerep2 @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Typerep_Otyperep_62)).
% 181.68/124.53 thf(2600,plain,((! [TA: $tType,TB: $tType]: (((typerep2 @ TB) & (typerep2 @ TA)) => (typerep2 @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[518])).
% 181.68/124.53 thf(515,axiom,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TB @ TA)]: ? [B:TB,C:TA]: (A = (product_Pair @ TB @ TA @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_surj__pair)).
% 181.68/124.53 thf(2583,plain,((! [TA: $tType,TB: $tType]: (! [A:(product_prod @ TB @ TA)]: ? [B:TB,C:TA]: (A = (product_Pair @ TB @ TA @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])).
% 181.68/124.53 thf(1003,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:(TA > (option @ TB))]: (((A @ B) = (none @ TB)) => ((map_add @ TA @ TB @ A @ C @ B) = (C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3403_map__add__left__None)).
% 181.68/124.53 thf(3965,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB)),B:TA,C:(TA > (option @ TB))]: (((A @ B) = (none @ TB)) => ((map_add @ TA @ TB @ (A) @ (C) @ B) = (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003])).
% 181.68/124.53 thf(484,axiom,(((minus_minus @ code_natural @ (zero_zero @ code_natural) @ (one_one @ code_natural)) = (zero_zero @ code_natural))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3662_natural__zero__minus__one)).
% 181.68/124.53 thf(2507,plain,(((minus_minus @ code_natural @ (zero_zero @ code_natural) @ (one_one @ code_natural)) = (zero_zero @ code_natural))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])).
% 181.68/124.53 thf(236,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/sandbox/benchmark/theBenchmark.p',fact_537_diff__diff__left)).
% 181.68/124.53 thf(1713,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)],[236])).
% 181.68/124.53 thf(673,axiom,((! [TA: $tType,TB: $tType]: ((semilattice_sup @ TA) => (sup @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osup)).
% 181.68/124.53 thf(3076,plain,((! [TA: $tType,TB: $tType]: ((semilattice_sup @ TA) => (sup @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[673])).
% 181.68/124.53 thf(34,axiom,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ (one_one @ nat) @ A) => ((suc @ (minus_minus @ nat @ B @ A)) = (minus_minus @ nat @ B @ (minus_minus @ nat @ A @ (one_one @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_Suc__n__minus__m__eq)).
% 181.68/124.53 thf(1120,plain,((! [A:nat,B:nat]: ((ord_less_eq @ nat @ A @ B) => ((ord_less @ nat @ (one_one @ nat) @ A) => ((suc @ (minus_minus @ nat @ B @ A)) = (minus_minus @ nat @ B @ (minus_minus @ nat @ A @ (one_one @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
% 181.68/124.53 thf(444,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB)]: ((comp @ (option @ TC) @ (option @ TB) @ TA @ (map_option @ TC @ TB @ A) @ (^ [B:TA]: (none @ TC))) = (^ [B:TA]: (none @ TB)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_map__option__o__empty)).
% 181.68/124.53 thf(2372,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB)]: ((comp @ (option @ TC) @ (option @ TB) @ TA @ (map_option @ TC @ TB @ A) @ (^ [B:TA]: (none @ TC))) = (^ [B:TA]: (none @ TB)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[444])).
% 181.68/124.53 thf(370,axiom,((! [A:(product_prod @ ((product_prod @ code_integer @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_integer @ code_integer))]: ~ (! [B:((product_prod @ code_integer @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_integer,D:code_integer]: (A != (product_Pair @ ((product_prod @ code_integer @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_integer @ code_integer) @ B @ (product_Pair @ code_integer @ code_integer @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1273_full__exhaustive__integer_H_Ocases)).
% 181.68/124.53 thf(2138,plain,((! [A:(product_prod @ ((product_prod @ code_integer @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_integer @ code_integer))]: ~ (! [B:((product_prod @ code_integer @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_integer,D:code_integer]: ~ (A = (product_Pair @ ((product_prod @ code_integer @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_integer @ code_integer) @ (B) @ (product_Pair @ code_integer @ code_integer @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[370])).
% 181.68/124.53 thf(695,axiom,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (list @ TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Quickcheck__Random_Orandom_293)).
% 181.68/124.53 thf(3128,plain,((! [TA: $tType]: ((quickcheck_random @ TA) => (quickcheck_random @ (list @ TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[695])).
% 181.68/124.53 thf(314,axiom,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit),C:TA,D:(heap_ext @ product_unit)]: (((product_Pair @ (ref @ TA) @ (heap_ext @ product_unit) @ A @ B) = (ref_alloc @ TA @ C @ D)) => (~ (ref_present @ TA @ D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5723_next__fresh)).
% 181.68/124.53 thf(1977,plain,((! [TA: $tType]: ((heap @ TA) => (! [A:(ref @ TA),B:(heap_ext @ product_unit),C:TA,D:(heap_ext @ product_unit)]: (((product_Pair @ (ref @ TA) @ (heap_ext @ product_unit) @ A @ B) = (ref_alloc @ TA @ C @ D)) => (~ (ref_present @ TA @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])).
