%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP066^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:16 AM UTC 2026
% Result : Theorem 129.09s 19.78s
% Output : Refutation 129.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP066^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 08:25:15 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.35 ---- Original DTF file ---
% 0.14/0.35 thf(spec,logic,$$dhol).
% 0.14/0.35 %------------------------------------------------------------------------------
% 0.14/0.35 % File : ITP066^2 : TPTP v9.2.1. Released v7.5.0.
% 0.14/0.35 % Domain : Interactive Theorem Proving
% 0.14/0.35 % Problem : Sledgehammer HeapImperative problem prob_1195__5351920_1
% 0.14/0.35 % Version : Especial.
% 0.14/0.35 % English :
% 0.14/0.35
% 0.14/0.35 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.14/0.35 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.14/0.35 % Source : [Des21]
% 0.14/0.35 % Names : HeapImperative/prob_1195__5351920_1 [Des21]
% 0.14/0.35
% 0.14/0.35 % Status : Theorem
% 0.14/0.35 % Rating : 0.33 v8.2.0, 0.67 v8.1.0, 0.25 v7.5.0
% 0.14/0.35 % Syntax : Number of formulae : 356 ( 98 unt; 81 typ; 0 def)
% 0.14/0.35 % Number of atoms : 779 ( 389 equ; 0 cnn)
% 0.14/0.35 % Maximal formula atoms : 12 ( 2 avg)
% 0.14/0.35 % Number of connectives : 5485 ( 84 ~; 10 |; 61 &;4971 @)
% 0.14/0.35 % ( 0 <=>; 359 =>; 0 <=; 0 <~>)
% 0.14/0.35 % Maximal formula depth : 28 ( 8 avg)
% 0.14/0.35 % Number of types : 2 ( 1 usr)
% 0.14/0.35 % Number of type conns : 223 ( 223 >; 0 *; 0 +; 0 <<)
% 0.14/0.35 % Number of symbols : 83 ( 80 usr; 14 con; 0-8 aty)
% 0.14/0.35 % Number of variables : 1341 ( 56 ^;1188 !; 19 ?;1341 :)
% 0.14/0.35 % ( 78 !>; 0 ?*; 0 @-; 0 @+)
% 0.14/0.35 % SPC : TH1_THM_EQU_NAR
% 0.14/0.35
% 0.14/0.35 % Comments : This file was generated by Sledgehammer 2021-02-23 16:17:35.238
% 0.14/0.35 %------------------------------------------------------------------------------
% 0.14/0.35 % Could-be-implicit typings (6)
% 0.14/0.35 thf(ty_t_Product__Type_Oprod,type,
% 0.14/0.35 product_prod: $tType > $tType > $tType ).
% 0.14/0.35
% 0.14/0.35 thf(ty_t_Multiset_Omultiset,type,
% 0.14/0.35 multiset: $tType > $tType ).
% 0.14/0.35
% 0.14/0.35 thf(ty_t_List_Olist,type,
% 0.14/0.35 list: $tType > $tType ).
% 0.14/0.35
% 0.14/0.35 thf(ty_t_Heap_OTree,type,
% 0.14/0.35 tree: $tType > $tType ).
% 0.14/0.35
% 0.14/0.35 thf(ty_t_Set_Oset,type,
% 0.14/0.35 set: $tType > $tType ).
% 0.14/0.35
% 0.14/0.35 thf(ty_tf_a,type,
% 0.14/0.35 a: $tType ).
% 0.14/0.35
% 0.14/0.35 % Explicit typings (75)
% 0.14/0.35 thf(sy_cl_HOL_Otype,type,
% 0.14/0.35 type:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Orderings_Opreorder,type,
% 0.14/0.35 preorder:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Ozero,type,
% 0.14/0.35 zero:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Num_Oneg__numeral,type,
% 0.14/0.35 neg_numeral:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Ogroup__add,type,
% 0.14/0.35 group_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Omonoid__add,type,
% 0.14/0.35 monoid_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Orderings_Olinorder,type,
% 0.14/0.35 linorder:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.14/0.35 semigroup_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.14/0.35 comm_monoid_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.14/0.35 ab_semigroup_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.14/0.35 cancel_semigroup_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.14/0.35 cancel1352612707id_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.14/0.35 linord219039673up_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.14/0.35 ordere216010020id_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.14/0.35 ordere779506340up_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.14/0.35 linord1659791738miring:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.14/0.35 canoni770627133id_add:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.14/0.35 ordere236663937imp_le:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 0.14/0.35 unique1598680935umeral:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.14/0.35 ordere516151231imp_le:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 0.14/0.35 semiri456707255roduct:
% 0.14/0.35 !>[A: $tType] : $o ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux,type,
% 0.14/0.35 unique455577585es_aux:
% 0.14/0.35 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.14/0.35 plus_plus:
% 0.14/0.35 !>[A: $tType] : ( A > A > A ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.14/0.35 zero_zero:
% 0.14/0.35 !>[A: $tType] : A ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HOL_ONO__MATCH,type,
% 0.14/0.35 nO_MATCH:
% 0.14/0.35 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oheapify,type,
% 0.14/0.35 heapIm818251801eapify:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Ohs__is__empty,type,
% 0.14/0.35 heapIm721255937_empty:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Ohs__of__list,type,
% 0.14/0.35 heapIm874063447f_list:
% 0.14/0.35 !>[A: $tType] : ( ( list @ A ) > ( tree @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Ohs__remove__max,type,
% 0.14/0.35 heapIm1542349758ve_max:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > ( product_prod @ A @ ( tree @ A ) ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oleft,type,
% 0.14/0.35 heapIm1271749598e_left:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oof__list__tree,type,
% 0.14/0.35 heapIm1912108042t_tree:
% 0.14/0.35 !>[A: $tType] : ( ( list @ A ) > ( tree @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_OremoveLeaf,type,
% 0.14/0.35 heapIm970386777veLeaf:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > ( product_prod @ A @ ( tree @ A ) ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oright,type,
% 0.14/0.35 heapIm1434396069_right:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_OsiftDown,type,
% 0.14/0.35 heapIm748920189ftDown:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Heap_OHeap,type,
% 0.14/0.35 heap:
% 0.14/0.35 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( tree @ A ) ) > ( B > ( product_prod @ A @ B ) ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Heap_OHeap__axioms,type,
% 0.14/0.35 heap_axioms:
% 0.14/0.35 !>[B: $tType,A: $tType] : ( ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( tree @ A ) ) > ( B > ( product_prod @ A @ B ) ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Heap_OTree_OE,type,
% 0.14/0.35 e:
% 0.14/0.35 !>[A: $tType] : ( tree @ A ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Heap_OTree_OT,type,
% 0.14/0.35 t:
% 0.14/0.35 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) > ( tree @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Heap_Oin__tree,type,
% 0.14/0.35 in_tree:
% 0.14/0.35 !>[A: $tType] : ( A > ( tree @ A ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Heap_Ois__heap,type,
% 0.14/0.35 is_heap:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Heap_Omultiset,type,
% 0.14/0.35 multiset2:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > ( multiset @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Heap_Oval,type,
% 0.14/0.35 val:
% 0.14/0.35 !>[A: $tType] : ( ( tree @ A ) > A ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_If,type,
% 0.14/0.35 if:
% 0.14/0.35 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Lattices__Big_Olinorder__class_OMax,type,
% 0.14/0.35 lattic929149872er_Max:
% 0.14/0.35 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Multiset_Oadd__mset,type,
% 0.14/0.35 add_mset:
% 0.14/0.35 !>[A: $tType] : ( A > ( multiset @ A ) > ( multiset @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Multiset_Ocomm__monoid__add_Osum__mset,type,
% 0.14/0.35 comm_monoid_sum_mset:
% 0.14/0.35 !>[A: $tType] : ( ( A > A > A ) > A > ( multiset @ A ) > A ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Multiset_Ois__empty,type,
% 0.14/0.35 is_empty:
% 0.14/0.35 !>[A: $tType] : ( ( multiset @ A ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Multiset_Omult,type,
% 0.14/0.35 mult:
% 0.14/0.35 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Multiset_Omult1,type,
% 0.14/0.35 mult1:
% 0.14/0.35 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Multiset_Oset__mset,type,
% 0.14/0.35 set_mset:
% 0.14/0.35 !>[A: $tType] : ( ( multiset @ A ) > ( set @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.14/0.35 ord_less_eq:
% 0.14/0.35 !>[A: $tType] : ( A > A > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Product__Type_OPair,type,
% 0.14/0.35 product_Pair:
% 0.14/0.35 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.14/0.35 produc2004651681e_prod:
% 0.14/0.35 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.14/0.35 product_rec_prod:
% 0.14/0.35 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 0.14/0.35 product_fst:
% 0.14/0.35 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 0.14/0.35 product_snd:
% 0.14/0.35 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Product__Type_Oprod_Oswap,type,
% 0.14/0.35 product_swap:
% 0.14/0.35 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > ( product_prod @ B @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Product__Type_Oscomp,type,
% 0.14/0.35 product_scomp:
% 0.14/0.35 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( product_prod @ B @ C ) ) > ( B > C > D ) > A > D ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Relation_Oirrefl,type,
% 0.14/0.35 irrefl:
% 0.14/0.35 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Relation_Otrans,type,
% 0.14/0.35 trans:
% 0.14/0.35 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_RemoveMax_OCollection,type,
% 0.14/0.35 collection:
% 0.14/0.35 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_Set_OCollect,type,
% 0.14/0.35 collect:
% 0.14/0.35 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_c_member,type,
% 0.14/0.35 member:
% 0.14/0.35 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_l1____,type,
% 0.14/0.35 l1: tree @ a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_l2____,type,
% 0.14/0.35 l2: tree @ a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_r1____,type,
% 0.14/0.35 r1: tree @ a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_r2____,type,
% 0.14/0.35 r2: tree @ a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_t,type,
% 0.14/0.35 t2: tree @ a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_t_H,type,
% 0.14/0.35 t3: tree @ a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_t_Ha____,type,
% 0.14/0.35 t_a: tree @ a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_v1____,type,
% 0.14/0.35 v1: a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_v2____,type,
% 0.14/0.35 v2: a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_v_H,type,
% 0.14/0.35 v: a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_v_Ha____,type,
% 0.14/0.35 v_a: a ).
% 0.14/0.35
% 0.14/0.35 thf(sy_v_v____,type,
% 0.14/0.35 v3: a ).
% 0.14/0.35
% 0.14/0.35 % Relevant facts (255)
% 0.14/0.35 thf(fact_0__C4__2_Oprems_C_I1_J,axiom,
% 0.14/0.35 ( ( product_Pair @ a @ ( tree @ a ) @ v_a @ t_a )
% 0.14/0.35 = ( heapIm970386777veLeaf @ a @ ( t @ a @ v3 @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % "4_2.prems"(1)
% 0.14/0.35 thf(fact_1_assms_I1_J,axiom,
% 0.14/0.35 ( ( product_Pair @ a @ ( tree @ a ) @ v @ t3 )
% 0.14/0.35 = ( heapIm970386777veLeaf @ a @ t2 ) ) ).
% 0.14/0.35
% 0.14/0.35 % assms(1)
% 0.14/0.35 thf(fact_2__C4__2_Oprems_C_I2_J,axiom,
% 0.14/0.35 ( ( t @ a @ v3 @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) )
% 0.14/0.35 != ( e @ a ) ) ).
% 0.14/0.35
% 0.14/0.35 % "4_2.prems"(2)
% 0.14/0.35 thf(fact_3__092_060open_062t_H_A_061_AT_Av_A_Isnd_A_IremoveLeaf_A_IT_Av1_Al1_Ar1_J_J_J_A_IT_Av2_Al2_Ar2_J_092_060close_062,axiom,
% 0.14/0.35 ( t_a
% 0.14/0.35 = ( t @ a @ v3 @ ( product_snd @ a @ ( tree @ a ) @ ( heapIm970386777veLeaf @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % \<open>t' = T v (snd (removeLeaf (T v1 l1 r1))) (T v2 l2 r2)\<close>
% 0.14/0.35 thf(fact_4_Tree_Oinject,axiom,
% 0.14/0.35 ! [A: $tType,X21: A,X22: tree @ A,X23: tree @ A,Y21: A,Y22: tree @ A,Y23: tree @ A] :
% 0.14/0.35 ( ( ( t @ A @ X21 @ X22 @ X23 )
% 0.14/0.35 = ( t @ A @ Y21 @ Y22 @ Y23 ) )
% 0.14/0.35 = ( ( X21 = Y21 )
% 0.14/0.35 & ( X22 = Y22 )
% 0.14/0.35 & ( X23 = Y23 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % Tree.inject
% 0.14/0.35 thf(fact_5_removeLeaf_Osimps_I5_J,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ! [V: A,Vd: A,Ve: tree @ A,Vf: tree @ A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.14/0.35 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.35 = ( product_Pair @ A @ ( tree @ A ) @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) @ ( t @ A @ V @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % removeLeaf.simps(5)
% 0.14/0.35 thf(fact_6_removeLeaf_Osimps_I4_J,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A] :
% 0.14/0.35 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 0.14/0.35 = ( product_Pair @ A @ ( tree @ A ) @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( t @ A @ V @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % removeLeaf.simps(4)
% 0.14/0.35 thf(fact_7_left_Osimps,axiom,
% 0.14/0.35 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 0.14/0.35 ( ( heapIm1271749598e_left @ A @ ( t @ A @ V @ L @ R ) )
% 0.14/0.35 = L ) ).
% 0.14/0.35
% 0.14/0.35 % left.simps
% 0.14/0.35 thf(fact_8_right_Osimps,axiom,
% 0.14/0.35 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 0.14/0.35 ( ( heapIm1434396069_right @ A @ ( t @ A @ V @ L @ R ) )
% 0.14/0.35 = R ) ).
% 0.14/0.35
% 0.14/0.35 % right.simps
% 0.14/0.35 thf(fact_9__C4__2_Ohyps_C_I1_J,axiom,
% 0.14/0.35 ! [V2: a,T2: tree @ a] :
% 0.14/0.35 ( ( ( product_Pair @ a @ ( tree @ a ) @ V2 @ T2 )
% 0.14/0.35 = ( heapIm970386777veLeaf @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
% 0.14/0.35 => ( ( ( t @ a @ v1 @ l1 @ r1 )
% 0.14/0.35 != ( e @ a ) )
% 0.14/0.35 => ( ( plus_plus @ ( multiset @ a ) @ ( add_mset @ a @ V2 @ ( zero_zero @ ( multiset @ a ) ) ) @ ( multiset2 @ a @ T2 ) )
% 0.14/0.35 = ( multiset2 @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % "4_2.hyps"(1)
% 0.14/0.35 thf(fact_10_removeLeaf_Osimps_I1_J,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ! [V: A] :
% 0.14/0.35 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) )
% 0.14/0.35 = ( product_Pair @ A @ ( tree @ A ) @ V @ ( e @ A ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % removeLeaf.simps(1)
% 0.14/0.35 thf(fact_11_fstI,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,X: product_prod @ A @ B,Y: A,Z: B] :
% 0.14/0.35 ( ( X
% 0.14/0.35 = ( product_Pair @ A @ B @ Y @ Z ) )
% 0.14/0.35 => ( ( product_fst @ A @ B @ X )
% 0.14/0.35 = Y ) ) ).
% 0.14/0.35
% 0.14/0.35 % fstI
% 0.14/0.35 thf(fact_12_fst__eqD,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,X: A,Y: B,A2: A] :
% 0.14/0.35 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X @ Y ) )
% 0.14/0.35 = A2 )
% 0.14/0.35 => ( X = A2 ) ) ).
% 0.14/0.35
% 0.14/0.35 % fst_eqD
% 0.14/0.35 thf(fact_13_fst__conv,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,X1: A,X2: B] :
% 0.14/0.35 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X1 @ X2 ) )
% 0.14/0.35 = X1 ) ).
% 0.14/0.35
% 0.14/0.35 % fst_conv
% 0.14/0.35 thf(fact_14_assms_I2_J,axiom,
% 0.14/0.35 ( t2
% 0.14/0.35 != ( e @ a ) ) ).
% 0.14/0.35
% 0.14/0.35 % assms(2)
% 0.14/0.35 thf(fact_15_prod_Oinject,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.14/0.35 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.14/0.35 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.14/0.35 = ( ( X1 = Y1 )
% 0.14/0.35 & ( X2 = Y2 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod.inject
% 0.14/0.35 thf(fact_16_old_Oprod_Oinject,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.14/0.35 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.14/0.35 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.14/0.35 = ( ( A2 = A3 )
% 0.14/0.35 & ( B2 = B3 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % old.prod.inject
% 0.14/0.35 thf(fact_17_prod_Ocollapse,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.14/0.35 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 0.14/0.35 = Prod ) ).
% 0.14/0.35
% 0.14/0.35 % prod.collapse
% 0.14/0.35 thf(fact_18_multiset_Osimps_I2_J,axiom,
% 0.14/0.35 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 0.14/0.35 ( ( multiset2 @ A @ ( t @ A @ V @ L @ R ) )
% 0.14/0.35 = ( plus_plus @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ ( multiset2 @ A @ L ) @ ( add_mset @ A @ V @ ( zero_zero @ ( multiset @ A ) ) ) ) @ ( multiset2 @ A @ R ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % multiset.simps(2)
% 0.14/0.35 thf(fact_19_multiset_Osimps_I1_J,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( multiset2 @ A @ ( e @ A ) )
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % multiset.simps(1)
% 0.14/0.35 thf(fact_20_sndI,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,X: product_prod @ A @ B,Y: A,Z: B] :
% 0.14/0.35 ( ( X
% 0.14/0.35 = ( product_Pair @ A @ B @ Y @ Z ) )
% 0.14/0.35 => ( ( product_snd @ A @ B @ X )
% 0.14/0.35 = Z ) ) ).
% 0.14/0.35
% 0.14/0.35 % sndI
% 0.14/0.35 thf(fact_21_snd__eqD,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,X: B,Y: A,A2: A] :
% 0.14/0.35 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 0.14/0.35 = A2 )
% 0.14/0.35 => ( Y = A2 ) ) ).
% 0.14/0.35
% 0.14/0.35 % snd_eqD
% 0.14/0.35 thf(fact_22_snd__conv,axiom,
% 0.14/0.35 ! [Aa: $tType,A: $tType,X1: Aa,X2: A] :
% 0.14/0.35 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X1 @ X2 ) )
% 0.14/0.35 = X2 ) ).
% 0.14/0.35
% 0.14/0.35 % snd_conv
% 0.14/0.35 thf(fact_23_surj__pair,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 0.14/0.35 ? [X3: A,Y3: B] :
% 0.14/0.35 ( P
% 0.14/0.35 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 0.14/0.35
% 0.14/0.35 % surj_pair
% 0.14/0.35 thf(fact_24_prod__cases,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 0.14/0.35 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.14/0.35 => ( P2 @ P ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_cases
% 0.14/0.35 thf(fact_25_Pair__inject,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.14/0.35 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.14/0.35 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.14/0.35 => ~ ( ( A2 = A3 )
% 0.14/0.35 => ( B2 != B3 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % Pair_inject
% 0.14/0.35 thf(fact_26_prod__cases3,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.14/0.35 ~ ! [A4: A,B4: B,C2: C] :
% 0.14/0.35 ( Y
% 0.14/0.35 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_cases3
% 0.14/0.35 thf(fact_27_prod__cases4,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.14/0.35 ~ ! [A4: A,B4: B,C2: C,D2: D] :
% 0.14/0.35 ( Y
% 0.14/0.35 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_cases4
% 0.14/0.35 thf(fact_28_prod__cases5,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.14/0.35 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E] :
% 0.14/0.35 ( Y
% 0.14/0.35 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_cases5
% 0.14/0.35 thf(fact_29_prod__cases6,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 0.14/0.35 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F] :
% 0.14/0.35 ( Y
% 0.14/0.35 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_cases6
% 0.14/0.35 thf(fact_30_prod__cases7,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.14/0.35 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F,G2: G] :
% 0.14/0.35 ( Y
% 0.14/0.35 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_cases7
% 0.14/0.35 thf(fact_31_prod__induct3,axiom,
% 0.14/0.35 ! [C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.14/0.35 ( ! [A4: A,B4: B,C2: C] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 0.14/0.35 => ( P2 @ X ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_induct3
% 0.14/0.35 thf(fact_32_prod__induct4,axiom,
% 0.14/0.35 ! [D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.14/0.35 ( ! [A4: A,B4: B,C2: C,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.14/0.35 => ( P2 @ X ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_induct4
% 0.14/0.35 thf(fact_33_prod__induct5,axiom,
% 0.14/0.35 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.14/0.35 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.14/0.35 => ( P2 @ X ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_induct5
% 0.14/0.35 thf(fact_34_prod__induct6,axiom,
% 0.14/0.35 ! [F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 0.14/0.35 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 0.14/0.35 => ( P2 @ X ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_induct6
% 0.14/0.35 thf(fact_35_prod__induct7,axiom,
% 0.14/0.35 ! [G: $tType,F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.14/0.35 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F,G2: G] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 0.14/0.35 => ( P2 @ X ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_induct7
% 0.14/0.35 thf(fact_36_old_Oprod_Oexhaust,axiom,
% 0.14/0.35 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.14/0.35 ~ ! [A4: A,B4: B] :
% 0.14/0.35 ( Y
% 0.14/0.35 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 0.14/0.35
% 0.14/0.35 % old.prod.exhaust
% 0.14/0.35 thf(fact_37_old_Oprod_Oinducts,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.14/0.35 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.14/0.35 => ( P2 @ Prod ) ) ).
% 0.14/0.35
% 0.14/0.35 % old.prod.inducts
% 0.14/0.35 thf(fact_38_HS_Omultiset__empty,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ( ( multiset2 @ A @ ( e @ A ) )
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % HS.multiset_empty
% 0.14/0.35 thf(fact_39_surjective__pairing,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,T3: product_prod @ A @ B] :
% 0.14/0.35 ( T3
% 0.14/0.35 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T3 ) @ ( product_snd @ A @ B @ T3 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % surjective_pairing
% 0.14/0.35 thf(fact_40_prod_Oexhaust__sel,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.14/0.35 ( Prod
% 0.14/0.35 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod.exhaust_sel
% 0.14/0.35 thf(fact_41_prod__eq__iff,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType] :
% 0.14/0.35 ( ( ^ [Y4: product_prod @ A @ B,Z2: product_prod @ A @ B] : ( Y4 = Z2 ) )
% 0.14/0.35 = ( ^ [S: product_prod @ A @ B,T4: product_prod @ A @ B] :
% 0.14/0.35 ( ( ( product_fst @ A @ B @ S )
% 0.14/0.35 = ( product_fst @ A @ B @ T4 ) )
% 0.14/0.35 & ( ( product_snd @ A @ B @ S )
% 0.14/0.35 = ( product_snd @ A @ B @ T4 ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_eq_iff
% 0.14/0.35 thf(fact_42_prod_Oexpand,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 0.14/0.35 ( ( ( ( product_fst @ A @ B @ Prod )
% 0.14/0.35 = ( product_fst @ A @ B @ Prod2 ) )
% 0.14/0.35 & ( ( product_snd @ A @ B @ Prod )
% 0.14/0.35 = ( product_snd @ A @ B @ Prod2 ) ) )
% 0.14/0.35 => ( Prod = Prod2 ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod.expand
% 0.14/0.35 thf(fact_43_prod__eqI,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,P: product_prod @ A @ B,Q: product_prod @ A @ B] :
% 0.14/0.35 ( ( ( product_fst @ A @ B @ P )
% 0.14/0.35 = ( product_fst @ A @ B @ Q ) )
% 0.14/0.35 => ( ( ( product_snd @ A @ B @ P )
% 0.14/0.35 = ( product_snd @ A @ B @ Q ) )
% 0.14/0.35 => ( P = Q ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % prod_eqI
% 0.14/0.35 thf(fact_44_is__heap_Ocases,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ! [X: tree @ A] :
% 0.14/0.35 ( ( X
% 0.14/0.35 != ( e @ A ) )
% 0.14/0.35 => ( ! [V3: A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( e @ A ) @ ( e @ A ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 0.14/0.35 => ~ ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % is_heap.cases
% 0.14/0.35 thf(fact_45_mem__Collect__eq,axiom,
% 0.14/0.35 ! [A: $tType,A2: A,P2: A > $o] :
% 0.14/0.35 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.14/0.35 = ( P2 @ A2 ) ) ).
% 0.14/0.35
% 0.14/0.35 % mem_Collect_eq
% 0.14/0.35 thf(fact_46_Collect__mem__eq,axiom,
% 0.14/0.35 ! [A: $tType,A5: set @ A] :
% 0.14/0.35 ( ( collect @ A
% 0.14/0.35 @ ^ [X4: A] : ( member @ A @ X4 @ A5 ) )
% 0.14/0.35 = A5 ) ).
% 0.14/0.35
% 0.14/0.35 % Collect_mem_eq
% 0.14/0.35 thf(fact_47_Collect__cong,axiom,
% 0.14/0.35 ! [A: $tType,P2: A > $o,Q2: A > $o] :
% 0.14/0.35 ( ! [X3: A] :
% 0.14/0.35 ( ( P2 @ X3 )
% 0.14/0.35 = ( Q2 @ X3 ) )
% 0.14/0.35 => ( ( collect @ A @ P2 )
% 0.14/0.35 = ( collect @ A @ Q2 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % Collect_cong
% 0.14/0.35 thf(fact_48_ext,axiom,
% 0.14/0.35 ! [B: $tType,A: $tType,F3: A > B,G3: A > B] :
% 0.14/0.35 ( ! [X3: A] :
% 0.14/0.35 ( ( F3 @ X3 )
% 0.14/0.35 = ( G3 @ X3 ) )
% 0.14/0.35 => ( F3 = G3 ) ) ).
% 0.14/0.35
% 0.14/0.35 % ext
% 0.14/0.35 thf(fact_49_Tree_Oexhaust,axiom,
% 0.14/0.35 ! [A: $tType,Y: tree @ A] :
% 0.14/0.35 ( ( Y
% 0.14/0.35 != ( e @ A ) )
% 0.14/0.35 => ~ ! [X212: A,X222: tree @ A,X232: tree @ A] :
% 0.14/0.35 ( Y
% 0.14/0.35 != ( t @ A @ X212 @ X222 @ X232 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % Tree.exhaust
% 0.14/0.35 thf(fact_50_Tree_Oinduct,axiom,
% 0.14/0.35 ! [A: $tType,P2: ( tree @ A ) > $o,Tree: tree @ A] :
% 0.14/0.35 ( ( P2 @ ( e @ A ) )
% 0.14/0.35 => ( ! [X12: A,X24: tree @ A,X32: tree @ A] :
% 0.14/0.35 ( ( P2 @ X24 )
% 0.14/0.35 => ( ( P2 @ X32 )
% 0.14/0.35 => ( P2 @ ( t @ A @ X12 @ X24 @ X32 ) ) ) )
% 0.14/0.35 => ( P2 @ Tree ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % Tree.induct
% 0.14/0.35 thf(fact_51_Tree_Odistinct_I1_J,axiom,
% 0.14/0.35 ! [A: $tType,X21: A,X22: tree @ A,X23: tree @ A] :
% 0.14/0.35 ( ( e @ A )
% 0.14/0.35 != ( t @ A @ X21 @ X22 @ X23 ) ) ).
% 0.14/0.35
% 0.14/0.35 % Tree.distinct(1)
% 0.14/0.35 thf(fact_52_removeLeaf_Oinduct,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ! [P2: ( tree @ A ) > $o,A0: tree @ A] :
% 0.14/0.35 ( ! [V3: A] : ( P2 @ ( t @ A @ V3 @ ( e @ A ) @ ( e @ A ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 0.14/0.35 => ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 0.14/0.35 => ( P2 @ ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 0.14/0.35 => ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 0.14/0.35 => ( P2 @ ( t @ A @ V3 @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 0.14/0.35 ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 0.14/0.35 => ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 0.14/0.35 => ( P2 @ ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) )
% 0.14/0.35 => ( ! [V3: A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( ( P2 @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) )
% 0.14/0.35 => ( ( P2 @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) )
% 0.14/0.35 => ( P2 @ ( t @ A @ V3 @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) )
% 0.14/0.35 => ( ( P2 @ ( e @ A ) )
% 0.14/0.35 => ( P2 @ A0 ) ) ) ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % removeLeaf.induct
% 0.14/0.35 thf(fact_53_removeLeaf_Ocases,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ! [X: tree @ A] :
% 0.14/0.35 ( ! [V3: A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( e @ A ) @ ( e @ A ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.14/0.35 => ( ! [V3: A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.14/0.35 => ( X
% 0.14/0.35 = ( e @ A ) ) ) ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % removeLeaf.cases
% 0.14/0.35 thf(fact_54_siftDown_Ocases,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ! [X: tree @ A] :
% 0.14/0.35 ( ( X
% 0.14/0.35 != ( e @ A ) )
% 0.14/0.35 => ( ! [V3: A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( e @ A ) @ ( e @ A ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 0.14/0.35 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.14/0.35 => ~ ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 0.14/0.35 ( X
% 0.14/0.35 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % siftDown.cases
% 0.14/0.35 thf(fact_55_removeLeaf_Osimps_I2_J,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.14/0.35 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 0.14/0.35 = ( product_Pair @ A @ ( tree @ A ) @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( t @ A @ V @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( e @ A ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % removeLeaf.simps(2)
% 0.14/0.35 thf(fact_56_removeLeaf_Osimps_I3_J,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( linorder @ A )
% 0.14/0.35 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.14/0.35 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.35 = ( product_Pair @ A @ ( tree @ A ) @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( t @ A @ V @ ( e @ A ) @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % removeLeaf.simps(3)
% 0.14/0.35 thf(fact_57_union__mset__add__mset__left,axiom,
% 0.14/0.35 ! [A: $tType,A2: A,A5: multiset @ A,B5: multiset @ A] :
% 0.14/0.35 ( ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ A2 @ A5 ) @ B5 )
% 0.14/0.35 = ( add_mset @ A @ A2 @ ( plus_plus @ ( multiset @ A ) @ A5 @ B5 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % union_mset_add_mset_left
% 0.14/0.35 thf(fact_58_union__mset__add__mset__right,axiom,
% 0.14/0.35 ! [A: $tType,A5: multiset @ A,A2: A,B5: multiset @ A] :
% 0.14/0.35 ( ( plus_plus @ ( multiset @ A ) @ A5 @ ( add_mset @ A @ A2 @ B5 ) )
% 0.14/0.35 = ( add_mset @ A @ A2 @ ( plus_plus @ ( multiset @ A ) @ A5 @ B5 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % union_mset_add_mset_right
% 0.14/0.35 thf(fact_59_single__eq__single,axiom,
% 0.14/0.35 ! [A: $tType,A2: A,B2: A] :
% 0.14/0.35 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.35 = ( add_mset @ A @ B2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.14/0.35 = ( A2 = B2 ) ) ).
% 0.14/0.35
% 0.14/0.35 % single_eq_single
% 0.14/0.35 thf(fact_60_add__mset__eq__single,axiom,
% 0.14/0.35 ! [A: $tType,B2: A,M: multiset @ A,A2: A] :
% 0.14/0.35 ( ( ( add_mset @ A @ B2 @ M )
% 0.14/0.35 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.14/0.35 = ( ( B2 = A2 )
% 0.14/0.35 & ( M
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % add_mset_eq_single
% 0.14/0.35 thf(fact_61_single__eq__add__mset,axiom,
% 0.14/0.35 ! [A: $tType,A2: A,B2: A,M: multiset @ A] :
% 0.14/0.35 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.35 = ( add_mset @ A @ B2 @ M ) )
% 0.14/0.35 = ( ( B2 = A2 )
% 0.14/0.35 & ( M
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % single_eq_add_mset
% 0.14/0.35 thf(fact_62_add__mset__eq__singleton__iff,axiom,
% 0.14/0.35 ! [A: $tType,X: A,M: multiset @ A,Y: A] :
% 0.14/0.35 ( ( ( add_mset @ A @ X @ M )
% 0.14/0.35 = ( add_mset @ A @ Y @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.14/0.35 = ( ( M
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.35 & ( X = Y ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % add_mset_eq_singleton_iff
% 0.14/0.35 thf(fact_63_empty__eq__union,axiom,
% 0.14/0.35 ! [A: $tType,M: multiset @ A,N: multiset @ A] :
% 0.14/0.35 ( ( ( zero_zero @ ( multiset @ A ) )
% 0.14/0.35 = ( plus_plus @ ( multiset @ A ) @ M @ N ) )
% 0.14/0.35 = ( ( M
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.35 & ( N
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % empty_eq_union
% 0.14/0.35 thf(fact_64_union__eq__empty,axiom,
% 0.14/0.35 ! [A: $tType,M: multiset @ A,N: multiset @ A] :
% 0.14/0.35 ( ( ( plus_plus @ ( multiset @ A ) @ M @ N )
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.35 = ( ( M
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.35 & ( N
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % union_eq_empty
% 0.14/0.35 thf(fact_65_subset__mset_Oadd__eq__0__iff__both__eq__0,axiom,
% 0.14/0.35 ! [A: $tType,X: multiset @ A,Y: multiset @ A] :
% 0.14/0.35 ( ( ( plus_plus @ ( multiset @ A ) @ X @ Y )
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.35 = ( ( X
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.35 & ( Y
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % subset_mset.add_eq_0_iff_both_eq_0
% 0.14/0.35 thf(fact_66_subset__mset_Ozero__eq__add__iff__both__eq__0,axiom,
% 0.14/0.35 ! [A: $tType,X: multiset @ A,Y: multiset @ A] :
% 0.14/0.35 ( ( ( zero_zero @ ( multiset @ A ) )
% 0.14/0.35 = ( plus_plus @ ( multiset @ A ) @ X @ Y ) )
% 0.14/0.35 = ( ( X
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.35 & ( Y
% 0.14/0.35 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % subset_mset.zero_eq_add_iff_both_eq_0
% 0.14/0.35 thf(fact_67_add_Oleft__neutral,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( monoid_add @ A )
% 0.14/0.35 => ! [A2: A] :
% 0.14/0.35 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.14/0.35 = A2 ) ) ).
% 0.14/0.35
% 0.14/0.35 % add.left_neutral
% 0.14/0.35 thf(fact_68_add__right__cancel,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( cancel_semigroup_add @ A )
% 0.14/0.35 => ! [B2: A,A2: A,C3: A] :
% 0.14/0.35 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.14/0.35 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.14/0.35 = ( B2 = C3 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % add_right_cancel
% 0.14/0.35 thf(fact_69_add__left__cancel,axiom,
% 0.14/0.35 ! [A: $tType] :
% 0.14/0.35 ( ( cancel_semigroup_add @ A )
% 0.14/0.35 => ! [A2: A,B2: A,C3: A] :
% 0.14/0.35 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.14/0.35 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.14/0.35 = ( B2 = C3 ) ) ) ).
% 0.14/0.35
% 0.14/0.35 % add_left_cancel
% 0.14/0.35 thf(fact_70_multi__self__add__other__not__self,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ A,X: A] :
% 0.14/0.36 ( M
% 0.14/0.36 != ( add_mset @ A @ X @ M ) ) ).
% 0.14/0.36
% 0.14/0.36 % multi_self_add_other_not_self
% 0.14/0.36 thf(fact_71_add__mset__add__mset__same__iff,axiom,
% 0.14/0.36 ! [A: $tType,A2: A,A5: multiset @ A,B5: multiset @ A] :
% 0.14/0.36 ( ( ( add_mset @ A @ A2 @ A5 )
% 0.14/0.36 = ( add_mset @ A @ A2 @ B5 ) )
% 0.14/0.36 = ( A5 = B5 ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_mset_add_mset_same_iff
% 0.14/0.36 thf(fact_72_zero__eq__add__iff__both__eq__0,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( canoni770627133id_add @ A )
% 0.14/0.36 => ! [X: A,Y: A] :
% 0.14/0.36 ( ( ( zero_zero @ A )
% 0.14/0.36 = ( plus_plus @ A @ X @ Y ) )
% 0.14/0.36 = ( ( X
% 0.14/0.36 = ( zero_zero @ A ) )
% 0.14/0.36 & ( Y
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % zero_eq_add_iff_both_eq_0
% 0.14/0.36 thf(fact_73_add__eq__0__iff__both__eq__0,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( canoni770627133id_add @ A )
% 0.14/0.36 => ! [X: A,Y: A] :
% 0.14/0.36 ( ( ( plus_plus @ A @ X @ Y )
% 0.14/0.36 = ( zero_zero @ A ) )
% 0.14/0.36 = ( ( X
% 0.14/0.36 = ( zero_zero @ A ) )
% 0.14/0.36 & ( Y
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_eq_0_iff_both_eq_0
% 0.14/0.36 thf(fact_74_add__cancel__right__right,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( cancel1352612707id_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( A2
% 0.14/0.36 = ( plus_plus @ A @ A2 @ B2 ) )
% 0.14/0.36 = ( B2
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_cancel_right_right
% 0.14/0.36 thf(fact_75_add__cancel__right__left,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( cancel1352612707id_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( A2
% 0.14/0.36 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.14/0.36 = ( B2
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_cancel_right_left
% 0.14/0.36 thf(fact_76_add__cancel__left__right,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( cancel1352612707id_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.14/0.36 = A2 )
% 0.14/0.36 = ( B2
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_cancel_left_right
% 0.14/0.36 thf(fact_77_add__cancel__left__left,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( cancel1352612707id_add @ A )
% 0.14/0.36 => ! [B2: A,A2: A] :
% 0.14/0.36 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.14/0.36 = A2 )
% 0.14/0.36 = ( B2
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_cancel_left_left
% 0.14/0.36 thf(fact_78_double__zero__sym,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linord219039673up_add @ A )
% 0.14/0.36 => ! [A2: A] :
% 0.14/0.36 ( ( ( zero_zero @ A )
% 0.14/0.36 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.14/0.36 = ( A2
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % double_zero_sym
% 0.14/0.36 thf(fact_79_double__zero,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linord219039673up_add @ A )
% 0.14/0.36 => ! [A2: A] :
% 0.14/0.36 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.14/0.36 = ( zero_zero @ A ) )
% 0.14/0.36 = ( A2
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % double_zero
% 0.14/0.36 thf(fact_80_add_Oright__neutral,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( monoid_add @ A )
% 0.14/0.36 => ! [A2: A] :
% 0.14/0.36 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.14/0.36 = A2 ) ) ).