% 181.68/124.53 thf(1007,axiom,((comm_semiring @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring_130)).
% 181.68/124.53 thf(3974,plain,((comm_semiring @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007])).
% 181.68/124.53 thf(268,axiom,((! [A:nat,B:nat]: ~ (ord_less @ nat @ (plus_plus @ nat @ A @ B) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_not__add__less2)).
% 181.68/124.53 thf(1827,plain,((! [A:nat,B:nat]: ~ (ord_less @ nat @ (plus_plus @ nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])).
% 181.68/124.53 thf(779,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA)]: ((heap_Time_Heap_ord @ TA @ A @ B) => ((heap_Time_Heap_ord @ TA @ B @ A) => (A = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_heap_Oleq__antisym)).
% 181.68/124.53 thf(3360,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA)]: ((heap_Time_Heap_ord @ TA @ A @ B) => ((heap_Time_Heap_ord @ TA @ B @ A) => (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[779])).
% 181.68/124.53 thf(127,axiom,((ordere580206878836729694up_add @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Groups_Oordered__cancel__ab__semigroup__add_436)).
% 181.68/124.53 thf(1378,plain,((ordere580206878836729694up_add @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
% 181.68/124.53 thf(194,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA),B:TB,C:TA,D:TA]: ((fun_upd @ TB @ TA @ (fun_upd @ TB @ TA @ A @ B @ C) @ B @ D) = (fun_upd @ TB @ TA @ A @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2717_fun__upd__upd)).
% 181.68/124.53 thf(1582,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > TA),B:TB,C:TA,D:TA]: ((fun_upd @ TB @ TA @ (fun_upd @ TB @ TA @ A @ B @ C) @ B @ D) = (fun_upd @ TB @ TA @ A @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
% 181.68/124.53 thf(408,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: ((map_add @ TB @ TA @ A @ (fun_upd @ TB @ (option @ TA) @ B @ C @ (some @ TA @ D))) = (fun_upd @ TB @ (option @ TA) @ (map_add @ TB @ TA @ A @ B) @ C @ (some @ TA @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3399_map__add__upd)).
% 181.68/124.53 thf(2265,plain,((! [TA: $tType,TB: $tType]: (! [A:(TB > (option @ TA)),B:(TB > (option @ TA)),C:TB,D:TA]: ((map_add @ TB @ TA @ A @ (fun_upd @ TB @ (option @ TA) @ B @ C @ (some @ TA @ D))) = (fun_upd @ TB @ (option @ TA) @ (map_add @ TB @ TA @ A @ B) @ C @ (some @ TA @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])).
% 181.68/124.53 thf(908,axiom,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:TA,D:(heap_ext @ product_unit),E:nat]: (((heap_Time_execute @ TA @ A @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))) => (heap_Time_effect @ TA @ A @ B @ D @ C @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_effectI)).
% 181.68/124.53 thf(3772,plain,((! [TA: $tType]: (! [A:(heap_Time_Heap @ TA),B:(heap_ext @ product_unit),C:TA,D:(heap_ext @ product_unit),E:nat]: (((heap_Time_execute @ TA @ A @ B) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ C @ (product_Pair @ (heap_ext @ product_unit) @ nat @ D @ E)))) => (heap_Time_effect @ TA @ A @ B @ D @ C @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[908])).
% 181.68/124.53 thf(185,axiom,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ B) => ((plus_plus @ TA @ (minus_minus @ TA @ B @ A) @ A) = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_ordered__cancel__comm__monoid__diff__class_Odiff__add)).
% 181.68/124.53 thf(1550,plain,((! [TA: $tType]: ((ordere1170586879665033532d_diff @ TA) => (! [A:TA,B:TA]: ((ord_less_eq @ TA @ A @ B) => ((plus_plus @ TA @ (minus_minus @ TA @ B @ A) @ A) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
% 181.68/124.53 thf(200,axiom,((preorder @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Orderings_Opreorder_557)).
% 181.68/124.53 thf(1597,plain,((preorder @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
% 181.68/124.53 thf(546,axiom,((! [A:nat]: ((ord_less_eq @ nat @ (one_one @ nat) @ A) = (A != (zero_zero @ nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_nat__geq__1__eq__neqz)).
% 181.68/124.53 thf(2687,plain,((! [A:nat]: ((ord_less_eq @ nat @ (one_one @ nat) @ A) = (~ (A = (zero_zero @ nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[546])).
% 181.68/124.53 thf(284,axiom,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less @ TA @ A @ B) & (ord_less_eq @ TA @ C @ D)) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_add__mono__thms__linordered__field_I3_J)).
% 181.68/124.53 thf(1880,plain,((! [TA: $tType]: ((ordere580206878836729694up_add @ TA) => (! [A:TA,B:TA,C:TA,D:TA]: (((ord_less @ TA @ A @ B) & (ord_less_eq @ TA @ C @ D)) => (ord_less @ TA @ (plus_plus @ TA @ A @ C) @ (plus_plus @ TA @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])).