% 0.14/0.36
% 0.14/0.36 % add.right_neutral
% 0.14/0.36 thf(fact_81_zero__reorient,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( zero @ A )
% 0.14/0.36 => ! [X: A] :
% 0.14/0.36 ( ( ( zero_zero @ A )
% 0.14/0.36 = X )
% 0.14/0.36 = ( X
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % zero_reorient
% 0.14/0.36 thf(fact_82_add__right__imp__eq,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( cancel_semigroup_add @ A )
% 0.14/0.36 => ! [B2: A,A2: A,C3: A] :
% 0.14/0.36 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.14/0.36 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.14/0.36 => ( B2 = C3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_right_imp_eq
% 0.14/0.36 thf(fact_83_add__left__imp__eq,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( cancel_semigroup_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A,C3: A] :
% 0.14/0.36 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.14/0.36 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.14/0.36 => ( B2 = C3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_left_imp_eq
% 0.14/0.36 thf(fact_84_add_Oleft__commute,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ab_semigroup_add @ A )
% 0.14/0.36 => ! [B2: A,A2: A,C3: A] :
% 0.14/0.36 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C3 ) )
% 0.14/0.36 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add.left_commute
% 0.14/0.36 thf(fact_85_add_Ocommute,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ab_semigroup_add @ A )
% 0.14/0.36 => ( ( plus_plus @ A )
% 0.14/0.36 = ( ^ [A6: A,B6: A] : ( plus_plus @ A @ B6 @ A6 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add.commute
% 0.14/0.36 thf(fact_86_add_Oright__cancel,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( group_add @ A )
% 0.14/0.36 => ! [B2: A,A2: A,C3: A] :
% 0.14/0.36 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.14/0.36 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.14/0.36 = ( B2 = C3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add.right_cancel
% 0.14/0.36 thf(fact_87_add_Oleft__cancel,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( group_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A,C3: A] :
% 0.14/0.36 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.14/0.36 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.14/0.36 = ( B2 = C3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add.left_cancel
% 0.14/0.36 thf(fact_88_add_Oassoc,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( semigroup_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A,C3: A] :
% 0.14/0.36 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 0.14/0.36 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add.assoc
% 0.14/0.36 thf(fact_89_group__cancel_Oadd2,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( comm_monoid_add @ A )
% 0.14/0.36 => ! [B5: A,K: A,B2: A,A2: A] :
% 0.14/0.36 ( ( B5
% 0.14/0.36 = ( plus_plus @ A @ K @ B2 ) )
% 0.14/0.36 => ( ( plus_plus @ A @ A2 @ B5 )
% 0.14/0.36 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % group_cancel.add2
% 0.14/0.36 thf(fact_90_group__cancel_Oadd1,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( comm_monoid_add @ A )
% 0.14/0.36 => ! [A5: A,K: A,A2: A,B2: A] :
% 0.14/0.36 ( ( A5
% 0.14/0.36 = ( plus_plus @ A @ K @ A2 ) )
% 0.14/0.36 => ( ( plus_plus @ A @ A5 @ B2 )
% 0.14/0.36 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % group_cancel.add1
% 0.14/0.36 thf(fact_91_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere779506340up_add @ A )
% 0.14/0.36 => ! [I: A,J: A,K: A,L: A] :
% 0.14/0.36 ( ( ( I = J )
% 0.14/0.36 & ( K = L ) )
% 0.14/0.36 => ( ( plus_plus @ A @ I @ K )
% 0.14/0.36 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_mono_thms_linordered_semiring(4)
% 0.14/0.36 thf(fact_92_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ab_semigroup_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A,C3: A] :
% 0.14/0.36 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 0.14/0.36 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % ab_semigroup_add_class.add_ac(1)
% 0.14/0.36 thf(fact_93_multi__union__self__other__eq,axiom,
% 0.14/0.36 ! [A: $tType,A5: multiset @ A,X5: multiset @ A,Y5: multiset @ A] :
% 0.14/0.36 ( ( ( plus_plus @ ( multiset @ A ) @ A5 @ X5 )
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ A5 @ Y5 ) )
% 0.14/0.36 => ( X5 = Y5 ) ) ).
% 0.14/0.36
% 0.14/0.36 % multi_union_self_other_eq
% 0.14/0.36 thf(fact_94_union__right__cancel,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ A,K2: multiset @ A,N: multiset @ A] :
% 0.14/0.36 ( ( ( plus_plus @ ( multiset @ A ) @ M @ K2 )
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ N @ K2 ) )
% 0.14/0.36 = ( M = N ) ) ).
% 0.14/0.36
% 0.14/0.36 % union_right_cancel
% 0.14/0.36 thf(fact_95_union__left__cancel,axiom,
% 0.14/0.36 ! [A: $tType,K2: multiset @ A,M: multiset @ A,N: multiset @ A] :
% 0.14/0.36 ( ( ( plus_plus @ ( multiset @ A ) @ K2 @ M )
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ K2 @ N ) )
% 0.14/0.36 = ( M = N ) ) ).
% 0.14/0.36
% 0.14/0.36 % union_left_cancel
% 0.14/0.36 thf(fact_96_union__commute,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( plus_plus @ ( multiset @ A ) )
% 0.14/0.36 = ( ^ [M2: multiset @ A,N2: multiset @ A] : ( plus_plus @ ( multiset @ A ) @ N2 @ M2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % union_commute
% 0.14/0.36 thf(fact_97_union__lcomm,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ A,N: multiset @ A,K2: multiset @ A] :
% 0.14/0.36 ( ( plus_plus @ ( multiset @ A ) @ M @ ( plus_plus @ ( multiset @ A ) @ N @ K2 ) )
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ N @ ( plus_plus @ ( multiset @ A ) @ M @ K2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % union_lcomm
% 0.14/0.36 thf(fact_98_union__assoc,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ A,N: multiset @ A,K2: multiset @ A] :
% 0.14/0.36 ( ( plus_plus @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ M @ N ) @ K2 )
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ M @ ( plus_plus @ ( multiset @ A ) @ N @ K2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % union_assoc
% 0.14/0.36 thf(fact_99_add__mset__commute,axiom,
% 0.14/0.36 ! [A: $tType,X: A,Y: A,M: multiset @ A] :
% 0.14/0.36 ( ( add_mset @ A @ X @ ( add_mset @ A @ Y @ M ) )
% 0.14/0.36 = ( add_mset @ A @ Y @ ( add_mset @ A @ X @ M ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_mset_commute
% 0.14/0.36 thf(fact_100_add__eq__conv__ex,axiom,
% 0.14/0.36 ! [A: $tType,A2: A,M: multiset @ A,B2: A,N: multiset @ A] :
% 0.14/0.36 ( ( ( add_mset @ A @ A2 @ M )
% 0.14/0.36 = ( add_mset @ A @ B2 @ N ) )
% 0.14/0.36 = ( ( ( M = N )
% 0.14/0.36 & ( A2 = B2 ) )
% 0.14/0.36 | ? [K3: multiset @ A] :
% 0.14/0.36 ( ( M
% 0.14/0.36 = ( add_mset @ A @ B2 @ K3 ) )
% 0.14/0.36 & ( N
% 0.14/0.36 = ( add_mset @ A @ A2 @ K3 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_eq_conv_ex
% 0.14/0.36 thf(fact_101_add_Ogroup__left__neutral,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( group_add @ A )
% 0.14/0.36 => ! [A2: A] :
% 0.14/0.36 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.14/0.36 = A2 ) ) ).
% 0.14/0.36
% 0.14/0.36 % add.group_left_neutral
% 0.14/0.36 thf(fact_102_add_Ocomm__neutral,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( comm_monoid_add @ A )
% 0.14/0.36 => ! [A2: A] :
% 0.14/0.36 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.14/0.36 = A2 ) ) ).
% 0.14/0.36
% 0.14/0.36 % add.comm_neutral
% 0.14/0.36 thf(fact_103_comm__monoid__add__class_Oadd__0,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( comm_monoid_add @ A )
% 0.14/0.36 => ! [A2: A] :
% 0.14/0.36 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.14/0.36 = A2 ) ) ).
% 0.14/0.36
% 0.14/0.36 % comm_monoid_add_class.add_0
% 0.14/0.36 thf(fact_104_empty__neutral_I1_J,axiom,
% 0.14/0.36 ! [A: $tType,X: multiset @ A] :
% 0.14/0.36 ( ( plus_plus @ ( multiset @ A ) @ ( zero_zero @ ( multiset @ A ) ) @ X )
% 0.14/0.36 = X ) ).
% 0.14/0.36
% 0.14/0.36 % empty_neutral(1)
% 0.14/0.36 thf(fact_105_empty__neutral_I2_J,axiom,
% 0.14/0.36 ! [A: $tType,X: multiset @ A] :
% 0.14/0.36 ( ( plus_plus @ ( multiset @ A ) @ X @ ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 = X ) ).
% 0.14/0.36
% 0.14/0.36 % empty_neutral(2)
% 0.14/0.36 thf(fact_106_multi__nonempty__split,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ A] :
% 0.14/0.36 ( ( M
% 0.14/0.36 != ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 => ? [A7: multiset @ A,A4: A] :
% 0.14/0.36 ( M
% 0.14/0.36 = ( add_mset @ A @ A4 @ A7 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multi_nonempty_split
% 0.14/0.36 thf(fact_107_empty__not__add__mset,axiom,
% 0.14/0.36 ! [A: $tType,A2: A,A5: multiset @ A] :
% 0.14/0.36 ( ( zero_zero @ ( multiset @ A ) )
% 0.14/0.36 != ( add_mset @ A @ A2 @ A5 ) ) ).
% 0.14/0.36
% 0.14/0.36 % empty_not_add_mset
% 0.14/0.36 thf(fact_108_multiset__induct2,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,P2: ( multiset @ A ) > ( multiset @ B ) > $o,M: multiset @ A,N: multiset @ B] :
% 0.14/0.36 ( ( P2 @ ( zero_zero @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ B ) ) )
% 0.14/0.36 => ( ! [A4: A,M3: multiset @ A,N3: multiset @ B] :
% 0.14/0.36 ( ( P2 @ M3 @ N3 )
% 0.14/0.36 => ( P2 @ ( add_mset @ A @ A4 @ M3 ) @ N3 ) )
% 0.14/0.36 => ( ! [A4: B,M3: multiset @ A,N3: multiset @ B] :
% 0.14/0.36 ( ( P2 @ M3 @ N3 )
% 0.14/0.36 => ( P2 @ M3 @ ( add_mset @ B @ A4 @ N3 ) ) )
% 0.14/0.36 => ( P2 @ M @ N ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multiset_induct2
% 0.14/0.36 thf(fact_109_multiset__induct,axiom,
% 0.14/0.36 ! [A: $tType,P2: ( multiset @ A ) > $o,M: multiset @ A] :
% 0.14/0.36 ( ( P2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 => ( ! [X3: A,M3: multiset @ A] :
% 0.14/0.36 ( ( P2 @ M3 )
% 0.14/0.36 => ( P2 @ ( add_mset @ A @ X3 @ M3 ) ) )
% 0.14/0.36 => ( P2 @ M ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multiset_induct
% 0.14/0.36 thf(fact_110_multiset__cases,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ A] :
% 0.14/0.36 ( ( M
% 0.14/0.36 != ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 => ~ ! [X3: A,N3: multiset @ A] :
% 0.14/0.36 ( M
% 0.14/0.36 != ( add_mset @ A @ X3 @ N3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multiset_cases
% 0.14/0.36 thf(fact_111_add__mset__add__single,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( add_mset @ A )
% 0.14/0.36 = ( ^ [A6: A,A8: multiset @ A] : ( plus_plus @ ( multiset @ A ) @ A8 @ ( add_mset @ A @ A6 @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_mset_add_single
% 0.14/0.36 thf(fact_112_union__is__single,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ A,N: multiset @ A,A2: A] :
% 0.14/0.36 ( ( ( plus_plus @ ( multiset @ A ) @ M @ N )
% 0.14/0.36 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.14/0.36 = ( ( ( M
% 0.14/0.36 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.14/0.36 & ( N
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) ) )
% 0.14/0.36 | ( ( M
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 & ( N
% 0.14/0.36 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % union_is_single
% 0.14/0.36 thf(fact_113_single__is__union,axiom,
% 0.14/0.36 ! [A: $tType,A2: A,M: multiset @ A,N: multiset @ A] :
% 0.14/0.36 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ M @ N ) )
% 0.14/0.36 = ( ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 = M )
% 0.14/0.36 & ( N
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) ) )
% 0.14/0.36 | ( ( M
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 & ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 = N ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % single_is_union
% 0.14/0.36 thf(fact_114_old_Oprod_Orec,axiom,
% 0.14/0.36 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.14/0.36 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.14/0.36 = ( F1 @ A2 @ B2 ) ) ).
% 0.14/0.36
% 0.14/0.36 % old.prod.rec
% 0.14/0.36 thf(fact_115_exI__realizer,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,P2: A > B > $o,Y: A,X: B] :
% 0.14/0.36 ( ( P2 @ Y @ X )
% 0.14/0.36 => ( P2 @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % exI_realizer
% 0.14/0.36 thf(fact_116_conjI__realizer,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,P2: A > $o,P: A,Q2: B > $o,Q: B] :
% 0.14/0.36 ( ( P2 @ P )
% 0.14/0.36 => ( ( Q2 @ Q )
% 0.14/0.36 => ( ( P2 @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P @ Q ) ) )
% 0.14/0.36 & ( Q2 @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P @ Q ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % conjI_realizer
% 0.14/0.36 thf(fact_117_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,P2: A > B > $o,X: A,Y: B,A2: product_prod @ A @ B] :
% 0.14/0.36 ( ( P2 @ X @ Y )
% 0.14/0.36 => ( ( A2
% 0.14/0.36 = ( product_Pair @ A @ B @ X @ Y ) )
% 0.14/0.36 => ( P2 @ ( product_fst @ A @ B @ A2 ) @ ( product_snd @ A @ B @ A2 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % BNF_Greatest_Fixpoint.subst_Pair
% 0.14/0.36 thf(fact_118_Multiset_Ois__empty__def,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( is_empty @ A )
% 0.14/0.36 = ( ^ [A8: multiset @ A] :
% 0.14/0.36 ( A8
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Multiset.is_empty_def
% 0.14/0.36 thf(fact_119_exE__realizer_H,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,P2: A > B > $o,P: product_prod @ B @ A] :
% 0.14/0.36 ( ( P2 @ ( product_snd @ B @ A @ P ) @ ( product_fst @ B @ A @ P ) )
% 0.14/0.36 => ~ ! [X3: B,Y3: A] :
% 0.14/0.36 ~ ( P2 @ Y3 @ X3 ) ) ).
% 0.14/0.36
% 0.14/0.36 % exE_realizer'
% 0.14/0.36 thf(fact_120_eq__snd__iff,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,B2: A,P: product_prod @ B @ A] :
% 0.14/0.36 ( ( B2
% 0.14/0.36 = ( product_snd @ B @ A @ P ) )
% 0.14/0.36 = ( ? [A6: B] :
% 0.14/0.36 ( P
% 0.14/0.36 = ( product_Pair @ B @ A @ A6 @ B2 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % eq_snd_iff
% 0.14/0.36 thf(fact_121_eq__fst__iff,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,A2: A,P: product_prod @ A @ B] :
% 0.14/0.36 ( ( A2
% 0.14/0.36 = ( product_fst @ A @ B @ P ) )
% 0.14/0.36 = ( ? [B6: B] :
% 0.14/0.36 ( P
% 0.14/0.36 = ( product_Pair @ A @ B @ A2 @ B6 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % eq_fst_iff
% 0.14/0.36 thf(fact_122_verit__sum__simplify,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( cancel1352612707id_add @ A )
% 0.14/0.36 => ! [A2: A] :
% 0.14/0.36 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.14/0.36 = A2 ) ) ).
% 0.14/0.36
% 0.14/0.36 % verit_sum_simplify
% 0.14/0.36 thf(fact_123_add__0__iff,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( semiri456707255roduct @ A )
% 0.14/0.36 => ! [B2: A,A2: A] :
% 0.14/0.36 ( ( B2
% 0.14/0.36 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.14/0.36 = ( A2
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_0_iff
% 0.14/0.36 thf(fact_124_HS_Ois__empty__as__list,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [E3: tree @ A] :
% 0.14/0.36 ( ( heapIm721255937_empty @ A @ E3 )
% 0.14/0.36 => ( ( multiset2 @ A @ E3 )
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % HS.is_empty_as_list
% 0.14/0.36 thf(fact_125_add__mset__replicate__mset__safe,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,M: multiset @ B,A2: B] :
% 0.14/0.36 ( ( nO_MATCH @ ( multiset @ A ) @ ( multiset @ B ) @ ( zero_zero @ ( multiset @ A ) ) @ M )
% 0.14/0.36 => ( ( add_mset @ B @ A2 @ M )
% 0.14/0.36 = ( plus_plus @ ( multiset @ B ) @ ( add_mset @ B @ A2 @ ( zero_zero @ ( multiset @ B ) ) ) @ M ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_mset_replicate_mset_safe
% 0.14/0.36 thf(fact_126_HS_Ois__empty__empty,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( heapIm721255937_empty @ A @ ( e @ A ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % HS.is_empty_empty
% 0.14/0.36 thf(fact_127_hs__is__empty__def,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( heapIm721255937_empty @ A )
% 0.14/0.36 = ( ^ [T4: tree @ A] :
% 0.14/0.36 ( T4
% 0.14/0.36 = ( e @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % hs_is_empty_def
% 0.14/0.36 thf(fact_128_HS_Ois__empty__inj,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [E3: tree @ A] :
% 0.14/0.36 ( ( heapIm721255937_empty @ A @ E3 )
% 0.14/0.36 => ( E3
% 0.14/0.36 = ( e @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % HS.is_empty_inj
% 0.14/0.36 thf(fact_129_prod_Oswap__def,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType] :
% 0.14/0.36 ( ( product_swap @ A @ B )
% 0.14/0.36 = ( ^ [P3: product_prod @ A @ B] : ( product_Pair @ B @ A @ ( product_snd @ A @ B @ P3 ) @ ( product_fst @ A @ B @ P3 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % prod.swap_def
% 0.14/0.36 thf(fact_130_removeLeaf__heap__is__heap,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [T3: tree @ A] :
% 0.14/0.36 ( ( is_heap @ A @ T3 )
% 0.14/0.36 => ( ( T3
% 0.14/0.36 != ( e @ A ) )
% 0.14/0.36 => ( is_heap @ A @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T3 ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % removeLeaf_heap_is_heap
% 0.14/0.36 thf(fact_131_NO__MATCH__cong,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType] :
% 0.14/0.36 ( ( nO_MATCH @ A @ B )
% 0.14/0.36 = ( nO_MATCH @ A @ B ) ) ).
% 0.14/0.36
% 0.14/0.36 % NO_MATCH_cong
% 0.14/0.36 thf(fact_132_NO__MATCH__def,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType] :
% 0.14/0.36 ( ( nO_MATCH @ A @ B )
% 0.14/0.36 = ( ^ [Pat: A,Val: B] : $true ) ) ).
% 0.14/0.36
% 0.14/0.36 % NO_MATCH_def
% 0.14/0.36 thf(fact_133_swap__swap,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,P: product_prod @ A @ B] :
% 0.14/0.36 ( ( product_swap @ B @ A @ ( product_swap @ A @ B @ P ) )
% 0.14/0.36 = P ) ).
% 0.14/0.36
% 0.14/0.36 % swap_swap
% 0.14/0.36 thf(fact_134_swap__simp,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,X: B,Y: A] :
% 0.14/0.36 ( ( product_swap @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 0.14/0.36 = ( product_Pair @ A @ B @ Y @ X ) ) ).
% 0.14/0.36
% 0.14/0.36 % swap_simp
% 0.14/0.36 thf(fact_135_snd__swap,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,X: product_prod @ A @ B] :
% 0.14/0.36 ( ( product_snd @ B @ A @ ( product_swap @ A @ B @ X ) )
% 0.14/0.36 = ( product_fst @ A @ B @ X ) ) ).
% 0.14/0.36
% 0.14/0.36 % snd_swap
% 0.14/0.36 thf(fact_136_fst__swap,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,X: product_prod @ B @ A] :
% 0.14/0.36 ( ( product_fst @ A @ B @ ( product_swap @ B @ A @ X ) )
% 0.14/0.36 = ( product_snd @ B @ A @ X ) ) ).
% 0.14/0.36
% 0.14/0.36 % fst_swap
% 0.14/0.36 thf(fact_137_is__heap_Osimps_I1_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( is_heap @ A @ ( e @ A ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % is_heap.simps(1)
% 0.14/0.36 thf(fact_138_is__heap_Osimps_I2_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [V: A] : ( is_heap @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % is_heap.simps(2)
% 0.14/0.36 thf(fact_139_removeLeaf__val__val,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [T3: tree @ A] :
% 0.14/0.36 ( ( ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T3 ) )
% 0.14/0.36 != ( e @ A ) )
% 0.14/0.36 => ( ( T3
% 0.14/0.36 != ( e @ A ) )
% 0.14/0.36 => ( ( val @ A @ T3 )
% 0.14/0.36 = ( val @ A @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T3 ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % removeLeaf_val_val
% 0.14/0.36 thf(fact_140_internal__case__prod__conv,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.14/0.36 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.14/0.36 = ( C3 @ A2 @ B2 ) ) ).
% 0.14/0.36
% 0.14/0.36 % internal_case_prod_conv
% 0.14/0.36 thf(fact_141_Heap__axioms__def,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( ( heap_axioms @ B @ A )
% 0.14/0.36 = ( ^ [Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),As_tree: B > ( tree @ A ),Remove_max: B > ( product_prod @ A @ B )] :
% 0.14/0.36 ( ! [L2: B] :
% 0.14/0.36 ( ( Multiset @ L2 )
% 0.14/0.36 = ( multiset2 @ A @ ( As_tree @ L2 ) ) )
% 0.14/0.36 & ! [I2: list @ A] : ( is_heap @ A @ ( As_tree @ ( Of_list @ I2 ) ) )
% 0.14/0.36 & ! [T4: B] :
% 0.14/0.36 ( ( ( As_tree @ T4 )
% 0.14/0.36 = ( e @ A ) )
% 0.14/0.36 = ( Is_empty @ T4 ) )
% 0.14/0.36 & ! [L2: B,M4: A,L3: B] :
% 0.14/0.36 ( ~ ( Is_empty @ L2 )
% 0.14/0.36 => ( ( ( product_Pair @ A @ B @ M4 @ L3 )
% 0.14/0.36 = ( Remove_max @ L2 ) )
% 0.14/0.36 => ( ( add_mset @ A @ M4 @ ( Multiset @ L3 ) )
% 0.14/0.36 = ( Multiset @ L2 ) ) ) )
% 0.14/0.36 & ! [L2: B,M4: A,L3: B] :
% 0.14/0.36 ( ~ ( Is_empty @ L2 )
% 0.14/0.36 => ( ( is_heap @ A @ ( As_tree @ L2 ) )
% 0.14/0.36 => ( ( ( product_Pair @ A @ B @ M4 @ L3 )
% 0.14/0.36 = ( Remove_max @ L2 ) )
% 0.14/0.36 => ( is_heap @ A @ ( As_tree @ L3 ) ) ) ) )
% 0.14/0.36 & ! [T4: B,M4: A,T5: B] :
% 0.14/0.36 ( ~ ( Is_empty @ T4 )
% 0.14/0.36 => ( ( ( product_Pair @ A @ B @ M4 @ T5 )
% 0.14/0.36 = ( Remove_max @ T4 ) )
% 0.14/0.36 => ( M4
% 0.14/0.36 = ( val @ A @ ( As_tree @ T4 ) ) ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap_axioms_def
% 0.14/0.36 thf(fact_142_Heap__axioms_Ointro,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Of_list2: ( list @ A ) > B,Is_empty2: B > $o,Remove_max2: B > ( product_prod @ A @ B )] :
% 0.14/0.36 ( ! [L4: B] :
% 0.14/0.36 ( ( Multiset2 @ L4 )
% 0.14/0.36 = ( multiset2 @ A @ ( As_tree2 @ L4 ) ) )
% 0.14/0.36 => ( ! [I3: list @ A] : ( is_heap @ A @ ( As_tree2 @ ( Of_list2 @ I3 ) ) )
% 0.14/0.36 => ( ! [T6: B] :
% 0.14/0.36 ( ( ( As_tree2 @ T6 )
% 0.14/0.36 = ( e @ A ) )
% 0.14/0.36 = ( Is_empty2 @ T6 ) )
% 0.14/0.36 => ( ! [L4: B,M5: A,L5: B] :
% 0.14/0.36 ( ~ ( Is_empty2 @ L4 )
% 0.14/0.36 => ( ( ( product_Pair @ A @ B @ M5 @ L5 )
% 0.14/0.36 = ( Remove_max2 @ L4 ) )
% 0.14/0.36 => ( ( add_mset @ A @ M5 @ ( Multiset2 @ L5 ) )
% 0.14/0.36 = ( Multiset2 @ L4 ) ) ) )
% 0.14/0.36 => ( ! [L4: B,M5: A,L5: B] :
% 0.14/0.36 ( ~ ( Is_empty2 @ L4 )
% 0.14/0.36 => ( ( is_heap @ A @ ( As_tree2 @ L4 ) )
% 0.14/0.36 => ( ( ( product_Pair @ A @ B @ M5 @ L5 )
% 0.14/0.36 = ( Remove_max2 @ L4 ) )
% 0.14/0.36 => ( is_heap @ A @ ( As_tree2 @ L5 ) ) ) ) )
% 0.14/0.36 => ( ! [T6: B,M5: A,T7: B] :
% 0.14/0.36 ( ~ ( Is_empty2 @ T6 )
% 0.14/0.36 => ( ( ( product_Pair @ A @ B @ M5 @ T7 )
% 0.14/0.36 = ( Remove_max2 @ T6 ) )
% 0.14/0.36 => ( M5
% 0.14/0.36 = ( val @ A @ ( As_tree2 @ T6 ) ) ) ) )
% 0.14/0.36 => ( heap_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 ) ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap_axioms.intro
% 0.14/0.36 thf(fact_143_val_Osimps,axiom,
% 0.14/0.36 ! [A: $tType,V: A,Uu: tree @ A,Uv: tree @ A] :
% 0.14/0.36 ( ( val @ A @ ( t @ A @ V @ Uu @ Uv ) )
% 0.14/0.36 = V ) ).
% 0.14/0.36
% 0.14/0.36 % val.simps
% 0.14/0.36 thf(fact_144_is__heap_Osimps_I4_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.14/0.36 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 0.14/0.36 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 & ( is_heap @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % is_heap.simps(4)
% 0.14/0.36 thf(fact_145_is__heap_Osimps_I3_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.14/0.36 ( ( is_heap @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 & ( is_heap @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % is_heap.simps(3)
% 0.14/0.36 thf(fact_146_divides__aux__eq,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( unique1598680935umeral @ A )
% 0.14/0.36 => ! [Q: A,R: A] :
% 0.14/0.36 ( ( unique455577585es_aux @ A @ ( product_Pair @ A @ A @ Q @ R ) )
% 0.14/0.36 = ( R
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % divides_aux_eq
% 0.14/0.36 thf(fact_147_Heap_Oremove__max__is__heap,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),L: B,M6: A,L6: B] :
% 0.14/0.36 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.14/0.36 => ( ~ ( Is_empty2 @ L )
% 0.14/0.36 => ( ( is_heap @ A @ ( As_tree2 @ L ) )
% 0.14/0.36 => ( ( ( product_Pair @ A @ B @ M6 @ L6 )
% 0.14/0.36 = ( Remove_max2 @ L ) )
% 0.14/0.36 => ( is_heap @ A @ ( As_tree2 @ L6 ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap.remove_max_is_heap
% 0.14/0.36 thf(fact_148_le__zero__eq,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( canoni770627133id_add @ A )
% 0.14/0.36 => ! [N4: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ N4 @ ( zero_zero @ A ) )
% 0.14/0.36 = ( N4
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % le_zero_eq
% 0.14/0.36 thf(fact_149_add__le__cancel__right,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere236663937imp_le @ A )
% 0.14/0.36 => ! [A2: A,C3: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.14/0.36 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_le_cancel_right
% 0.14/0.36 thf(fact_150_add__le__cancel__left,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere236663937imp_le @ A )
% 0.14/0.36 => ! [C3: A,A2: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.14/0.36 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_le_cancel_left
% 0.14/0.36 thf(fact_151_add__le__same__cancel1,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere516151231imp_le @ A )
% 0.14/0.36 => ! [B2: A,A2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.14/0.36 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_le_same_cancel1
% 0.14/0.36 thf(fact_152_add__le__same__cancel2,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere516151231imp_le @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.14/0.36 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_le_same_cancel2
% 0.14/0.36 thf(fact_153_le__add__same__cancel1,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere516151231imp_le @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.14/0.36 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % le_add_same_cancel1
% 0.14/0.36 thf(fact_154_le__add__same__cancel2,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere516151231imp_le @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.14/0.36 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % le_add_same_cancel2
% 0.14/0.36 thf(fact_155_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linord219039673up_add @ A )
% 0.14/0.36 => ! [A2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.14/0.36 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % double_add_le_zero_iff_single_add_le_zero
% 0.14/0.36 thf(fact_156_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linord219039673up_add @ A )
% 0.14/0.36 => ! [A2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.14/0.36 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % zero_le_double_add_iff_zero_le_single_add
% 0.14/0.36 thf(fact_157_verit__la__disequality,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( A2 = B2 )
% 0.14/0.36 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 0.14/0.36 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % verit_la_disequality
% 0.14/0.36 thf(fact_158_add__le__imp__le__right,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere236663937imp_le @ A )
% 0.14/0.36 => ! [A2: A,C3: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.14/0.36 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_le_imp_le_right
% 0.14/0.36 thf(fact_159_add__le__imp__le__left,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere236663937imp_le @ A )
% 0.14/0.36 => ! [C3: A,A2: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.14/0.36 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_le_imp_le_left
% 0.14/0.36 thf(fact_160_le__iff__add,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( canoni770627133id_add @ A )
% 0.14/0.36 => ( ( ord_less_eq @ A )
% 0.14/0.36 = ( ^ [A6: A,B6: A] :
% 0.14/0.36 ? [C4: A] :
% 0.14/0.36 ( B6
% 0.14/0.36 = ( plus_plus @ A @ A6 @ C4 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % le_iff_add
% 0.14/0.36 thf(fact_161_add__right__mono,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere779506340up_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A,C3: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.14/0.36 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_right_mono
% 0.14/0.36 thf(fact_162_less__eqE,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( canoni770627133id_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.14/0.36 => ~ ! [C2: A] :
% 0.14/0.36 ( B2
% 0.14/0.36 != ( plus_plus @ A @ A2 @ C2 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % less_eqE
% 0.14/0.36 thf(fact_163_add__left__mono,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere779506340up_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A,C3: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.14/0.36 => ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_left_mono
% 0.14/0.36 thf(fact_164_add__mono,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere779506340up_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A,C3: A,D3: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.14/0.36 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 0.14/0.36 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_mono
% 0.14/0.36 thf(fact_165_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere779506340up_add @ A )
% 0.14/0.36 => ! [I: A,J: A,K: A,L: A] :
% 0.14/0.36 ( ( ( ord_less_eq @ A @ I @ J )
% 0.14/0.36 & ( ord_less_eq @ A @ K @ L ) )
% 0.14/0.36 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_mono_thms_linordered_semiring(1)
% 0.14/0.36 thf(fact_166_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere779506340up_add @ A )
% 0.14/0.36 => ! [I: A,J: A,K: A,L: A] :
% 0.14/0.36 ( ( ( I = J )
% 0.14/0.36 & ( ord_less_eq @ A @ K @ L ) )
% 0.14/0.36 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_mono_thms_linordered_semiring(2)
% 0.14/0.36 thf(fact_167_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere779506340up_add @ A )
% 0.14/0.36 => ! [I: A,J: A,K: A,L: A] :
% 0.14/0.36 ( ( ( ord_less_eq @ A @ I @ J )
% 0.14/0.36 & ( K = L ) )
% 0.14/0.36 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_mono_thms_linordered_semiring(3)
% 0.14/0.36 thf(fact_168_zero__le,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( canoni770627133id_add @ A )
% 0.14/0.36 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.14/0.36
% 0.14/0.36 % zero_le
% 0.14/0.36 thf(fact_169_add__decreasing,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere216010020id_add @ A )
% 0.14/0.36 => ! [A2: A,C3: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.14/0.36 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 0.14/0.36 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ B2 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_decreasing
% 0.14/0.36 thf(fact_170_add__increasing,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere216010020id_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A,C3: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.14/0.36 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.14/0.36 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C3 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_increasing
% 0.14/0.36 thf(fact_171_add__decreasing2,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere216010020id_add @ A )
% 0.14/0.36 => ! [C3: A,A2: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ C3 @ ( zero_zero @ A ) )
% 0.14/0.36 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.14/0.36 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ B2 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_decreasing2
% 0.14/0.36 thf(fact_172_add__increasing2,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere216010020id_add @ A )
% 0.14/0.36 => ! [C3: A,B2: A,A2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C3 )
% 0.14/0.36 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.14/0.36 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C3 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_increasing2
% 0.14/0.36 thf(fact_173_add__nonneg__nonneg,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere216010020id_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.14/0.36 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.14/0.36 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_nonneg_nonneg
% 0.14/0.36 thf(fact_174_add__nonpos__nonpos,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere216010020id_add @ A )
% 0.14/0.36 => ! [A2: A,B2: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.14/0.36 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.14/0.36 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_nonpos_nonpos
% 0.14/0.36 thf(fact_175_add__nonneg__eq__0__iff,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere216010020id_add @ A )
% 0.14/0.36 => ! [X: A,Y: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.14/0.36 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 0.14/0.36 => ( ( ( plus_plus @ A @ X @ Y )
% 0.14/0.36 = ( zero_zero @ A ) )
% 0.14/0.36 = ( ( X
% 0.14/0.36 = ( zero_zero @ A ) )
% 0.14/0.36 & ( Y
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_nonneg_eq_0_iff
% 0.14/0.36 thf(fact_176_add__nonpos__eq__0__iff,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( ordere216010020id_add @ A )
% 0.14/0.36 => ! [X: A,Y: A] :
% 0.14/0.36 ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 0.14/0.36 => ( ( ord_less_eq @ A @ Y @ ( zero_zero @ A ) )
% 0.14/0.36 => ( ( ( plus_plus @ A @ X @ Y )
% 0.14/0.36 = ( zero_zero @ A ) )
% 0.14/0.36 = ( ( X
% 0.14/0.36 = ( zero_zero @ A ) )
% 0.14/0.36 & ( Y
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % add_nonpos_eq_0_iff
% 0.14/0.36 thf(fact_177_Heap_Oas__tree__empty,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),T3: B] :
% 0.14/0.36 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.14/0.36 => ( ( ( As_tree2 @ T3 )
% 0.14/0.36 = ( e @ A ) )
% 0.14/0.36 = ( Is_empty2 @ T3 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap.as_tree_empty
% 0.14/0.36 thf(fact_178_Heap_Ois__heap__of__list,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),I: list @ A] :
% 0.14/0.36 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.14/0.36 => ( is_heap @ A @ ( As_tree2 @ ( Of_list2 @ I ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap.is_heap_of_list
% 0.14/0.36 thf(fact_179_Heap_Omultiset,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),L: B] :
% 0.14/0.36 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.14/0.36 => ( ( Multiset2 @ L )
% 0.14/0.36 = ( multiset2 @ A @ ( As_tree2 @ L ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap.multiset
% 0.14/0.36 thf(fact_180_divides__aux__def,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( unique1598680935umeral @ A )
% 0.14/0.36 => ( ( unique455577585es_aux @ A )
% 0.14/0.36 = ( ^ [Qr: product_prod @ A @ A] :
% 0.14/0.36 ( ( product_snd @ A @ A @ Qr )
% 0.14/0.36 = ( zero_zero @ A ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % divides_aux_def
% 0.14/0.36 thf(fact_181_Heap_Oaxioms_I2_J,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B )] :
% 0.14/0.36 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.14/0.36 => ( heap_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap.axioms(2)
% 0.14/0.36 thf(fact_182_is__heap_Osimps_I6_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [V: A,Vd: A,Ve: tree @ A,Vf: tree @ A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.14/0.36 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 & ( is_heap @ A @ ( t @ A @ Va @ Vb @ Vc ) )
% 0.14/0.36 & ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 0.14/0.36 & ( is_heap @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % is_heap.simps(6)
% 0.14/0.36 thf(fact_183_is__heap_Osimps_I5_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A] :
% 0.14/0.36 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 0.14/0.36 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 0.14/0.36 & ( is_heap @ A @ ( t @ A @ Vd @ Ve @ Vf ) )
% 0.14/0.36 & ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 & ( is_heap @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % is_heap.simps(5)
% 0.14/0.36 thf(fact_184_Heap_Oremove__max__multiset_H,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),L: B,M6: A,L6: B] :
% 0.14/0.36 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.14/0.36 => ( ~ ( Is_empty2 @ L )
% 0.14/0.36 => ( ( ( product_Pair @ A @ B @ M6 @ L6 )
% 0.14/0.36 = ( Remove_max2 @ L ) )
% 0.14/0.36 => ( ( add_mset @ A @ M6 @ ( Multiset2 @ L6 ) )
% 0.14/0.36 = ( Multiset2 @ L ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap.remove_max_multiset'
% 0.14/0.36 thf(fact_185_Heap_Oremove__max__val,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),T3: B,M6: A,T2: B] :
% 0.14/0.36 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.14/0.36 => ( ~ ( Is_empty2 @ T3 )
% 0.14/0.36 => ( ( ( product_Pair @ A @ B @ M6 @ T2 )
% 0.14/0.36 = ( Remove_max2 @ T3 ) )
% 0.14/0.36 => ( M6
% 0.14/0.36 = ( val @ A @ ( As_tree2 @ T3 ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap.remove_max_val
% 0.14/0.36 thf(fact_186_siftDown_Osimps_I4_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Va: A,Vb: tree @ A,Vc: tree @ A,V: A] :
% 0.14/0.36 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 = ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) )
% 0.14/0.36 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 = ( t @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( e @ A ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown.simps(4)
% 0.14/0.36 thf(fact_187_siftDown_Osimps_I3_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Va: A,Vb: tree @ A,Vc: tree @ A,V: A] :
% 0.14/0.36 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 0.14/0.36 = ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) ) )
% 0.14/0.36 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 0.14/0.36 = ( t @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) @ ( e @ A ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown.simps(3)
% 0.14/0.36 thf(fact_188_siftDown_Osimps_I5_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Vd: A,Ve: tree @ A,Vf: tree @ A,Va: A,Vb: tree @ A,Vc: tree @ A,V: A] :
% 0.14/0.36 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 0.14/0.36 = ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) )
% 0.14/0.36 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 0.14/0.36 = ( t @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) )
% 0.14/0.36 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 0.14/0.36 = ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) )
% 0.14/0.36 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 0.14/0.36 = ( t @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( t @ A @ Va @ Vb @ Vc ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown.simps(5)
% 0.14/0.36 thf(fact_189_siftDown_Osimps_I1_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( e @ A ) )
% 0.14/0.36 = ( e @ A ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown.simps(1)
% 0.14/0.36 thf(fact_190_siftDown__multiset,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [T3: tree @ A] :
% 0.14/0.36 ( ( multiset2 @ A @ ( heapIm748920189ftDown @ A @ T3 ) )
% 0.14/0.36 = ( multiset2 @ A @ T3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown_multiset
% 0.14/0.36 thf(fact_191_siftDown__Node,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [T3: tree @ A,V: A,L: tree @ A,R: tree @ A] :
% 0.14/0.36 ( ( T3
% 0.14/0.36 = ( t @ A @ V @ L @ R ) )
% 0.14/0.36 => ? [L5: tree @ A,V4: A,R2: tree @ A] :
% 0.14/0.36 ( ( ( heapIm748920189ftDown @ A @ T3 )
% 0.14/0.36 = ( t @ A @ V4 @ L5 @ R2 ) )
% 0.14/0.36 & ( ord_less_eq @ A @ V @ V4 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown_Node
% 0.14/0.36 thf(fact_192_siftDown_Osimps_I2_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [V: A] :
% 0.14/0.36 ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) )
% 0.14/0.36 = ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown.simps(2)
% 0.14/0.36 thf(fact_193_siftDown__heap__is__heap,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [L: tree @ A,R: tree @ A,T3: tree @ A,V: A] :
% 0.14/0.36 ( ( is_heap @ A @ L )
% 0.14/0.36 => ( ( is_heap @ A @ R )
% 0.14/0.36 => ( ( T3
% 0.14/0.36 = ( t @ A @ V @ L @ R ) )
% 0.14/0.36 => ( is_heap @ A @ ( heapIm748920189ftDown @ A @ T3 ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown_heap_is_heap
% 0.14/0.36 thf(fact_194_siftDown_Osimps_I6_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A,V: A] :
% 0.14/0.36 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 0.14/0.36 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 = ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) )
% 0.14/0.36 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 = ( t @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) )
% 0.14/0.36 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 0.14/0.36 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 = ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) )
% 0.14/0.36 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 0.14/0.36 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.14/0.36 = ( t @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( t @ A @ Vd @ Ve @ Vf ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown.simps(6)
% 0.14/0.36 thf(fact_195_siftDown__in__tree,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [T3: tree @ A] :
% 0.14/0.36 ( ( T3
% 0.14/0.36 != ( e @ A ) )
% 0.14/0.36 => ( in_tree @ A @ ( val @ A @ ( heapIm748920189ftDown @ A @ T3 ) ) @ T3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown_in_tree
% 0.14/0.36 thf(fact_196_is__heap__max,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [V: A,T3: tree @ A] :
% 0.14/0.36 ( ( in_tree @ A @ V @ T3 )
% 0.14/0.36 => ( ( is_heap @ A @ T3 )
% 0.14/0.36 => ( ord_less_eq @ A @ V @ ( val @ A @ T3 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % is_heap_max
% 0.14/0.36 thf(fact_197_in__tree_Osimps_I2_J,axiom,
% 0.14/0.36 ! [A: $tType,V: A,V2: A,L: tree @ A,R: tree @ A] :
% 0.14/0.36 ( ( in_tree @ A @ V @ ( t @ A @ V2 @ L @ R ) )
% 0.14/0.36 = ( ( V = V2 )
% 0.14/0.36 | ( in_tree @ A @ V @ L )
% 0.14/0.36 | ( in_tree @ A @ V @ R ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % in_tree.simps(2)
% 0.14/0.36 thf(fact_198_in__tree_Osimps_I1_J,axiom,
% 0.14/0.36 ! [A: $tType,V: A] :
% 0.14/0.36 ~ ( in_tree @ A @ V @ ( e @ A ) ) ).
% 0.14/0.36
% 0.14/0.36 % in_tree.simps(1)
% 0.14/0.36 thf(fact_199_siftDown__in__tree__set,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( ( in_tree @ A )
% 0.14/0.36 = ( ^ [V5: A,T4: tree @ A] : ( in_tree @ A @ V5 @ ( heapIm748920189ftDown @ A @ T4 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % siftDown_in_tree_set
% 0.14/0.36 thf(fact_200_le__numeral__extra_I3_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linord1659791738miring @ A )
% 0.14/0.36 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % le_numeral_extra(3)
% 0.14/0.36 thf(fact_201_hs__remove__max__def,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( ( heapIm1542349758ve_max @ A )
% 0.14/0.36 = ( ^ [T4: tree @ A] :
% 0.14/0.36 ( if @ ( product_prod @ A @ ( tree @ A ) )
% 0.14/0.36 @ ( ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T4 ) )
% 0.14/0.36 = ( e @ A ) )
% 0.14/0.36 @ ( product_Pair @ A @ ( tree @ A ) @ ( val @ A @ T4 ) @ ( e @ A ) )
% 0.14/0.36 @ ( product_Pair @ A @ ( tree @ A ) @ ( val @ A @ T4 ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T4 ) ) @ ( heapIm1271749598e_left @ A @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T4 ) ) ) @ ( heapIm1434396069_right @ A @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T4 ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % hs_remove_max_def
% 0.14/0.36 thf(fact_202_is__num__normalize_I1_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( neg_numeral @ A )
% 0.14/0.36 => ! [A2: A,B2: A,C3: A] :
% 0.14/0.36 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 0.14/0.36 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % is_num_normalize(1)
% 0.14/0.36 thf(fact_203_scomp__unfold,axiom,
% 0.14/0.36 ! [D: $tType,C: $tType,B: $tType,A: $tType] :
% 0.14/0.36 ( ( product_scomp @ A @ B @ C @ D )
% 0.14/0.36 = ( ^ [F4: A > ( product_prod @ B @ C ),G4: B > C > D,X4: A] : ( G4 @ ( product_fst @ B @ C @ ( F4 @ X4 ) ) @ ( product_snd @ B @ C @ ( F4 @ X4 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % scomp_unfold
% 0.14/0.36 thf(fact_204_heapify_Osimps_I2_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [V: A,L: tree @ A,R: tree @ A] :
% 0.14/0.36 ( ( heapIm818251801eapify @ A @ ( t @ A @ V @ L @ R ) )
% 0.14/0.36 = ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm818251801eapify @ A @ L ) @ ( heapIm818251801eapify @ A @ R ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % heapify.simps(2)
% 0.14/0.36 thf(fact_205_scomp__scomp,axiom,
% 0.14/0.36 ! [A: $tType,C: $tType,D: $tType,B: $tType,F: $tType,E: $tType,F3: A > ( product_prod @ E @ F ),G3: E > F > ( product_prod @ C @ D ),H: C > D > B] :
% 0.14/0.36 ( ( product_scomp @ A @ C @ D @ B @ ( product_scomp @ A @ E @ F @ ( product_prod @ C @ D ) @ F3 @ G3 ) @ H )
% 0.14/0.36 = ( product_scomp @ A @ E @ F @ B @ F3
% 0.14/0.36 @ ^ [X4: E] : ( product_scomp @ F @ C @ D @ B @ ( G3 @ X4 ) @ H ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % scomp_scomp
% 0.14/0.36 thf(fact_206_Pair__scomp,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,C: $tType,X: C,F3: C > A > B] :
% 0.14/0.36 ( ( product_scomp @ A @ C @ A @ B @ ( product_Pair @ C @ A @ X ) @ F3 )
% 0.14/0.36 = ( F3 @ X ) ) ).
% 0.14/0.36
% 0.14/0.36 % Pair_scomp
% 0.14/0.36 thf(fact_207_scomp__Pair,axiom,
% 0.14/0.36 ! [C: $tType,B: $tType,A: $tType,X: A > ( product_prod @ B @ C )] :
% 0.14/0.36 ( ( product_scomp @ A @ B @ C @ ( product_prod @ B @ C ) @ X @ ( product_Pair @ B @ C ) )
% 0.14/0.36 = X ) ).
% 0.14/0.36
% 0.14/0.36 % scomp_Pair
% 0.14/0.36 thf(fact_208_heapify_Osimps_I1_J,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( ( heapIm818251801eapify @ A @ ( e @ A ) )
% 0.14/0.36 = ( e @ A ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % heapify.simps(1)
% 0.14/0.36 thf(fact_209_heapify__heap__is__heap,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [T3: tree @ A] : ( is_heap @ A @ ( heapIm818251801eapify @ A @ T3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % heapify_heap_is_heap
% 0.14/0.36 thf(fact_210_multiset__heapify,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [T3: tree @ A] :
% 0.14/0.36 ( ( multiset2 @ A @ ( heapIm818251801eapify @ A @ T3 ) )
% 0.14/0.36 = ( multiset2 @ A @ T3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multiset_heapify
% 0.14/0.36 thf(fact_211_Heap__def,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( ( heap @ B @ A )
% 0.14/0.36 = ( ^ [Empty2: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),As_tree: B > ( tree @ A ),Remove_max: B > ( product_prod @ A @ B )] :
% 0.14/0.36 ( ( collection @ B @ A @ Empty2 @ Is_empty @ Of_list @ Multiset )
% 0.14/0.36 & ( heap_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap_def
% 0.14/0.36 thf(fact_212_Heap_Ointro,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B )] :
% 0.14/0.36 ( ( collection @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 )
% 0.14/0.36 => ( ( heap_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.14/0.36 => ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap.intro
% 0.14/0.36 thf(fact_213_Heap_Oaxioms_I1_J,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B )] :
% 0.14/0.36 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.14/0.36 => ( collection @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Heap.axioms(1)
% 0.14/0.36 thf(fact_214_HS_OCollection__axioms,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( collection @ ( tree @ A ) @ A @ ( e @ A ) @ ( heapIm721255937_empty @ A ) @ ( heapIm874063447f_list @ A ) @ ( multiset2 @ A ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % HS.Collection_axioms
% 0.14/0.36 thf(fact_215_Collection_Omultiset__empty,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A )] :
% 0.14/0.36 ( ( collection @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 )
% 0.14/0.36 => ( ( Multiset2 @ Empty )
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Collection.multiset_empty
% 0.14/0.36 thf(fact_216_Collection_Ois__empty__as__list,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),E3: B] :
% 0.14/0.36 ( ( collection @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 )
% 0.14/0.36 => ( ( Is_empty2 @ E3 )
% 0.14/0.36 => ( ( Multiset2 @ E3 )
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % Collection.is_empty_as_list
% 0.14/0.36 thf(fact_217_hs__of__list__def,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( ( heapIm874063447f_list @ A )
% 0.14/0.36 = ( ^ [L2: list @ A] : ( heapIm818251801eapify @ A @ ( heapIm1912108042t_tree @ A @ L2 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % hs_of_list_def
% 0.14/0.36 thf(fact_218_pred__equals__eq2,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 0.14/0.36 ( ( ( ^ [X4: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y6 ) @ R3 ) )
% 0.14/0.36 = ( ^ [X4: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y6 ) @ S2 ) ) )
% 0.14/0.36 = ( R3 = S2 ) ) ).
% 0.14/0.36
% 0.14/0.36 % pred_equals_eq2
% 0.14/0.36 thf(fact_219_subrelI,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S3: set @ ( product_prod @ A @ B )] :
% 0.14/0.36 ( ! [X3: A,Y3: B] :
% 0.14/0.36 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 0.14/0.36 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S3 ) )
% 0.14/0.36 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S3 ) ) ).
% 0.14/0.36
% 0.14/0.36 % subrelI
% 0.14/0.36 thf(fact_220_pred__subset__eq2,axiom,
% 0.14/0.36 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 0.14/0.36 ( ( ord_less_eq @ ( A > B > $o )
% 0.14/0.36 @ ^ [X4: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y6 ) @ R3 )
% 0.14/0.36 @ ^ [X4: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y6 ) @ S2 ) )
% 0.14/0.36 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S2 ) ) ).
% 0.14/0.36
% 0.14/0.36 % pred_subset_eq2
% 0.14/0.36 thf(fact_221_fun__cong__unused__0,axiom,
% 0.14/0.36 ! [A: $tType,B: $tType,C: $tType] :
% 0.14/0.36 ( ( zero @ B )
% 0.14/0.36 => ! [F3: ( A > B ) > C,G3: C] :
% 0.14/0.36 ( ( F3
% 0.14/0.36 = ( ^ [X4: A > B] : G3 ) )
% 0.14/0.36 => ( ( F3
% 0.14/0.36 @ ^ [X4: A] : ( zero_zero @ B ) )
% 0.14/0.36 = G3 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % fun_cong_unused_0
% 0.14/0.36 thf(fact_222_heap__top__geq,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [A2: A,T3: tree @ A] :
% 0.14/0.36 ( ( member @ A @ A2 @ ( set_mset @ A @ ( multiset2 @ A @ T3 ) ) )
% 0.14/0.36 => ( ( is_heap @ A @ T3 )
% 0.14/0.36 => ( ord_less_eq @ A @ A2 @ ( val @ A @ T3 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % heap_top_geq
% 0.14/0.36 thf(fact_223_multi__member__last,axiom,
% 0.14/0.36 ! [A: $tType,X: A] : ( member @ A @ X @ ( set_mset @ A @ ( add_mset @ A @ X @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multi_member_last
% 0.14/0.36 thf(fact_224_union__single__eq__member,axiom,
% 0.14/0.36 ! [A: $tType,X: A,M: multiset @ A,N: multiset @ A] :
% 0.14/0.36 ( ( ( add_mset @ A @ X @ M )
% 0.14/0.36 = N )
% 0.14/0.36 => ( member @ A @ X @ ( set_mset @ A @ N ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % union_single_eq_member
% 0.14/0.36 thf(fact_225_insert__noteq__member,axiom,
% 0.14/0.36 ! [A: $tType,B2: A,B5: multiset @ A,C3: A,C5: multiset @ A] :
% 0.14/0.36 ( ( ( add_mset @ A @ B2 @ B5 )
% 0.14/0.36 = ( add_mset @ A @ C3 @ C5 ) )
% 0.14/0.36 => ( ( B2 != C3 )
% 0.14/0.36 => ( member @ A @ C3 @ ( set_mset @ A @ B5 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % insert_noteq_member
% 0.14/0.36 thf(fact_226_multi__member__split,axiom,
% 0.14/0.36 ! [A: $tType,X: A,M: multiset @ A] :
% 0.14/0.36 ( ( member @ A @ X @ ( set_mset @ A @ M ) )
% 0.14/0.36 => ? [A7: multiset @ A] :
% 0.14/0.36 ( M
% 0.14/0.36 = ( add_mset @ A @ X @ A7 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multi_member_split
% 0.14/0.36 thf(fact_227_mset__add,axiom,
% 0.14/0.36 ! [A: $tType,A2: A,A5: multiset @ A] :
% 0.14/0.36 ( ( member @ A @ A2 @ ( set_mset @ A @ A5 ) )
% 0.14/0.36 => ~ ! [B7: multiset @ A] :
% 0.14/0.36 ( A5
% 0.14/0.36 != ( add_mset @ A @ A2 @ B7 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % mset_add
% 0.14/0.36 thf(fact_228_union__iff,axiom,
% 0.14/0.36 ! [A: $tType,A2: A,A5: multiset @ A,B5: multiset @ A] :
% 0.14/0.36 ( ( member @ A @ A2 @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ A5 @ B5 ) ) )
% 0.14/0.36 = ( ( member @ A @ A2 @ ( set_mset @ A @ A5 ) )
% 0.14/0.36 | ( member @ A @ A2 @ ( set_mset @ A @ B5 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % union_iff
% 0.14/0.36 thf(fact_229_multiset__nonemptyE,axiom,
% 0.14/0.36 ! [A: $tType,A5: multiset @ A] :
% 0.14/0.36 ( ( A5
% 0.14/0.36 != ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 => ~ ! [X3: A] :
% 0.14/0.36 ~ ( member @ A @ X3 @ ( set_mset @ A @ A5 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multiset_nonemptyE
% 0.14/0.36 thf(fact_230_ge__eq__refl,axiom,
% 0.14/0.36 ! [A: $tType,R3: A > A > $o,X: A] :
% 0.14/0.36 ( ( ord_less_eq @ ( A > A > $o )
% 0.14/0.36 @ ^ [Y4: A,Z2: A] : ( Y4 = Z2 )
% 0.14/0.36 @ R3 )
% 0.14/0.36 => ( R3 @ X @ X ) ) ).
% 0.14/0.36
% 0.14/0.36 % ge_eq_refl
% 0.14/0.36 thf(fact_231_refl__ge__eq,axiom,
% 0.14/0.36 ! [A: $tType,R3: A > A > $o] :
% 0.14/0.36 ( ! [X3: A] : ( R3 @ X3 @ X3 )
% 0.14/0.36 => ( ord_less_eq @ ( A > A > $o )
% 0.14/0.36 @ ^ [Y4: A,Z2: A] : ( Y4 = Z2 )
% 0.14/0.36 @ R3 ) ) ).
% 0.14/0.36
% 0.14/0.36 % refl_ge_eq
% 0.14/0.36 thf(fact_232_subset__CollectI,axiom,
% 0.14/0.36 ! [A: $tType,B5: set @ A,A5: set @ A,Q2: A > $o,P2: A > $o] :
% 0.14/0.36 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 0.14/0.36 => ( ! [X3: A] :
% 0.14/0.36 ( ( member @ A @ X3 @ B5 )
% 0.14/0.36 => ( ( Q2 @ X3 )
% 0.14/0.36 => ( P2 @ X3 ) ) )
% 0.14/0.36 => ( ord_less_eq @ ( set @ A )
% 0.14/0.36 @ ( collect @ A
% 0.14/0.36 @ ^ [X4: A] :
% 0.14/0.36 ( ( member @ A @ X4 @ B5 )
% 0.14/0.36 & ( Q2 @ X4 ) ) )
% 0.14/0.36 @ ( collect @ A
% 0.14/0.36 @ ^ [X4: A] :
% 0.14/0.36 ( ( member @ A @ X4 @ A5 )
% 0.14/0.36 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % subset_CollectI
% 0.14/0.36 thf(fact_233_subset__Collect__iff,axiom,
% 0.14/0.36 ! [A: $tType,B5: set @ A,A5: set @ A,P2: A > $o] :
% 0.14/0.36 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 0.14/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B5
% 0.14/0.36 @ ( collect @ A
% 0.14/0.36 @ ^ [X4: A] :
% 0.14/0.36 ( ( member @ A @ X4 @ A5 )
% 0.14/0.36 & ( P2 @ X4 ) ) ) )
% 0.14/0.36 = ( ! [X4: A] :
% 0.14/0.36 ( ( member @ A @ X4 @ B5 )
% 0.14/0.36 => ( P2 @ X4 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % subset_Collect_iff
% 0.14/0.36 thf(fact_234_multiset__induct__min,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [P2: ( multiset @ A ) > $o,M: multiset @ A] :
% 0.14/0.36 ( ( P2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 => ( ! [X3: A,M3: multiset @ A] :
% 0.14/0.36 ( ( P2 @ M3 )
% 0.14/0.36 => ( ! [Xa: A] :
% 0.14/0.36 ( ( member @ A @ Xa @ ( set_mset @ A @ M3 ) )
% 0.14/0.36 => ( ord_less_eq @ A @ X3 @ Xa ) )
% 0.14/0.36 => ( P2 @ ( add_mset @ A @ X3 @ M3 ) ) ) )
% 0.14/0.36 => ( P2 @ M ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multiset_induct_min
% 0.14/0.36 thf(fact_235_multiset__induct__max,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [P2: ( multiset @ A ) > $o,M: multiset @ A] :
% 0.14/0.36 ( ( P2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 => ( ! [X3: A,M3: multiset @ A] :
% 0.14/0.36 ( ( P2 @ M3 )
% 0.14/0.36 => ( ! [Xa: A] :
% 0.14/0.36 ( ( member @ A @ Xa @ ( set_mset @ A @ M3 ) )
% 0.14/0.36 => ( ord_less_eq @ A @ Xa @ X3 ) )
% 0.14/0.36 => ( P2 @ ( add_mset @ A @ X3 @ M3 ) ) ) )
% 0.14/0.36 => ( P2 @ M ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multiset_induct_max
% 0.14/0.36 thf(fact_236_multi__member__skip,axiom,
% 0.14/0.36 ! [A: $tType,X: A,XS: multiset @ A,Y: A] :
% 0.14/0.36 ( ( member @ A @ X @ ( set_mset @ A @ XS ) )
% 0.14/0.36 => ( member @ A @ X @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ Y @ ( zero_zero @ ( multiset @ A ) ) ) @ XS ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multi_member_skip
% 0.14/0.36 thf(fact_237_multi__member__this,axiom,
% 0.14/0.36 ! [A: $tType,X: A,XS: multiset @ A] : ( member @ A @ X @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ X @ ( zero_zero @ ( multiset @ A ) ) ) @ XS ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % multi_member_this
% 0.14/0.36 thf(fact_238_less__add,axiom,
% 0.14/0.36 ! [A: $tType,N: multiset @ A,A2: A,M0: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 0.14/0.36 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ ( add_mset @ A @ A2 @ M0 ) ) @ ( mult1 @ A @ R ) )
% 0.14/0.36 => ( ? [M3: multiset @ A] :
% 0.14/0.36 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M3 @ M0 ) @ ( mult1 @ A @ R ) )
% 0.14/0.36 & ( N
% 0.14/0.36 = ( add_mset @ A @ A2 @ M3 ) ) )
% 0.14/0.36 | ? [K4: multiset @ A] :
% 0.14/0.36 ( ! [B8: A] :
% 0.14/0.36 ( ( member @ A @ B8 @ ( set_mset @ A @ K4 ) )
% 0.14/0.36 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B8 @ A2 ) @ R ) )
% 0.14/0.36 & ( N
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ M0 @ K4 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % less_add
% 0.14/0.36 thf(fact_239_mult1I,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ A,A2: A,M0: multiset @ A,N: multiset @ A,K2: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 0.14/0.36 ( ( M
% 0.14/0.36 = ( add_mset @ A @ A2 @ M0 ) )
% 0.14/0.36 => ( ( N
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ M0 @ K2 ) )
% 0.14/0.36 => ( ! [B4: A] :
% 0.14/0.36 ( ( member @ A @ B4 @ ( set_mset @ A @ K2 ) )
% 0.14/0.36 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A2 ) @ R ) )
% 0.14/0.36 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M ) @ ( mult1 @ A @ R ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % mult1I
% 0.14/0.36 thf(fact_240_mono__mult1,axiom,
% 0.14/0.36 ! [A: $tType,R: set @ ( product_prod @ A @ A ),R4: set @ ( product_prod @ A @ A )] :
% 0.14/0.36 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ R4 )
% 0.14/0.36 => ( ord_less_eq @ ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) @ ( mult1 @ A @ R ) @ ( mult1 @ A @ R4 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % mono_mult1
% 0.14/0.36 thf(fact_241_mult1__union,axiom,
% 0.14/0.36 ! [A: $tType,B5: multiset @ A,D4: multiset @ A,R: set @ ( product_prod @ A @ A ),C5: multiset @ A] :
% 0.14/0.36 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ B5 @ D4 ) @ ( mult1 @ A @ R ) )
% 0.14/0.36 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ C5 @ B5 ) @ ( plus_plus @ ( multiset @ A ) @ C5 @ D4 ) ) @ ( mult1 @ A @ R ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % mult1_union
% 0.14/0.36 thf(fact_242_not__less__empty,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 0.14/0.36 ~ ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M @ ( zero_zero @ ( multiset @ A ) ) ) @ ( mult1 @ A @ R ) ) ).
% 0.14/0.36
% 0.14/0.36 % not_less_empty
% 0.14/0.36 thf(fact_243_mult1E,axiom,
% 0.14/0.36 ! [A: $tType,N: multiset @ A,M: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 0.14/0.36 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M ) @ ( mult1 @ A @ R ) )
% 0.14/0.36 => ~ ! [A4: A,M02: multiset @ A] :
% 0.14/0.36 ( ( M
% 0.14/0.36 = ( add_mset @ A @ A4 @ M02 ) )
% 0.14/0.36 => ! [K4: multiset @ A] :
% 0.14/0.36 ( ( N
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ M02 @ K4 ) )
% 0.14/0.36 => ~ ! [B8: A] :
% 0.14/0.36 ( ( member @ A @ B8 @ ( set_mset @ A @ K4 ) )
% 0.14/0.36 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B8 @ A4 ) @ R ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % mult1E
% 0.14/0.36 thf(fact_244_one__step__implies__mult,axiom,
% 0.14/0.36 ! [A: $tType,J2: multiset @ A,K2: multiset @ A,R: set @ ( product_prod @ A @ A ),I4: multiset @ A] :
% 0.14/0.36 ( ( J2
% 0.14/0.36 != ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 => ( ! [X3: A] :
% 0.14/0.36 ( ( member @ A @ X3 @ ( set_mset @ A @ K2 ) )
% 0.14/0.36 => ? [Xa: A] :
% 0.14/0.36 ( ( member @ A @ Xa @ ( set_mset @ A @ J2 ) )
% 0.14/0.36 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Xa ) @ R ) ) )
% 0.14/0.36 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ I4 @ K2 ) @ ( plus_plus @ ( multiset @ A ) @ I4 @ J2 ) ) @ ( mult @ A @ R ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % one_step_implies_mult
% 0.14/0.36 thf(fact_245_heap__top__max,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ! [T3: tree @ A] :
% 0.14/0.36 ( ( T3
% 0.14/0.36 != ( e @ A ) )
% 0.14/0.36 => ( ( is_heap @ A @ T3 )
% 0.14/0.36 => ( ( val @ A @ T3 )
% 0.14/0.36 = ( lattic929149872er_Max @ A @ ( set_mset @ A @ ( multiset2 @ A @ T3 ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % heap_top_max
% 0.14/0.36 thf(fact_246_mono__mult,axiom,
% 0.14/0.36 ! [A: $tType,R: set @ ( product_prod @ A @ A ),R4: set @ ( product_prod @ A @ A )] :
% 0.14/0.36 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ R4 )
% 0.14/0.36 => ( ord_less_eq @ ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) @ ( mult @ A @ R ) @ ( mult @ A @ R4 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % mono_mult
% 0.14/0.36 thf(fact_247_mult__implies__one__step,axiom,
% 0.14/0.36 ! [A: $tType,R: set @ ( product_prod @ A @ A ),M: multiset @ A,N: multiset @ A] :
% 0.14/0.36 ( ( trans @ A @ R )
% 0.14/0.36 => ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M @ N ) @ ( mult @ A @ R ) )
% 0.14/0.36 => ? [I5: multiset @ A,J3: multiset @ A] :
% 0.14/0.36 ( ( N
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ I5 @ J3 ) )
% 0.14/0.36 & ? [K4: multiset @ A] :
% 0.14/0.36 ( ( M
% 0.14/0.36 = ( plus_plus @ ( multiset @ A ) @ I5 @ K4 ) )
% 0.14/0.36 & ( J3
% 0.14/0.36 != ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 & ! [X6: A] :
% 0.14/0.36 ( ( member @ A @ X6 @ ( set_mset @ A @ K4 ) )
% 0.14/0.36 => ? [Xa2: A] :
% 0.14/0.36 ( ( member @ A @ Xa2 @ ( set_mset @ A @ J3 ) )
% 0.14/0.36 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X6 @ Xa2 ) @ R ) ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % mult_implies_one_step
% 0.14/0.36 thf(fact_248_subset__mset_Osum__mset__0__iff,axiom,
% 0.14/0.36 ! [A: $tType,M: multiset @ ( multiset @ A )] :
% 0.14/0.36 ( ( ( comm_monoid_sum_mset @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ A ) ) @ M )
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) )
% 0.14/0.36 = ( ! [X4: multiset @ A] :
% 0.14/0.36 ( ( member @ ( multiset @ A ) @ X4 @ ( set_mset @ ( multiset @ A ) @ M ) )
% 0.14/0.36 => ( X4
% 0.14/0.36 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % subset_mset.sum_mset_0_iff
% 0.14/0.36 thf(fact_249_comm__monoid__add_Osum__mset_Ocong,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( comm_monoid_sum_mset @ A )
% 0.14/0.36 = ( comm_monoid_sum_mset @ A ) ) ).
% 0.14/0.36
% 0.14/0.36 % comm_monoid_add.sum_mset.cong
% 0.14/0.36 thf(fact_250_transD,axiom,
% 0.14/0.36 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A,Z: A] :
% 0.14/0.36 ( ( trans @ A @ R )
% 0.14/0.36 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 0.14/0.36 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z ) @ R )
% 0.14/0.36 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ R ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % transD
% 0.14/0.36 thf(fact_251_transE,axiom,
% 0.14/0.36 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A,Z: A] :
% 0.14/0.36 ( ( trans @ A @ R )
% 0.14/0.36 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 0.14/0.36 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z ) @ R )
% 0.14/0.36 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ R ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % transE
% 0.14/0.36 thf(fact_252_transI,axiom,
% 0.14/0.36 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 0.14/0.36 ( ! [X3: A,Y3: A,Z3: A] :
% 0.14/0.36 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 0.14/0.36 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ Z3 ) @ R )
% 0.14/0.36 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Z3 ) @ R ) ) )
% 0.14/0.36 => ( trans @ A @ R ) ) ).
% 0.14/0.36
% 0.14/0.36 % transI
% 0.14/0.36 thf(fact_253_trans__def,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( trans @ A )
% 0.14/0.36 = ( ^ [R5: set @ ( product_prod @ A @ A )] :
% 0.14/0.36 ! [X4: A,Y6: A,Z4: A] :
% 0.14/0.36 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y6 ) @ R5 )
% 0.14/0.36 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ Z4 ) @ R5 )
% 0.14/0.36 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Z4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % trans_def
% 0.14/0.36 thf(fact_254_mult__cancel__add__mset,axiom,
% 0.14/0.36 ! [A: $tType,S3: set @ ( product_prod @ A @ A ),Uu: A,X5: multiset @ A,Y5: multiset @ A] :
% 0.14/0.36 ( ( trans @ A @ S3 )
% 0.14/0.36 => ( ( irrefl @ A @ S3 )
% 0.14/0.36 => ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( add_mset @ A @ Uu @ X5 ) @ ( add_mset @ A @ Uu @ Y5 ) ) @ ( mult @ A @ S3 ) )
% 0.14/0.36 = ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ X5 @ Y5 ) @ ( mult @ A @ S3 ) ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 % mult_cancel_add_mset
% 0.14/0.36
% 0.14/0.36 % Subclasses (2)
% 0.14/0.36 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( type @ A ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.14/0.36 ! [A: $tType] :
% 0.14/0.36 ( ( linorder @ A )
% 0.14/0.36 => ( preorder @ A ) ) ).
% 0.14/0.36
% 0.14/0.36 % Type constructors (13)
% 0.14/0.36 thf(tcon_Multiset_Omultiset___Orderings_Opreorder,axiom,
% 0.14/0.36 ! [A9: $tType] :
% 0.14/0.36 ( ( preorder @ A9 )
% 0.14/0.36 => ( preorder @ ( multiset @ A9 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_HOL_Obool___Orderings_Opreorder_1,axiom,
% 0.14/0.36 preorder @ $o ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.14/0.36 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_fun___Orderings_Opreorder_3,axiom,
% 0.14/0.36 ! [A9: $tType,A10: $tType] :
% 0.14/0.36 ( ( preorder @ A10 )
% 0.14/0.36 => ( preorder @ ( A9 > A10 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.14/0.36 linorder @ $o ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_Multiset_Omultiset___Groups_Oordered__ab__semigroup__add,axiom,
% 0.14/0.36 ! [A9: $tType] :
% 0.14/0.36 ( ( preorder @ A9 )
% 0.14/0.36 => ( ordere779506340up_add @ ( multiset @ A9 ) ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add,axiom,
% 0.14/0.36 ! [A9: $tType] : ( cancel1352612707id_add @ ( multiset @ A9 ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_Multiset_Omultiset___Groups_Ocancel__semigroup__add,axiom,
% 0.14/0.36 ! [A9: $tType] : ( cancel_semigroup_add @ ( multiset @ A9 ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_Multiset_Omultiset___Groups_Oab__semigroup__add,axiom,
% 0.14/0.36 ! [A9: $tType] : ( ab_semigroup_add @ ( multiset @ A9 ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_Multiset_Omultiset___Groups_Ocomm__monoid__add,axiom,
% 0.14/0.36 ! [A9: $tType] : ( comm_monoid_add @ ( multiset @ A9 ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_Multiset_Omultiset___Groups_Osemigroup__add,axiom,
% 0.14/0.36 ! [A9: $tType] : ( semigroup_add @ ( multiset @ A9 ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_Multiset_Omultiset___Groups_Omonoid__add,axiom,
% 0.14/0.36 ! [A9: $tType] : ( monoid_add @ ( multiset @ A9 ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(tcon_Multiset_Omultiset___Groups_Ozero,axiom,
% 0.14/0.36 ! [A9: $tType] : ( zero @ ( multiset @ A9 ) ) ).
% 0.14/0.36
% 0.14/0.36 % Helper facts (3)
% 0.14/0.36 thf(help_If_3_1_T,axiom,
% 0.14/0.36 ! [P2: $o] :
% 0.14/0.36 ( ( P2 = $true )
% 0.14/0.36 | ( P2 = $false ) ) ).
% 0.14/0.36
% 0.14/0.36 thf(help_If_2_1_T,axiom,
% 0.14/0.36 ! [A: $tType,X: A,Y: A] :
% 0.14/0.36 ( ( if @ A @ $false @ X @ Y )
% 0.14/0.36 = Y ) ).
% 0.14/0.36
% 0.14/0.36 thf(help_If_1_1_T,axiom,
% 0.14/0.36 ! [A: $tType,X: A,Y: A] :
% 0.14/0.36 ( ( if @ A @ $true @ X @ Y )
% 0.14/0.36 = X ) ).
% 0.14/0.36
% 0.14/0.36 % Free types (1)
% 0.14/0.36 thf(tfree_0,hypothesis,
% 0.14/0.36 linorder @ a ).
% 0.14/0.36
% 0.14/0.36 % Conjectures (1)
% 0.14/0.36 thf(conj_0,conjecture,
% 0.14/0.36 ( v_a
% 0.14/0.36 = ( product_fst @ a @ ( tree @ a ) @ ( heapIm970386777veLeaf @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ).
% 0.14/0.36
% 0.14/0.36 %------------------------------------------------------------------------------
% 0.14/0.36 ------------------------
% 2.54/1.58 ---- Embedded in THF ---
% 2.54/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.54/1.58 %%% Generated on Tue Feb 24 08:25:17 EST 2026
% 2.54/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.54/1.58 %%% Logic specification used:
% 2.54/1.58 %%% thf(spec, logic, $$dhol).
% 2.54/1.58
% 2.54/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.P5IR1jFQuE/DTF2DTF10235.p
% 2.54/1.58 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.54/1.58 thf(ty_t_Multiset_Omultiset, type, multiset: ($tType > $tType)).
% 2.54/1.58 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.54/1.58 thf(ty_t_Heap_OTree, type, tree: ($tType > $tType)).
% 2.54/1.58 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.54/1.58 thf(ty_tf_a, type, a: $tType).
% 2.54/1.58 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Oordered__comm__monoid__add, type, ordere216010020id_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral, type, unique1598680935umeral: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le, type, ordere516151231imp_le: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, type, semiri456707255roduct: (!> [A:$tType]: ($o))).
% 2.54/1.58 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux, type, unique455577585es_aux: (!> [A:$tType]: ((((product_prod @ A) @ A) > $o)))).
% 2.54/1.58 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.54/1.58 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.54/1.58 thf(sy_c_HOL_ONO__MATCH, type, nO_MATCH: (!> [A:$tType,B:$tType]: ((A > (B > $o))))).
% 2.54/1.58 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oheapify, type, heapIm818251801eapify: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.54/1.58 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Ohs__is__empty, type, heapIm721255937_empty: (!> [A:$tType]: (((tree @ A) > $o)))).
% 2.54/1.58 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Ohs__of__list, type, heapIm874063447f_list: (!> [A:$tType]: (((list @ A) > (tree @ A))))).
% 2.54/1.58 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Ohs__remove__max, type, heapIm1542349758ve_max: (!> [A:$tType]: (((tree @ A) > ((product_prod @ A) @ (tree @ A)))))).
% 2.54/1.58 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oleft, type, heapIm1271749598e_left: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.54/1.58 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oof__list__tree, type, heapIm1912108042t_tree: (!> [A:$tType]: (((list @ A) > (tree @ A))))).
% 2.54/1.58 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_OremoveLeaf, type, heapIm970386777veLeaf: (!> [A:$tType]: (((tree @ A) > ((product_prod @ A) @ (tree @ A)))))).
% 2.54/1.58 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oright, type, heapIm1434396069_right: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.54/1.58 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_OsiftDown, type, heapIm748920189ftDown: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.54/1.58 thf(sy_c_Heap_OHeap, type, heap: (!> [B:$tType,A:$tType]: ((B > ((B > $o) > (((list @ A) > B) > ((B > (multiset @ A)) > ((B > (tree @ A)) > ((B > ((product_prod @ A) @ B)) > $o))))))))).
% 2.54/1.58 thf(sy_c_Heap_OHeap__axioms, type, heap_axioms: (!> [B:$tType,A:$tType]: (((B > $o) > (((list @ A) > B) > ((B > (multiset @ A)) > ((B > (tree @ A)) > ((B > ((product_prod @ A) @ B)) > $o)))))))).
% 2.54/1.58 thf(sy_c_Heap_OTree_OE, type, e: (!> [A:$tType]: ((tree @ A)))).
% 2.54/1.58 thf(sy_c_Heap_OTree_OT, type, t: (!> [A:$tType]: ((A > ((tree @ A) > ((tree @ A) > (tree @ A))))))).
% 2.54/1.58 thf(sy_c_Heap_Oin__tree, type, in_tree: (!> [A:$tType]: ((A > ((tree @ A) > $o))))).
% 2.54/1.58 thf(sy_c_Heap_Ois__heap, type, is_heap: (!> [A:$tType]: (((tree @ A) > $o)))).
% 2.54/1.58 thf(sy_c_Heap_Omultiset, type, multiset2: (!> [A:$tType]: (((tree @ A) > (multiset @ A))))).
% 2.54/1.58 thf(sy_c_Heap_Oval, type, val: (!> [A:$tType]: (((tree @ A) > A)))).
% 2.54/1.58 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.54/1.58 thf(sy_c_Lattices__Big_Olinorder__class_OMax, type, lattic929149872er_Max: (!> [A:$tType]: (((set @ A) > A)))).
% 2.54/1.58 thf(sy_c_Multiset_Oadd__mset, type, add_mset: (!> [A:$tType]: ((A > ((multiset @ A) > (multiset @ A)))))).
% 2.54/1.58 thf(sy_c_Multiset_Ocomm__monoid__add_Osum__mset, type, comm_monoid_sum_mset: (!> [A:$tType]: (((A > (A > A)) > (A > ((multiset @ A) > A)))))).
% 2.54/1.58 thf(sy_c_Multiset_Ois__empty, type, is_empty: (!> [A:$tType]: (((multiset @ A) > $o)))).
% 2.54/1.58 thf(sy_c_Multiset_Omult, type, mult: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (multiset @ A)) @ (multiset @ A))))))).
% 2.54/1.58 thf(sy_c_Multiset_Omult1, type, mult1: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (multiset @ A)) @ (multiset @ A))))))).
% 2.54/1.58 thf(sy_c_Multiset_Oset__mset, type, set_mset: (!> [A:$tType]: (((multiset @ A) > (set @ A))))).
% 2.54/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.54/1.58 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.54/1.58 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.54/1.58 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.54/1.58 thf(sy_c_Product__Type_Oprod_Ofst, type, product_fst: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > A)))).
% 2.54/1.58 thf(sy_c_Product__Type_Oprod_Osnd, type, product_snd: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > B)))).
% 2.54/1.58 thf(sy_c_Product__Type_Oprod_Oswap, type, product_swap: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > ((product_prod @ B) @ A))))).
% 2.54/1.58 thf(sy_c_Product__Type_Oscomp, type, product_scomp: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: (((A > ((product_prod @ B) @ C)) > ((B > (C > D)) > (A > D)))))).
% 2.54/1.58 thf(sy_c_Relation_Oirrefl, type, irrefl: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.54/1.58 thf(sy_c_Relation_Otrans, type, trans: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.54/1.58 thf(sy_c_RemoveMax_OCollection, type, collection: (!> [B:$tType,A:$tType]: ((B > ((B > $o) > (((list @ A) > B) > ((B > (multiset @ A)) > $o))))))).
% 2.54/1.58 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.54/1.58 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.54/1.58 thf(sy_v_l1____, type, l1: (tree @ a)).
% 2.54/1.58 thf(sy_v_l2____, type, l2: (tree @ a)).
% 2.54/1.58 thf(sy_v_r1____, type, r1: (tree @ a)).
% 2.54/1.58 thf(sy_v_r2____, type, r2: (tree @ a)).
% 2.54/1.58 thf(sy_v_t, type, t2: (tree @ a)).
% 2.54/1.58 thf(sy_v_t_H, type, t3: (tree @ a)).