% 181.68/124.53 thf(550,axiom,((! [TA: $tType]: ((combine_options @ TA) = (^ [A:(TA > (TA > TA)),B:(option @ TA),C:(option @ TA)]: (case_option @ (option @ TA) @ TA @ C @ (^ [D:TA]: (case_option @ (option @ TA) @ TA @ (some @ TA @ D) @ (^ [E:TA]: (some @ TA @ (A @ D @ E))) @ C)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_combine__options__def)).
% 181.68/124.53 thf(2699,plain,((! [TA: $tType]: ((combine_options @ TA) = (^ [A:(TA > (TA > TA)),B:(option @ TA),C:(option @ TA)]: (case_option @ (option @ TA) @ TA @ C @ (^ [D:TA]: (case_option @ (option @ TA) @ TA @ (some @ TA @ D) @ (^ [E:TA]: (some @ TA @ (A @ D @ E))) @ C)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[550])).
% 181.68/124.53 thf(929,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: ((map_add @ TA @ TB @ A @ (^ [B:TA]: (none @ TB))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3397_map__add__empty)).
% 181.68/124.53 thf(3812,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (option @ TB))]: ((map_add @ TA @ TB @ A @ (^ [B:TA]: (none @ TB))) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[929])).
% 181.68/124.53 thf(134,axiom,((ord_less_eq @ code_integer @ (zero_zero @ code_integer) @ (zero_zero @ code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1270_less__eq__integer__code_I1_J)).
% 181.68/124.53 thf(1399,plain,((ord_less_eq @ code_integer @ (zero_zero @ code_integer) @ (zero_zero @ code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
% 181.68/124.53 thf(981,axiom,((complete_Inf @ nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Complete__Lattices_OInf_124)).
% 181.68/124.53 thf(3918,plain,((complete_Inf @ nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[981])).
% 181.68/124.53 thf(898,axiom,((bounded_lattice @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Obounded__lattice_408)).
% 181.68/124.53 thf(3753,plain,((bounded_lattice @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[898])).
% 181.68/124.53 thf(112,axiom,((! [A:(product_prod @ (code_integer > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_integer @ code_integer))]: ~ (! [B:(code_integer > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_integer,D:code_integer]: (A != (product_Pair @ (code_integer > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_integer @ code_integer) @ B @ (product_Pair @ code_integer @ code_integer @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1272_exhaustive__integer_H_Ocases)).
% 181.68/124.53 thf(1331,plain,((! [A:(product_prod @ (code_integer > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_integer @ code_integer))]: ~ (! [B:(code_integer > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_integer,D:code_integer]: ~ (A = (product_Pair @ (code_integer > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_integer @ code_integer) @ (B) @ (product_Pair @ code_integer @ code_integer @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
% 181.68/124.53 thf(123,axiom,((! [TA: $tType]: (! [A:TA,B:TA,C:(set @ (product_prod @ TA @ TA)),D:TA,E:nat]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ C) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ D) @ (compow @ (set @ (product_prod @ TA @ TA)) @ E @ C)) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ D) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ E) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4986_relpow__Suc__I2)).
% 181.68/124.53 thf(1367,plain,((! [TA: $tType]: (! [A:TA,B:TA,C:(set @ (product_prod @ TA @ TA)),D:TA,E:nat]: ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ B) @ C) => ((member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ B @ D) @ (compow @ (set @ (product_prod @ TA @ TA)) @ E @ C)) => (member @ (product_prod @ TA @ TA) @ (product_Pair @ TA @ TA @ A @ D) @ (compow @ (set @ (product_prod @ TA @ TA)) @ (suc @ E) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
% 181.68/124.53 thf(857,axiom,((! [TA: $tType]: ((cancel_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: (((plus_plus @ TA @ A @ B) = (plus_plus @ TA @ A @ C)) => (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_add__left__imp__eq)).
% 181.68/124.53 thf(3626,plain,((! [TA: $tType]: ((cancel_semigroup_add @ TA) => (! [A:TA,B:TA,C:TA]: (((plus_plus @ TA @ A @ B) = (plus_plus @ TA @ A @ C)) => (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[857])).
% 181.68/124.53 thf(343,axiom,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA,C:TA]: ((accp @ TA @ A @ B) => ((A @ C @ B) => (accp @ TA @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_accp__downward)).
% 181.68/124.53 thf(2059,plain,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA,C:TA]: ((accp @ TA @ (A) @ B) => ((A @ C @ B) => (accp @ TA @ (A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])).
% 181.68/124.53 thf(296,axiom,((! [TA: $tType]: (countable @ (ref @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Heap_Oref___Countable_Ocountable_289)).
% 181.68/124.53 thf(1917,plain,((! [TA: $tType]: (countable @ (ref @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])).