% 2.54/1.58 thf(sy_v_t_Ha____, type, t_a: (tree @ a)).
% 2.54/1.58 thf(sy_v_v1____, type, v1: a).
% 2.54/1.58 thf(sy_v_v2____, type, v2: a).
% 2.54/1.58 thf(sy_v_v_H, type, v: a).
% 2.54/1.58 thf(sy_v_v_Ha____, type, v_a: a).
% 2.54/1.58 thf(sy_v_v____, type, v3: a).
% 2.54/1.58 thf(fact_0__C4__2_Oprems_C_I1_J, axiom, (((((product_Pair @ a) @ (tree @ a)) @ v_a) @ t_a) = ((heapIm970386777veLeaf @ a) @ ((((t @ a) @ v3) @ ((((t @ a) @ v1) @ l1) @ r1)) @ ((((t @ a) @ v2) @ l2) @ r2))))).
% 2.54/1.58 thf(fact_1_assms_I1_J, axiom, (((((product_Pair @ a) @ (tree @ a)) @ v) @ t3) = ((heapIm970386777veLeaf @ a) @ t2))).
% 2.54/1.58 thf(fact_2__C4__2_Oprems_C_I2_J, axiom, (((((t @ a) @ v3) @ ((((t @ a) @ v1) @ l1) @ r1)) @ ((((t @ a) @ v2) @ l2) @ r2)) != (e @ a))).
% 2.54/1.58 thf(fact_3__092_060open_062t_H_A_061_AT_Av_A_Isnd_A_IremoveLeaf_A_IT_Av1_Al1_Ar1_J_J_J_A_IT_Av2_Al2_Ar2_J_092_060close_062, axiom, (t_a = ((((t @ a) @ v3) @ (((product_snd @ a) @ (tree @ a)) @ ((heapIm970386777veLeaf @ a) @ ((((t @ a) @ v1) @ l1) @ r1)))) @ ((((t @ a) @ v2) @ l2) @ r2)))).
% 2.54/1.58 thf(fact_4_Tree_Oinject, axiom, (! [A:$tType,X21:A,X22:(tree @ A),X23:(tree @ A),Y21:A,Y22:(tree @ A),Y23:(tree @ A)]: (((((((t @ A) @ X21) @ X22) @ X23) = ((((t @ A) @ Y21) @ Y22) @ Y23)) = ((X21 = Y21) & ((X22 = Y22) & (X23 = Y23))))))).
% 2.54/1.58 thf(fact_5_removeLeaf_Osimps_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Vd:A,Ve:(tree @ A),Vf:(tree @ A),Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((((heapIm970386777veLeaf @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((product_Pair @ A) @ (tree @ A)) @ (((product_fst @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf)))) @ ((((t @ A) @ V) @ (((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf)))) @ ((((t @ A) @ Va) @ Vb) @ Vc)))))))))).
% 2.54/1.58 thf(fact_6_removeLeaf_Osimps_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Va:A,Vb:(tree @ A),Vc:(tree @ A),Vd:A,Ve:(tree @ A),Vf:(tree @ A)]: ((((heapIm970386777veLeaf @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) = ((((product_Pair @ A) @ (tree @ A)) @ (((product_fst @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))) @ ((((t @ A) @ V) @ (((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))) @ ((((t @ A) @ Vd) @ Ve) @ Vf)))))))))).
% 2.54/1.58 thf(fact_7_left_Osimps, axiom, (! [A:$tType,V:A,L:(tree @ A),R:(tree @ A)]: ((((heapIm1271749598e_left @ A) @ ((((t @ A) @ V) @ L) @ R)) = L)))).
% 2.54/1.58 thf(fact_8_right_Osimps, axiom, (! [A:$tType,V:A,L:(tree @ A),R:(tree @ A)]: ((((heapIm1434396069_right @ A) @ ((((t @ A) @ V) @ L) @ R)) = R)))).
% 2.54/1.58 thf(fact_9__C4__2_Ohyps_C_I1_J, axiom, (! [V2:a,T2:(tree @ a)]: (((((((product_Pair @ a) @ (tree @ a)) @ V2) @ T2) = ((heapIm970386777veLeaf @ a) @ ((((t @ a) @ v1) @ l1) @ r1))) => ((((((t @ a) @ v1) @ l1) @ r1) != (e @ a)) => ((((plus_plus @ (multiset @ a)) @ (((add_mset @ a) @ V2) @ (zero_zero @ (multiset @ a)))) @ ((multiset2 @ a) @ T2)) = ((multiset2 @ a) @ ((((t @ a) @ v1) @ l1) @ r1)))))))).
% 2.54/1.58 thf(fact_10_removeLeaf_Osimps_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A]: ((((heapIm970386777veLeaf @ A) @ ((((t @ A) @ V) @ (e @ A)) @ (e @ A))) = ((((product_Pair @ A) @ (tree @ A)) @ V) @ (e @ A))))))))).
% 2.54/1.58 thf(fact_11_fstI, axiom, (! [B:$tType,A:$tType,X:((product_prod @ A) @ B),Y:A,Z:B]: (((X = ((((product_Pair @ A) @ B) @ Y) @ Z)) => ((((product_fst @ A) @ B) @ X) = Y))))).
% 2.54/1.58 thf(fact_12_fst__eqD, axiom, (! [B:$tType,A:$tType,X:A,Y:B,A2:A]: ((((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X) @ Y)) = A2) => (X = A2))))).
% 2.54/1.58 thf(fact_13_fst__conv, axiom, (! [B:$tType,A:$tType,X1:A,X2:B]: (((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X1) @ X2)) = X1)))).
% 2.54/1.58 thf(fact_14_assms_I2_J, axiom, (t2 != (e @ a))).
% 2.54/1.58 thf(fact_15_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 2.54/1.58 thf(fact_16_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((A2 = A3) & (B2 = B3)))))).
% 2.54/1.58 thf(fact_17_prod_Ocollapse, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)) = Prod)))).
% 2.54/1.58 thf(fact_18_multiset_Osimps_I2_J, axiom, (! [A:$tType,V:A,L:(tree @ A),R:(tree @ A)]: ((((multiset2 @ A) @ ((((t @ A) @ V) @ L) @ R)) = (((plus_plus @ (multiset @ A)) @ (((plus_plus @ (multiset @ A)) @ ((multiset2 @ A) @ L)) @ (((add_mset @ A) @ V) @ (zero_zero @ (multiset @ A))))) @ ((multiset2 @ A) @ R)))))).
% 2.54/1.58 thf(fact_19_multiset_Osimps_I1_J, axiom, (! [A:$tType]: ((((multiset2 @ A) @ (e @ A)) = (zero_zero @ (multiset @ A)))))).
% 2.54/1.58 thf(fact_20_sndI, axiom, (! [A:$tType,B:$tType,X:((product_prod @ A) @ B),Y:A,Z:B]: (((X = ((((product_Pair @ A) @ B) @ Y) @ Z)) => ((((product_snd @ A) @ B) @ X) = Z))))).
% 2.54/1.58 thf(fact_21_snd__eqD, axiom, (! [B:$tType,A:$tType,X:B,Y:A,A2:A]: ((((((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y)) = A2) => (Y = A2))))).
% 2.54/1.58 thf(fact_22_snd__conv, axiom, (! [Aa:$tType,A:$tType,X1:Aa,X2:A]: (((((product_snd @ Aa) @ A) @ ((((product_Pair @ Aa) @ A) @ X1) @ X2)) = X2)))).
% 2.54/1.58 thf(fact_23_surj__pair, axiom, (! [A:$tType,B:$tType,P:((product_prod @ A) @ B)]: ((? [X3:A,Y3:B]: ((P = ((((product_Pair @ A) @ B) @ X3) @ Y3))))))).
% 2.54/1.58 thf(fact_24_prod__cases, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),P:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P2 @ P))))).
% 2.54/1.58 thf(fact_25_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) => (~ (((A2 = A3) => (B2 != B3)))))))).
% 2.54/1.58 thf(fact_26_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A4:A,B4:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C2)))))))))).
% 2.54/1.58 thf(fact_27_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 2.54/1.58 thf(fact_28_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.54/1.58 thf(fact_29_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E2:E,F2:F]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F)) @ D2) @ ((((product_Pair @ E) @ F) @ E2) @ F2))))))))))))).
% 2.54/1.58 thf(fact_30_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F:$tType,G:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E2:E,F2:F,G2:G]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2)))))))))))))).
% 2.54/1.58 thf(fact_31_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A4:A,B4:B,C2:C]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C2))))) => (P2 @ X))))).
% 2.54/1.58 thf(fact_32_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A4:A,B4:B,C2:C,D2:D]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P2 @ X))))).
% 2.54/1.58 thf(fact_33_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A4:A,B4:B,C2:C,D2:D,E2:E]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P2 @ X))))).
% 2.54/1.58 thf(fact_34_prod__induct6, axiom, (! [F:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))))]: (((! [A4:A,B4:B,C2:C,D2:D,E2:E,F2:F]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F)) @ D2) @ ((((product_Pair @ E) @ F) @ E2) @ F2)))))))) => (P2 @ X))))).
% 2.54/1.58 thf(fact_35_prod__induct7, axiom, (! [G:$tType,F:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: (((! [A4:A,B4:B,C2:C,D2:D,E2:E,F2:F,G2:G]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2))))))))) => (P2 @ X))))).
% 2.54/1.58 thf(fact_36_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A4) @ B4))))))))).
% 2.54/1.58 thf(fact_37_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P2 @ Prod))))).
% 2.54/1.58 thf(fact_38_HS_Omultiset__empty, axiom, (! [A:$tType]: (((linorder @ A) => (((multiset2 @ A) @ (e @ A)) = (zero_zero @ (multiset @ A))))))).
% 2.54/1.58 thf(fact_39_surjective__pairing, axiom, (! [B:$tType,A:$tType,T3:((product_prod @ A) @ B)]: ((T3 = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ T3)) @ (((product_snd @ A) @ B) @ T3)))))).
% 2.54/1.58 thf(fact_40_prod_Oexhaust__sel, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((Prod = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)))))).
% 2.54/1.58 thf(fact_41_prod__eq__iff, axiom, (! [B:$tType,A:$tType]: (((^ [Y4:((product_prod @ A) @ B),Z2:((product_prod @ A) @ B)]: ((Y4 = Z2))) = (^ [S:((product_prod @ A) @ B),T4:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ S) = (((product_fst @ A) @ B) @ T4)) & ((((product_snd @ A) @ B) @ S) = (((product_snd @ A) @ B) @ T4))))))))).
% 2.54/1.58 thf(fact_42_prod_Oexpand, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B),Prod2:((product_prod @ A) @ B)]: (((((((product_fst @ A) @ B) @ Prod) = (((product_fst @ A) @ B) @ Prod2)) & ((((product_snd @ A) @ B) @ Prod) = (((product_snd @ A) @ B) @ Prod2))) => (Prod = Prod2))))).
% 2.54/1.58 thf(fact_43_prod__eqI, axiom, (! [B:$tType,A:$tType,P:((product_prod @ A) @ B),Q:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ P) = (((product_fst @ A) @ B) @ Q)) => (((((product_snd @ A) @ B) @ P) = (((product_snd @ A) @ B) @ Q)) => (P = Q)))))).
% 2.54/1.58 thf(fact_44_is__heap_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:(tree @ A)]: (((X != (e @ A)) => ((! [V3:A]: ((X != ((((t @ A) @ V3) @ (e @ A)) @ (e @ A))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ (e @ A)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ (e @ A))))) => (~ ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A),Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))))))))))))))))).
% 2.54/1.58 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 2.54/1.58 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A5)))) = A5)))).
% 2.54/1.58 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q2:(A > $o)]: (((! [X3:A]: (((P2 @ X3) = (Q2 @ X3)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q2)))))).
% 2.54/1.58 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G3:(A > B)]: (((! [X3:A]: (((F3 @ X3) = (G3 @ X3)))) => (F3 = G3))))).
% 2.54/1.58 thf(fact_49_Tree_Oexhaust, axiom, (! [A:$tType,Y:(tree @ A)]: (((Y != (e @ A)) => (~ ((! [X212:A,X222:(tree @ A),X232:(tree @ A)]: ((Y != ((((t @ A) @ X212) @ X222) @ X232)))))))))).
% 2.54/1.58 thf(fact_50_Tree_Oinduct, axiom, (! [A:$tType,P2:((tree @ A) > $o),Tree:(tree @ A)]: (((P2 @ (e @ A)) => ((! [X12:A,X24:(tree @ A),X32:(tree @ A)]: (((P2 @ X24) => ((P2 @ X32) => (P2 @ ((((t @ A) @ X12) @ X24) @ X32)))))) => (P2 @ Tree)))))).
% 2.54/1.58 thf(fact_51_Tree_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(tree @ A),X23:(tree @ A)]: (((e @ A) != ((((t @ A) @ X21) @ X22) @ X23))))).
% 2.54/1.58 thf(fact_52_removeLeaf_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:((tree @ A) > $o),A0:(tree @ A)]: (((! [V3:A]: ((P2 @ ((((t @ A) @ V3) @ (e @ A)) @ (e @ A))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: (((P2 @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) => ((P2 @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) => (P2 @ ((((t @ A) @ V3) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ (e @ A))))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: (((P2 @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) => ((P2 @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) => (P2 @ ((((t @ A) @ V3) @ (e @ A)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A),Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A)]: (((P2 @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) => ((P2 @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) => (P2 @ ((((t @ A) @ V3) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))))))) => ((! [V3:A,Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A),Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: (((P2 @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) => ((P2 @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) => (P2 @ ((((t @ A) @ V3) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))))))) => ((P2 @ (e @ A)) => (P2 @ A0))))))))))))).
% 2.54/1.58 thf(fact_53_removeLeaf_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:(tree @ A)]: (((! [V3:A]: ((X != ((((t @ A) @ V3) @ (e @ A)) @ (e @ A))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ (e @ A))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ (e @ A)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A),Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))))) => ((! [V3:A,Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A),Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))))) => (X = (e @ A))))))))))))).
% 2.54/1.58 thf(fact_54_siftDown_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:(tree @ A)]: (((X != (e @ A)) => ((! [V3:A]: ((X != ((((t @ A) @ V3) @ (e @ A)) @ (e @ A))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ (e @ A))))) => ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ (e @ A)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))))) => (~ ((! [V3:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A),Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A)]: ((X != ((((t @ A) @ V3) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))))))))))))))))).
% 2.54/1.58 thf(fact_55_removeLeaf_Osimps_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((((heapIm970386777veLeaf @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ (e @ A))) = ((((product_Pair @ A) @ (tree @ A)) @ (((product_fst @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))) @ ((((t @ A) @ V) @ (((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))) @ (e @ A)))))))))).
% 2.54/1.58 thf(fact_56_removeLeaf_Osimps_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((((heapIm970386777veLeaf @ A) @ ((((t @ A) @ V) @ (e @ A)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((product_Pair @ A) @ (tree @ A)) @ (((product_fst @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))) @ ((((t @ A) @ V) @ (e @ A)) @ (((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))))))))))).
% 2.54/1.58 thf(fact_57_union__mset__add__mset__left, axiom, (! [A:$tType,A2:A,A5:(multiset @ A),B5:(multiset @ A)]: (((((plus_plus @ (multiset @ A)) @ (((add_mset @ A) @ A2) @ A5)) @ B5) = (((add_mset @ A) @ A2) @ (((plus_plus @ (multiset @ A)) @ A5) @ B5)))))).
% 2.54/1.58 thf(fact_58_union__mset__add__mset__right, axiom, (! [A:$tType,A5:(multiset @ A),A2:A,B5:(multiset @ A)]: (((((plus_plus @ (multiset @ A)) @ A5) @ (((add_mset @ A) @ A2) @ B5)) = (((add_mset @ A) @ A2) @ (((plus_plus @ (multiset @ A)) @ A5) @ B5)))))).
% 2.54/1.58 thf(fact_59_single__eq__single, axiom, (! [A:$tType,A2:A,B2:A]: ((((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = (((add_mset @ A) @ B2) @ (zero_zero @ (multiset @ A)))) = (A2 = B2))))).
% 2.54/1.58 thf(fact_60_add__mset__eq__single, axiom, (! [A:$tType,B2:A,M:(multiset @ A),A2:A]: ((((((add_mset @ A) @ B2) @ M) = (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))) = ((B2 = A2) & (M = (zero_zero @ (multiset @ A)))))))).
% 2.54/1.58 thf(fact_61_single__eq__add__mset, axiom, (! [A:$tType,A2:A,B2:A,M:(multiset @ A)]: ((((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = (((add_mset @ A) @ B2) @ M)) = ((B2 = A2) & (M = (zero_zero @ (multiset @ A)))))))).
% 2.54/1.58 thf(fact_62_add__mset__eq__singleton__iff, axiom, (! [A:$tType,X:A,M:(multiset @ A),Y:A]: ((((((add_mset @ A) @ X) @ M) = (((add_mset @ A) @ Y) @ (zero_zero @ (multiset @ A)))) = ((M = (zero_zero @ (multiset @ A))) & (X = Y)))))).
% 2.54/1.58 thf(fact_63_empty__eq__union, axiom, (! [A:$tType,M:(multiset @ A),N:(multiset @ A)]: ((((zero_zero @ (multiset @ A)) = (((plus_plus @ (multiset @ A)) @ M) @ N)) = ((M = (zero_zero @ (multiset @ A))) & (N = (zero_zero @ (multiset @ A)))))))).
% 2.54/1.58 thf(fact_64_union__eq__empty, axiom, (! [A:$tType,M:(multiset @ A),N:(multiset @ A)]: ((((((plus_plus @ (multiset @ A)) @ M) @ N) = (zero_zero @ (multiset @ A))) = ((M = (zero_zero @ (multiset @ A))) & (N = (zero_zero @ (multiset @ A)))))))).
% 2.54/1.58 thf(fact_65_subset__mset_Oadd__eq__0__iff__both__eq__0, axiom, (! [A:$tType,X:(multiset @ A),Y:(multiset @ A)]: ((((((plus_plus @ (multiset @ A)) @ X) @ Y) = (zero_zero @ (multiset @ A))) = ((X = (zero_zero @ (multiset @ A))) & (Y = (zero_zero @ (multiset @ A)))))))).
% 2.54/1.58 thf(fact_66_subset__mset_Ozero__eq__add__iff__both__eq__0, axiom, (! [A:$tType,X:(multiset @ A),Y:(multiset @ A)]: ((((zero_zero @ (multiset @ A)) = (((plus_plus @ (multiset @ A)) @ X) @ Y)) = ((X = (zero_zero @ (multiset @ A))) & (Y = (zero_zero @ (multiset @ A)))))))).
% 2.54/1.58 thf(fact_67_add_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.54/1.58 thf(fact_68_add__right__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C3) @ A2)) = (B2 = C3)))))))).
% 2.54/1.58 thf(fact_69_add__left__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C3)) = (B2 = C3)))))))).
% 2.54/1.58 thf(fact_70_multi__self__add__other__not__self, axiom, (! [A:$tType,M:(multiset @ A),X:A]: ((M != (((add_mset @ A) @ X) @ M))))).
% 2.54/1.58 thf(fact_71_add__mset__add__mset__same__iff, axiom, (! [A:$tType,A2:A,A5:(multiset @ A),B5:(multiset @ A)]: ((((((add_mset @ A) @ A2) @ A5) = (((add_mset @ A) @ A2) @ B5)) = (A5 = B5))))).
% 2.54/1.58 thf(fact_72_zero__eq__add__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A,Y:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ X) @ Y)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))).
% 2.54/1.58 thf(fact_73_add__eq__0__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A,Y:A]: ((((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))).
% 2.54/1.58 thf(fact_74_add__cancel__right__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ A2) @ B2)) = (B2 = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_75_add__cancel__right__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ B2) @ A2)) = (B2 = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_76_add__cancel__left__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: ((((((plus_plus @ A) @ A2) @ B2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_77_add__cancel__left__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [B2:A,A2:A]: ((((((plus_plus @ A) @ B2) @ A2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_78_double__zero__sym, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ A2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_79_double__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((((plus_plus @ A) @ A2) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_80_add_Oright__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.54/1.58 thf(fact_81_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_82_add__right__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C3) @ A2)) => (B2 = C3)))))))).
% 2.54/1.58 thf(fact_83_add__left__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C3)) => (B2 = C3)))))))).
% 2.54/1.58 thf(fact_84_add_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [B2:A,A2:A,C3:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C3)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 2.54/1.58 thf(fact_85_add_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => ((plus_plus @ A) = (^ [A6:A,B6:A]: ((((plus_plus @ A) @ B6) @ A6)))))))).
% 2.54/1.58 thf(fact_86_add_Oright__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [B2:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C3) @ A2)) = (B2 = C3)))))))).
% 2.54/1.58 thf(fact_87_add_Oleft__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C3)) = (B2 = C3)))))))).
% 2.54/1.58 thf(fact_88_add_Oassoc, axiom, (! [A:$tType]: (((semigroup_add @ A) => (! [A2:A,B2:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 2.54/1.58 thf(fact_89_group__cancel_Oadd2, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [B5:A,K:A,B2:A,A2:A]: (((B5 = (((plus_plus @ A) @ K) @ B2)) => ((((plus_plus @ A) @ A2) @ B5) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.54/1.58 thf(fact_90_group__cancel_Oadd1, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A5:A,K:A,A2:A,B2:A]: (((A5 = (((plus_plus @ A) @ K) @ A2)) => ((((plus_plus @ A) @ A5) @ B2) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.54/1.58 thf(fact_91_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 2.54/1.58 thf(fact_92_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [A2:A,B2:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 2.54/1.58 thf(fact_93_multi__union__self__other__eq, axiom, (! [A:$tType,A5:(multiset @ A),X5:(multiset @ A),Y5:(multiset @ A)]: ((((((plus_plus @ (multiset @ A)) @ A5) @ X5) = (((plus_plus @ (multiset @ A)) @ A5) @ Y5)) => (X5 = Y5))))).
% 2.54/1.58 thf(fact_94_union__right__cancel, axiom, (! [A:$tType,M:(multiset @ A),K2:(multiset @ A),N:(multiset @ A)]: ((((((plus_plus @ (multiset @ A)) @ M) @ K2) = (((plus_plus @ (multiset @ A)) @ N) @ K2)) = (M = N))))).
% 2.54/1.58 thf(fact_95_union__left__cancel, axiom, (! [A:$tType,K2:(multiset @ A),M:(multiset @ A),N:(multiset @ A)]: ((((((plus_plus @ (multiset @ A)) @ K2) @ M) = (((plus_plus @ (multiset @ A)) @ K2) @ N)) = (M = N))))).
% 2.54/1.58 thf(fact_96_union__commute, axiom, (! [A:$tType]: (((plus_plus @ (multiset @ A)) = (^ [M2:(multiset @ A),N2:(multiset @ A)]: ((((plus_plus @ (multiset @ A)) @ N2) @ M2))))))).
% 2.54/1.58 thf(fact_97_union__lcomm, axiom, (! [A:$tType,M:(multiset @ A),N:(multiset @ A),K2:(multiset @ A)]: (((((plus_plus @ (multiset @ A)) @ M) @ (((plus_plus @ (multiset @ A)) @ N) @ K2)) = (((plus_plus @ (multiset @ A)) @ N) @ (((plus_plus @ (multiset @ A)) @ M) @ K2)))))).
% 2.54/1.58 thf(fact_98_union__assoc, axiom, (! [A:$tType,M:(multiset @ A),N:(multiset @ A),K2:(multiset @ A)]: (((((plus_plus @ (multiset @ A)) @ (((plus_plus @ (multiset @ A)) @ M) @ N)) @ K2) = (((plus_plus @ (multiset @ A)) @ M) @ (((plus_plus @ (multiset @ A)) @ N) @ K2)))))).
% 2.54/1.58 thf(fact_99_add__mset__commute, axiom, (! [A:$tType,X:A,Y:A,M:(multiset @ A)]: (((((add_mset @ A) @ X) @ (((add_mset @ A) @ Y) @ M)) = (((add_mset @ A) @ Y) @ (((add_mset @ A) @ X) @ M)))))).
% 2.54/1.58 thf(fact_100_add__eq__conv__ex, axiom, (! [A:$tType,A2:A,M:(multiset @ A),B2:A,N:(multiset @ A)]: ((((((add_mset @ A) @ A2) @ M) = (((add_mset @ A) @ B2) @ N)) = (((M = N) & (A2 = B2)) | (? [K3:(multiset @ A)]: (((M = (((add_mset @ A) @ B2) @ K3)) & (N = (((add_mset @ A) @ A2) @ K3)))))))))).
% 2.54/1.58 thf(fact_101_add_Ogroup__left__neutral, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.54/1.58 thf(fact_102_add_Ocomm__neutral, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.54/1.58 thf(fact_103_comm__monoid__add__class_Oadd__0, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.54/1.58 thf(fact_104_empty__neutral_I1_J, axiom, (! [A:$tType,X:(multiset @ A)]: (((((plus_plus @ (multiset @ A)) @ (zero_zero @ (multiset @ A))) @ X) = X)))).
% 2.54/1.58 thf(fact_105_empty__neutral_I2_J, axiom, (! [A:$tType,X:(multiset @ A)]: (((((plus_plus @ (multiset @ A)) @ X) @ (zero_zero @ (multiset @ A))) = X)))).
% 2.54/1.58 thf(fact_106_multi__nonempty__split, axiom, (! [A:$tType,M:(multiset @ A)]: (((M != (zero_zero @ (multiset @ A))) => (? [A7:(multiset @ A),A4:A]: ((M = (((add_mset @ A) @ A4) @ A7)))))))).
% 2.54/1.58 thf(fact_107_empty__not__add__mset, axiom, (! [A:$tType,A2:A,A5:(multiset @ A)]: (((zero_zero @ (multiset @ A)) != (((add_mset @ A) @ A2) @ A5))))).
% 2.54/1.58 thf(fact_108_multiset__induct2, axiom, (! [A:$tType,B:$tType,P2:((multiset @ A) > ((multiset @ B) > $o)),M:(multiset @ A),N:(multiset @ B)]: ((((P2 @ (zero_zero @ (multiset @ A))) @ (zero_zero @ (multiset @ B))) => ((! [A4:A,M3:(multiset @ A),N3:(multiset @ B)]: ((((P2 @ M3) @ N3) => ((P2 @ (((add_mset @ A) @ A4) @ M3)) @ N3)))) => ((! [A4:B,M3:(multiset @ A),N3:(multiset @ B)]: ((((P2 @ M3) @ N3) => ((P2 @ M3) @ (((add_mset @ B) @ A4) @ N3))))) => ((P2 @ M) @ N))))))).
% 2.54/1.58 thf(fact_109_multiset__induct, axiom, (! [A:$tType,P2:((multiset @ A) > $o),M:(multiset @ A)]: (((P2 @ (zero_zero @ (multiset @ A))) => ((! [X3:A,M3:(multiset @ A)]: (((P2 @ M3) => (P2 @ (((add_mset @ A) @ X3) @ M3))))) => (P2 @ M)))))).
% 2.54/1.58 thf(fact_110_multiset__cases, axiom, (! [A:$tType,M:(multiset @ A)]: (((M != (zero_zero @ (multiset @ A))) => (~ ((! [X3:A,N3:(multiset @ A)]: ((M != (((add_mset @ A) @ X3) @ N3)))))))))).
% 2.54/1.58 thf(fact_111_add__mset__add__single, axiom, (! [A:$tType]: (((add_mset @ A) = (^ [A6:A,A8:(multiset @ A)]: ((((plus_plus @ (multiset @ A)) @ A8) @ (((add_mset @ A) @ A6) @ (zero_zero @ (multiset @ A)))))))))).
% 2.54/1.58 thf(fact_112_union__is__single, axiom, (! [A:$tType,M:(multiset @ A),N:(multiset @ A),A2:A]: ((((((plus_plus @ (multiset @ A)) @ M) @ N) = (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))) = (((M = (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))) & (N = (zero_zero @ (multiset @ A)))) | ((M = (zero_zero @ (multiset @ A))) & (N = (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))))))))).
% 2.54/1.58 thf(fact_113_single__is__union, axiom, (! [A:$tType,A2:A,M:(multiset @ A),N:(multiset @ A)]: ((((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = (((plus_plus @ (multiset @ A)) @ M) @ N)) = ((((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = M) & (N = (zero_zero @ (multiset @ A)))) | ((M = (zero_zero @ (multiset @ A))) & ((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = N))))))).
% 2.54/1.58 thf(fact_114_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.54/1.58 thf(fact_115_exI__realizer, axiom, (! [B:$tType,A:$tType,P2:(A > (B > $o)),Y:A,X:B]: ((((P2 @ Y) @ X) => ((P2 @ (((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y))) @ (((product_fst @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y))))))).
% 2.54/1.58 thf(fact_116_conjI__realizer, axiom, (! [A:$tType,B:$tType,P2:(A > $o),P:A,Q2:(B > $o),Q:B]: (((P2 @ P) => ((Q2 @ Q) => ((P2 @ (((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ P) @ Q))) & (Q2 @ (((product_snd @ A) @ B) @ ((((product_Pair @ A) @ B) @ P) @ Q))))))))).
% 2.54/1.58 thf(fact_117_BNF__Greatest__Fixpoint_Osubst__Pair, axiom, (! [B:$tType,A:$tType,P2:(A > (B > $o)),X:A,Y:B,A2:((product_prod @ A) @ B)]: ((((P2 @ X) @ Y) => ((A2 = ((((product_Pair @ A) @ B) @ X) @ Y)) => ((P2 @ (((product_fst @ A) @ B) @ A2)) @ (((product_snd @ A) @ B) @ A2))))))).
% 2.54/1.58 thf(fact_118_Multiset_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A8:(multiset @ A)]: ((A8 = (zero_zero @ (multiset @ A))))))))).
% 2.54/1.58 thf(fact_119_exE__realizer_H, axiom, (! [A:$tType,B:$tType,P2:(A > (B > $o)),P:((product_prod @ B) @ A)]: ((((P2 @ (((product_snd @ B) @ A) @ P)) @ (((product_fst @ B) @ A) @ P)) => (~ ((! [X3:B,Y3:A]: ((~ (((P2 @ Y3) @ X3))))))))))).
% 2.54/1.58 thf(fact_120_eq__snd__iff, axiom, (! [A:$tType,B:$tType,B2:A,P:((product_prod @ B) @ A)]: (((B2 = (((product_snd @ B) @ A) @ P)) = (? [A6:B]: ((P = ((((product_Pair @ B) @ A) @ A6) @ B2)))))))).
% 2.54/1.58 thf(fact_121_eq__fst__iff, axiom, (! [A:$tType,B:$tType,A2:A,P:((product_prod @ A) @ B)]: (((A2 = (((product_fst @ A) @ B) @ P)) = (? [B6:B]: ((P = ((((product_Pair @ A) @ B) @ A2) @ B6)))))))).
% 2.54/1.58 thf(fact_122_verit__sum__simplify, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.54/1.58 thf(fact_123_add__0__iff, axiom, (! [A:$tType]: (((semiri456707255roduct @ A) => (! [B2:A,A2:A]: (((B2 = (((plus_plus @ A) @ B2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_124_HS_Ois__empty__as__list, axiom, (! [A:$tType]: (((linorder @ A) => (! [E3:(tree @ A)]: ((((heapIm721255937_empty @ A) @ E3) => (((multiset2 @ A) @ E3) = (zero_zero @ (multiset @ A)))))))))).
% 2.54/1.58 thf(fact_125_add__mset__replicate__mset__safe, axiom, (! [A:$tType,B:$tType,M:(multiset @ B),A2:B]: ((((((nO_MATCH @ (multiset @ A)) @ (multiset @ B)) @ (zero_zero @ (multiset @ A))) @ M) => ((((add_mset @ B) @ A2) @ M) = (((plus_plus @ (multiset @ B)) @ (((add_mset @ B) @ A2) @ (zero_zero @ (multiset @ B)))) @ M)))))).
% 2.54/1.58 thf(fact_126_HS_Ois__empty__empty, axiom, (! [A:$tType]: (((linorder @ A) => ((heapIm721255937_empty @ A) @ (e @ A)))))).
% 2.54/1.58 thf(fact_127_hs__is__empty__def, axiom, (! [A:$tType]: (((heapIm721255937_empty @ A) = (^ [T4:(tree @ A)]: ((T4 = (e @ A)))))))).
% 2.54/1.58 thf(fact_128_HS_Ois__empty__inj, axiom, (! [A:$tType]: (((linorder @ A) => (! [E3:(tree @ A)]: ((((heapIm721255937_empty @ A) @ E3) => (E3 = (e @ A))))))))).
% 2.54/1.58 thf(fact_129_prod_Oswap__def, axiom, (! [B:$tType,A:$tType]: ((((product_swap @ A) @ B) = (^ [P3:((product_prod @ A) @ B)]: (((((product_Pair @ B) @ A) @ (((product_snd @ A) @ B) @ P3)) @ (((product_fst @ A) @ B) @ P3)))))))).
% 2.54/1.58 thf(fact_130_removeLeaf__heap__is__heap, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:(tree @ A)]: ((((is_heap @ A) @ T3) => ((T3 != (e @ A)) => ((is_heap @ A) @ (((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ T3))))))))))).
% 2.54/1.58 thf(fact_131_NO__MATCH__cong, axiom, (! [B:$tType,A:$tType]: ((((nO_MATCH @ A) @ B) = ((nO_MATCH @ A) @ B))))).
% 2.54/1.58 thf(fact_132_NO__MATCH__def, axiom, (! [B:$tType,A:$tType]: ((((nO_MATCH @ A) @ B) = (^ [Pat:A,Val:B]: ($true)))))).
% 2.54/1.58 thf(fact_133_swap__swap, axiom, (! [B:$tType,A:$tType,P:((product_prod @ A) @ B)]: (((((product_swap @ B) @ A) @ (((product_swap @ A) @ B) @ P)) = P)))).
% 2.54/1.58 thf(fact_134_swap__simp, axiom, (! [A:$tType,B:$tType,X:B,Y:A]: (((((product_swap @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y)) = ((((product_Pair @ A) @ B) @ Y) @ X))))).
% 2.54/1.58 thf(fact_135_snd__swap, axiom, (! [B:$tType,A:$tType,X:((product_prod @ A) @ B)]: (((((product_snd @ B) @ A) @ (((product_swap @ A) @ B) @ X)) = (((product_fst @ A) @ B) @ X))))).
% 2.54/1.58 thf(fact_136_fst__swap, axiom, (! [A:$tType,B:$tType,X:((product_prod @ B) @ A)]: (((((product_fst @ A) @ B) @ (((product_swap @ B) @ A) @ X)) = (((product_snd @ B) @ A) @ X))))).
% 2.54/1.58 thf(fact_137_is__heap_Osimps_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => ((is_heap @ A) @ (e @ A)))))).
% 2.54/1.58 thf(fact_138_is__heap_Osimps_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A]: (((is_heap @ A) @ ((((t @ A) @ V) @ (e @ A)) @ (e @ A))))))))).
% 2.54/1.58 thf(fact_139_removeLeaf__val__val, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:(tree @ A)]: ((((((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ T3)) != (e @ A)) => ((T3 != (e @ A)) => (((val @ A) @ T3) = ((val @ A) @ (((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ T3)))))))))))).
% 2.54/1.58 thf(fact_140_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C3 @ A2) @ B2))))).
% 2.54/1.58 thf(fact_141_Heap__axioms__def, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (((heap_axioms @ B) @ A) = (^ [Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B))]: (((! [L2:B]: (((Multiset @ L2) = ((multiset2 @ A) @ (As_tree @ L2))))) & ((! [I2:(list @ A)]: (((is_heap @ A) @ (As_tree @ (Of_list @ I2))))) & ((! [T4:B]: ((((As_tree @ T4) = (e @ A)) = (Is_empty @ T4)))) & ((! [L2:B,M4:A,L3:B]: (((~ ((Is_empty @ L2))) => ((((((product_Pair @ A) @ B) @ M4) @ L3) = (Remove_max @ L2)) => ((((add_mset @ A) @ M4) @ (Multiset @ L3)) = (Multiset @ L2)))))) & ((! [L2:B,M4:A,L3:B]: (((~ ((Is_empty @ L2))) => (((is_heap @ A) @ (As_tree @ L2)) => ((((((product_Pair @ A) @ B) @ M4) @ L3) = (Remove_max @ L2)) => ((is_heap @ A) @ (As_tree @ L3))))))) & (! [T4:B,M4:A,T5:B]: (((~ ((Is_empty @ T4))) => ((((((product_Pair @ A) @ B) @ M4) @ T5) = (Remove_max @ T4)) => (M4 = ((val @ A) @ (As_tree @ T4))))))))))))))))))).
% 2.54/1.58 thf(fact_142_Heap__axioms_Ointro, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Of_list2:((list @ A) > B),Is_empty2:(B > $o),Remove_max2:(B > ((product_prod @ A) @ B))]: (((! [L4:B]: (((Multiset2 @ L4) = ((multiset2 @ A) @ (As_tree2 @ L4))))) => ((! [I3:(list @ A)]: (((is_heap @ A) @ (As_tree2 @ (Of_list2 @ I3))))) => ((! [T6:B]: ((((As_tree2 @ T6) = (e @ A)) = (Is_empty2 @ T6)))) => ((! [L4:B,M5:A,L5:B]: (((~ ((Is_empty2 @ L4))) => ((((((product_Pair @ A) @ B) @ M5) @ L5) = (Remove_max2 @ L4)) => ((((add_mset @ A) @ M5) @ (Multiset2 @ L5)) = (Multiset2 @ L4)))))) => ((! [L4:B,M5:A,L5:B]: (((~ ((Is_empty2 @ L4))) => (((is_heap @ A) @ (As_tree2 @ L4)) => ((((((product_Pair @ A) @ B) @ M5) @ L5) = (Remove_max2 @ L4)) => ((is_heap @ A) @ (As_tree2 @ L5))))))) => ((! [T6:B,M5:A,T7:B]: (((~ ((Is_empty2 @ T6))) => ((((((product_Pair @ A) @ B) @ M5) @ T7) = (Remove_max2 @ T6)) => (M5 = ((val @ A) @ (As_tree2 @ T6))))))) => (((((((heap_axioms @ B) @ A) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2))))))))))))).
% 2.54/1.58 thf(fact_143_val_Osimps, axiom, (! [A:$tType,V:A,Uu:(tree @ A),Uv:(tree @ A)]: ((((val @ A) @ ((((t @ A) @ V) @ Uu) @ Uv)) = V)))).
% 2.54/1.58 thf(fact_144_is__heap_Osimps_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((((is_heap @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ (e @ A))) = ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V) & ((is_heap @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))))))))).
% 2.54/1.58 thf(fact_145_is__heap_Osimps_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((((is_heap @ A) @ ((((t @ A) @ V) @ (e @ A)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V) & ((is_heap @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))))))))).
% 2.54/1.58 thf(fact_146_divides__aux__eq, axiom, (! [A:$tType]: (((unique1598680935umeral @ A) => (! [Q:A,R:A]: ((((unique455577585es_aux @ A) @ ((((product_Pair @ A) @ A) @ Q) @ R)) = (R = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_147_Heap_Oremove__max__is__heap, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B)),L:B,M6:A,L6:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2) => ((~ ((Is_empty2 @ L))) => (((is_heap @ A) @ (As_tree2 @ L)) => ((((((product_Pair @ A) @ B) @ M6) @ L6) = (Remove_max2 @ L)) => ((is_heap @ A) @ (As_tree2 @ L6)))))))))))).
% 2.54/1.58 thf(fact_148_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N4:A]: (((((ord_less_eq @ A) @ N4) @ (zero_zero @ A)) = (N4 = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_149_add__le__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C3:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.54/1.58 thf(fact_150_add__le__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C3:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.54/1.58 thf(fact_151_add__le__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ B2) @ A2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_152_add__le__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_153_le__add__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.54/1.58 thf(fact_154_le__add__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ B2) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.54/1.58 thf(fact_155_double__add__le__zero__iff__single__add__le__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_156_zero__le__double__add__iff__zero__le__single__add, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ A2)))))))).
% 2.54/1.58 thf(fact_157_verit__la__disequality, axiom, (! [A:$tType]: (((linorder @ A) => (! [A2:A,B2:A]: (((A2 = B2) | ((~ ((((ord_less_eq @ A) @ A2) @ B2))) | (~ ((((ord_less_eq @ A) @ B2) @ A2))))))))))).
% 2.54/1.58 thf(fact_158_add__le__imp__le__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C3:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.54/1.58 thf(fact_159_add__le__imp__le__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C3:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.54/1.58 thf(fact_160_le__iff__add, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => ((ord_less_eq @ A) = (^ [A6:A,B6:A]: ((? [C4:A]: ((B6 = (((plus_plus @ A) @ A6) @ C4))))))))))).
% 2.54/1.58 thf(fact_161_add__right__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 2.54/1.58 thf(fact_162_less__eqE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (~ ((! [C2:A]: ((B2 != (((plus_plus @ A) @ A2) @ C2))))))))))))).
% 2.54/1.58 thf(fact_163_add__left__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2))))))))).
% 2.54/1.58 thf(fact_164_add__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C3:A,D3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C3) @ D3) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ D3)))))))))).
% 2.54/1.58 thf(fact_165_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.54/1.58 thf(fact_166_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.54/1.58 thf(fact_167_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (K = L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.54/1.58 thf(fact_168_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X))))))).
% 2.54/1.58 thf(fact_169_add__decreasing, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,C3:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ C3) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ B2))))))))).
% 2.54/1.58 thf(fact_170_add__increasing, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ C3) => (((ord_less_eq @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C3)))))))))).
% 2.54/1.58 thf(fact_171_add__decreasing2, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [C3:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ C3) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ B2))))))))).
% 2.54/1.58 thf(fact_172_add__increasing2, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [C3:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ C3) => ((((ord_less_eq @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C3)))))))))).
% 2.54/1.58 thf(fact_173_add__nonneg__nonneg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.54/1.58 thf(fact_174_add__nonpos__nonpos, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.54/1.58 thf(fact_175_add__nonneg__eq__0__iff, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y) => (((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))))).
% 2.54/1.58 thf(fact_176_add__nonpos__eq__0__iff, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ Y) @ (zero_zero @ A)) => (((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))))).
% 2.54/1.58 thf(fact_177_Heap_Oas__tree__empty, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B)),T3:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2) => (((As_tree2 @ T3) = (e @ A)) = (Is_empty2 @ T3))))))))).
% 2.54/1.58 thf(fact_178_Heap_Ois__heap__of__list, axiom, (! [B:$tType,A:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B)),I:(list @ A)]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2) => ((is_heap @ A) @ (As_tree2 @ (Of_list2 @ I)))))))))).
% 2.54/1.58 thf(fact_179_Heap_Omultiset, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B)),L:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2) => ((Multiset2 @ L) = ((multiset2 @ A) @ (As_tree2 @ L)))))))))).
% 2.54/1.58 thf(fact_180_divides__aux__def, axiom, (! [A:$tType]: (((unique1598680935umeral @ A) => ((unique455577585es_aux @ A) = (^ [Qr:((product_prod @ A) @ A)]: (((((product_snd @ A) @ A) @ Qr) = (zero_zero @ A))))))))).
% 2.54/1.58 thf(fact_181_Heap_Oaxioms_I2_J, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B))]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2) => (((((((heap_axioms @ B) @ A) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2)))))))).
% 2.54/1.58 thf(fact_182_is__heap_Osimps_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Vd:A,Ve:(tree @ A),Vf:(tree @ A),Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((((is_heap @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V) & (((is_heap @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)) & ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ V) & ((is_heap @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf)))))))))))).
% 2.54/1.58 thf(fact_183_is__heap_Osimps_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Va:A,Vb:(tree @ A),Vc:(tree @ A),Vd:A,Ve:(tree @ A),Vf:(tree @ A)]: ((((is_heap @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) = ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ V) & (((is_heap @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) & ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V) & ((is_heap @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))))))))))).
% 2.54/1.58 thf(fact_184_Heap_Oremove__max__multiset_H, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B)),L:B,M6:A,L6:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2) => ((~ ((Is_empty2 @ L))) => ((((((product_Pair @ A) @ B) @ M6) @ L6) = (Remove_max2 @ L)) => ((((add_mset @ A) @ M6) @ (Multiset2 @ L6)) = (Multiset2 @ L))))))))))).
% 2.54/1.58 thf(fact_185_Heap_Oremove__max__val, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B)),T3:B,M6:A,T2:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2) => ((~ ((Is_empty2 @ T3))) => ((((((product_Pair @ A) @ B) @ M6) @ T2) = (Remove_max2 @ T3)) => (M6 = ((val @ A) @ (As_tree2 @ T3)))))))))))).
% 2.54/1.58 thf(fact_186_siftDown_Osimps_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [Va:A,Vb:(tree @ A),Vc:(tree @ A),V:A]: ((((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ (e @ A)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((t @ A) @ V) @ (e @ A)) @ ((((t @ A) @ Va) @ Vb) @ Vc)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ (e @ A)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ (e @ A)) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))))))))))))).
% 2.54/1.58 thf(fact_187_siftDown_Osimps_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [Va:A,Vb:(tree @ A),Vc:(tree @ A),V:A]: ((((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ (e @ A))) = ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ (e @ A)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ (e @ A))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))))) @ (e @ A))))))))))).
% 2.54/1.58 thf(fact_188_siftDown_Osimps_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [Vd:A,Ve:(tree @ A),Vf:(tree @ A),Va:A,Vb:(tree @ A),Vc:(tree @ A),V:A]: ((((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) => (((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) = ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))))) @ ((((t @ A) @ Vd) @ Ve) @ Vf)))))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))))) => (((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) = ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf)))))))))))))))).
% 2.54/1.58 thf(fact_189_siftDown_Osimps_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (((heapIm748920189ftDown @ A) @ (e @ A)) = (e @ A)))))).
% 2.54/1.58 thf(fact_190_siftDown__multiset, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:(tree @ A)]: ((((multiset2 @ A) @ ((heapIm748920189ftDown @ A) @ T3)) = ((multiset2 @ A) @ T3)))))))).
% 2.54/1.58 thf(fact_191_siftDown__Node, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:(tree @ A),V:A,L:(tree @ A),R:(tree @ A)]: (((T3 = ((((t @ A) @ V) @ L) @ R)) => (? [L5:(tree @ A),V4:A,R2:(tree @ A)]: (((((heapIm748920189ftDown @ A) @ T3) = ((((t @ A) @ V4) @ L5) @ R2)) & (((ord_less_eq @ A) @ V) @ V4))))))))))).
% 2.54/1.58 thf(fact_192_siftDown_Osimps_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A]: ((((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ (e @ A)) @ (e @ A))) = ((((t @ A) @ V) @ (e @ A)) @ (e @ A))))))))).
% 2.54/1.58 thf(fact_193_siftDown__heap__is__heap, axiom, (! [A:$tType]: (((linorder @ A) => (! [L:(tree @ A),R:(tree @ A),T3:(tree @ A),V:A]: ((((is_heap @ A) @ L) => (((is_heap @ A) @ R) => ((T3 = ((((t @ A) @ V) @ L) @ R)) => ((is_heap @ A) @ ((heapIm748920189ftDown @ A) @ T3))))))))))).
% 2.54/1.58 thf(fact_194_siftDown_Osimps_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [Va:A,Vb:(tree @ A),Vc:(tree @ A),Vd:A,Ve:(tree @ A),Vf:(tree @ A),V:A]: ((((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) => (((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((t @ A) @ V) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) @ ((((t @ A) @ Va) @ Vb) @ Vc)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))))) @ ((((t @ A) @ Va) @ Vb) @ Vc)))))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ ((val @ A) @ ((((t @ A) @ Vd) @ Ve) @ Vf))))) => (((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((t @ A) @ V) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) @ ((((t @ A) @ Va) @ Vb) @ Vc)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) @ ((((t @ A) @ Va) @ Vb) @ Vc))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ ((((t @ A) @ Vd) @ Ve) @ Vf)) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Va) @ Vb) @ Vc)))))))))))))))).
% 2.54/1.58 thf(fact_195_siftDown__in__tree, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:(tree @ A)]: (((T3 != (e @ A)) => (((in_tree @ A) @ ((val @ A) @ ((heapIm748920189ftDown @ A) @ T3))) @ T3)))))))).
% 2.54/1.58 thf(fact_196_is__heap__max, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,T3:(tree @ A)]: (((((in_tree @ A) @ V) @ T3) => (((is_heap @ A) @ T3) => (((ord_less_eq @ A) @ V) @ ((val @ A) @ T3)))))))))).
% 2.54/1.58 thf(fact_197_in__tree_Osimps_I2_J, axiom, (! [A:$tType,V:A,V2:A,L:(tree @ A),R:(tree @ A)]: (((((in_tree @ A) @ V) @ ((((t @ A) @ V2) @ L) @ R)) = ((V = V2) | ((((in_tree @ A) @ V) @ L) | (((in_tree @ A) @ V) @ R))))))).
% 2.54/1.58 thf(fact_198_in__tree_Osimps_I1_J, axiom, (! [A:$tType,V:A]: ((~ ((((in_tree @ A) @ V) @ (e @ A))))))).
% 2.54/1.58 thf(fact_199_siftDown__in__tree__set, axiom, (! [A:$tType]: (((linorder @ A) => ((in_tree @ A) = (^ [V5:A,T4:(tree @ A)]: ((((in_tree @ A) @ V5) @ ((heapIm748920189ftDown @ A) @ T4))))))))).
% 2.54/1.58 thf(fact_200_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.54/1.58 thf(fact_201_hs__remove__max__def, axiom, (! [A:$tType]: (((linorder @ A) => ((heapIm1542349758ve_max @ A) = (^ [T4:(tree @ A)]: (((((if @ ((product_prod @ A) @ (tree @ A))) @ ((((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ T4)) = (e @ A))) @ ((((product_Pair @ A) @ (tree @ A)) @ ((val @ A) @ T4)) @ (e @ A))) @ ((((product_Pair @ A) @ (tree @ A)) @ ((val @ A) @ T4)) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ (((product_fst @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ T4))) @ ((heapIm1271749598e_left @ A) @ (((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ T4)))) @ ((heapIm1434396069_right @ A) @ (((product_snd @ A) @ (tree @ A)) @ ((heapIm970386777veLeaf @ A) @ T4)))))))))))))).
% 2.54/1.58 thf(fact_202_is__num__normalize_I1_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (! [A2:A,B2:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 2.54/1.58 thf(fact_203_scomp__unfold, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType]: ((((((product_scomp @ A) @ B) @ C) @ D) = (^ [F4:(A > ((product_prod @ B) @ C)),G4:(B > (C > D)),X4:A]: (((G4 @ (((product_fst @ B) @ C) @ (F4 @ X4))) @ (((product_snd @ B) @ C) @ (F4 @ X4))))))))).
% 2.54/1.58 thf(fact_204_heapify_Osimps_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,L:(tree @ A),R:(tree @ A)]: ((((heapIm818251801eapify @ A) @ ((((t @ A) @ V) @ L) @ R)) = ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm818251801eapify @ A) @ L)) @ ((heapIm818251801eapify @ A) @ R)))))))))).
% 2.54/1.58 thf(fact_205_scomp__scomp, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,F:$tType,E:$tType,F3:(A > ((product_prod @ E) @ F)),G3:(E > (F > ((product_prod @ C) @ D))),H:(C > (D > B))]: ((((((((product_scomp @ A) @ C) @ D) @ B) @ ((((((product_scomp @ A) @ E) @ F) @ ((product_prod @ C) @ D)) @ F3) @ G3)) @ H) = ((((((product_scomp @ A) @ E) @ F) @ B) @ F3) @ (^ [X4:E]: (((((((product_scomp @ F) @ C) @ D) @ B) @ (G3 @ X4)) @ H)))))))).
% 2.54/1.58 thf(fact_206_Pair__scomp, axiom, (! [A:$tType,B:$tType,C:$tType,X:C,F3:(C > (A > B))]: ((((((((product_scomp @ A) @ C) @ A) @ B) @ (((product_Pair @ C) @ A) @ X)) @ F3) = (F3 @ X))))).
% 2.54/1.58 thf(fact_207_scomp__Pair, axiom, (! [C:$tType,B:$tType,A:$tType,X:(A > ((product_prod @ B) @ C))]: ((((((((product_scomp @ A) @ B) @ C) @ ((product_prod @ B) @ C)) @ X) @ ((product_Pair @ B) @ C)) = X)))).
% 2.54/1.58 thf(fact_208_heapify_Osimps_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (((heapIm818251801eapify @ A) @ (e @ A)) = (e @ A)))))).
% 2.54/1.58 thf(fact_209_heapify__heap__is__heap, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:(tree @ A)]: (((is_heap @ A) @ ((heapIm818251801eapify @ A) @ T3)))))))).
% 2.54/1.58 thf(fact_210_multiset__heapify, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:(tree @ A)]: ((((multiset2 @ A) @ ((heapIm818251801eapify @ A) @ T3)) = ((multiset2 @ A) @ T3)))))))).
% 2.54/1.58 thf(fact_211_Heap__def, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (((heap @ B) @ A) = (^ [Empty2:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B))]: ((((((((collection @ B) @ A) @ Empty2) @ Is_empty) @ Of_list) @ Multiset) & (((((((heap_axioms @ B) @ A) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max))))))))).
% 2.54/1.58 thf(fact_212_Heap_Ointro, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B))]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) => ((((((((heap_axioms @ B) @ A) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2) => ((((((((heap @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2))))))))).
% 2.54/1.58 thf(fact_213_Heap_Oaxioms_I1_J, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B))]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2) => ((((((collection @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2)))))))).
% 2.54/1.58 thf(fact_214_HS_OCollection__axioms, axiom, (! [A:$tType]: (((linorder @ A) => ((((((collection @ (tree @ A)) @ A) @ (e @ A)) @ (heapIm721255937_empty @ A)) @ (heapIm874063447f_list @ A)) @ (multiset2 @ A)))))).
% 2.54/1.58 thf(fact_215_Collection_Omultiset__empty, axiom, (! [B:$tType,A:$tType,Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A))]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) => ((Multiset2 @ Empty) = (zero_zero @ (multiset @ A))))))).
% 2.54/1.58 thf(fact_216_Collection_Ois__empty__as__list, axiom, (! [B:$tType,A:$tType,Empty:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),E3:B]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty2) @ Of_list2) @ Multiset2) => ((Is_empty2 @ E3) => ((Multiset2 @ E3) = (zero_zero @ (multiset @ A)))))))).
% 2.54/1.58 thf(fact_217_hs__of__list__def, axiom, (! [A:$tType]: (((linorder @ A) => ((heapIm874063447f_list @ A) = (^ [L2:(list @ A)]: (((heapIm818251801eapify @ A) @ ((heapIm1912108042t_tree @ A) @ L2))))))))).
% 2.54/1.58 thf(fact_218_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),S2:(set @ ((product_prod @ A) @ B))]: ((((^ [X4:A,Y6:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y6)) @ R3))) = (^ [X4:A,Y6:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y6)) @ S2)))) = (R3 = S2))))).
% 2.54/1.58 thf(fact_219_subrelI, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S3:(set @ ((product_prod @ A) @ B))]: (((! [X3:A,Y3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ R) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ S3)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R) @ S3))))).
% 2.54/1.58 thf(fact_220_pred__subset__eq2, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),S2:(set @ ((product_prod @ A) @ B))]: (((((ord_less_eq @ (A > (B > $o))) @ (^ [X4:A,Y6:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y6)) @ R3)))) @ (^ [X4:A,Y6:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y6)) @ S2)))) = (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R3) @ S2))))).
% 2.54/1.58 thf(fact_221_fun__cong__unused__0, axiom, (! [A:$tType,B:$tType,C:$tType]: (((zero @ B) => (! [F3:((A > B) > C),G3:C]: (((F3 = (^ [X4:(A > B)]: (G3))) => ((F3 @ (^ [X4:A]: ((zero_zero @ B)))) = G3)))))))).
% 2.54/1.58 thf(fact_222_heap__top__geq, axiom, (! [A:$tType]: (((linorder @ A) => (! [A2:A,T3:(tree @ A)]: (((((member @ A) @ A2) @ ((set_mset @ A) @ ((multiset2 @ A) @ T3))) => (((is_heap @ A) @ T3) => (((ord_less_eq @ A) @ A2) @ ((val @ A) @ T3)))))))))).
% 2.54/1.58 thf(fact_223_multi__member__last, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ ((set_mset @ A) @ (((add_mset @ A) @ X) @ (zero_zero @ (multiset @ A)))))))).
% 2.54/1.58 thf(fact_224_union__single__eq__member, axiom, (! [A:$tType,X:A,M:(multiset @ A),N:(multiset @ A)]: ((((((add_mset @ A) @ X) @ M) = N) => (((member @ A) @ X) @ ((set_mset @ A) @ N)))))).
% 2.54/1.58 thf(fact_225_insert__noteq__member, axiom, (! [A:$tType,B2:A,B5:(multiset @ A),C3:A,C5:(multiset @ A)]: ((((((add_mset @ A) @ B2) @ B5) = (((add_mset @ A) @ C3) @ C5)) => ((B2 != C3) => (((member @ A) @ C3) @ ((set_mset @ A) @ B5))))))).
% 2.54/1.58 thf(fact_226_multi__member__split, axiom, (! [A:$tType,X:A,M:(multiset @ A)]: (((((member @ A) @ X) @ ((set_mset @ A) @ M)) => (? [A7:(multiset @ A)]: ((M = (((add_mset @ A) @ X) @ A7)))))))).
% 2.54/1.58 thf(fact_227_mset__add, axiom, (! [A:$tType,A2:A,A5:(multiset @ A)]: (((((member @ A) @ A2) @ ((set_mset @ A) @ A5)) => (~ ((! [B7:(multiset @ A)]: ((A5 != (((add_mset @ A) @ A2) @ B7)))))))))).
% 2.54/1.58 thf(fact_228_union__iff, axiom, (! [A:$tType,A2:A,A5:(multiset @ A),B5:(multiset @ A)]: (((((member @ A) @ A2) @ ((set_mset @ A) @ (((plus_plus @ (multiset @ A)) @ A5) @ B5))) = ((((member @ A) @ A2) @ ((set_mset @ A) @ A5)) | (((member @ A) @ A2) @ ((set_mset @ A) @ B5))))))).
% 2.54/1.58 thf(fact_229_multiset__nonemptyE, axiom, (! [A:$tType,A5:(multiset @ A)]: (((A5 != (zero_zero @ (multiset @ A))) => (~ ((! [X3:A]: ((~ ((((member @ A) @ X3) @ ((set_mset @ A) @ A5)))))))))))).
% 2.54/1.58 thf(fact_230_ge__eq__refl, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A]: (((((ord_less_eq @ (A > (A > $o))) @ (^ [Y4:A,Z2:A]: ((Y4 = Z2)))) @ R3) => ((R3 @ X) @ X))))).
% 2.54/1.58 thf(fact_231_refl__ge__eq, axiom, (! [A:$tType,R3:(A > (A > $o))]: (((! [X3:A]: (((R3 @ X3) @ X3))) => (((ord_less_eq @ (A > (A > $o))) @ (^ [Y4:A,Z2:A]: ((Y4 = Z2)))) @ R3))))).
% 2.54/1.58 thf(fact_232_subset__CollectI, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A),Q2:(A > $o),P2:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B5) @ A5) => ((! [X3:A]: (((((member @ A) @ X3) @ B5) => ((Q2 @ X3) => (P2 @ X3))))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ B5) & (Q2 @ X4)))))) @ ((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ A5) & (P2 @ X4))))))))))).
% 2.54/1.58 thf(fact_233_subset__Collect__iff, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A),P2:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B5) @ A5) => ((((ord_less_eq @ (set @ A)) @ B5) @ ((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ A5) & (P2 @ X4)))))) = (! [X4:A]: (((((member @ A) @ X4) @ B5) => (P2 @ X4))))))))).
% 2.54/1.58 thf(fact_234_multiset__induct__min, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:((multiset @ A) > $o),M:(multiset @ A)]: (((P2 @ (zero_zero @ (multiset @ A))) => ((! [X3:A,M3:(multiset @ A)]: (((P2 @ M3) => ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set_mset @ A) @ M3)) => (((ord_less_eq @ A) @ X3) @ Xa)))) => (P2 @ (((add_mset @ A) @ X3) @ M3)))))) => (P2 @ M))))))))).
% 2.54/1.58 thf(fact_235_multiset__induct__max, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:((multiset @ A) > $o),M:(multiset @ A)]: (((P2 @ (zero_zero @ (multiset @ A))) => ((! [X3:A,M3:(multiset @ A)]: (((P2 @ M3) => ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set_mset @ A) @ M3)) => (((ord_less_eq @ A) @ Xa) @ X3)))) => (P2 @ (((add_mset @ A) @ X3) @ M3)))))) => (P2 @ M))))))))).
% 2.54/1.58 thf(fact_236_multi__member__skip, axiom, (! [A:$tType,X:A,XS:(multiset @ A),Y:A]: (((((member @ A) @ X) @ ((set_mset @ A) @ XS)) => (((member @ A) @ X) @ ((set_mset @ A) @ (((plus_plus @ (multiset @ A)) @ (((add_mset @ A) @ Y) @ (zero_zero @ (multiset @ A)))) @ XS))))))).
% 2.54/1.58 thf(fact_237_multi__member__this, axiom, (! [A:$tType,X:A,XS:(multiset @ A)]: ((((member @ A) @ X) @ ((set_mset @ A) @ (((plus_plus @ (multiset @ A)) @ (((add_mset @ A) @ X) @ (zero_zero @ (multiset @ A)))) @ XS)))))).
% 2.54/1.58 thf(fact_238_less__add, axiom, (! [A:$tType,N:(multiset @ A),A2:A,M0:(multiset @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ N) @ (((add_mset @ A) @ A2) @ M0))) @ ((mult1 @ A) @ R)) => ((? [M3:(multiset @ A)]: (((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ M3) @ M0)) @ ((mult1 @ A) @ R)) & (N = (((add_mset @ A) @ A2) @ M3))))) | (? [K4:(multiset @ A)]: (((! [B8:A]: (((((member @ A) @ B8) @ ((set_mset @ A) @ K4)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B8) @ A2)) @ R)))) & (N = (((plus_plus @ (multiset @ A)) @ M0) @ K4)))))))))).
% 2.54/1.58 thf(fact_239_mult1I, axiom, (! [A:$tType,M:(multiset @ A),A2:A,M0:(multiset @ A),N:(multiset @ A),K2:(multiset @ A),R:(set @ ((product_prod @ A) @ A))]: (((M = (((add_mset @ A) @ A2) @ M0)) => ((N = (((plus_plus @ (multiset @ A)) @ M0) @ K2)) => ((! [B4:A]: (((((member @ A) @ B4) @ ((set_mset @ A) @ K2)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B4) @ A2)) @ R)))) => (((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ N) @ M)) @ ((mult1 @ A) @ R)))))))).
% 2.54/1.58 thf(fact_240_mono__mult1, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),R4:(set @ ((product_prod @ A) @ A))]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ R) @ R4) => (((ord_less_eq @ (set @ ((product_prod @ (multiset @ A)) @ (multiset @ A)))) @ ((mult1 @ A) @ R)) @ ((mult1 @ A) @ R4)))))).
% 2.54/1.58 thf(fact_241_mult1__union, axiom, (! [A:$tType,B5:(multiset @ A),D4:(multiset @ A),R:(set @ ((product_prod @ A) @ A)),C5:(multiset @ A)]: (((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ B5) @ D4)) @ ((mult1 @ A) @ R)) => (((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ (((plus_plus @ (multiset @ A)) @ C5) @ B5)) @ (((plus_plus @ (multiset @ A)) @ C5) @ D4))) @ ((mult1 @ A) @ R)))))).
% 2.54/1.58 thf(fact_242_not__less__empty, axiom, (! [A:$tType,M:(multiset @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ M) @ (zero_zero @ (multiset @ A)))) @ ((mult1 @ A) @ R))))))).
% 2.54/1.58 thf(fact_243_mult1E, axiom, (! [A:$tType,N:(multiset @ A),M:(multiset @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ N) @ M)) @ ((mult1 @ A) @ R)) => (~ ((! [A4:A,M02:(multiset @ A)]: (((M = (((add_mset @ A) @ A4) @ M02)) => (! [K4:(multiset @ A)]: (((N = (((plus_plus @ (multiset @ A)) @ M02) @ K4)) => (~ ((! [B8:A]: (((((member @ A) @ B8) @ ((set_mset @ A) @ K4)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B8) @ A4)) @ R)))))))))))))))))).
% 2.54/1.58 thf(fact_244_one__step__implies__mult, axiom, (! [A:$tType,J2:(multiset @ A),K2:(multiset @ A),R:(set @ ((product_prod @ A) @ A)),I4:(multiset @ A)]: (((J2 != (zero_zero @ (multiset @ A))) => ((! [X3:A]: (((((member @ A) @ X3) @ ((set_mset @ A) @ K2)) => (? [Xa:A]: (((((member @ A) @ Xa) @ ((set_mset @ A) @ J2)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Xa)) @ R))))))) => (((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ (((plus_plus @ (multiset @ A)) @ I4) @ K2)) @ (((plus_plus @ (multiset @ A)) @ I4) @ J2))) @ ((mult @ A) @ R))))))).
% 2.54/1.58 thf(fact_245_heap__top__max, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:(tree @ A)]: (((T3 != (e @ A)) => (((is_heap @ A) @ T3) => (((val @ A) @ T3) = ((lattic929149872er_Max @ A) @ ((set_mset @ A) @ ((multiset2 @ A) @ T3)))))))))))).
% 2.54/1.58 thf(fact_246_mono__mult, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),R4:(set @ ((product_prod @ A) @ A))]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ R) @ R4) => (((ord_less_eq @ (set @ ((product_prod @ (multiset @ A)) @ (multiset @ A)))) @ ((mult @ A) @ R)) @ ((mult @ A) @ R4)))))).
% 2.54/1.58 thf(fact_247_mult__implies__one__step, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),M:(multiset @ A),N:(multiset @ A)]: ((((trans @ A) @ R) => ((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ M) @ N)) @ ((mult @ A) @ R)) => (? [I5:(multiset @ A),J3:(multiset @ A)]: (((N = (((plus_plus @ (multiset @ A)) @ I5) @ J3)) & (? [K4:(multiset @ A)]: (((M = (((plus_plus @ (multiset @ A)) @ I5) @ K4)) & ((J3 != (zero_zero @ (multiset @ A))) & (! [X6:A]: (((((member @ A) @ X6) @ ((set_mset @ A) @ K4)) => (? [Xa2:A]: (((((member @ A) @ Xa2) @ ((set_mset @ A) @ J3)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X6) @ Xa2)) @ R))))))))))))))))))).
% 2.54/1.58 thf(fact_248_subset__mset_Osum__mset__0__iff, axiom, (! [A:$tType,M:(multiset @ (multiset @ A))]: (((((((comm_monoid_sum_mset @ (multiset @ A)) @ (plus_plus @ (multiset @ A))) @ (zero_zero @ (multiset @ A))) @ M) = (zero_zero @ (multiset @ A))) = (! [X4:(multiset @ A)]: (((((member @ (multiset @ A)) @ X4) @ ((set_mset @ (multiset @ A)) @ M)) => (X4 = (zero_zero @ (multiset @ A)))))))))).
% 2.54/1.58 thf(fact_249_comm__monoid__add_Osum__mset_Ocong, axiom, (! [A:$tType]: (((comm_monoid_sum_mset @ A) = (comm_monoid_sum_mset @ A))))).
% 2.54/1.58 thf(fact_250_transD, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X:A,Y:A,Z:A]: ((((trans @ A) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ Z)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z)) @ R))))))).
% 2.54/1.58 thf(fact_251_transE, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X:A,Y:A,Z:A]: ((((trans @ A) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ Z)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z)) @ R))))))).
% 2.54/1.58 thf(fact_252_transI, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A))]: (((! [X3:A,Y3:A,Z3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y3) @ Z3)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Z3)) @ R))))) => ((trans @ A) @ R))))).
% 2.54/1.58 thf(fact_253_trans__def, axiom, (! [A:$tType]: (((trans @ A) = (^ [R5:(set @ ((product_prod @ A) @ A))]: ((! [X4:A,Y6:A,Z4:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Y6)) @ R5) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ Z4)) @ R5) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Z4)) @ R5))))))))))).
% 2.54/1.58 thf(fact_254_mult__cancel__add__mset, axiom, (! [A:$tType,S3:(set @ ((product_prod @ A) @ A)),Uu:A,X5:(multiset @ A),Y5:(multiset @ A)]: ((((trans @ A) @ S3) => (((irrefl @ A) @ S3) => ((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ (((add_mset @ A) @ Uu) @ X5)) @ (((add_mset @ A) @ Uu) @ Y5))) @ ((mult @ A) @ S3)) = (((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ X5) @ Y5)) @ ((mult @ A) @ S3)))))))).
% 2.54/1.58 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: (((linorder @ A) => (type @ A))))).
% 2.54/1.58 thf(subcl_Orderings_Olinorder___Orderings_Opreorder, axiom, (! [A:$tType]: (((linorder @ A) => (preorder @ A))))).
% 2.54/1.58 thf(tcon_Multiset_Omultiset___Orderings_Opreorder, axiom, (! [A9:$tType]: (((preorder @ A9) => (preorder @ (multiset @ A9)))))).
% 2.54/1.58 thf(tcon_HOL_Obool___Orderings_Opreorder_1, axiom, (preorder @ $o)).
% 2.54/1.58 thf(tcon_Set_Oset___Orderings_Opreorder_2, axiom, (! [A9:$tType]: ((preorder @ (set @ A9))))).
% 2.54/1.58 thf(tcon_fun___Orderings_Opreorder_3, axiom, (! [A9:$tType,A10:$tType]: (((preorder @ A10) => (preorder @ (A9 > A10)))))).
% 2.54/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.54/1.58 thf(tcon_Multiset_Omultiset___Groups_Oordered__ab__semigroup__add, axiom, (! [A9:$tType]: (((preorder @ A9) => (ordere779506340up_add @ (multiset @ A9)))))).
% 2.54/1.58 thf(tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add, axiom, (! [A9:$tType]: ((cancel1352612707id_add @ (multiset @ A9))))).
% 2.54/1.58 thf(tcon_Multiset_Omultiset___Groups_Ocancel__semigroup__add, axiom, (! [A9:$tType]: ((cancel_semigroup_add @ (multiset @ A9))))).
% 2.54/1.58 thf(tcon_Multiset_Omultiset___Groups_Oab__semigroup__add, axiom, (! [A9:$tType]: ((ab_semigroup_add @ (multiset @ A9))))).
% 2.54/1.58 thf(tcon_Multiset_Omultiset___Groups_Ocomm__monoid__add, axiom, (! [A9:$tType]: ((comm_monoid_add @ (multiset @ A9))))).
% 2.54/1.58 thf(tcon_Multiset_Omultiset___Groups_Osemigroup__add, axiom, (! [A9:$tType]: ((semigroup_add @ (multiset @ A9))))).
% 2.54/1.58 thf(tcon_Multiset_Omultiset___Groups_Omonoid__add, axiom, (! [A9:$tType]: ((monoid_add @ (multiset @ A9))))).
% 2.54/1.58 thf(tcon_Multiset_Omultiset___Groups_Ozero, axiom, (! [A9:$tType]: ((zero @ (multiset @ A9))))).
% 2.54/1.58 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 2.54/1.58 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.54/1.58 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.54/1.58 thf(tfree_0, hypothesis, (linorder @ a)).
% 2.54/1.58 thf(conj_0, conjecture, (v_a = (((product_fst @ a) @ (tree @ a)) @ ((heapIm970386777veLeaf @ a) @ ((((t @ a) @ v1) @ l1) @ r1))))).
% 2.54/1.58 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.P5IR1jFQuE/DTF2DTF10235.p
% 2.54/1.58 ------------------------
% 2.76/1.61 ---- Cleaned THF ---
% 2.76/1.61 thf(ty_t_Product__Type_Oprod,type,
% 2.76/1.61 product_prod: $tType > $tType > $tType ).
% 2.76/1.61
% 2.76/1.61 thf(ty_t_Multiset_Omultiset,type,
% 2.76/1.61 multiset: $tType > $tType ).
% 2.76/1.61
% 2.76/1.61 thf(ty_t_List_Olist,type,
% 2.76/1.61 list: $tType > $tType ).
% 2.76/1.61
% 2.76/1.61 thf(ty_t_Heap_OTree,type,
% 2.76/1.61 tree: $tType > $tType ).
% 2.76/1.61
% 2.76/1.61 thf(ty_t_Set_Oset,type,
% 2.76/1.61 set: $tType > $tType ).
% 2.76/1.61
% 2.76/1.61 thf(ty_tf_a,type,
% 2.76/1.61 a: $tType ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_HOL_Otype,type,
% 2.76/1.61 type:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Orderings_Opreorder,type,
% 2.76/1.61 preorder:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Ozero,type,
% 2.76/1.61 zero:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Num_Oneg__numeral,type,
% 2.76/1.61 neg_numeral:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Ogroup__add,type,
% 2.76/1.61 group_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Omonoid__add,type,
% 2.76/1.61 monoid_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Orderings_Olinorder,type,
% 2.76/1.61 linorder:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.76/1.61 semigroup_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.76/1.61 comm_monoid_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.76/1.61 ab_semigroup_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.76/1.61 cancel_semigroup_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.76/1.61 cancel1352612707id_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.76/1.61 linord219039673up_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 2.76/1.61 ordere216010020id_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.76/1.61 ordere779506340up_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.76/1.61 linord1659791738miring:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.76/1.61 canoni770627133id_add:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.76/1.61 ordere236663937imp_le:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 2.76/1.61 unique1598680935umeral:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 2.76/1.61 ordere516151231imp_le:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 2.76/1.61 semiri456707255roduct:
% 2.76/1.61 !>[A: $tType] : $o ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux,type,
% 2.76/1.61 unique455577585es_aux:
% 2.76/1.61 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.76/1.61 plus_plus:
% 2.76/1.61 !>[A: $tType] : ( A > A > A ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.76/1.61 zero_zero:
% 2.76/1.61 !>[A: $tType] : A ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HOL_ONO__MATCH,type,
% 2.76/1.61 nO_MATCH:
% 2.76/1.61 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oheapify,type,
% 2.76/1.61 heapIm818251801eapify:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Ohs__is__empty,type,
% 2.76/1.61 heapIm721255937_empty:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Ohs__of__list,type,
% 2.76/1.61 heapIm874063447f_list:
% 2.76/1.61 !>[A: $tType] : ( ( list @ A ) > ( tree @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Ohs__remove__max,type,
% 2.76/1.61 heapIm1542349758ve_max:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > ( product_prod @ A @ ( tree @ A ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oleft,type,
% 2.76/1.61 heapIm1271749598e_left:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oof__list__tree,type,
% 2.76/1.61 heapIm1912108042t_tree:
% 2.76/1.61 !>[A: $tType] : ( ( list @ A ) > ( tree @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_OremoveLeaf,type,
% 2.76/1.61 heapIm970386777veLeaf:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > ( product_prod @ A @ ( tree @ A ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oright,type,
% 2.76/1.61 heapIm1434396069_right:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_OsiftDown,type,
% 2.76/1.61 heapIm748920189ftDown:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Heap_OHeap,type,
% 2.76/1.61 heap:
% 2.76/1.61 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( tree @ A ) ) > ( B > ( product_prod @ A @ B ) ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Heap_OHeap__axioms,type,
% 2.76/1.61 heap_axioms:
% 2.76/1.61 !>[B: $tType,A: $tType] : ( ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( tree @ A ) ) > ( B > ( product_prod @ A @ B ) ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Heap_OTree_OE,type,
% 2.76/1.61 e:
% 2.76/1.61 !>[A: $tType] : ( tree @ A ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Heap_OTree_OT,type,
% 2.76/1.61 t:
% 2.76/1.61 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) > ( tree @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Heap_Oin__tree,type,
% 2.76/1.61 in_tree:
% 2.76/1.61 !>[A: $tType] : ( A > ( tree @ A ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Heap_Ois__heap,type,
% 2.76/1.61 is_heap:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Heap_Omultiset,type,
% 2.76/1.61 multiset2:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > ( multiset @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Heap_Oval,type,
% 2.76/1.61 val:
% 2.76/1.61 !>[A: $tType] : ( ( tree @ A ) > A ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_If,type,
% 2.76/1.61 if:
% 2.76/1.61 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Lattices__Big_Olinorder__class_OMax,type,
% 2.76/1.61 lattic929149872er_Max:
% 2.76/1.61 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Multiset_Oadd__mset,type,
% 2.76/1.61 add_mset:
% 2.76/1.61 !>[A: $tType] : ( A > ( multiset @ A ) > ( multiset @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Multiset_Ocomm__monoid__add_Osum__mset,type,
% 2.76/1.61 comm_monoid_sum_mset:
% 2.76/1.61 !>[A: $tType] : ( ( A > A > A ) > A > ( multiset @ A ) > A ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Multiset_Ois__empty,type,
% 2.76/1.61 is_empty:
% 2.76/1.61 !>[A: $tType] : ( ( multiset @ A ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Multiset_Omult,type,
% 2.76/1.61 mult:
% 2.76/1.61 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Multiset_Omult1,type,
% 2.76/1.61 mult1:
% 2.76/1.61 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Multiset_Oset__mset,type,
% 2.76/1.61 set_mset:
% 2.76/1.61 !>[A: $tType] : ( ( multiset @ A ) > ( set @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.76/1.61 ord_less_eq:
% 2.76/1.61 !>[A: $tType] : ( A > A > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Product__Type_OPair,type,
% 2.76/1.61 product_Pair:
% 2.76/1.61 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.76/1.61 produc2004651681e_prod:
% 2.76/1.61 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.76/1.61 product_rec_prod:
% 2.76/1.61 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 2.76/1.61 product_fst:
% 2.76/1.61 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 2.76/1.61 product_snd:
% 2.76/1.61 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Product__Type_Oprod_Oswap,type,
% 2.76/1.61 product_swap:
% 2.76/1.61 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > ( product_prod @ B @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Product__Type_Oscomp,type,
% 2.76/1.61 product_scomp:
% 2.76/1.61 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( product_prod @ B @ C ) ) > ( B > C > D ) > A > D ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Relation_Oirrefl,type,
% 2.76/1.61 irrefl:
% 2.76/1.61 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Relation_Otrans,type,
% 2.76/1.61 trans:
% 2.76/1.61 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_RemoveMax_OCollection,type,
% 2.76/1.61 collection:
% 2.76/1.61 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_Set_OCollect,type,
% 2.76/1.61 collect:
% 2.76/1.61 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_c_member,type,
% 2.76/1.61 member:
% 2.76/1.61 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_l1____,type,
% 2.76/1.61 l1: tree @ a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_l2____,type,
% 2.76/1.61 l2: tree @ a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_r1____,type,
% 2.76/1.61 r1: tree @ a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_r2____,type,
% 2.76/1.61 r2: tree @ a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_t,type,
% 2.76/1.61 t2: tree @ a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_t_H,type,
% 2.76/1.61 t3: tree @ a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_t_Ha____,type,
% 2.76/1.61 t_a: tree @ a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_v1____,type,
% 2.76/1.61 v1: a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_v2____,type,
% 2.76/1.61 v2: a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_v_H,type,
% 2.76/1.61 v: a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_v_Ha____,type,
% 2.76/1.61 v_a: a ).