% 181.68/124.53 thf(24,axiom,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA)),B:(set @ (product_prod @ TA @ TA)),C:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ B) @ (init_seg_of @ TA)) => (member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ (minus_minus @ (set @ (product_prod @ TA @ TA)) @ A @ C) @ (minus_minus @ (set @ (product_prod @ TA @ TA)) @ B @ C)) @ (init_seg_of @ TA)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4361_initial__segment__of__Diff)).
% 181.68/124.53 thf(1088,plain,((! [TA: $tType]: (! [A:(set @ (product_prod @ TA @ TA)),B:(set @ (product_prod @ TA @ TA)),C:(set @ (product_prod @ TA @ TA))]: ((member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ A @ B) @ (init_seg_of @ TA)) => (member @ (product_prod @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA))) @ (product_Pair @ (set @ (product_prod @ TA @ TA)) @ (set @ (product_prod @ TA @ TA)) @ (minus_minus @ (set @ (product_prod @ TA @ TA)) @ A @ C) @ (minus_minus @ (set @ (product_prod @ TA @ TA)) @ B @ C)) @ (init_seg_of @ TA)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 181.68/124.53 thf(758,axiom,((! [TA: $tType]: ((refine_Imp_refines @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA)]: ! [C:(heap_ext @ product_unit)]: (case_option @ $o @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ ($true) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ $o @ (^ [D:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ $o @ (^ [E:(heap_ext @ product_unit),F:nat]: ((heap_Time_execute @ TA @ A @ C) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ F)))))))) @ (heap_Time_execute @ TA @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2862_refines__def)).
% 181.68/124.53 thf(3296,plain,((! [TA: $tType]: ((refine_Imp_refines @ TA) = (^ [A:(heap_Time_Heap @ TA),B:(heap_Time_Heap @ TA)]: ! [C:(heap_ext @ product_unit)]: (case_option @ $o @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ ($true) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ $o @ (^ [D:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ $o @ (^ [E:(heap_ext @ product_unit),F:nat]: ((heap_Time_execute @ TA @ A @ C) = (some @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (product_Pair @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ D @ (product_Pair @ (heap_ext @ product_unit) @ nat @ E @ F)))))))) @ (heap_Time_execute @ TA @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[758])).
% 181.68/124.53 thf(657,axiom,((! [TA: $tType,TB: $tType]: (((quickc3360725361186068524ustive @ TA) & (cl_HOL_Oequal @ TB) & (quickc3360725361186068524ustive @ TB)) => (! [A:(product_prod @ ((product_prod @ (TB > TA) @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:((product_prod @ (TB > TA) @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_natural,D:code_natural]: (A != (product_Pair @ ((product_prod @ (TB > TA) @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural) @ B @ (product_Pair @ code_natural @ code_natural @ C @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4216_full__exhaustive__fun_H_Ocases)).
% 181.68/124.53 thf(3035,plain,((! [TA: $tType,TB: $tType]: (((quickc3360725361186068524ustive @ TA) & (cl_HOL_Oequal @ TB) & (quickc3360725361186068524ustive @ TB)) => (! [A:(product_prod @ ((product_prod @ (TB > TA) @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural))]: ~ (! [B:((product_prod @ (TB > TA) @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))),C:code_natural,D:code_natural]: ~ (A = (product_Pair @ ((product_prod @ (TB > TA) @ (product_unit > code_term)) > (option @ (product_prod @ $o @ (list @ code_term)))) @ (product_prod @ code_natural @ code_natural) @ (B) @ (product_Pair @ code_natural @ code_natural @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[657])).
% 181.68/124.53 thf(1014,axiom,((! [TA: $tType]: (! [A:(list @ char)]: ((heap_Time_execute @ TA @ (heap_Time_raise @ TA @ A)) = (^ [B:(heap_ext @ product_unit)]: (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_execute__raise)).
% 181.68/124.53 thf(4002,plain,((! [TA: $tType]: (! [A:(list @ char)]: ((heap_Time_execute @ TA @ (heap_Time_raise @ TA @ A)) = (^ [B:(heap_ext @ product_unit)]: (none @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014])).
% 181.68/124.53 thf(279,axiom,((! [TA: $tType,TB: $tType]: (! [A:assn,B:(heap_Time_Heap @ TB),C:(TB > assn),D:(TB > (heap_Time_Heap @ TA)),E:(TA > assn)]: ((hoare_hoare_triple @ TB @ A @ B @ C) => ((! [F:TB]: (hoare_hoare_triple @ TA @ (C @ F) @ (D @ F) @ E)) => (hoare_hoare_triple @ TA @ A @ (heap_Time_bind @ TB @ TA @ B @ D) @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5658_bind__rule)).
% 181.68/124.53 thf(1870,plain,((! [TA: $tType,TB: $tType]: (! [A:assn,B:(heap_Time_Heap @ TB),C:(TB > assn),D:(TB > (heap_Time_Heap @ TA)),E:(TA > assn)]: ((hoare_hoare_triple @ TB @ A @ B @ (C)) => ((! [F:TB]: (hoare_hoare_triple @ TA @ (C @ F) @ (D @ F) @ (E))) => (hoare_hoare_triple @ TA @ A @ (heap_Time_bind @ TB @ TA @ B @ (D)) @ (E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])).
% 181.68/124.53 thf(841,axiom,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA),C:(option @ TA)]: ((! [D:TA,E:TA]: ((A @ D @ E) = (A @ E @ D))) => ((combine_options @ TA @ A @ B @ C) = (combine_options @ TA @ A @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_combine__options__commute)).
% 181.68/124.53 thf(3580,plain,((! [TA: $tType]: (! [A:(TA > (TA > TA)),B:(option @ TA),C:(option @ TA)]: ((! [D:TA,E:TA]: ((A @ D @ E) = (A @ E @ D))) => ((combine_options @ TA @ (A) @ B @ C) = (combine_options @ TA @ (A) @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[841])).
% 181.68/124.53 thf(814,axiom,((! [TA: $tType]: (cl_HOL_Oequal @ (option @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___HOL_Oequal_334)).
% 181.68/124.53 thf(3461,plain,((! [TA: $tType]: (cl_HOL_Oequal @ (option @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[814])).
% 181.68/124.53 thf(727,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/sandbox/benchmark/theBenchmark.p',fact_453_less__eqE)).
% 181.68/124.53 thf(3212,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)],[727])).
% 181.68/124.53 thf(759,axiom,((! [TA: $tType]: ((sup @ TA) => ((sup_sup @ (option @ TA)) = (^ [A:(option @ TA),B:(option @ TA)]: (case_option @ (option @ TA) @ TA @ B @ (^ [C:TA]: (case_option @ (option @ TA) @ TA @ A @ (^ [D:TA]: (some @ TA @ (sup_sup @ TA @ C @ D))) @ B)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2686_sup__option__def)).
% 181.68/124.53 thf(3299,plain,((! [TA: $tType]: ((sup @ TA) => ((sup_sup @ (option @ TA)) = (^ [A:(option @ TA),B:(option @ TA)]: (case_option @ (option @ TA) @ TA @ B @ (^ [C:TA]: (case_option @ (option @ TA) @ TA @ A @ (^ [D:TA]: (some @ TA @ (sup_sup @ TA @ C @ D))) @ B)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[759])).
% 181.68/124.53 thf(244,axiom,((! [TA: $tType]: (! [A:$o,B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit),D:(heap_Time_Heap @ TA)]: (((A) => (heap_Time_success @ TA @ B @ C)) => (((~ (A)) => (heap_Time_success @ TA @ D @ C)) => (heap_Time_success @ TA @ (if @ (heap_Time_Heap @ TA) @ A @ B @ D) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_success__ifI)).
% 181.68/124.53 thf(1737,plain,((! [TA: $tType]: (! [A:$o,B:(heap_Time_Heap @ TA),C:(heap_ext @ product_unit),D:(heap_Time_Heap @ TA)]: (((A) => (heap_Time_success @ TA @ B @ C)) => (((~ (A)) => (heap_Time_success @ TA @ D @ C)) => (heap_Time_success @ TA @ (if @ (heap_Time_Heap @ TA) @ A @ B @ D) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
% 181.68/124.53 thf(681,axiom,((! [TA: $tType]: (semilattice_sup @ (set @ TA)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_248)).
% 181.68/124.53 thf(3096,plain,((! [TA: $tType]: (semilattice_sup @ (set @ TA)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[681])).
% 181.68/124.53 thf(950,axiom,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TA),B:(TA > (heap_Time_Heap @ TB)),C:(heap_ext @ product_unit)]: ((heap_Time_execute @ TB @ (heap_Time_bind @ TA @ TB @ A @ B) @ C) = (case_option @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (none @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [D:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [E:(heap_ext @ product_unit),F:nat]: (heap_Time_timeFrame @ TB @ F @ (heap_Time_execute @ TB @ (B @ D) @ E)))))) @ (heap_Time_execute @ TA @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_execute__bind__case)).
% 181.68/124.53 thf(3854,plain,((! [TA: $tType,TB: $tType]: (! [A:(heap_Time_Heap @ TA),B:(TA > (heap_Time_Heap @ TB)),C:(heap_ext @ product_unit)]: ((heap_Time_execute @ TB @ (heap_Time_bind @ TA @ TB @ A @ (B)) @ C) = (case_option @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (product_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat)) @ (none @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (product_case_prod @ TA @ (product_prod @ (heap_ext @ product_unit) @ nat) @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [D:TA]: (product_case_prod @ (heap_ext @ product_unit) @ nat @ (option @ (product_prod @ TB @ (product_prod @ (heap_ext @ product_unit) @ nat))) @ (^ [E:(heap_ext @ product_unit),F:nat]: (heap_Time_timeFrame @ TB @ F @ (heap_Time_execute @ TB @ (B @ D) @ E)))))) @ (heap_Time_execute @ TA @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[950])).
% 181.68/124.53 thf(389,axiom,((! [A:nat]: ((ord_less @ nat @ A @ (one_one @ nat)) = (A = (zero_zero @ nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_less__one)).