% 2.76/1.61
% 2.76/1.61 thf(sy_v_v____,type,
% 2.76/1.61 v3: a ).
% 2.76/1.61
% 2.76/1.61 thf(fact_0__C4__2_Oprems_C_I1_J,axiom,
% 2.76/1.61 ( ( product_Pair @ a @ ( tree @ a ) @ v_a @ t_a )
% 2.76/1.61 = ( heapIm970386777veLeaf @ a @ ( t @ a @ v3 @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_1_assms_I1_J,axiom,
% 2.76/1.61 ( ( product_Pair @ a @ ( tree @ a ) @ v @ t3 )
% 2.76/1.61 = ( heapIm970386777veLeaf @ a @ t2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_2__C4__2_Oprems_C_I2_J,axiom,
% 2.76/1.61 ( ( t @ a @ v3 @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) )
% 2.76/1.61 != ( e @ a ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_3__092_060open_062t_H_A_061_AT_Av_A_Isnd_A_IremoveLeaf_A_IT_Av1_Al1_Ar1_J_J_J_A_IT_Av2_Al2_Ar2_J_092_060close_062,axiom,
% 2.76/1.61 ( t_a
% 2.76/1.61 = ( t @ a @ v3 @ ( product_snd @ a @ ( tree @ a ) @ ( heapIm970386777veLeaf @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_4_Tree_Oinject,axiom,
% 2.76/1.61 ! [A: $tType,X21: A,X22: tree @ A,X23: tree @ A,Y21: A,Y22: tree @ A,Y23: tree @ A] :
% 2.76/1.61 ( ( ( t @ A @ X21 @ X22 @ X23 )
% 2.76/1.61 = ( t @ A @ Y21 @ Y22 @ Y23 ) )
% 2.76/1.61 = ( ( X21 = Y21 )
% 2.76/1.61 & ( X22 = Y22 )
% 2.76/1.61 & ( X23 = Y23 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_5_removeLeaf_Osimps_I5_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,Vd: A,Ve: tree @ A,Vf: tree @ A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.76/1.61 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( product_Pair @ A @ ( tree @ A ) @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) @ ( t @ A @ V @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_6_removeLeaf_Osimps_I4_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A] :
% 2.76/1.61 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 2.76/1.61 = ( product_Pair @ A @ ( tree @ A ) @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( t @ A @ V @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_7_left_Osimps,axiom,
% 2.76/1.61 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 2.76/1.61 ( ( heapIm1271749598e_left @ A @ ( t @ A @ V @ L @ R ) )
% 2.76/1.61 = L ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_8_right_Osimps,axiom,
% 2.76/1.61 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 2.76/1.61 ( ( heapIm1434396069_right @ A @ ( t @ A @ V @ L @ R ) )
% 2.76/1.61 = R ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_9__C4__2_Ohyps_C_I1_J,axiom,
% 2.76/1.61 ! [V2: a,T2: tree @ a] :
% 2.76/1.61 ( ( ( product_Pair @ a @ ( tree @ a ) @ V2 @ T2 )
% 2.76/1.61 = ( heapIm970386777veLeaf @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
% 2.76/1.61 => ( ( ( t @ a @ v1 @ l1 @ r1 )
% 2.76/1.61 != ( e @ a ) )
% 2.76/1.61 => ( ( plus_plus @ ( multiset @ a ) @ ( add_mset @ a @ V2 @ ( zero_zero @ ( multiset @ a ) ) ) @ ( multiset2 @ a @ T2 ) )
% 2.76/1.61 = ( multiset2 @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_10_removeLeaf_Osimps_I1_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A] :
% 2.76/1.61 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) )
% 2.76/1.61 = ( product_Pair @ A @ ( tree @ A ) @ V @ ( e @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_11_fstI,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,X: product_prod @ A @ B,Y: A,Z: B] :
% 2.76/1.61 ( ( X
% 2.76/1.61 = ( product_Pair @ A @ B @ Y @ Z ) )
% 2.76/1.61 => ( ( product_fst @ A @ B @ X )
% 2.76/1.61 = Y ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_12_fst__eqD,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,X: A,Y: B,A2: A] :
% 2.76/1.61 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X @ Y ) )
% 2.76/1.61 = A2 )
% 2.76/1.61 => ( X = A2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_13_fst__conv,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,X1: A,X2: B] :
% 2.76/1.61 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X1 @ X2 ) )
% 2.76/1.61 = X1 ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_14_assms_I2_J,axiom,
% 2.76/1.61 ( t2
% 2.76/1.61 != ( e @ a ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_15_prod_Oinject,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 2.76/1.61 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 2.76/1.61 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 2.76/1.61 = ( ( X1 = Y1 )
% 2.76/1.61 & ( X2 = Y2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_16_old_Oprod_Oinject,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 2.76/1.61 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.76/1.61 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.76/1.61 = ( ( A2 = A3 )
% 2.76/1.61 & ( B2 = B3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_17_prod_Ocollapse,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 2.76/1.61 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 2.76/1.61 = Prod ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_18_multiset_Osimps_I2_J,axiom,
% 2.76/1.61 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 2.76/1.61 ( ( multiset2 @ A @ ( t @ A @ V @ L @ R ) )
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ ( multiset2 @ A @ L ) @ ( add_mset @ A @ V @ ( zero_zero @ ( multiset @ A ) ) ) ) @ ( multiset2 @ A @ R ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_19_multiset_Osimps_I1_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( multiset2 @ A @ ( e @ A ) )
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_20_sndI,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,X: product_prod @ A @ B,Y: A,Z: B] :
% 2.76/1.61 ( ( X
% 2.76/1.61 = ( product_Pair @ A @ B @ Y @ Z ) )
% 2.76/1.61 => ( ( product_snd @ A @ B @ X )
% 2.76/1.61 = Z ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_21_snd__eqD,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,X: B,Y: A,A2: A] :
% 2.76/1.61 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 2.76/1.61 = A2 )
% 2.76/1.61 => ( Y = A2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_22_snd__conv,axiom,
% 2.76/1.61 ! [Aa: $tType,A: $tType,X1: Aa,X2: A] :
% 2.76/1.61 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X1 @ X2 ) )
% 2.76/1.61 = X2 ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_23_surj__pair,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 2.76/1.61 ? [X3: A,Y3: B] :
% 2.76/1.61 ( P
% 2.76/1.61 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_24_prod__cases,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 2.76/1.61 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.76/1.61 => ( P2 @ P ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_25_Pair__inject,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 2.76/1.61 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.76/1.61 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.76/1.61 => ~ ( ( A2 = A3 )
% 2.76/1.61 => ( B2 != B3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_26_prod__cases3,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.76/1.61 ~ ! [A4: A,B4: B,C2: C] :
% 2.76/1.61 ( Y
% 2.76/1.61 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_27_prod__cases4,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.76/1.61 ~ ! [A4: A,B4: B,C2: C,D2: D] :
% 2.76/1.61 ( Y
% 2.76/1.61 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_28_prod__cases5,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.76/1.61 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E] :
% 2.76/1.61 ( Y
% 2.76/1.61 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_29_prod__cases6,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 2.76/1.61 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F] :
% 2.76/1.61 ( Y
% 2.76/1.61 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_30_prod__cases7,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 2.76/1.61 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F,G2: G] :
% 2.76/1.61 ( Y
% 2.76/1.61 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_31_prod__induct3,axiom,
% 2.76/1.61 ! [C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.76/1.61 ( ! [A4: A,B4: B,C2: C] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 2.76/1.61 => ( P2 @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_32_prod__induct4,axiom,
% 2.76/1.61 ! [D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.76/1.61 ( ! [A4: A,B4: B,C2: C,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 2.76/1.61 => ( P2 @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_33_prod__induct5,axiom,
% 2.76/1.61 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.76/1.61 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 2.76/1.61 => ( P2 @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_34_prod__induct6,axiom,
% 2.76/1.61 ! [F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 2.76/1.61 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 2.76/1.61 => ( P2 @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_35_prod__induct7,axiom,
% 2.76/1.61 ! [G: $tType,F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 2.76/1.61 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F,G2: G] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 2.76/1.61 => ( P2 @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_36_old_Oprod_Oexhaust,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.76/1.61 ~ ! [A4: A,B4: B] :
% 2.76/1.61 ( Y
% 2.76/1.61 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_37_old_Oprod_Oinducts,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.76/1.61 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.76/1.61 => ( P2 @ Prod ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_38_HS_Omultiset__empty,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( ( multiset2 @ A @ ( e @ A ) )
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_39_surjective__pairing,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,T3: product_prod @ A @ B] :
% 2.76/1.61 ( T3
% 2.76/1.61 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T3 ) @ ( product_snd @ A @ B @ T3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_40_prod_Oexhaust__sel,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 2.76/1.61 ( Prod
% 2.76/1.61 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_41_prod__eq__iff,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType] :
% 2.76/1.61 ( ( ^ [Y4: product_prod @ A @ B,Z2: product_prod @ A @ B] : ( Y4 = Z2 ) )
% 2.76/1.61 = ( ^ [S: product_prod @ A @ B,T4: product_prod @ A @ B] :
% 2.76/1.61 ( ( ( product_fst @ A @ B @ S )
% 2.76/1.61 = ( product_fst @ A @ B @ T4 ) )
% 2.76/1.61 & ( ( product_snd @ A @ B @ S )
% 2.76/1.61 = ( product_snd @ A @ B @ T4 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_42_prod_Oexpand,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 2.76/1.61 ( ( ( ( product_fst @ A @ B @ Prod )
% 2.76/1.61 = ( product_fst @ A @ B @ Prod2 ) )
% 2.76/1.61 & ( ( product_snd @ A @ B @ Prod )
% 2.76/1.61 = ( product_snd @ A @ B @ Prod2 ) ) )
% 2.76/1.61 => ( Prod = Prod2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_43_prod__eqI,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,P: product_prod @ A @ B,Q: product_prod @ A @ B] :
% 2.76/1.61 ( ( ( product_fst @ A @ B @ P )
% 2.76/1.61 = ( product_fst @ A @ B @ Q ) )
% 2.76/1.61 => ( ( ( product_snd @ A @ B @ P )
% 2.76/1.61 = ( product_snd @ A @ B @ Q ) )
% 2.76/1.61 => ( P = Q ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_44_is__heap_Ocases,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [X: tree @ A] :
% 2.76/1.61 ( ( X
% 2.76/1.61 != ( e @ A ) )
% 2.76/1.61 => ( ! [V3: A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( e @ A ) @ ( e @ A ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 2.76/1.61 => ~ ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_45_mem__Collect__eq,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,P2: A > $o] :
% 2.76/1.61 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 2.76/1.61 = ( P2 @ A2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_46_Collect__mem__eq,axiom,
% 2.76/1.61 ! [A: $tType,A5: set @ A] :
% 2.76/1.61 ( ( collect @ A
% 2.76/1.61 @ ^ [X4: A] : ( member @ A @ X4 @ A5 ) )
% 2.76/1.61 = A5 ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_47_Collect__cong,axiom,
% 2.76/1.61 ! [A: $tType,P2: A > $o,Q2: A > $o] :
% 2.76/1.61 ( ! [X3: A] :
% 2.76/1.61 ( ( P2 @ X3 )
% 2.76/1.61 = ( Q2 @ X3 ) )
% 2.76/1.61 => ( ( collect @ A @ P2 )
% 2.76/1.61 = ( collect @ A @ Q2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_48_ext,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,F3: A > B,G3: A > B] :
% 2.76/1.61 ( ! [X3: A] :
% 2.76/1.61 ( ( F3 @ X3 )
% 2.76/1.61 = ( G3 @ X3 ) )
% 2.76/1.61 => ( F3 = G3 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_49_Tree_Oexhaust,axiom,
% 2.76/1.61 ! [A: $tType,Y: tree @ A] :
% 2.76/1.61 ( ( Y
% 2.76/1.61 != ( e @ A ) )
% 2.76/1.61 => ~ ! [X212: A,X222: tree @ A,X232: tree @ A] :
% 2.76/1.61 ( Y
% 2.76/1.61 != ( t @ A @ X212 @ X222 @ X232 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_50_Tree_Oinduct,axiom,
% 2.76/1.61 ! [A: $tType,P2: ( tree @ A ) > $o,Tree: tree @ A] :
% 2.76/1.61 ( ( P2 @ ( e @ A ) )
% 2.76/1.61 => ( ! [X12: A,X24: tree @ A,X32: tree @ A] :
% 2.76/1.61 ( ( P2 @ X24 )
% 2.76/1.61 => ( ( P2 @ X32 )
% 2.76/1.61 => ( P2 @ ( t @ A @ X12 @ X24 @ X32 ) ) ) )
% 2.76/1.61 => ( P2 @ Tree ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_51_Tree_Odistinct_I1_J,axiom,
% 2.76/1.61 ! [A: $tType,X21: A,X22: tree @ A,X23: tree @ A] :
% 2.76/1.61 ( ( e @ A )
% 2.76/1.61 != ( t @ A @ X21 @ X22 @ X23 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_52_removeLeaf_Oinduct,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [P2: ( tree @ A ) > $o,A0: tree @ A] :
% 2.76/1.61 ( ! [V3: A] : ( P2 @ ( t @ A @ V3 @ ( e @ A ) @ ( e @ A ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 2.76/1.61 => ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 2.76/1.61 => ( P2 @ ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 2.76/1.61 => ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 2.76/1.61 => ( P2 @ ( t @ A @ V3 @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 2.76/1.61 ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 2.76/1.61 => ( ( P2 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 2.76/1.61 => ( P2 @ ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) )
% 2.76/1.61 => ( ! [V3: A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( ( P2 @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) )
% 2.76/1.61 => ( ( P2 @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) )
% 2.76/1.61 => ( P2 @ ( t @ A @ V3 @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) )
% 2.76/1.61 => ( ( P2 @ ( e @ A ) )
% 2.76/1.61 => ( P2 @ A0 ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_53_removeLeaf_Ocases,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [X: tree @ A] :
% 2.76/1.61 ( ! [V3: A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( e @ A ) @ ( e @ A ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.76/1.61 => ( ! [V3: A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.76/1.61 => ( X
% 2.76/1.61 = ( e @ A ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_54_siftDown_Ocases,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [X: tree @ A] :
% 2.76/1.61 ( ( X
% 2.76/1.61 != ( e @ A ) )
% 2.76/1.61 => ( ! [V3: A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( e @ A ) @ ( e @ A ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 2.76/1.61 => ( ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.76/1.61 => ~ ! [V3: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 2.76/1.61 ( X
% 2.76/1.61 != ( t @ A @ V3 @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_55_removeLeaf_Osimps_I2_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.76/1.61 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 2.76/1.61 = ( product_Pair @ A @ ( tree @ A ) @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( t @ A @ V @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( e @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_56_removeLeaf_Osimps_I3_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.76/1.61 ( ( heapIm970386777veLeaf @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( product_Pair @ A @ ( tree @ A ) @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) @ ( t @ A @ V @ ( e @ A ) @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_57_union__mset__add__mset__left,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,A5: multiset @ A,B5: multiset @ A] :
% 2.76/1.61 ( ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ A2 @ A5 ) @ B5 )
% 2.76/1.61 = ( add_mset @ A @ A2 @ ( plus_plus @ ( multiset @ A ) @ A5 @ B5 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_58_union__mset__add__mset__right,axiom,
% 2.76/1.61 ! [A: $tType,A5: multiset @ A,A2: A,B5: multiset @ A] :
% 2.76/1.61 ( ( plus_plus @ ( multiset @ A ) @ A5 @ ( add_mset @ A @ A2 @ B5 ) )
% 2.76/1.61 = ( add_mset @ A @ A2 @ ( plus_plus @ ( multiset @ A ) @ A5 @ B5 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_59_single__eq__single,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,B2: A] :
% 2.76/1.61 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 = ( add_mset @ A @ B2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.76/1.61 = ( A2 = B2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_60_add__mset__eq__single,axiom,
% 2.76/1.61 ! [A: $tType,B2: A,M: multiset @ A,A2: A] :
% 2.76/1.61 ( ( ( add_mset @ A @ B2 @ M )
% 2.76/1.61 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.76/1.61 = ( ( B2 = A2 )
% 2.76/1.61 & ( M
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_61_single__eq__add__mset,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,B2: A,M: multiset @ A] :
% 2.76/1.61 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 = ( add_mset @ A @ B2 @ M ) )
% 2.76/1.61 = ( ( B2 = A2 )
% 2.76/1.61 & ( M
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_62_add__mset__eq__singleton__iff,axiom,
% 2.76/1.61 ! [A: $tType,X: A,M: multiset @ A,Y: A] :
% 2.76/1.61 ( ( ( add_mset @ A @ X @ M )
% 2.76/1.61 = ( add_mset @ A @ Y @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.76/1.61 = ( ( M
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 & ( X = Y ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_63_empty__eq__union,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A,N: multiset @ A] :
% 2.76/1.61 ( ( ( zero_zero @ ( multiset @ A ) )
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ M @ N ) )
% 2.76/1.61 = ( ( M
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 & ( N
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_64_union__eq__empty,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A,N: multiset @ A] :
% 2.76/1.61 ( ( ( plus_plus @ ( multiset @ A ) @ M @ N )
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 = ( ( M
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 & ( N
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_65_subset__mset_Oadd__eq__0__iff__both__eq__0,axiom,
% 2.76/1.61 ! [A: $tType,X: multiset @ A,Y: multiset @ A] :
% 2.76/1.61 ( ( ( plus_plus @ ( multiset @ A ) @ X @ Y )
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 = ( ( X
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 & ( Y
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_66_subset__mset_Ozero__eq__add__iff__both__eq__0,axiom,
% 2.76/1.61 ! [A: $tType,X: multiset @ A,Y: multiset @ A] :
% 2.76/1.61 ( ( ( zero_zero @ ( multiset @ A ) )
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ X @ Y ) )
% 2.76/1.61 = ( ( X
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 & ( Y
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_67_add_Oleft__neutral,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( monoid_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.61 = A2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_68_add__right__cancel,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( cancel_semigroup_add @ A )
% 2.76/1.61 => ! [B2: A,A2: A,C3: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.76/1.61 = ( plus_plus @ A @ C3 @ A2 ) )
% 2.76/1.61 = ( B2 = C3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_69_add__left__cancel,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( cancel_semigroup_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.76/1.61 = ( plus_plus @ A @ A2 @ C3 ) )
% 2.76/1.61 = ( B2 = C3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_70_multi__self__add__other__not__self,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A,X: A] :
% 2.76/1.61 ( M
% 2.76/1.61 != ( add_mset @ A @ X @ M ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_71_add__mset__add__mset__same__iff,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,A5: multiset @ A,B5: multiset @ A] :
% 2.76/1.61 ( ( ( add_mset @ A @ A2 @ A5 )
% 2.76/1.61 = ( add_mset @ A @ A2 @ B5 ) )
% 2.76/1.61 = ( A5 = B5 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_72_zero__eq__add__iff__both__eq__0,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( canoni770627133id_add @ A )
% 2.76/1.61 => ! [X: A,Y: A] :
% 2.76/1.61 ( ( ( zero_zero @ A )
% 2.76/1.61 = ( plus_plus @ A @ X @ Y ) )
% 2.76/1.61 = ( ( X
% 2.76/1.61 = ( zero_zero @ A ) )
% 2.76/1.61 & ( Y
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_73_add__eq__0__iff__both__eq__0,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( canoni770627133id_add @ A )
% 2.76/1.61 => ! [X: A,Y: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ X @ Y )
% 2.76/1.61 = ( zero_zero @ A ) )
% 2.76/1.61 = ( ( X
% 2.76/1.61 = ( zero_zero @ A ) )
% 2.76/1.61 & ( Y
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_74_add__cancel__right__right,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( cancel1352612707id_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( A2
% 2.76/1.61 = ( plus_plus @ A @ A2 @ B2 ) )
% 2.76/1.61 = ( B2
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_75_add__cancel__right__left,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( cancel1352612707id_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( A2
% 2.76/1.61 = ( plus_plus @ A @ B2 @ A2 ) )
% 2.76/1.61 = ( B2
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_76_add__cancel__left__right,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( cancel1352612707id_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.76/1.61 = A2 )
% 2.76/1.61 = ( B2
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_77_add__cancel__left__left,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( cancel1352612707id_add @ A )
% 2.76/1.61 => ! [B2: A,A2: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.76/1.61 = A2 )
% 2.76/1.61 = ( B2
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_78_double__zero__sym,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linord219039673up_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( ( zero_zero @ A )
% 2.76/1.61 = ( plus_plus @ A @ A2 @ A2 ) )
% 2.76/1.61 = ( A2
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_79_double__zero,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linord219039673up_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ A2 @ A2 )
% 2.76/1.61 = ( zero_zero @ A ) )
% 2.76/1.61 = ( A2
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_80_add_Oright__neutral,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( monoid_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.61 = A2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_81_zero__reorient,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( zero @ A )
% 2.76/1.61 => ! [X: A] :
% 2.76/1.61 ( ( ( zero_zero @ A )
% 2.76/1.61 = X )
% 2.76/1.61 = ( X
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_82_add__right__imp__eq,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( cancel_semigroup_add @ A )
% 2.76/1.61 => ! [B2: A,A2: A,C3: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.76/1.61 = ( plus_plus @ A @ C3 @ A2 ) )
% 2.76/1.61 => ( B2 = C3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_83_add__left__imp__eq,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( cancel_semigroup_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.76/1.61 = ( plus_plus @ A @ A2 @ C3 ) )
% 2.76/1.61 => ( B2 = C3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_84_add_Oleft__commute,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ab_semigroup_add @ A )
% 2.76/1.61 => ! [B2: A,A2: A,C3: A] :
% 2.76/1.61 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C3 ) )
% 2.76/1.61 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_85_add_Ocommute,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ab_semigroup_add @ A )
% 2.76/1.61 => ( ( plus_plus @ A )
% 2.76/1.61 = ( ^ [A6: A,B6: A] : ( plus_plus @ A @ B6 @ A6 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_86_add_Oright__cancel,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( group_add @ A )
% 2.76/1.61 => ! [B2: A,A2: A,C3: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.76/1.61 = ( plus_plus @ A @ C3 @ A2 ) )
% 2.76/1.61 = ( B2 = C3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_87_add_Oleft__cancel,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( group_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A] :
% 2.76/1.61 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.76/1.61 = ( plus_plus @ A @ A2 @ C3 ) )
% 2.76/1.61 = ( B2 = C3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_88_add_Oassoc,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( semigroup_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A] :
% 2.76/1.61 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 2.76/1.61 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_89_group__cancel_Oadd2,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( comm_monoid_add @ A )
% 2.76/1.61 => ! [B5: A,K: A,B2: A,A2: A] :
% 2.76/1.61 ( ( B5
% 2.76/1.61 = ( plus_plus @ A @ K @ B2 ) )
% 2.76/1.61 => ( ( plus_plus @ A @ A2 @ B5 )
% 2.76/1.61 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_90_group__cancel_Oadd1,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( comm_monoid_add @ A )
% 2.76/1.61 => ! [A5: A,K: A,A2: A,B2: A] :
% 2.76/1.61 ( ( A5
% 2.76/1.61 = ( plus_plus @ A @ K @ A2 ) )
% 2.76/1.61 => ( ( plus_plus @ A @ A5 @ B2 )
% 2.76/1.61 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_91_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere779506340up_add @ A )
% 2.76/1.61 => ! [I: A,J: A,K: A,L: A] :
% 2.76/1.61 ( ( ( I = J )
% 2.76/1.61 & ( K = L ) )
% 2.76/1.61 => ( ( plus_plus @ A @ I @ K )
% 2.76/1.61 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_92_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ab_semigroup_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A] :
% 2.76/1.61 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 2.76/1.61 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_93_multi__union__self__other__eq,axiom,
% 2.76/1.61 ! [A: $tType,A5: multiset @ A,X5: multiset @ A,Y5: multiset @ A] :
% 2.76/1.61 ( ( ( plus_plus @ ( multiset @ A ) @ A5 @ X5 )
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ A5 @ Y5 ) )
% 2.76/1.61 => ( X5 = Y5 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_94_union__right__cancel,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A,K2: multiset @ A,N: multiset @ A] :
% 2.76/1.61 ( ( ( plus_plus @ ( multiset @ A ) @ M @ K2 )
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ N @ K2 ) )
% 2.76/1.61 = ( M = N ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_95_union__left__cancel,axiom,
% 2.76/1.61 ! [A: $tType,K2: multiset @ A,M: multiset @ A,N: multiset @ A] :
% 2.76/1.61 ( ( ( plus_plus @ ( multiset @ A ) @ K2 @ M )
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ K2 @ N ) )
% 2.76/1.61 = ( M = N ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_96_union__commute,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( plus_plus @ ( multiset @ A ) )
% 2.76/1.61 = ( ^ [M2: multiset @ A,N2: multiset @ A] : ( plus_plus @ ( multiset @ A ) @ N2 @ M2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_97_union__lcomm,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A,N: multiset @ A,K2: multiset @ A] :
% 2.76/1.61 ( ( plus_plus @ ( multiset @ A ) @ M @ ( plus_plus @ ( multiset @ A ) @ N @ K2 ) )
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ N @ ( plus_plus @ ( multiset @ A ) @ M @ K2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_98_union__assoc,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A,N: multiset @ A,K2: multiset @ A] :
% 2.76/1.61 ( ( plus_plus @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ M @ N ) @ K2 )
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ M @ ( plus_plus @ ( multiset @ A ) @ N @ K2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_99_add__mset__commute,axiom,
% 2.76/1.61 ! [A: $tType,X: A,Y: A,M: multiset @ A] :
% 2.76/1.61 ( ( add_mset @ A @ X @ ( add_mset @ A @ Y @ M ) )
% 2.76/1.61 = ( add_mset @ A @ Y @ ( add_mset @ A @ X @ M ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_100_add__eq__conv__ex,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,M: multiset @ A,B2: A,N: multiset @ A] :
% 2.76/1.61 ( ( ( add_mset @ A @ A2 @ M )
% 2.76/1.61 = ( add_mset @ A @ B2 @ N ) )
% 2.76/1.61 = ( ( ( M = N )
% 2.76/1.61 & ( A2 = B2 ) )
% 2.76/1.61 | ? [K3: multiset @ A] :
% 2.76/1.61 ( ( M
% 2.76/1.61 = ( add_mset @ A @ B2 @ K3 ) )
% 2.76/1.61 & ( N
% 2.76/1.61 = ( add_mset @ A @ A2 @ K3 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_101_add_Ogroup__left__neutral,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( group_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.61 = A2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_102_add_Ocomm__neutral,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( comm_monoid_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.61 = A2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_103_comm__monoid__add__class_Oadd__0,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( comm_monoid_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.61 = A2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_104_empty__neutral_I1_J,axiom,
% 2.76/1.61 ! [A: $tType,X: multiset @ A] :
% 2.76/1.61 ( ( plus_plus @ ( multiset @ A ) @ ( zero_zero @ ( multiset @ A ) ) @ X )
% 2.76/1.61 = X ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_105_empty__neutral_I2_J,axiom,
% 2.76/1.61 ! [A: $tType,X: multiset @ A] :
% 2.76/1.61 ( ( plus_plus @ ( multiset @ A ) @ X @ ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 = X ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_106_multi__nonempty__split,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A] :
% 2.76/1.61 ( ( M
% 2.76/1.61 != ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 => ? [A7: multiset @ A,A4: A] :
% 2.76/1.61 ( M
% 2.76/1.61 = ( add_mset @ A @ A4 @ A7 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_107_empty__not__add__mset,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,A5: multiset @ A] :
% 2.76/1.61 ( ( zero_zero @ ( multiset @ A ) )
% 2.76/1.61 != ( add_mset @ A @ A2 @ A5 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_108_multiset__induct2,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,P2: ( multiset @ A ) > ( multiset @ B ) > $o,M: multiset @ A,N: multiset @ B] :
% 2.76/1.61 ( ( P2 @ ( zero_zero @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ B ) ) )
% 2.76/1.61 => ( ! [A4: A,M3: multiset @ A,N3: multiset @ B] :
% 2.76/1.61 ( ( P2 @ M3 @ N3 )
% 2.76/1.61 => ( P2 @ ( add_mset @ A @ A4 @ M3 ) @ N3 ) )
% 2.76/1.61 => ( ! [A4: B,M3: multiset @ A,N3: multiset @ B] :
% 2.76/1.61 ( ( P2 @ M3 @ N3 )
% 2.76/1.61 => ( P2 @ M3 @ ( add_mset @ B @ A4 @ N3 ) ) )
% 2.76/1.61 => ( P2 @ M @ N ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_109_multiset__induct,axiom,
% 2.76/1.61 ! [A: $tType,P2: ( multiset @ A ) > $o,M: multiset @ A] :
% 2.76/1.61 ( ( P2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 => ( ! [X3: A,M3: multiset @ A] :
% 2.76/1.61 ( ( P2 @ M3 )
% 2.76/1.61 => ( P2 @ ( add_mset @ A @ X3 @ M3 ) ) )
% 2.76/1.61 => ( P2 @ M ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_110_multiset__cases,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A] :
% 2.76/1.61 ( ( M
% 2.76/1.61 != ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 => ~ ! [X3: A,N3: multiset @ A] :
% 2.76/1.61 ( M
% 2.76/1.61 != ( add_mset @ A @ X3 @ N3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_111_add__mset__add__single,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( add_mset @ A )
% 2.76/1.61 = ( ^ [A6: A,A8: multiset @ A] : ( plus_plus @ ( multiset @ A ) @ A8 @ ( add_mset @ A @ A6 @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_112_union__is__single,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A,N: multiset @ A,A2: A] :
% 2.76/1.61 ( ( ( plus_plus @ ( multiset @ A ) @ M @ N )
% 2.76/1.61 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.76/1.61 = ( ( ( M
% 2.76/1.61 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.76/1.61 & ( N
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) )
% 2.76/1.61 | ( ( M
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 & ( N
% 2.76/1.61 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_113_single__is__union,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,M: multiset @ A,N: multiset @ A] :
% 2.76/1.61 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ M @ N ) )
% 2.76/1.61 = ( ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 = M )
% 2.76/1.61 & ( N
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) )
% 2.76/1.61 | ( ( M
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 & ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 = N ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_114_old_Oprod_Orec,axiom,
% 2.76/1.61 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.76/1.61 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.76/1.61 = ( F1 @ A2 @ B2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_115_exI__realizer,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,P2: A > B > $o,Y: A,X: B] :
% 2.76/1.61 ( ( P2 @ Y @ X )
% 2.76/1.61 => ( P2 @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_116_conjI__realizer,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,P2: A > $o,P: A,Q2: B > $o,Q: B] :
% 2.76/1.61 ( ( P2 @ P )
% 2.76/1.61 => ( ( Q2 @ Q )
% 2.76/1.61 => ( ( P2 @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P @ Q ) ) )
% 2.76/1.61 & ( Q2 @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P @ Q ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_117_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,P2: A > B > $o,X: A,Y: B,A2: product_prod @ A @ B] :
% 2.76/1.61 ( ( P2 @ X @ Y )
% 2.76/1.61 => ( ( A2
% 2.76/1.61 = ( product_Pair @ A @ B @ X @ Y ) )
% 2.76/1.61 => ( P2 @ ( product_fst @ A @ B @ A2 ) @ ( product_snd @ A @ B @ A2 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_118_Multiset_Ois__empty__def,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( is_empty @ A )
% 2.76/1.61 = ( ^ [A8: multiset @ A] :
% 2.76/1.61 ( A8
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_119_exE__realizer_H,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,P2: A > B > $o,P: product_prod @ B @ A] :
% 2.76/1.61 ( ( P2 @ ( product_snd @ B @ A @ P ) @ ( product_fst @ B @ A @ P ) )
% 2.76/1.61 => ~ ! [X3: B,Y3: A] :
% 2.76/1.61 ~ ( P2 @ Y3 @ X3 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_120_eq__snd__iff,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,B2: A,P: product_prod @ B @ A] :
% 2.76/1.61 ( ( B2
% 2.76/1.61 = ( product_snd @ B @ A @ P ) )
% 2.76/1.61 = ( ? [A6: B] :
% 2.76/1.61 ( P
% 2.76/1.61 = ( product_Pair @ B @ A @ A6 @ B2 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_121_eq__fst__iff,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,A2: A,P: product_prod @ A @ B] :
% 2.76/1.61 ( ( A2
% 2.76/1.61 = ( product_fst @ A @ B @ P ) )
% 2.76/1.61 = ( ? [B6: B] :
% 2.76/1.61 ( P
% 2.76/1.61 = ( product_Pair @ A @ B @ A2 @ B6 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_122_verit__sum__simplify,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( cancel1352612707id_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.61 = A2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_123_add__0__iff,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( semiri456707255roduct @ A )
% 2.76/1.61 => ! [B2: A,A2: A] :
% 2.76/1.61 ( ( B2
% 2.76/1.61 = ( plus_plus @ A @ B2 @ A2 ) )
% 2.76/1.61 = ( A2
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_124_HS_Ois__empty__as__list,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [E3: tree @ A] :
% 2.76/1.61 ( ( heapIm721255937_empty @ A @ E3 )
% 2.76/1.61 => ( ( multiset2 @ A @ E3 )
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_125_add__mset__replicate__mset__safe,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,M: multiset @ B,A2: B] :
% 2.76/1.61 ( ( nO_MATCH @ ( multiset @ A ) @ ( multiset @ B ) @ ( zero_zero @ ( multiset @ A ) ) @ M )
% 2.76/1.61 => ( ( add_mset @ B @ A2 @ M )
% 2.76/1.61 = ( plus_plus @ ( multiset @ B ) @ ( add_mset @ B @ A2 @ ( zero_zero @ ( multiset @ B ) ) ) @ M ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_126_HS_Ois__empty__empty,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( heapIm721255937_empty @ A @ ( e @ A ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_127_hs__is__empty__def,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( heapIm721255937_empty @ A )
% 2.76/1.61 = ( ^ [T4: tree @ A] :
% 2.76/1.61 ( T4
% 2.76/1.61 = ( e @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_128_HS_Ois__empty__inj,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [E3: tree @ A] :
% 2.76/1.61 ( ( heapIm721255937_empty @ A @ E3 )
% 2.76/1.61 => ( E3
% 2.76/1.61 = ( e @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_129_prod_Oswap__def,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType] :
% 2.76/1.61 ( ( product_swap @ A @ B )
% 2.76/1.61 = ( ^ [P3: product_prod @ A @ B] : ( product_Pair @ B @ A @ ( product_snd @ A @ B @ P3 ) @ ( product_fst @ A @ B @ P3 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_130_removeLeaf__heap__is__heap,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [T3: tree @ A] :
% 2.76/1.61 ( ( is_heap @ A @ T3 )
% 2.76/1.61 => ( ( T3
% 2.76/1.61 != ( e @ A ) )
% 2.76/1.61 => ( is_heap @ A @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T3 ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_131_NO__MATCH__cong,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType] :
% 2.76/1.61 ( ( nO_MATCH @ A @ B )
% 2.76/1.61 = ( nO_MATCH @ A @ B ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_132_NO__MATCH__def,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType] :
% 2.76/1.61 ( ( nO_MATCH @ A @ B )
% 2.76/1.61 = ( ^ [Pat: A,Val: B] : $true ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_133_swap__swap,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,P: product_prod @ A @ B] :
% 2.76/1.61 ( ( product_swap @ B @ A @ ( product_swap @ A @ B @ P ) )
% 2.76/1.61 = P ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_134_swap__simp,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,X: B,Y: A] :
% 2.76/1.61 ( ( product_swap @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 2.76/1.61 = ( product_Pair @ A @ B @ Y @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_135_snd__swap,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,X: product_prod @ A @ B] :
% 2.76/1.61 ( ( product_snd @ B @ A @ ( product_swap @ A @ B @ X ) )
% 2.76/1.61 = ( product_fst @ A @ B @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_136_fst__swap,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,X: product_prod @ B @ A] :
% 2.76/1.61 ( ( product_fst @ A @ B @ ( product_swap @ B @ A @ X ) )
% 2.76/1.61 = ( product_snd @ B @ A @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_137_is__heap_Osimps_I1_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( is_heap @ A @ ( e @ A ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_138_is__heap_Osimps_I2_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A] : ( is_heap @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_139_removeLeaf__val__val,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [T3: tree @ A] :
% 2.76/1.61 ( ( ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T3 ) )
% 2.76/1.61 != ( e @ A ) )
% 2.76/1.61 => ( ( T3
% 2.76/1.61 != ( e @ A ) )
% 2.76/1.61 => ( ( val @ A @ T3 )
% 2.76/1.61 = ( val @ A @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T3 ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_140_internal__case__prod__conv,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 2.76/1.61 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.76/1.61 = ( C3 @ A2 @ B2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_141_Heap__axioms__def,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( ( heap_axioms @ B @ A )
% 2.76/1.61 = ( ^ [Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),As_tree: B > ( tree @ A ),Remove_max: B > ( product_prod @ A @ B )] :
% 2.76/1.61 ( ! [L2: B] :
% 2.76/1.61 ( ( Multiset @ L2 )
% 2.76/1.61 = ( multiset2 @ A @ ( As_tree @ L2 ) ) )
% 2.76/1.61 & ! [I2: list @ A] : ( is_heap @ A @ ( As_tree @ ( Of_list @ I2 ) ) )
% 2.76/1.61 & ! [T4: B] :
% 2.76/1.61 ( ( ( As_tree @ T4 )
% 2.76/1.61 = ( e @ A ) )
% 2.76/1.61 = ( Is_empty @ T4 ) )
% 2.76/1.61 & ! [L2: B,M4: A,L3: B] :
% 2.76/1.61 ( ~ ( Is_empty @ L2 )
% 2.76/1.61 => ( ( ( product_Pair @ A @ B @ M4 @ L3 )
% 2.76/1.61 = ( Remove_max @ L2 ) )
% 2.76/1.61 => ( ( add_mset @ A @ M4 @ ( Multiset @ L3 ) )
% 2.76/1.61 = ( Multiset @ L2 ) ) ) )
% 2.76/1.61 & ! [L2: B,M4: A,L3: B] :
% 2.76/1.61 ( ~ ( Is_empty @ L2 )
% 2.76/1.61 => ( ( is_heap @ A @ ( As_tree @ L2 ) )
% 2.76/1.61 => ( ( ( product_Pair @ A @ B @ M4 @ L3 )
% 2.76/1.61 = ( Remove_max @ L2 ) )
% 2.76/1.61 => ( is_heap @ A @ ( As_tree @ L3 ) ) ) ) )
% 2.76/1.61 & ! [T4: B,M4: A,T5: B] :
% 2.76/1.61 ( ~ ( Is_empty @ T4 )
% 2.76/1.61 => ( ( ( product_Pair @ A @ B @ M4 @ T5 )
% 2.76/1.61 = ( Remove_max @ T4 ) )
% 2.76/1.61 => ( M4
% 2.76/1.61 = ( val @ A @ ( As_tree @ T4 ) ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_142_Heap__axioms_Ointro,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Of_list2: ( list @ A ) > B,Is_empty2: B > $o,Remove_max2: B > ( product_prod @ A @ B )] :
% 2.76/1.61 ( ! [L4: B] :
% 2.76/1.61 ( ( Multiset2 @ L4 )
% 2.76/1.61 = ( multiset2 @ A @ ( As_tree2 @ L4 ) ) )
% 2.76/1.61 => ( ! [I3: list @ A] : ( is_heap @ A @ ( As_tree2 @ ( Of_list2 @ I3 ) ) )