% 181.68/124.53 thf(2206,plain,((! [A:nat]: ((ord_less @ nat @ A @ (one_one @ nat)) = (A = (zero_zero @ nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])).
% 181.68/124.53 thf(227,axiom,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ (heap_Time_ureturn @ TA @ A) @ B @ C @ D @ E) => (~ ((D = A) => ((C = B) => (E != (zero_zero @ nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_effect__ureturnE)).
% 181.68/124.53 thf(1681,plain,((! [TA: $tType]: (! [A:TA,B:(heap_ext @ product_unit),C:(heap_ext @ product_unit),D:TA,E:nat]: ((heap_Time_effect @ TA @ (heap_Time_ureturn @ TA @ A) @ B @ C @ D @ E) => (~ ((D = A) => ((C = B) => (~ (E = (zero_zero @ nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])).
% 181.68/124.53 thf(54,axiom,((quickc658316121487927005ustive @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Quickcheck__Exhaustive_Oexhaustive_447)).
% 181.68/124.53 thf(1184,plain,((quickc658316121487927005ustive @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
% 181.68/124.53 thf(547,axiom,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TE > TD),B:(TA > TE),C:(TB > TD),D:(TA > TB),E:(TD > TC),F:(TB > TC)]: (((comp @ TE @ TD @ TA @ A @ B) = (comp @ TB @ TD @ TA @ C @ D)) => (((comp @ TD @ TC @ TB @ E @ C) = F) => ((comp @ TE @ TC @ TA @ (comp @ TD @ TC @ TE @ E @ A) @ B) = (comp @ TB @ TC @ TA @ F @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_rewriteR__comp__comp2)).
% 181.68/124.53 thf(2690,plain,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType]: (! [A:(TE > TD),B:(TA > TE),C:(TB > TD),D:(TA > TB),E:(TD > TC),F:(TB > TC)]: (((comp @ TE @ TD @ TA @ A @ B) = (comp @ TB @ TD @ TA @ C @ D)) => (((comp @ TD @ TC @ TB @ E @ C) = (F)) => ((comp @ TE @ TC @ TA @ (comp @ TD @ TC @ TE @ E @ A) @ B) = (comp @ TB @ TC @ TA @ F @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[547])).
% 181.68/124.53 thf(157,axiom,((typerep2 @ code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Ointeger___Typerep_Otyperep_4)).
% 181.68/124.53 thf(1463,plain,((typerep2 @ code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])).
% 181.68/124.53 thf(189,axiom,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA]: ((~ (accp @ TA @ A @ B)) => (~ (! [C:TA]: ((A @ C @ B) => (accp @ TA @ A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_not__accp__down)).
% 181.68/124.53 thf(1565,plain,((! [TA: $tType]: (! [A:(TA > (TA > $o)),B:TA]: ((~ (accp @ TA @ (A) @ B)) => (~ (! [C:TA]: ((A @ C @ B) => (accp @ TA @ (A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
% 181.68/124.53 thf(415,axiom,((comm_monoid_diff @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__diff_541)).
% 181.68/124.53 thf(2297,plain,((comm_monoid_diff @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])).
% 181.68/124.53 thf(467,axiom,((! [TA: $tType,TB: $tType]: (! [A:$o]: (((A) => ((collect @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ (^ [B:TA,C:TB]: (A)))) = (top_top @ (set @ (product_prod @ TA @ TB))))) & ((~ (A)) => ((collect @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ (^ [B:TA,C:TB]: (A)))) = (bot_bot @ (set @ (product_prod @ TA @ TB))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2337_Collect__const__case__prod)).
% 181.68/124.53 thf(2438,plain,((! [TA: $tType,TB: $tType]: (! [A:$o]: (((A) => ((collect @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ (^ [B:TA,C:TB]: (A)))) = (top_top @ (set @ (product_prod @ TA @ TB))))) & ((~ (A)) => ((collect @ (product_prod @ TA @ TB) @ (product_case_prod @ TA @ TB @ $o @ (^ [B:TA,C:TB]: (A)))) = (bot_bot @ (set @ (product_prod @ TA @ TB))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])).
% 181.68/124.53 thf(401,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(list @ TA)]: ((map @ TC @ TB @ A @ (map @ TA @ TC @ B @ C)) = (map @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3483_list_Omap__comp)).
% 181.68/124.53 thf(2238,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TC > TB),B:(TA > TC),C:(list @ TA)]: ((map @ TC @ TB @ (A) @ (map @ TA @ TC @ (B) @ C)) = (map @ TA @ TB @ (comp @ TC @ TB @ TA @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])).
% 181.68/124.53 thf(642,axiom,((! [TA: $tType,TB: $tType]: (((enum @ TB) & (cl_HOL_Oequal @ TA)) => (cl_HOL_Oequal @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___HOL_Oequal)).
% 181.68/124.53 thf(2993,plain,((! [TA: $tType,TB: $tType]: (((enum @ TB) & (cl_HOL_Oequal @ TA)) => (cl_HOL_Oequal @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[642])).
% 181.68/124.53 thf(263,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/sandbox/benchmark/theBenchmark.p',fact_211_add__less__mono1)).
% 181.68/124.53 thf(1812,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)],[263])).
% 181.68/124.53 thf(360,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/sandbox/benchmark/theBenchmark.p',fact_508_mono__nat__linear__lb)).
% 181.68/124.53 thf(2106,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)],[360])).
% 181.68/124.53 thf(355,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/sandbox/benchmark/theBenchmark.p',fact_285_less__imp__add__positive)).
% 181.68/124.53 thf(2087,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)],[355])).
% 181.68/124.53 thf(990,axiom,((uminus @ product_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Groups_Ouminus_419)).
% 181.68/124.53 thf(3933,plain,((uminus @ product_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[990])).
% 181.68/124.53 thf(833,axiom,((! [TA: $tType]: ((zero @ TA) => (! [A:TA]: (((zero_zero @ TA) = A) = (A = (zero_zero @ TA))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_zero__reorient)).
% 181.68/124.53 thf(3553,plain,((! [TA: $tType]: ((zero @ TA) => (! [A:TA]: (((zero_zero @ TA) = A) = (A = (zero_zero @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[833])).
% 181.68/124.53 thf(661,axiom,((! [TA: $tType,TB: $tType]: (((cl_HOL_Oequal @ TB) & (quickc3360725361186068524ustive @ TB) & (quickc3360725361186068524ustive @ TA)) => (quickc3360725361186068524ustive @ (TB > TA))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Quickcheck__Exhaustive_Ofull__exhaustive)).
% 181.68/124.53 thf(3047,plain,((! [TA: $tType,TB: $tType]: (((cl_HOL_Oequal @ TB) & (quickc3360725361186068524ustive @ TB) & (quickc3360725361186068524ustive @ TA)) => (quickc3360725361186068524ustive @ (TB > TA))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[661])).
% 181.68/124.53 thf(476,axiom,((semiring @ code_natural)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Osemiring_564)).
% 181.68/124.53 thf(2470,plain,((semiring @ code_natural)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[476])).
% 181.68/124.53 thf(4039,plain,(($false)),inference(e,[status(thm)],[3021,2630,2612,1454,3798,3698,2463,3969,2544,1950,1369,2889,2295,3053,4005,1633,2778,3399,2263,3930,3863,3830,2787,3449,4015,1179,2331,1818,1295,1750,3072,3317,1882,2495,3417,3285,2676,1591,3498,3402,1692,1041,2363,3680,1200,2077,4037,2976,2117,2940,1406,2622,3858,3905,3762,1569,2248,3098,1073,1728,3108,3012,1205,2114,1269,1173,1486,3848,1671,1655,3120,1756,3044,3446,1872,3616,1327,1640,3313,3577,1078,3217,3049,3745,3332,3367,3648,3942,4011,1867,2184,3175,2476,2627,2168,1919,1988,3414,3121,3481,1507,3895,3717,2360,3370,3335,3103,2348,3088,1613,3898,4030,2516,2400,2405,2869,2957,3836,2216,3629,2763,3915,2227,1576,3308,2010,1935,1601,1386,3809,1366,2819,1803,3880,1904,1518,1228,1623,3891,1287,3275,2667,3574,2682,1455,1132,2571,1055,1409,3938,3195,1760,1660,1298,3617,1330,2444,1323,3653,1313,1279,3749,2562,2897,1191,2126,3803,2466,1545,1922,1800,3998,2403,1147,2049,1704,3084,2158,3708,1815,1362,3180,3231,3840,3463,1379,1572,3919,2635,2929,3902,1931,2388,2533,1232,3268,4008,2007,2616,3075,4018,2782,3163,2880,3438,2540,2335,1283,3771,1489,2950,3887,2027,3199,3934,3670,4001,1418,3453,2451,2236,3923,2555,1843,1886,2530,3157,3756,1433,2750,3870,3406,4033,3189,2424,2979,2799,4038,2804,2965,3588,1104,1242,3559,3211,2392,1521,2586,2982,2884,3510,1564,2954,2011,3857,3503,2473,3567,2574,1306,1153,3995,1915,2641,3795,1163,1074,1604,3899,1311,2307,2660,1768,2382,2061,3550,2773,2000,2673,2589,2705,2249,1042,1123,1502,1666,3610,3816,3261,1223,3827,2428,3711,1343,2560,3972,3989,3239,3069,3233,3884,2937,3154,3134,2132,2414,3250,2528