% 2.76/1.61 => ( ! [T6: B] :
% 2.76/1.61 ( ( ( As_tree2 @ T6 )
% 2.76/1.61 = ( e @ A ) )
% 2.76/1.61 = ( Is_empty2 @ T6 ) )
% 2.76/1.61 => ( ! [L4: B,M5: A,L5: B] :
% 2.76/1.61 ( ~ ( Is_empty2 @ L4 )
% 2.76/1.61 => ( ( ( product_Pair @ A @ B @ M5 @ L5 )
% 2.76/1.61 = ( Remove_max2 @ L4 ) )
% 2.76/1.61 => ( ( add_mset @ A @ M5 @ ( Multiset2 @ L5 ) )
% 2.76/1.61 = ( Multiset2 @ L4 ) ) ) )
% 2.76/1.61 => ( ! [L4: B,M5: A,L5: B] :
% 2.76/1.61 ( ~ ( Is_empty2 @ L4 )
% 2.76/1.61 => ( ( is_heap @ A @ ( As_tree2 @ L4 ) )
% 2.76/1.61 => ( ( ( product_Pair @ A @ B @ M5 @ L5 )
% 2.76/1.61 = ( Remove_max2 @ L4 ) )
% 2.76/1.61 => ( is_heap @ A @ ( As_tree2 @ L5 ) ) ) ) )
% 2.76/1.61 => ( ! [T6: B,M5: A,T7: B] :
% 2.76/1.61 ( ~ ( Is_empty2 @ T6 )
% 2.76/1.61 => ( ( ( product_Pair @ A @ B @ M5 @ T7 )
% 2.76/1.61 = ( Remove_max2 @ T6 ) )
% 2.76/1.61 => ( M5
% 2.76/1.61 = ( val @ A @ ( As_tree2 @ T6 ) ) ) ) )
% 2.76/1.61 => ( heap_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_143_val_Osimps,axiom,
% 2.76/1.61 ! [A: $tType,V: A,Uu: tree @ A,Uv: tree @ A] :
% 2.76/1.61 ( ( val @ A @ ( t @ A @ V @ Uu @ Uv ) )
% 2.76/1.61 = V ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_144_is__heap_Osimps_I4_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.76/1.61 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 2.76/1.61 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 & ( is_heap @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_145_is__heap_Osimps_I3_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.76/1.61 ( ( is_heap @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 & ( is_heap @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_146_divides__aux__eq,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( unique1598680935umeral @ A )
% 2.76/1.61 => ! [Q: A,R: A] :
% 2.76/1.61 ( ( unique455577585es_aux @ A @ ( product_Pair @ A @ A @ Q @ R ) )
% 2.76/1.61 = ( R
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_147_Heap_Oremove__max__is__heap,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),L: B,M6: A,L6: B] :
% 2.76/1.61 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 2.76/1.61 => ( ~ ( Is_empty2 @ L )
% 2.76/1.61 => ( ( is_heap @ A @ ( As_tree2 @ L ) )
% 2.76/1.61 => ( ( ( product_Pair @ A @ B @ M6 @ L6 )
% 2.76/1.61 = ( Remove_max2 @ L ) )
% 2.76/1.61 => ( is_heap @ A @ ( As_tree2 @ L6 ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_148_le__zero__eq,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( canoni770627133id_add @ A )
% 2.76/1.61 => ! [N4: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ N4 @ ( zero_zero @ A ) )
% 2.76/1.61 = ( N4
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_149_add__le__cancel__right,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere236663937imp_le @ A )
% 2.76/1.61 => ! [A2: A,C3: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 2.76/1.61 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_150_add__le__cancel__left,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere236663937imp_le @ A )
% 2.76/1.61 => ! [C3: A,A2: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 2.76/1.61 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_151_add__le__same__cancel1,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere516151231imp_le @ A )
% 2.76/1.61 => ! [B2: A,A2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 2.76/1.61 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_152_add__le__same__cancel2,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere516151231imp_le @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.76/1.61 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_153_le__add__same__cancel1,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere516151231imp_le @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 2.76/1.61 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_154_le__add__same__cancel2,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere516151231imp_le @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 2.76/1.61 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_155_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linord219039673up_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.76/1.61 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_156_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linord219039673up_add @ A )
% 2.76/1.61 => ! [A2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.76/1.61 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_157_verit__la__disequality,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( A2 = B2 )
% 2.76/1.61 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.61 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_158_add__le__imp__le__right,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere236663937imp_le @ A )
% 2.76/1.61 => ! [A2: A,C3: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 2.76/1.61 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_159_add__le__imp__le__left,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere236663937imp_le @ A )
% 2.76/1.61 => ! [C3: A,A2: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 2.76/1.61 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_160_le__iff__add,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( canoni770627133id_add @ A )
% 2.76/1.61 => ( ( ord_less_eq @ A )
% 2.76/1.61 = ( ^ [A6: A,B6: A] :
% 2.76/1.61 ? [C4: A] :
% 2.76/1.61 ( B6
% 2.76/1.61 = ( plus_plus @ A @ A6 @ C4 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_161_add__right__mono,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere779506340up_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.61 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_162_less__eqE,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( canoni770627133id_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.61 => ~ ! [C2: A] :
% 2.76/1.61 ( B2
% 2.76/1.61 != ( plus_plus @ A @ A2 @ C2 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_163_add__left__mono,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere779506340up_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.61 => ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_164_add__mono,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere779506340up_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A,D3: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.61 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 2.76/1.61 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_165_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere779506340up_add @ A )
% 2.76/1.61 => ! [I: A,J: A,K: A,L: A] :
% 2.76/1.61 ( ( ( ord_less_eq @ A @ I @ J )
% 2.76/1.61 & ( ord_less_eq @ A @ K @ L ) )
% 2.76/1.61 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_166_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere779506340up_add @ A )
% 2.76/1.61 => ! [I: A,J: A,K: A,L: A] :
% 2.76/1.61 ( ( ( I = J )
% 2.76/1.61 & ( ord_less_eq @ A @ K @ L ) )
% 2.76/1.61 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_167_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere779506340up_add @ A )
% 2.76/1.61 => ! [I: A,J: A,K: A,L: A] :
% 2.76/1.61 ( ( ( ord_less_eq @ A @ I @ J )
% 2.76/1.61 & ( K = L ) )
% 2.76/1.61 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_168_zero__le,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( canoni770627133id_add @ A )
% 2.76/1.61 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_169_add__decreasing,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere216010020id_add @ A )
% 2.76/1.61 => ! [A2: A,C3: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.61 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 2.76/1.61 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ B2 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_170_add__increasing,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere216010020id_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.61 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 2.76/1.61 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C3 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_171_add__decreasing2,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere216010020id_add @ A )
% 2.76/1.61 => ! [C3: A,A2: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ C3 @ ( zero_zero @ A ) )
% 2.76/1.61 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.76/1.61 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ B2 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_172_add__increasing2,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere216010020id_add @ A )
% 2.76/1.61 => ! [C3: A,B2: A,A2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C3 )
% 2.76/1.61 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.76/1.61 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C3 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_173_add__nonneg__nonneg,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere216010020id_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.76/1.61 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.76/1.61 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_174_add__nonpos__nonpos,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere216010020id_add @ A )
% 2.76/1.61 => ! [A2: A,B2: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.76/1.61 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.76/1.61 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_175_add__nonneg__eq__0__iff,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere216010020id_add @ A )
% 2.76/1.61 => ! [X: A,Y: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 2.76/1.61 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 2.76/1.61 => ( ( ( plus_plus @ A @ X @ Y )
% 2.76/1.61 = ( zero_zero @ A ) )
% 2.76/1.61 = ( ( X
% 2.76/1.61 = ( zero_zero @ A ) )
% 2.76/1.61 & ( Y
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_176_add__nonpos__eq__0__iff,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( ordere216010020id_add @ A )
% 2.76/1.61 => ! [X: A,Y: A] :
% 2.76/1.61 ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 2.76/1.61 => ( ( ord_less_eq @ A @ Y @ ( zero_zero @ A ) )
% 2.76/1.61 => ( ( ( plus_plus @ A @ X @ Y )
% 2.76/1.61 = ( zero_zero @ A ) )
% 2.76/1.61 = ( ( X
% 2.76/1.61 = ( zero_zero @ A ) )
% 2.76/1.61 & ( Y
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_177_Heap_Oas__tree__empty,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),T3: B] :
% 2.76/1.61 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 2.76/1.61 => ( ( ( As_tree2 @ T3 )
% 2.76/1.61 = ( e @ A ) )
% 2.76/1.61 = ( Is_empty2 @ T3 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_178_Heap_Ois__heap__of__list,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),I: list @ A] :
% 2.76/1.61 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 2.76/1.61 => ( is_heap @ A @ ( As_tree2 @ ( Of_list2 @ I ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_179_Heap_Omultiset,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),L: B] :
% 2.76/1.61 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 2.76/1.61 => ( ( Multiset2 @ L )
% 2.76/1.61 = ( multiset2 @ A @ ( As_tree2 @ L ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_180_divides__aux__def,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( unique1598680935umeral @ A )
% 2.76/1.61 => ( ( unique455577585es_aux @ A )
% 2.76/1.61 = ( ^ [Qr: product_prod @ A @ A] :
% 2.76/1.61 ( ( product_snd @ A @ A @ Qr )
% 2.76/1.61 = ( zero_zero @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_181_Heap_Oaxioms_I2_J,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B )] :
% 2.76/1.61 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 2.76/1.61 => ( heap_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_182_is__heap_Osimps_I6_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,Vd: A,Ve: tree @ A,Vf: tree @ A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.76/1.61 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 & ( is_heap @ A @ ( t @ A @ Va @ Vb @ Vc ) )
% 2.76/1.61 & ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 2.76/1.61 & ( is_heap @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_183_is__heap_Osimps_I5_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A] :
% 2.76/1.61 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 2.76/1.61 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 2.76/1.61 & ( is_heap @ A @ ( t @ A @ Vd @ Ve @ Vf ) )
% 2.76/1.61 & ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 & ( is_heap @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_184_Heap_Oremove__max__multiset_H,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),L: B,M6: A,L6: B] :
% 2.76/1.61 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 2.76/1.61 => ( ~ ( Is_empty2 @ L )
% 2.76/1.61 => ( ( ( product_Pair @ A @ B @ M6 @ L6 )
% 2.76/1.61 = ( Remove_max2 @ L ) )
% 2.76/1.61 => ( ( add_mset @ A @ M6 @ ( Multiset2 @ L6 ) )
% 2.76/1.61 = ( Multiset2 @ L ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_185_Heap_Oremove__max__val,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B ),T3: B,M6: A,T2: B] :
% 2.76/1.61 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 2.76/1.61 => ( ~ ( Is_empty2 @ T3 )
% 2.76/1.61 => ( ( ( product_Pair @ A @ B @ M6 @ T2 )
% 2.76/1.61 = ( Remove_max2 @ T3 ) )
% 2.76/1.61 => ( M6
% 2.76/1.61 = ( val @ A @ ( As_tree2 @ T3 ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_186_siftDown_Osimps_I4_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Va: A,Vb: tree @ A,Vc: tree @ A,V: A] :
% 2.76/1.61 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) )
% 2.76/1.61 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( t @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( e @ A ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_187_siftDown_Osimps_I3_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Va: A,Vb: tree @ A,Vc: tree @ A,V: A] :
% 2.76/1.61 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 2.76/1.61 = ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) ) )
% 2.76/1.61 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 2.76/1.61 = ( t @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) @ ( e @ A ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_188_siftDown_Osimps_I5_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Vd: A,Ve: tree @ A,Vf: tree @ A,Va: A,Vb: tree @ A,Vc: tree @ A,V: A] :
% 2.76/1.61 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 2.76/1.61 = ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) )
% 2.76/1.61 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 2.76/1.61 = ( t @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) )
% 2.76/1.61 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 2.76/1.61 = ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) )
% 2.76/1.61 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 2.76/1.61 = ( t @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( t @ A @ Va @ Vb @ Vc ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_189_siftDown_Osimps_I1_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( e @ A ) )
% 2.76/1.61 = ( e @ A ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_190_siftDown__multiset,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [T3: tree @ A] :
% 2.76/1.61 ( ( multiset2 @ A @ ( heapIm748920189ftDown @ A @ T3 ) )
% 2.76/1.61 = ( multiset2 @ A @ T3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_191_siftDown__Node,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [T3: tree @ A,V: A,L: tree @ A,R: tree @ A] :
% 2.76/1.61 ( ( T3
% 2.76/1.61 = ( t @ A @ V @ L @ R ) )
% 2.76/1.61 => ? [L5: tree @ A,V4: A,R2: tree @ A] :
% 2.76/1.61 ( ( ( heapIm748920189ftDown @ A @ T3 )
% 2.76/1.61 = ( t @ A @ V4 @ L5 @ R2 ) )
% 2.76/1.61 & ( ord_less_eq @ A @ V @ V4 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_192_siftDown_Osimps_I2_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A] :
% 2.76/1.61 ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) )
% 2.76/1.61 = ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_193_siftDown__heap__is__heap,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [L: tree @ A,R: tree @ A,T3: tree @ A,V: A] :
% 2.76/1.61 ( ( is_heap @ A @ L )
% 2.76/1.61 => ( ( is_heap @ A @ R )
% 2.76/1.61 => ( ( T3
% 2.76/1.61 = ( t @ A @ V @ L @ R ) )
% 2.76/1.61 => ( is_heap @ A @ ( heapIm748920189ftDown @ A @ T3 ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_194_siftDown_Osimps_I6_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A,V: A] :
% 2.76/1.61 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 2.76/1.61 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) )
% 2.76/1.61 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( t @ A @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) )
% 2.76/1.61 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( val @ A @ ( t @ A @ Vd @ Ve @ Vf ) ) )
% 2.76/1.61 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) ) )
% 2.76/1.61 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ V )
% 2.76/1.61 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd @ Ve @ Vf ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.76/1.61 = ( t @ A @ ( val @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( t @ A @ Vd @ Ve @ Vf ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va @ Vb @ Vc ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va @ Vb @ Vc ) ) ) ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_195_siftDown__in__tree,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [T3: tree @ A] :
% 2.76/1.61 ( ( T3
% 2.76/1.61 != ( e @ A ) )
% 2.76/1.61 => ( in_tree @ A @ ( val @ A @ ( heapIm748920189ftDown @ A @ T3 ) ) @ T3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_196_is__heap__max,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,T3: tree @ A] :
% 2.76/1.61 ( ( in_tree @ A @ V @ T3 )
% 2.76/1.61 => ( ( is_heap @ A @ T3 )
% 2.76/1.61 => ( ord_less_eq @ A @ V @ ( val @ A @ T3 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_197_in__tree_Osimps_I2_J,axiom,
% 2.76/1.61 ! [A: $tType,V: A,V2: A,L: tree @ A,R: tree @ A] :
% 2.76/1.61 ( ( in_tree @ A @ V @ ( t @ A @ V2 @ L @ R ) )
% 2.76/1.61 = ( ( V = V2 )
% 2.76/1.61 | ( in_tree @ A @ V @ L )
% 2.76/1.61 | ( in_tree @ A @ V @ R ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_198_in__tree_Osimps_I1_J,axiom,
% 2.76/1.61 ! [A: $tType,V: A] :
% 2.76/1.61 ~ ( in_tree @ A @ V @ ( e @ A ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_199_siftDown__in__tree__set,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( ( in_tree @ A )
% 2.76/1.61 = ( ^ [V5: A,T4: tree @ A] : ( in_tree @ A @ V5 @ ( heapIm748920189ftDown @ A @ T4 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_200_le__numeral__extra_I3_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linord1659791738miring @ A )
% 2.76/1.61 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_201_hs__remove__max__def,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( ( heapIm1542349758ve_max @ A )
% 2.76/1.61 = ( ^ [T4: tree @ A] :
% 2.76/1.61 ( if @ ( product_prod @ A @ ( tree @ A ) )
% 2.76/1.61 @ ( ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T4 ) )
% 2.76/1.61 = ( e @ A ) )
% 2.76/1.61 @ ( product_Pair @ A @ ( tree @ A ) @ ( val @ A @ T4 ) @ ( e @ A ) )
% 2.76/1.61 @ ( product_Pair @ A @ ( tree @ A ) @ ( val @ A @ T4 ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ ( product_fst @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T4 ) ) @ ( heapIm1271749598e_left @ A @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T4 ) ) ) @ ( heapIm1434396069_right @ A @ ( product_snd @ A @ ( tree @ A ) @ ( heapIm970386777veLeaf @ A @ T4 ) ) ) ) ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_202_is__num__normalize_I1_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( neg_numeral @ A )
% 2.76/1.61 => ! [A2: A,B2: A,C3: A] :
% 2.76/1.61 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 2.76/1.61 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_203_scomp__unfold,axiom,
% 2.76/1.61 ! [D: $tType,C: $tType,B: $tType,A: $tType] :
% 2.76/1.61 ( ( product_scomp @ A @ B @ C @ D )
% 2.76/1.61 = ( ^ [F4: A > ( product_prod @ B @ C ),G4: B > C > D,X4: A] : ( G4 @ ( product_fst @ B @ C @ ( F4 @ X4 ) ) @ ( product_snd @ B @ C @ ( F4 @ X4 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_204_heapify_Osimps_I2_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [V: A,L: tree @ A,R: tree @ A] :
% 2.76/1.61 ( ( heapIm818251801eapify @ A @ ( t @ A @ V @ L @ R ) )
% 2.76/1.61 = ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm818251801eapify @ A @ L ) @ ( heapIm818251801eapify @ A @ R ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_205_scomp__scomp,axiom,
% 2.76/1.61 ! [A: $tType,C: $tType,D: $tType,B: $tType,F: $tType,E: $tType,F3: A > ( product_prod @ E @ F ),G3: E > F > ( product_prod @ C @ D ),H: C > D > B] :
% 2.76/1.61 ( ( product_scomp @ A @ C @ D @ B @ ( product_scomp @ A @ E @ F @ ( product_prod @ C @ D ) @ F3 @ G3 ) @ H )
% 2.76/1.61 = ( product_scomp @ A @ E @ F @ B @ F3
% 2.76/1.61 @ ^ [X4: E] : ( product_scomp @ F @ C @ D @ B @ ( G3 @ X4 ) @ H ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_206_Pair__scomp,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,C: $tType,X: C,F3: C > A > B] :
% 2.76/1.61 ( ( product_scomp @ A @ C @ A @ B @ ( product_Pair @ C @ A @ X ) @ F3 )
% 2.76/1.61 = ( F3 @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_207_scomp__Pair,axiom,
% 2.76/1.61 ! [C: $tType,B: $tType,A: $tType,X: A > ( product_prod @ B @ C )] :
% 2.76/1.61 ( ( product_scomp @ A @ B @ C @ ( product_prod @ B @ C ) @ X @ ( product_Pair @ B @ C ) )
% 2.76/1.61 = X ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_208_heapify_Osimps_I1_J,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( ( heapIm818251801eapify @ A @ ( e @ A ) )
% 2.76/1.61 = ( e @ A ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_209_heapify__heap__is__heap,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [T3: tree @ A] : ( is_heap @ A @ ( heapIm818251801eapify @ A @ T3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_210_multiset__heapify,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [T3: tree @ A] :
% 2.76/1.61 ( ( multiset2 @ A @ ( heapIm818251801eapify @ A @ T3 ) )
% 2.76/1.61 = ( multiset2 @ A @ T3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_211_Heap__def,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( ( heap @ B @ A )
% 2.76/1.61 = ( ^ [Empty2: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),As_tree: B > ( tree @ A ),Remove_max: B > ( product_prod @ A @ B )] :
% 2.76/1.61 ( ( collection @ B @ A @ Empty2 @ Is_empty @ Of_list @ Multiset )
% 2.76/1.61 & ( heap_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_212_Heap_Ointro,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B )] :
% 2.76/1.61 ( ( collection @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 )
% 2.76/1.61 => ( ( heap_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 2.76/1.61 => ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_213_Heap_Oaxioms_I1_J,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),As_tree2: B > ( tree @ A ),Remove_max2: B > ( product_prod @ A @ B )] :
% 2.76/1.61 ( ( heap @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 2.76/1.61 => ( collection @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_214_HS_OCollection__axioms,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( collection @ ( tree @ A ) @ A @ ( e @ A ) @ ( heapIm721255937_empty @ A ) @ ( heapIm874063447f_list @ A ) @ ( multiset2 @ A ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_215_Collection_Omultiset__empty,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A )] :
% 2.76/1.61 ( ( collection @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 )
% 2.76/1.61 => ( ( Multiset2 @ Empty )
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_216_Collection_Ois__empty__as__list,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,Empty: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),E3: B] :
% 2.76/1.61 ( ( collection @ B @ A @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 )
% 2.76/1.61 => ( ( Is_empty2 @ E3 )
% 2.76/1.61 => ( ( Multiset2 @ E3 )
% 2.76/1.61 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_217_hs__of__list__def,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ( ( heapIm874063447f_list @ A )
% 2.76/1.61 = ( ^ [L2: list @ A] : ( heapIm818251801eapify @ A @ ( heapIm1912108042t_tree @ A @ L2 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_218_pred__equals__eq2,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 2.76/1.61 ( ( ( ^ [X4: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y6 ) @ R3 ) )
% 2.76/1.61 = ( ^ [X4: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y6 ) @ S2 ) ) )
% 2.76/1.61 = ( R3 = S2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_219_subrelI,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S3: set @ ( product_prod @ A @ B )] :
% 2.76/1.61 ( ! [X3: A,Y3: B] :
% 2.76/1.61 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 2.76/1.61 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S3 ) )
% 2.76/1.61 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S3 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_220_pred__subset__eq2,axiom,
% 2.76/1.61 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 2.76/1.61 ( ( ord_less_eq @ ( A > B > $o )
% 2.76/1.61 @ ^ [X4: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y6 ) @ R3 )
% 2.76/1.61 @ ^ [X4: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y6 ) @ S2 ) )
% 2.76/1.61 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S2 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_221_fun__cong__unused__0,axiom,
% 2.76/1.61 ! [A: $tType,B: $tType,C: $tType] :
% 2.76/1.61 ( ( zero @ B )
% 2.76/1.61 => ! [F3: ( A > B ) > C,G3: C] :
% 2.76/1.61 ( ( F3
% 2.76/1.61 = ( ^ [X4: A > B] : G3 ) )
% 2.76/1.61 => ( ( F3
% 2.76/1.61 @ ^ [X4: A] : ( zero_zero @ B ) )
% 2.76/1.61 = G3 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_222_heap__top__geq,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [A2: A,T3: tree @ A] :
% 2.76/1.61 ( ( member @ A @ A2 @ ( set_mset @ A @ ( multiset2 @ A @ T3 ) ) )
% 2.76/1.61 => ( ( is_heap @ A @ T3 )
% 2.76/1.61 => ( ord_less_eq @ A @ A2 @ ( val @ A @ T3 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_223_multi__member__last,axiom,
% 2.76/1.61 ! [A: $tType,X: A] : ( member @ A @ X @ ( set_mset @ A @ ( add_mset @ A @ X @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_224_union__single__eq__member,axiom,
% 2.76/1.61 ! [A: $tType,X: A,M: multiset @ A,N: multiset @ A] :
% 2.76/1.61 ( ( ( add_mset @ A @ X @ M )
% 2.76/1.61 = N )
% 2.76/1.61 => ( member @ A @ X @ ( set_mset @ A @ N ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_225_insert__noteq__member,axiom,
% 2.76/1.61 ! [A: $tType,B2: A,B5: multiset @ A,C3: A,C5: multiset @ A] :
% 2.76/1.61 ( ( ( add_mset @ A @ B2 @ B5 )
% 2.76/1.61 = ( add_mset @ A @ C3 @ C5 ) )
% 2.76/1.61 => ( ( B2 != C3 )
% 2.76/1.61 => ( member @ A @ C3 @ ( set_mset @ A @ B5 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_226_multi__member__split,axiom,
% 2.76/1.61 ! [A: $tType,X: A,M: multiset @ A] :
% 2.76/1.61 ( ( member @ A @ X @ ( set_mset @ A @ M ) )
% 2.76/1.61 => ? [A7: multiset @ A] :
% 2.76/1.61 ( M
% 2.76/1.61 = ( add_mset @ A @ X @ A7 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_227_mset__add,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,A5: multiset @ A] :
% 2.76/1.61 ( ( member @ A @ A2 @ ( set_mset @ A @ A5 ) )
% 2.76/1.61 => ~ ! [B7: multiset @ A] :
% 2.76/1.61 ( A5
% 2.76/1.61 != ( add_mset @ A @ A2 @ B7 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_228_union__iff,axiom,
% 2.76/1.61 ! [A: $tType,A2: A,A5: multiset @ A,B5: multiset @ A] :
% 2.76/1.61 ( ( member @ A @ A2 @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ A5 @ B5 ) ) )
% 2.76/1.61 = ( ( member @ A @ A2 @ ( set_mset @ A @ A5 ) )
% 2.76/1.61 | ( member @ A @ A2 @ ( set_mset @ A @ B5 ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_229_multiset__nonemptyE,axiom,
% 2.76/1.61 ! [A: $tType,A5: multiset @ A] :
% 2.76/1.61 ( ( A5
% 2.76/1.61 != ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 => ~ ! [X3: A] :
% 2.76/1.61 ~ ( member @ A @ X3 @ ( set_mset @ A @ A5 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_230_ge__eq__refl,axiom,
% 2.76/1.61 ! [A: $tType,R3: A > A > $o,X: A] :
% 2.76/1.61 ( ( ord_less_eq @ ( A > A > $o )
% 2.76/1.61 @ ^ [Y4: A,Z2: A] : ( Y4 = Z2 )
% 2.76/1.61 @ R3 )
% 2.76/1.61 => ( R3 @ X @ X ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_231_refl__ge__eq,axiom,
% 2.76/1.61 ! [A: $tType,R3: A > A > $o] :
% 2.76/1.61 ( ! [X3: A] : ( R3 @ X3 @ X3 )
% 2.76/1.61 => ( ord_less_eq @ ( A > A > $o )
% 2.76/1.61 @ ^ [Y4: A,Z2: A] : ( Y4 = Z2 )
% 2.76/1.61 @ R3 ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_232_subset__CollectI,axiom,
% 2.76/1.61 ! [A: $tType,B5: set @ A,A5: set @ A,Q2: A > $o,P2: A > $o] :
% 2.76/1.61 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 2.76/1.61 => ( ! [X3: A] :
% 2.76/1.61 ( ( member @ A @ X3 @ B5 )
% 2.76/1.61 => ( ( Q2 @ X3 )
% 2.76/1.61 => ( P2 @ X3 ) ) )
% 2.76/1.61 => ( ord_less_eq @ ( set @ A )
% 2.76/1.61 @ ( collect @ A
% 2.76/1.61 @ ^ [X4: A] :
% 2.76/1.61 ( ( member @ A @ X4 @ B5 )
% 2.76/1.61 & ( Q2 @ X4 ) ) )
% 2.76/1.61 @ ( collect @ A
% 2.76/1.61 @ ^ [X4: A] :
% 2.76/1.61 ( ( member @ A @ X4 @ A5 )
% 2.76/1.61 & ( P2 @ X4 ) ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_233_subset__Collect__iff,axiom,
% 2.76/1.61 ! [A: $tType,B5: set @ A,A5: set @ A,P2: A > $o] :
% 2.76/1.61 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 2.76/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B5
% 2.76/1.61 @ ( collect @ A
% 2.76/1.61 @ ^ [X4: A] :
% 2.76/1.61 ( ( member @ A @ X4 @ A5 )
% 2.76/1.61 & ( P2 @ X4 ) ) ) )
% 2.76/1.61 = ( ! [X4: A] :
% 2.76/1.61 ( ( member @ A @ X4 @ B5 )
% 2.76/1.61 => ( P2 @ X4 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_234_multiset__induct__min,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [P2: ( multiset @ A ) > $o,M: multiset @ A] :
% 2.76/1.61 ( ( P2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 => ( ! [X3: A,M3: multiset @ A] :
% 2.76/1.61 ( ( P2 @ M3 )
% 2.76/1.61 => ( ! [Xa: A] :
% 2.76/1.61 ( ( member @ A @ Xa @ ( set_mset @ A @ M3 ) )
% 2.76/1.61 => ( ord_less_eq @ A @ X3 @ Xa ) )
% 2.76/1.61 => ( P2 @ ( add_mset @ A @ X3 @ M3 ) ) ) )
% 2.76/1.61 => ( P2 @ M ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_235_multiset__induct__max,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [P2: ( multiset @ A ) > $o,M: multiset @ A] :
% 2.76/1.61 ( ( P2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 => ( ! [X3: A,M3: multiset @ A] :
% 2.76/1.61 ( ( P2 @ M3 )
% 2.76/1.61 => ( ! [Xa: A] :
% 2.76/1.61 ( ( member @ A @ Xa @ ( set_mset @ A @ M3 ) )
% 2.76/1.61 => ( ord_less_eq @ A @ Xa @ X3 ) )
% 2.76/1.61 => ( P2 @ ( add_mset @ A @ X3 @ M3 ) ) ) )
% 2.76/1.61 => ( P2 @ M ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_236_multi__member__skip,axiom,
% 2.76/1.61 ! [A: $tType,X: A,XS: multiset @ A,Y: A] :
% 2.76/1.61 ( ( member @ A @ X @ ( set_mset @ A @ XS ) )
% 2.76/1.61 => ( member @ A @ X @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ Y @ ( zero_zero @ ( multiset @ A ) ) ) @ XS ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_237_multi__member__this,axiom,
% 2.76/1.61 ! [A: $tType,X: A,XS: multiset @ A] : ( member @ A @ X @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ X @ ( zero_zero @ ( multiset @ A ) ) ) @ XS ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_238_less__add,axiom,
% 2.76/1.61 ! [A: $tType,N: multiset @ A,A2: A,M0: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 2.76/1.61 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ ( add_mset @ A @ A2 @ M0 ) ) @ ( mult1 @ A @ R ) )
% 2.76/1.61 => ( ? [M3: multiset @ A] :
% 2.76/1.61 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M3 @ M0 ) @ ( mult1 @ A @ R ) )
% 2.76/1.61 & ( N
% 2.76/1.61 = ( add_mset @ A @ A2 @ M3 ) ) )
% 2.76/1.61 | ? [K4: multiset @ A] :
% 2.76/1.61 ( ! [B8: A] :
% 2.76/1.61 ( ( member @ A @ B8 @ ( set_mset @ A @ K4 ) )
% 2.76/1.61 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B8 @ A2 ) @ R ) )
% 2.76/1.61 & ( N
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ M0 @ K4 ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_239_mult1I,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A,A2: A,M0: multiset @ A,N: multiset @ A,K2: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 2.76/1.61 ( ( M
% 2.76/1.61 = ( add_mset @ A @ A2 @ M0 ) )
% 2.76/1.61 => ( ( N
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ M0 @ K2 ) )
% 2.76/1.61 => ( ! [B4: A] :
% 2.76/1.61 ( ( member @ A @ B4 @ ( set_mset @ A @ K2 ) )
% 2.76/1.61 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A2 ) @ R ) )
% 2.76/1.61 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M ) @ ( mult1 @ A @ R ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_240_mono__mult1,axiom,
% 2.76/1.61 ! [A: $tType,R: set @ ( product_prod @ A @ A ),R4: set @ ( product_prod @ A @ A )] :
% 2.76/1.61 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ R4 )
% 2.76/1.61 => ( ord_less_eq @ ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) @ ( mult1 @ A @ R ) @ ( mult1 @ A @ R4 ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_241_mult1__union,axiom,
% 2.76/1.61 ! [A: $tType,B5: multiset @ A,D4: multiset @ A,R: set @ ( product_prod @ A @ A ),C5: multiset @ A] :
% 2.76/1.61 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ B5 @ D4 ) @ ( mult1 @ A @ R ) )
% 2.76/1.61 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ C5 @ B5 ) @ ( plus_plus @ ( multiset @ A ) @ C5 @ D4 ) ) @ ( mult1 @ A @ R ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_242_not__less__empty,axiom,
% 2.76/1.61 ! [A: $tType,M: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 2.76/1.61 ~ ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M @ ( zero_zero @ ( multiset @ A ) ) ) @ ( mult1 @ A @ R ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_243_mult1E,axiom,
% 2.76/1.61 ! [A: $tType,N: multiset @ A,M: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 2.76/1.61 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M ) @ ( mult1 @ A @ R ) )
% 2.76/1.61 => ~ ! [A4: A,M02: multiset @ A] :
% 2.76/1.61 ( ( M
% 2.76/1.61 = ( add_mset @ A @ A4 @ M02 ) )
% 2.76/1.61 => ! [K4: multiset @ A] :
% 2.76/1.61 ( ( N
% 2.76/1.61 = ( plus_plus @ ( multiset @ A ) @ M02 @ K4 ) )
% 2.76/1.61 => ~ ! [B8: A] :
% 2.76/1.61 ( ( member @ A @ B8 @ ( set_mset @ A @ K4 ) )
% 2.76/1.61 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B8 @ A4 ) @ R ) ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_244_one__step__implies__mult,axiom,
% 2.76/1.61 ! [A: $tType,J2: multiset @ A,K2: multiset @ A,R: set @ ( product_prod @ A @ A ),I4: multiset @ A] :
% 2.76/1.61 ( ( J2
% 2.76/1.61 != ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.61 => ( ! [X3: A] :
% 2.76/1.61 ( ( member @ A @ X3 @ ( set_mset @ A @ K2 ) )
% 2.76/1.61 => ? [Xa: A] :
% 2.76/1.61 ( ( member @ A @ Xa @ ( set_mset @ A @ J2 ) )
% 2.76/1.61 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Xa ) @ R ) ) )
% 2.76/1.61 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ I4 @ K2 ) @ ( plus_plus @ ( multiset @ A ) @ I4 @ J2 ) ) @ ( mult @ A @ R ) ) ) ) ).
% 2.76/1.61
% 2.76/1.61 thf(fact_245_heap__top__max,axiom,
% 2.76/1.61 ! [A: $tType] :
% 2.76/1.61 ( ( linorder @ A )
% 2.76/1.61 => ! [T3: tree @ A] :
% 2.76/1.61 ( ( T3
% 2.76/1.61 != ( e @ A ) )
% 2.76/1.61 => ( ( is_heap @ A @ T3 )
% 2.76/1.61 => ( ( val @ A @ T3 )
% 2.76/1.61 = ( lattic929149872er_Max @ A @ ( set_mset @ A @ ( multiset2 @ A @ T3 ) ) ) ) ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(fact_246_mono__mult,axiom,
% 2.76/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),R4: set @ ( product_prod @ A @ A )] :
% 2.76/1.62 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ R4 )
% 2.76/1.62 => ( ord_less_eq @ ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) @ ( mult @ A @ R ) @ ( mult @ A @ R4 ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(fact_247_mult__implies__one__step,axiom,
% 2.76/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),M: multiset @ A,N: multiset @ A] :
% 2.76/1.62 ( ( trans @ A @ R )
% 2.76/1.62 => ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M @ N ) @ ( mult @ A @ R ) )
% 2.76/1.62 => ? [I5: multiset @ A,J3: multiset @ A] :
% 2.76/1.62 ( ( N
% 2.76/1.62 = ( plus_plus @ ( multiset @ A ) @ I5 @ J3 ) )
% 2.76/1.62 & ? [K4: multiset @ A] :
% 2.76/1.62 ( ( M
% 2.76/1.62 = ( plus_plus @ ( multiset @ A ) @ I5 @ K4 ) )
% 2.76/1.62 & ( J3
% 2.76/1.62 != ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.62 & ! [X6: A] :
% 2.76/1.62 ( ( member @ A @ X6 @ ( set_mset @ A @ K4 ) )
% 2.76/1.62 => ? [Xa2: A] :
% 2.76/1.62 ( ( member @ A @ Xa2 @ ( set_mset @ A @ J3 ) )
% 2.76/1.62 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X6 @ Xa2 ) @ R ) ) ) ) ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(fact_248_subset__mset_Osum__mset__0__iff,axiom,
% 2.76/1.62 ! [A: $tType,M: multiset @ ( multiset @ A )] :
% 2.76/1.62 ( ( ( comm_monoid_sum_mset @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ A ) ) @ M )
% 2.76/1.62 = ( zero_zero @ ( multiset @ A ) ) )
% 2.76/1.62 = ( ! [X4: multiset @ A] :
% 2.76/1.62 ( ( member @ ( multiset @ A ) @ X4 @ ( set_mset @ ( multiset @ A ) @ M ) )
% 2.76/1.62 => ( X4
% 2.76/1.62 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(fact_249_comm__monoid__add_Osum__mset_Ocong,axiom,
% 2.76/1.62 ! [A: $tType] :
% 2.76/1.62 ( ( comm_monoid_sum_mset @ A )
% 2.76/1.62 = ( comm_monoid_sum_mset @ A ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(fact_250_transD,axiom,
% 2.76/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A,Z: A] :
% 2.76/1.62 ( ( trans @ A @ R )
% 2.76/1.62 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 2.76/1.62 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z ) @ R )
% 2.76/1.62 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ R ) ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(fact_251_transE,axiom,
% 2.76/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A,Z: A] :
% 2.76/1.62 ( ( trans @ A @ R )
% 2.76/1.62 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 2.76/1.62 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z ) @ R )
% 2.76/1.62 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ R ) ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(fact_252_transI,axiom,
% 2.76/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 2.76/1.62 ( ! [X3: A,Y3: A,Z3: A] :
% 2.76/1.62 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 2.76/1.62 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ Z3 ) @ R )
% 2.76/1.62 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Z3 ) @ R ) ) )
% 2.76/1.62 => ( trans @ A @ R ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(fact_253_trans__def,axiom,
% 2.76/1.62 ! [A: $tType] :
% 2.76/1.62 ( ( trans @ A )
% 2.76/1.62 = ( ^ [R5: set @ ( product_prod @ A @ A )] :
% 2.76/1.62 ! [X4: A,Y6: A,Z4: A] :
% 2.76/1.62 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y6 ) @ R5 )
% 2.76/1.62 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ Z4 ) @ R5 )
% 2.76/1.62 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Z4 ) @ R5 ) ) ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(fact_254_mult__cancel__add__mset,axiom,
% 2.76/1.62 ! [A: $tType,S3: set @ ( product_prod @ A @ A ),Uu: A,X5: multiset @ A,Y5: multiset @ A] :
% 2.76/1.62 ( ( trans @ A @ S3 )
% 2.76/1.62 => ( ( irrefl @ A @ S3 )
% 2.76/1.62 => ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( add_mset @ A @ Uu @ X5 ) @ ( add_mset @ A @ Uu @ Y5 ) ) @ ( mult @ A @ S3 ) )
% 2.76/1.62 = ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ X5 @ Y5 ) @ ( mult @ A @ S3 ) ) ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.76/1.62 ! [A: $tType] :
% 2.76/1.62 ( ( linorder @ A )
% 2.76/1.62 => ( type @ A ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 2.76/1.62 ! [A: $tType] :
% 2.76/1.62 ( ( linorder @ A )
% 2.76/1.62 => ( preorder @ A ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Multiset_Omultiset___Orderings_Opreorder,axiom,
% 2.76/1.62 ! [A9: $tType] :
% 2.76/1.62 ( ( preorder @ A9 )
% 2.76/1.62 => ( preorder @ ( multiset @ A9 ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_HOL_Obool___Orderings_Opreorder_1,axiom,
% 2.76/1.62 preorder @ $o ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 2.76/1.62 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_fun___Orderings_Opreorder_3,axiom,
% 2.76/1.62 ! [A9: $tType,A10: $tType] :
% 2.76/1.62 ( ( preorder @ A10 )
% 2.76/1.62 => ( preorder @ ( A9 > A10 ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.76/1.62 linorder @ $o ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Multiset_Omultiset___Groups_Oordered__ab__semigroup__add,axiom,
% 2.76/1.62 ! [A9: $tType] :
% 2.76/1.62 ( ( preorder @ A9 )
% 2.76/1.62 => ( ordere779506340up_add @ ( multiset @ A9 ) ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add,axiom,
% 2.76/1.62 ! [A9: $tType] : ( cancel1352612707id_add @ ( multiset @ A9 ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Multiset_Omultiset___Groups_Ocancel__semigroup__add,axiom,
% 2.76/1.62 ! [A9: $tType] : ( cancel_semigroup_add @ ( multiset @ A9 ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Multiset_Omultiset___Groups_Oab__semigroup__add,axiom,
% 2.76/1.62 ! [A9: $tType] : ( ab_semigroup_add @ ( multiset @ A9 ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Multiset_Omultiset___Groups_Ocomm__monoid__add,axiom,
% 2.76/1.62 ! [A9: $tType] : ( comm_monoid_add @ ( multiset @ A9 ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Multiset_Omultiset___Groups_Osemigroup__add,axiom,
% 2.76/1.62 ! [A9: $tType] : ( semigroup_add @ ( multiset @ A9 ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Multiset_Omultiset___Groups_Omonoid__add,axiom,
% 2.76/1.62 ! [A9: $tType] : ( monoid_add @ ( multiset @ A9 ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(tcon_Multiset_Omultiset___Groups_Ozero,axiom,
% 2.76/1.62 ! [A9: $tType] : ( zero @ ( multiset @ A9 ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(help_If_3_1_T,axiom,
% 2.76/1.62 ! [P2: $o] :
% 2.76/1.62 ( ( P2 = $true )
% 2.76/1.62 | ( P2 = $false ) ) ).