,3664,3207,2396,3682,4021,3778,2015,3889,1883,1560,3282,2433,2332,2200,2327,3028,2741,3667,3033,3271,3166,3958,3191,1938,2873,1032,3269,2670,3810,3090,2565,3198,3750,3349,3556,1888,3877,3546,3144,1159,2344,2313,1128,2769,4027,3731,3968,3782,1983,2801,3862,2895,2694,2509,3386,3632,3078,3941,2638,2268,3105,3467,3699,2300,1762,2100,1851,1772,1259,2990,1534,1953,1375,2973,3381,1064,1540,3963,2724,1719,3650,4012,3060,3087,3018,1361,3922,1182,3714,3596,2080,1414,2613,3643,1889,2649,3573,3935,2460,1493,1160,3775,3141,1292,3622,1424,3441,2317,3294,3242,1825,3656,2845,3743,3222,1947,2813,3115,3064,3920,3215,1588,1099,1150,1478,3126,3541,1451,2304,1530,1382,1266,3354,2900,1668,1974,2851,2243,2581,2465,3819,3390,3760,3409,2766,2052,2482,1246,3201,1393,3147,3755,3802,3225,1695,3592,1187,1167,2995,3841,1732,3807,3824,1857,1991,1318,1202,2203,2702,2546,2043,3279,2963,3321,1035,2408,1663,1515,4036,2662,1185,2235,3130,2176,2904,1698,1219,1273,1747,3262,2602,3792,3343,1146,2292,3871,2033,3738,2028,1301,3888,3839,2524,2376,2727,3768,3504,1389,3811,1125,2525,1620,4032,3900,2806,2716,3868,1256,3741,1833,2970,3319,3636,3925,1652,3736,3081,1929,3266,2568,1403,3458,1795,1701,3590,2827,3599,1503,2326,1707,3646,1058,3700,1897,2425,1464,3302,1428,2161,3118,2220,3964,3340,1239,1997,2759,3436,3783,2055,1092,2166,1765,1090,2148,2358,2521,3815,1894,1806,1524,2097,2246,1722,1043,3138,3384,1439,1969,2065,1194,2346,1209,2721,2538,1408,2084,2624,3038,2422,3779,1048,1771,2945,3456,1877,2111,1862,3614,3451,3583,2553,2911,3219,2824,2025,2632,1339,2605,3027,3055,4009,2314,2129,1821,1731,2542,1460,3150,1061,1171,2075,2212,1066,3110,3687,1176,2931,2797,2535,1496,3512,2999,3908,1841,1396,1926,2365,2725,1594,3423,1044,1245,3159,2064,2369,3674,3363,3310,2967,1250,2069,2867,3444,2952,1208,2471,2037,2878,1509,2564,3292,3571,3849,1413,3881,1626,3009,2914,2816,1304,1873,3193,3427,3161,1905,1081,2927,3975,2684,2202,3921,1340,3278,1958,2942,2513,1547,3376,1961,2192,3754,1941,3949,3228,1531,1484,2831,1798,2298,3391,3640,3315,1598,2397,3507,1070,3112,2375,1156,1225,1743,1400,3833,3659,2821,3209,1753,3786,3058,1098,2888,2747,2092,1186,1038,1785,3475,3544,1085,1336,1220,2354,1987,1716,2454,3305,1432,3818,3691,1637,3273,3655,1262,1235,3823,2337,3801,1980,1317,1830,1538,2486,3847,2903,3623,3412,1130,1579,3041,3853,2948,2411,1543,2558,3124,2379,2579,1427,3024,3961,3366,3007,1617,2056,1358,1221,1284,2279,2357,1955,2145,1972,2320,1052,2711,1506,1585,1094,3943,2030,1372,3256,2892,1272,3914,3684,3288,1421,3620,1649,2479,3548,2215,2919,1108,2875,3168,2435,2760,3433,3946,1459,3092,2818,3067,2696,1553,3171,2960,2310,3874,2611,3928,1216,2209,2743,2997,2187,3346,2226,1453,1866,2071,2775,1734,2792,1646,1326,3864,2273,2389,2853,2135,2532,1481,1101,1629,3748,1854,3501,4010,3136,3252,1276,1590,3613,1253,1674,3789,2608,3235,3662,3780,2934,2152,2447,2956,3324,1607,3351,2120,2095,2739,1994,2019,3420,1689,2081,3694,2786,3844,3585,3430,1308,3896,2576,2066,1077,3677,2162,2680,1212,2230,2036,2917,3761,2123,2287,1512,2155,1097,1229,3892,3100,1876,3132,3992,2003,2142,3379,1678,3785,3865,2719,3373,3464,2736,1986,1527,3337,3203,3062,3822,3015,1436,1657,3850,3479,1789,2366,2040,2340,1610,2651,2783,2549,3897,2201,1363,1314,3177,3804,1335,4024,1288,1710,1197,2714,1891,3030,3765,2223,2795,2619,1065,2353,3244,2241,2810,2430,2803,2600,2583,3965,2507,1713,3076,1120,2372,2138,3128,1977,3974,1827,3360,1378,1582,2265,3772,1550,1597,2687,1880,2699,3812,1399,3918,3753,1331,1367,3626,2059,1917,1088,3296,3035,4002,1870,3580,3461,3212,3299,1737,3096,3854,2206,1681,1184,2690,1463,1565,2297,2438,2238,2993,1812,2106,2087,3933,3553,3047,2470])).
% 181.68/124.53 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 181.68/124.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------