% 2.76/1.62
% 2.76/1.62 thf(help_If_2_1_T,axiom,
% 2.76/1.62 ! [A: $tType,X: A,Y: A] :
% 2.76/1.62 ( ( if @ A @ $false @ X @ Y )
% 2.76/1.62 = Y ) ).
% 2.76/1.62
% 2.76/1.62 thf(help_If_1_1_T,axiom,
% 2.76/1.62 ! [A: $tType,X: A,Y: A] :
% 2.76/1.62 ( ( if @ A @ $true @ X @ Y )
% 2.76/1.62 = X ) ).
% 2.76/1.62
% 2.76/1.62 thf(tfree_0,hypothesis,
% 2.76/1.62 linorder @ a ).
% 2.76/1.62
% 2.76/1.62 thf(conj_0,conjecture,
% 2.76/1.62 ( v_a
% 2.76/1.62 = ( product_fst @ a @ ( tree @ a ) @ ( heapIm970386777veLeaf @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ).
% 2.76/1.62 ------------------------
% 2.76/1.64 % (10490)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/183Mi)
% 2.76/1.64 % (10491)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/4Mi)
% 2.76/1.64 % (10492)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/27Mi)
% 2.76/1.64 % (10494)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/2Mi)
% 2.76/1.64 % (10495)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/275Mi)
% 2.76/1.64 % (10496)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/18Mi)
% 2.76/1.64 % (10493)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/2Mi)
% 2.76/1.64 % (10494)Instruction limit reached!
% 2.76/1.64 % (10494)------------------------------
% 2.76/1.64 % (10494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.64 % (10494)Termination reason: Unknown
% 2.76/1.64 % (10494)Termination phase: shuffling
% 2.76/1.64
% 2.76/1.64 % (10494)Memory used [KB]: 1407
% 2.76/1.64 % (10494)Time elapsed: 0.002 s
% 2.76/1.64 % (10494)Instructions burned: 2 (million)
% 2.76/1.64 % (10494)------------------------------
% 2.76/1.64 % (10494)------------------------------
% 2.76/1.64 % (10491)Instruction limit reached!
% 2.76/1.64 % (10491)------------------------------
% 2.76/1.64 % (10491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.64 % (10491)Termination reason: Unknown
% 2.76/1.64 % (10491)Termination phase: shuffling
% 2.76/1.64
% 2.76/1.64 % (10491)Memory used [KB]: 1535
% 2.76/1.64 % (10491)Time elapsed: 0.003 s
% 2.76/1.64 % (10491)Instructions burned: 5 (million)
% 2.76/1.64 % (10491)------------------------------
% 2.76/1.64 % (10491)------------------------------
% 2.76/1.64 % (10493)Instruction limit reached!
% 2.76/1.64 % (10493)------------------------------
% 2.76/1.64 % (10493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.64 % (10493)Termination reason: Unknown
% 2.76/1.64 % (10493)Termination phase: shuffling
% 2.76/1.64
% 2.76/1.64 % (10493)Memory used [KB]: 1535
% 2.76/1.64 % (10493)Time elapsed: 0.003 s
% 2.76/1.64 % (10493)Instructions burned: 4 (million)
% 2.76/1.64 % (10493)------------------------------
% 2.76/1.64 % (10493)------------------------------
% 2.76/1.64 % (10496)Instruction limit reached!
% 2.76/1.64 % (10496)------------------------------
% 2.76/1.64 % (10496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.64 % (10496)Termination reason: Unknown
% 2.76/1.64 % (10496)Termination phase: shuffling
% 2.76/1.64
% 2.76/1.64 % (10496)Memory used [KB]: 1791
% 2.76/1.64 % (10496)Time elapsed: 0.008 s
% 2.76/1.64 % (10496)Instructions burned: 20 (million)
% 2.76/1.64 % (10496)------------------------------
% 2.76/1.64 % (10496)------------------------------
% 2.76/1.65 % (10492)Instruction limit reached!
% 2.76/1.65 % (10492)------------------------------
% 2.76/1.65 % (10492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.65 % (10492)Termination reason: Unknown
% 2.76/1.65 % (10492)Termination phase: shuffling
% 2.76/1.65
% 2.76/1.65 % (10492)Memory used [KB]: 2046
% 2.76/1.65 % (10492)Time elapsed: 0.011 s
% 2.76/1.65 % (10492)Instructions burned: 29 (million)
% 2.76/1.65 % (10492)------------------------------
% 2.76/1.65 % (10492)------------------------------
% 2.76/1.65 % (10506)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/3Mi)
% 2.76/1.65 % (10507)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/37Mi)
% 2.76/1.65 % (10506)Instruction limit reached!
% 2.76/1.65 % (10506)------------------------------
% 2.76/1.65 % (10506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.65 % (10506)Termination reason: Unknown
% 2.76/1.65 % (10506)Termination phase: shuffling
% 2.76/1.65
% 2.76/1.65 % (10506)Memory used [KB]: 1407
% 2.76/1.65 % (10506)Time elapsed: 0.002 s
% 2.76/1.65 % (10506)Instructions burned: 3 (million)
% 2.76/1.65 % (10506)------------------------------
% 2.76/1.65 % (10506)------------------------------
% 2.76/1.65 % (10509)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/15Mi)
% 2.76/1.65 % (10512)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/3Mi)
% 2.76/1.65 % (10512)Instruction limit reached!
% 2.76/1.65 % (10512)------------------------------
% 2.76/1.65 % (10512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.65 % (10512)Termination reason: Unknown
% 2.76/1.65 % (10512)Termination phase: shuffling
% 2.76/1.65
% 2.76/1.65 % (10512)Memory used [KB]: 1407
% 2.76/1.65 % (10512)Time elapsed: 0.002 s
% 2.76/1.65 % (10512)Instructions burned: 3 (million)
% 2.76/1.65 % (10512)------------------------------
% 2.76/1.65 % (10512)------------------------------
% 2.76/1.65 % (10509)Instruction limit reached!
% 2.76/1.65 % (10509)------------------------------
% 2.76/1.65 % (10509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.65 % (10509)Termination reason: Unknown
% 2.76/1.65 % (10509)Termination phase: shuffling
% 2.76/1.65
% 2.76/1.65 % (10509)Memory used [KB]: 1663
% 2.76/1.65 % (10509)Time elapsed: 0.007 s
% 2.76/1.65 % (10509)Instructions burned: 17 (million)
% 2.76/1.65 % (10509)------------------------------
% 2.76/1.65 % (10509)------------------------------
% 2.76/1.66 % (10513)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/1041Mi)
% 2.76/1.66 % (10507)Instruction limit reached!
% 2.76/1.66 % (10507)------------------------------
% 2.76/1.66 % (10507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.66 % (10507)Termination reason: Unknown
% 2.76/1.66 % (10507)Termination phase: shuffling
% 2.76/1.66
% 2.76/1.66 % (10507)Memory used [KB]: 2174
% 2.76/1.66 % (10507)Time elapsed: 0.012 s
% 2.76/1.66 % (10507)Instructions burned: 39 (million)
% 2.76/1.66 % (10507)------------------------------
% 2.76/1.66 % (10507)------------------------------
% 2.76/1.66 % (10515)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/7Mi)
% 2.76/1.66 % (10515)Instruction limit reached!
% 2.76/1.66 % (10515)------------------------------
% 2.76/1.66 % (10515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.66 % (10515)Termination reason: Unknown
% 2.76/1.66 % (10515)Termination phase: shuffling
% 2.76/1.66
% 2.76/1.66 % (10515)Memory used [KB]: 1535
% 2.76/1.66 % (10515)Time elapsed: 0.004 s
% 2.76/1.66 % (10515)Instructions burned: 8 (million)
% 2.76/1.66 % (10515)------------------------------
% 2.76/1.66 % (10515)------------------------------
% 2.76/1.66 % (10519)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/16Mi)
% 2.76/1.66 % (10520)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/3Mi)
% 2.76/1.66 % (10520)Instruction limit reached!
% 2.76/1.66 % (10520)------------------------------
% 2.76/1.66 % (10520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.66 % (10520)Termination reason: Unknown
% 2.76/1.66 % (10520)Termination phase: shuffling
% 2.76/1.66
% 2.76/1.66 % (10520)Memory used [KB]: 1407
% 2.76/1.66 % (10520)Time elapsed: 0.002 s
% 2.76/1.66 % (10520)Instructions burned: 3 (million)
% 2.76/1.66 % (10520)------------------------------
% 2.76/1.66 % (10520)------------------------------
% 2.76/1.67 % (10522)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/3Mi)
% 2.76/1.67 % (10519)Instruction limit reached!
% 2.76/1.67 % (10519)------------------------------
% 2.76/1.67 % (10519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.67 % (10519)Termination reason: Unknown
% 2.76/1.67 % (10519)Termination phase: shuffling
% 2.76/1.67
% 2.76/1.67 % (10519)Memory used [KB]: 1791
% 2.76/1.67 % (10519)Time elapsed: 0.007 s
% 2.76/1.67 % (10519)Instructions burned: 18 (million)
% 2.76/1.67 % (10519)------------------------------
% 2.76/1.67 % (10519)------------------------------
% 2.76/1.67 % (10522)Instruction limit reached!
% 2.76/1.67 % (10522)------------------------------
% 2.76/1.67 % (10522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.67 % (10522)Termination reason: Unknown
% 2.76/1.67 % (10522)Termination phase: shuffling
% 2.76/1.67
% 2.76/1.67 % (10522)Memory used [KB]: 1535
% 2.76/1.67 % (10522)Time elapsed: 0.003 s
% 2.76/1.67 % (10522)Instructions burned: 6 (million)
% 2.76/1.67 % (10522)------------------------------
% 2.76/1.67 % (10522)------------------------------
% 2.76/1.67 % (10525)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/7Mi)
% 2.76/1.67 % (10495)Refutation not found, incomplete strategy
% 2.76/1.67 % (10495)------------------------------
% 2.76/1.67 % (10495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.67 % (10495)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.67
% 2.76/1.67
% 2.76/1.67 % (10495)Memory used [KB]: 7419
% 2.76/1.67 % (10495)Time elapsed: 0.037 s
% 2.76/1.67 % (10495)Instructions burned: 115 (million)
% 2.76/1.67 % (10495)------------------------------
% 2.76/1.67 % (10495)------------------------------
% 2.76/1.67 % (10525)Instruction limit reached!
% 2.76/1.67 % (10525)------------------------------
% 2.76/1.67 % (10525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.67 % (10525)Termination reason: Unknown
% 2.76/1.67 % (10525)Termination phase: shuffling
% 2.76/1.67
% 2.76/1.67 % (10525)Memory used [KB]: 1535
% 2.76/1.67 % (10525)Time elapsed: 0.004 s
% 2.76/1.67 % (10525)Instructions burned: 9 (million)
% 2.76/1.67 % (10525)------------------------------
% 2.76/1.67 % (10525)------------------------------
% 2.76/1.67 % (10526)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/3Mi)
% 2.76/1.68 % (10526)Instruction limit reached!
% 2.76/1.68 % (10526)------------------------------
% 2.76/1.68 % (10526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.68 % (10526)Termination reason: Unknown
% 2.76/1.68 % (10526)Termination phase: shuffling
% 2.76/1.68
% 2.76/1.68 % (10526)Memory used [KB]: 1407
% 2.76/1.68 % (10526)Time elapsed: 0.002 s
% 2.76/1.68 % (10526)Instructions burned: 3 (million)
% 2.76/1.68 % (10526)------------------------------
% 2.76/1.68 % (10526)------------------------------
% 2.76/1.68 % (10528)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/4Mi)
% 2.76/1.68 % (10530)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/18Mi)
% 2.76/1.68 % (10528)Instruction limit reached!
% 2.76/1.68 % (10528)------------------------------
% 2.76/1.68 % (10528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.68 % (10528)Termination reason: Unknown
% 2.76/1.68 % (10528)Termination phase: shuffling
% 2.76/1.68
% 2.76/1.68 % (10528)Memory used [KB]: 1535
% 2.76/1.68 % (10528)Time elapsed: 0.003 s
% 2.76/1.68 % (10528)Instructions burned: 6 (million)
% 2.76/1.68 % (10528)------------------------------
% 2.76/1.68 % (10528)------------------------------
% 2.76/1.68 % (10533)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/710Mi)
% 2.76/1.68 % (10534)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/6Mi)
% 2.76/1.68 % (10537)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/902Mi)
% 2.76/1.68 % (10534)Instruction limit reached!
% 2.76/1.68 % (10534)------------------------------
% 2.76/1.68 % (10534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.68 % (10534)Termination reason: Unknown
% 2.76/1.68 % (10534)Termination phase: shuffling
% 2.76/1.68
% 2.76/1.68 % (10534)Memory used [KB]: 1535
% 2.76/1.68 % (10534)Time elapsed: 0.003 s
% 2.76/1.68 % (10534)Instructions burned: 6 (million)
% 2.76/1.68 % (10534)------------------------------
% 2.76/1.68 % (10534)------------------------------
% 2.76/1.69 % (10530)Instruction limit reached!
% 2.76/1.69 % (10530)------------------------------
% 2.76/1.69 % (10530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.69 % (10530)Termination reason: Unknown
% 2.76/1.69 % (10530)Termination phase: shuffling
% 2.76/1.69
% 2.76/1.69 % (10530)Memory used [KB]: 1791
% 2.76/1.69 % (10530)Time elapsed: 0.007 s
% 2.76/1.69 % (10530)Instructions burned: 18 (million)
% 2.76/1.69 % (10530)------------------------------
% 2.76/1.69 % (10530)------------------------------
% 2.76/1.69 % (10540)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/21Mi)
% 2.76/1.69 % (10490)Instruction limit reached!
% 2.76/1.69 % (10490)------------------------------
% 2.76/1.69 % (10490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.69 % (10490)Termination reason: Unknown
% 2.76/1.69 % (10490)Termination phase: Saturation
% 2.76/1.69
% 2.76/1.69 % (10490)Memory used [KB]: 7419
% 2.76/1.69 % (10490)Time elapsed: 0.055 s
% 2.76/1.69 % (10490)Instructions burned: 183 (million)
% 2.76/1.69 % (10490)------------------------------
% 2.76/1.69 % (10490)------------------------------
% 2.76/1.69 % (10541)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/5Mi)
% 2.76/1.69 % (10542)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/6Mi)
% 2.79/1.70 % (10541)Instruction limit reached!
% 2.79/1.70 % (10541)------------------------------
% 2.79/1.70 % (10541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.70 % (10541)Termination reason: Unknown
% 2.79/1.70 % (10541)Termination phase: shuffling
% 2.79/1.70
% 2.79/1.70 % (10541)Memory used [KB]: 1535
% 2.79/1.70 % (10541)Time elapsed: 0.003 s
% 2.79/1.70 % (10541)Instructions burned: 7 (million)
% 2.79/1.70 % (10541)------------------------------
% 2.79/1.70 % (10541)------------------------------
% 2.79/1.70 % (10542)Instruction limit reached!
% 2.79/1.70 % (10542)------------------------------
% 2.79/1.70 % (10542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.70 % (10542)Termination reason: Unknown
% 2.79/1.70 % (10542)Termination phase: shuffling
% 2.79/1.70
% 2.79/1.70 % (10542)Memory used [KB]: 1535
% 2.79/1.70 % (10542)Time elapsed: 0.003 s
% 2.79/1.70 % (10542)Instructions burned: 7 (million)
% 2.79/1.70 % (10542)------------------------------
% 2.79/1.70 % (10542)------------------------------
% 2.79/1.70 % (10540)Instruction limit reached!
% 2.79/1.70 % (10540)------------------------------
% 2.79/1.70 % (10540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.70 % (10540)Termination reason: Unknown
% 2.79/1.70 % (10540)Termination phase: shuffling
% 2.79/1.70
% 2.79/1.70 % (10540)Memory used [KB]: 1918
% 2.79/1.70 % (10540)Time elapsed: 0.009 s
% 2.79/1.70 % (10540)Instructions burned: 23 (million)
% 2.79/1.70 % (10540)------------------------------
% 2.79/1.70 % (10540)------------------------------
% 2.79/1.70 % (10546)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/377Mi)
% 2.79/1.71 % (10550)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/779Mi)
% 2.79/1.71 % (10551)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/19Mi)
% 2.79/1.71 % (10552)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/879Mi)
% 2.79/1.71 % (10551)Instruction limit reached!
% 2.79/1.71 % (10551)------------------------------
% 2.79/1.71 % (10551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.71 % (10551)Termination reason: Unknown
% 2.79/1.71 % (10551)Termination phase: shuffling
% 2.79/1.71
% 2.79/1.71 % (10551)Memory used [KB]: 1791
% 2.79/1.71 % (10551)Time elapsed: 0.007 s
% 2.79/1.71 % (10551)Instructions burned: 20 (million)
% 2.79/1.71 % (10551)------------------------------
% 2.79/1.71 % (10551)------------------------------
% 2.79/1.72 % (10558)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10235 for (2999ds/17Mi)
% 2.79/1.73 % (10558)Instruction limit reached!
% 2.79/1.73 % (10558)------------------------------
% 2.79/1.73 % (10558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.73 % (10558)Termination reason: Unknown
% 2.79/1.73 % (10558)Termination phase: shuffling
% 2.79/1.73
% 2.79/1.73 % (10558)Memory used [KB]: 1791
% 2.79/1.73 % (10558)Time elapsed: 0.008 s
% 2.79/1.73 % (10558)Instructions burned: 19 (million)
% 2.79/1.73 % (10558)------------------------------
% 2.79/1.73 % (10558)------------------------------
% 2.79/1.74 % (10575)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10235 for (2998ds/3Mi)
% 2.79/1.74 % (10537)Refutation not found, incomplete strategy
% 2.79/1.74 % (10537)------------------------------
% 2.79/1.74 % (10537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.74 % (10537)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.74
% 2.79/1.74
% 2.79/1.74 % (10537)Memory used [KB]: 7803
% 2.79/1.74 % (10537)Time elapsed: 0.055 s
% 2.79/1.74 % (10537)Instructions burned: 174 (million)
% 2.79/1.74 % (10537)------------------------------
% 2.79/1.74 % (10537)------------------------------
% 2.79/1.74 % (10575)Instruction limit reached!
% 2.79/1.74 % (10575)------------------------------
% 2.79/1.74 % (10575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.74 % (10575)Termination reason: Unknown
% 2.79/1.74 % (10575)Termination phase: shuffling
% 2.79/1.74
% 2.79/1.74 % (10575)Memory used [KB]: 1535
% 2.79/1.74 % (10575)Time elapsed: 0.003 s
% 2.79/1.74 % (10575)Instructions burned: 5 (million)
% 2.79/1.74 % (10575)------------------------------
% 2.79/1.74 % (10575)------------------------------
% 2.79/1.75 % (10587)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10235 for (2998ds/30Mi)
% 2.79/1.75 % (10588)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10235 for (2998ds/127Mi)
% 2.79/1.76 % (10587)Instruction limit reached!
% 2.79/1.76 % (10587)------------------------------
% 2.79/1.76 % (10587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.76 % (10587)Termination reason: Unknown
% 2.79/1.76 % (10587)Termination phase: shuffling
% 2.79/1.76
% 2.79/1.76 % (10587)Memory used [KB]: 2046
% 2.79/1.76 % (10587)Time elapsed: 0.011 s
% 2.79/1.76 % (10587)Instructions burned: 30 (million)
% 2.79/1.76 % (10587)------------------------------
% 2.79/1.76 % (10587)------------------------------
% 2.79/1.77 % (10599)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10235 for (2998ds/100Mi)
% 2.79/1.79 % (10588)Instruction limit reached!
% 2.79/1.79 % (10588)------------------------------
% 2.79/1.79 % (10588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.79 % (10588)Termination reason: Unknown
% 2.79/1.79 % (10588)Termination phase: Saturation
% 2.79/1.79
% 2.79/1.79 % (10588)Memory used [KB]: 7164
% 2.79/1.79 % (10588)Time elapsed: 0.038 s
% 2.79/1.79 % (10588)Instructions burned: 127 (million)
% 2.79/1.79 % (10588)------------------------------
% 2.79/1.79 % (10588)------------------------------
% 2.79/1.80 % (10600)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_10235 for (2998ds/3Mi)
% 2.79/1.80 % (10600)Instruction limit reached!
% 2.79/1.80 % (10600)------------------------------
% 2.79/1.80 % (10600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.80 % (10600)Termination reason: Unknown
% 2.79/1.80 % (10600)Termination phase: shuffling
% 2.79/1.80
% 2.79/1.80 % (10600)Memory used [KB]: 1407
% 2.79/1.80 % (10600)Time elapsed: 0.002 s
% 2.79/1.80 % (10600)Instructions burned: 3 (million)
% 2.79/1.80 % (10600)------------------------------
% 2.79/1.80 % (10600)------------------------------
% 2.79/1.80 % (10599)Instruction limit reached!
% 2.79/1.80 % (10599)------------------------------
% 2.79/1.80 % (10599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.80 % (10599)Termination reason: Unknown
% 2.79/1.80 % (10599)Termination phase: Preprocessing 3
% 2.79/1.80
% 2.79/1.80 % (10599)Memory used [KB]: 2814
% 2.79/1.80 % (10599)Time elapsed: 0.030 s
% 2.79/1.80 % (10599)Instructions burned: 102 (million)
% 2.79/1.80 % (10599)------------------------------
% 2.79/1.80 % (10599)------------------------------
% 2.79/1.81 % (10601)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_10235 for (2998ds/20Mi)
% 2.79/1.81 % (10602)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_10235 for (2998ds/86Mi)
% 2.79/1.81 % (10601)Instruction limit reached!
% 2.79/1.81 % (10601)------------------------------
% 2.79/1.81 % (10601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.81 % (10601)Termination reason: Unknown
% 2.79/1.81 % (10601)Termination phase: shuffling
% 2.79/1.81
% 2.79/1.81 % (10601)Memory used [KB]: 1791
% 2.79/1.81 % (10601)Time elapsed: 0.008 s
% 2.79/1.81 % (10601)Instructions burned: 20 (million)
% 2.79/1.81 % (10601)------------------------------
% 2.79/1.81 % (10601)------------------------------
% 2.79/1.81 % (10546)Instruction limit reached!
% 2.79/1.81 % (10546)------------------------------
% 2.79/1.81 % (10546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.81 % (10546)Termination reason: Unknown
% 2.79/1.81 % (10546)Termination phase: Saturation
% 2.79/1.81
% 2.79/1.81 % (10546)Memory used [KB]: 8443
% 2.79/1.81 % (10546)Time elapsed: 0.116 s
% 2.79/1.81 % (10546)Instructions burned: 379 (million)
% 2.79/1.81 % (10546)------------------------------
% 2.79/1.81 % (10546)------------------------------
% 2.79/1.82 % (10603)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_10235 for (2998ds/107Mi)
% 2.79/1.82 % (10604)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_10235 for (2998ds/39Mi)
% 2.79/1.83 % (10602)Instruction limit reached!
% 2.79/1.83 % (10602)------------------------------
% 2.79/1.83 % (10602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.83 % (10602)Termination reason: Unknown
% 2.79/1.83 % (10602)Termination phase: Property scanning
% 2.79/1.83
% 2.79/1.83 % (10602)Memory used [KB]: 2686
% 2.79/1.83 % (10602)Time elapsed: 0.028 s
% 2.79/1.83 % (10602)Instructions burned: 88 (million)
% 2.79/1.83 % (10602)------------------------------
% 2.79/1.83 % (10602)------------------------------
% 2.79/1.84 % (10604)Instruction limit reached!
% 2.79/1.84 % (10604)------------------------------
% 2.79/1.84 % (10604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.84 % (10604)Termination reason: Unknown
% 2.79/1.84 % (10604)Termination phase: shuffling
% 2.79/1.84
% 2.79/1.84 % (10604)Memory used [KB]: 2174
% 2.79/1.84 % (10604)Time elapsed: 0.013 s
% 2.79/1.84 % (10604)Instructions burned: 41 (million)
% 2.79/1.84 % (10604)------------------------------
% 2.79/1.84 % (10604)------------------------------
% 2.79/1.84 % (10605)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_10235 for (2997ds/448Mi)
% 2.79/1.85 % (10606)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_10235 for (2997ds/46Mi)
% 2.79/1.85 % (10603)Instruction limit reached!
% 2.79/1.85 % (10603)------------------------------
% 2.79/1.85 % (10603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.85 % (10603)Termination reason: Unknown
% 2.79/1.85 % (10603)Termination phase: Property scanning
% 2.79/1.85
% 2.79/1.85 % (10603)Memory used [KB]: 2558
% 2.79/1.85 % (10603)Time elapsed: 0.033 s
% 2.79/1.85 % (10603)Instructions burned: 108 (million)
% 2.79/1.85 % (10603)------------------------------
% 2.79/1.85 % (10603)------------------------------
% 2.79/1.86 % (10606)Instruction limit reached!
% 2.79/1.86 % (10606)------------------------------
% 2.79/1.86 % (10606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.86 % (10606)Termination reason: Unknown
% 2.79/1.86 % (10606)Termination phase: Property scanning
% 2.79/1.86
% 2.79/1.86 % (10606)Memory used [KB]: 2174
% 2.79/1.86 % (10606)Time elapsed: 0.015 s
% 2.79/1.86 % (10606)Instructions burned: 46 (million)
% 2.79/1.86 % (10606)------------------------------
% 2.79/1.86 % (10606)------------------------------
% 2.79/1.86 % (10607)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_10235 for (2997ds/98Mi)
% 2.79/1.87 % (10608)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_10235 for (2997ds/507Mi)
% 2.79/1.89 % (10607)Instruction limit reached!
% 2.79/1.89 % (10607)------------------------------
% 2.79/1.89 % (10607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.89 % (10607)Termination reason: Unknown
% 2.79/1.89 % (10607)Termination phase: Preprocessing 3
% 2.79/1.89
% 2.79/1.89 % (10607)Memory used [KB]: 2558
% 2.79/1.89 % (10607)Time elapsed: 0.028 s
% 2.79/1.89 % (10607)Instructions burned: 99 (million)
% 2.79/1.89 % (10607)------------------------------
% 2.79/1.89 % (10607)------------------------------
% 2.79/1.90 % (10609)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_10235 for (2997ds/149Mi)
% 2.79/1.90 % (10533)Instruction limit reached!
% 2.79/1.90 % (10533)------------------------------
% 2.79/1.90 % (10533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.90 % (10533)Termination reason: Unknown
% 2.79/1.90 % (10533)Termination phase: Saturation
% 2.79/1.90
% 2.79/1.90 % (10533)Memory used [KB]: 8571
% 2.79/1.90 % (10533)Time elapsed: 0.223 s
% 2.79/1.90 % (10533)Instructions burned: 712 (million)
% 2.79/1.90 % (10533)------------------------------
% 2.79/1.90 % (10533)------------------------------
% 2.79/1.91 % (10610)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_10235 for (2997ds/39Mi)
% 2.79/1.92 % (10608)Refutation not found, incomplete strategy
% 2.79/1.92 % (10608)------------------------------
% 2.79/1.92 % (10608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.92 % (10608)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.92
% 2.79/1.92
% 2.79/1.92 % (10608)Memory used [KB]: 7931
% 2.79/1.92 % (10608)Time elapsed: 0.078 s
% 2.79/1.92 % (10608)Instructions burned: 187 (million)
% 2.79/1.92 % (10608)------------------------------
% 2.79/1.92 % (10608)------------------------------
% 2.79/1.93 % (10610)Instruction limit reached!
% 2.79/1.93 % (10610)------------------------------
% 2.79/1.93 % (10610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.93 % (10610)Termination reason: Unknown
% 2.79/1.93 % (10610)Termination phase: Property scanning
% 2.79/1.93
% 2.79/1.93 % (10610)Memory used [KB]: 2046
% 2.79/1.93 % (10610)Time elapsed: 0.014 s
% 2.79/1.93 % (10610)Instructions burned: 41 (million)
% 2.79/1.93 % (10610)------------------------------
% 2.79/1.93 % (10610)------------------------------
% 2.79/1.93 % (10611)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/6Mi)
% 2.79/1.94 % (10611)Instruction limit reached!
% 2.79/1.94 % (10611)------------------------------
% 2.79/1.94 % (10611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.94 % (10611)Termination reason: Unknown
% 2.79/1.94 % (10611)Termination phase: shuffling
% 2.79/1.94
% 2.79/1.94 % (10611)Memory used [KB]: 1535
% 2.79/1.94 % (10611)Time elapsed: 0.003 s
% 2.79/1.94 % (10611)Instructions burned: 6 (million)
% 2.79/1.94 % (10611)------------------------------
% 2.79/1.94 % (10611)------------------------------
% 2.79/1.94 % (10612)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/1087Mi)
% 2.79/1.94 % (10609)Instruction limit reached!
% 2.79/1.94 % (10609)------------------------------
% 2.79/1.94 % (10609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.94 % (10609)Termination reason: Unknown
% 2.79/1.94 % (10609)Termination phase: Property scanning
% 2.79/1.94
% 2.79/1.94 % (10609)Memory used [KB]: 2686
% 2.79/1.94 % (10609)Time elapsed: 0.042 s
% 2.79/1.94 % (10609)Instructions burned: 149 (million)
% 2.79/1.94 % (10609)------------------------------
% 2.79/1.94 % (10609)------------------------------
% 2.79/1.94 % (10550)Instruction limit reached!
% 2.79/1.94 % (10550)------------------------------
% 2.79/1.94 % (10550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.94 % (10550)Termination reason: Unknown
% 2.79/1.94 % (10550)Termination phase: Saturation
% 2.79/1.94
% 2.79/1.94 % (10550)Memory used [KB]: 8827
% 2.79/1.94 % (10550)Time elapsed: 0.238 s
% 2.79/1.94 % (10550)Instructions burned: 780 (million)
% 2.79/1.94 % (10550)------------------------------
% 2.79/1.94 % (10550)------------------------------
% 2.79/1.95 % (10613)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/47Mi)
% 2.79/1.95 % (10614)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/44Mi)
% 2.79/1.95 % (10615)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/432Mi)
% 2.79/1.96 % (10613)Instruction limit reached!
% 2.79/1.96 % (10613)------------------------------
% 2.79/1.96 % (10613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.96 % (10613)Termination reason: Unknown
% 2.79/1.96 % (10613)Termination phase: Property scanning
% 2.79/1.96
% 2.79/1.96 % (10613)Memory used [KB]: 2046
% 2.79/1.96 % (10613)Time elapsed: 0.016 s
% 2.79/1.96 % (10613)Instructions burned: 49 (million)
% 2.79/1.96 % (10613)------------------------------
% 2.79/1.96 % (10613)------------------------------
% 2.79/1.96 % (10614)Instruction limit reached!
% 2.79/1.96 % (10614)------------------------------
% 2.79/1.96 % (10614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.96 % (10614)Termination reason: Unknown
% 2.79/1.96 % (10614)Termination phase: shuffling
% 2.79/1.96
% 2.79/1.96 % (10614)Memory used [KB]: 2302
% 2.79/1.96 % (10614)Time elapsed: 0.014 s
% 2.79/1.96 % (10614)Instructions burned: 46 (million)
% 2.79/1.96 % (10614)------------------------------
% 2.79/1.96 % (10614)------------------------------
% 2.79/1.97 % (10513)Instruction limit reached!
% 2.79/1.97 % (10513)------------------------------
% 2.79/1.97 % (10513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.97 % (10513)Termination reason: Unknown
% 2.79/1.97 % (10513)Termination phase: Saturation
% 2.79/1.97
% 2.79/1.97 % (10513)Memory used [KB]: 9722
% 2.79/1.97 % (10513)Time elapsed: 0.315 s
% 2.79/1.97 % (10513)Instructions burned: 1042 (million)
% 2.79/1.97 % (10513)------------------------------
% 2.79/1.97 % (10513)------------------------------
% 2.79/1.97 % (10616)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/62Mi)
% 2.79/1.97 % (10617)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/31Mi)
% 2.79/1.97 % (10605)Instruction limit reached!
% 2.79/1.97 % (10605)------------------------------
% 2.79/1.97 % (10605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.97 % (10605)Termination reason: Unknown
% 2.79/1.97 % (10605)Termination phase: Saturation
% 2.79/1.97
% 2.79/1.97 % (10605)Memory used [KB]: 8955
% 2.79/1.97 % (10605)Time elapsed: 0.131 s
% 2.79/1.97 % (10605)Instructions burned: 448 (million)
% 2.79/1.97 % (10605)------------------------------
% 2.79/1.97 % (10605)------------------------------
% 2.79/1.98 % (10618)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/96Mi)
% 2.79/1.98 % (10552)Instruction limit reached!
% 2.79/1.98 % (10552)------------------------------
% 2.79/1.98 % (10552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.98 % (10552)Termination reason: Unknown
% 2.79/1.98 % (10552)Termination phase: Saturation
% 2.79/1.98
% 2.79/1.98 % (10552)Memory used [KB]: 8443
% 2.79/1.98 % (10552)Time elapsed: 0.274 s
% 2.79/1.98 % (10552)Instructions burned: 882 (million)
% 2.79/1.98 % (10552)------------------------------
% 2.79/1.98 % (10552)------------------------------
% 2.79/1.98 % (10619)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/453Mi)
% 2.79/1.98 % (10617)Instruction limit reached!
% 2.79/1.98 % (10617)------------------------------
% 2.79/1.98 % (10617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.98 % (10617)Termination reason: Unknown
% 2.79/1.98 % (10617)Termination phase: shuffling
% 2.79/1.98
% 2.79/1.98 % (10617)Memory used [KB]: 2046
% 2.79/1.98 % (10617)Time elapsed: 0.012 s
% 2.79/1.98 % (10617)Instructions burned: 33 (million)
% 2.79/1.98 % (10617)------------------------------
% 2.79/1.98 % (10617)------------------------------
% 2.79/1.99 % (10616)Instruction limit reached!
% 2.79/1.99 % (10616)------------------------------
% 2.79/1.99 % (10616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.99 % (10616)Termination reason: Unknown
% 2.79/1.99 % (10616)Termination phase: Property scanning
% 2.79/1.99
% 2.79/1.99 % (10616)Memory used [KB]: 2430
% 2.79/1.99 % (10616)Time elapsed: 0.019 s
% 2.79/1.99 % (10616)Instructions burned: 65 (million)
% 2.79/1.99 % (10616)------------------------------
% 2.79/1.99 % (10616)------------------------------
% 2.79/1.99 % (10620)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/71Mi)
% 2.79/1.99 % (10621)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/83Mi)
% 2.79/2.00 % (10622)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/11Mi)
% 2.79/2.00 % (10622)Instruction limit reached!
% 2.79/2.00 % (10622)------------------------------
% 2.79/2.00 % (10622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/2.00 % (10622)Termination reason: Unknown
% 2.79/2.00 % (10622)Termination phase: shuffling
% 2.79/2.00
% 2.79/2.00 % (10622)Memory used [KB]: 1663
% 2.79/2.00 % (10622)Time elapsed: 0.004 s
% 2.79/2.00 % (10622)Instructions burned: 11 (million)
% 2.79/2.00 % (10622)------------------------------
% 2.79/2.00 % (10622)------------------------------
% 2.79/2.01 % (10618)Instruction limit reached!
% 2.79/2.01 % (10618)------------------------------
% 2.79/2.01 % (10618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/2.01 % (10618)Termination reason: Unknown
% 2.79/2.01 % (10618)Termination phase: Function definition elimination
% 2.79/2.01
% 2.79/2.01 % (10618)Memory used [KB]: 2558
% 2.79/2.01 % (10618)Time elapsed: 0.030 s
% 2.79/2.01 % (10618)Instructions burned: 97 (million)
% 2.79/2.01 % (10618)------------------------------
% 2.79/2.01 % (10618)------------------------------
% 2.79/2.01 % (10623)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/41Mi)
% 5.38/2.01 % (10620)Instruction limit reached!
% 5.38/2.01 % (10620)------------------------------
% 5.38/2.01 % (10620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.38/2.01 % (10620)Termination reason: Unknown
% 5.38/2.01 % (10620)Termination phase: Preprocessing 3
% 5.38/2.01
% 5.38/2.01 % (10620)Memory used [KB]: 2430
% 5.38/2.01 % (10620)Time elapsed: 0.024 s
% 5.38/2.01 % (10620)Instructions burned: 72 (million)
% 5.38/2.01 % (10620)------------------------------
% 5.38/2.01 % (10620)------------------------------
% 5.38/2.02 % (10624)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/6Mi)
% 5.38/2.02 % (10621)Instruction limit reached!
% 5.38/2.02 % (10621)------------------------------
% 5.38/2.02 % (10621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.38/2.02 % (10621)Termination reason: Unknown
% 5.38/2.02 % (10621)Termination phase: Property scanning
% 5.38/2.02
% 5.38/2.02 % (10621)Memory used [KB]: 2302
% 5.38/2.02 % (10621)Time elapsed: 0.026 s
% 5.38/2.02 % (10621)Instructions burned: 84 (million)
% 5.38/2.02 % (10621)------------------------------
% 5.38/2.02 % (10621)------------------------------
% 5.38/2.02 % (10624)Instruction limit reached!
% 5.38/2.02 % (10624)------------------------------
% 5.38/2.02 % (10624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.38/2.02 % (10624)Termination reason: Unknown
% 5.38/2.02 % (10624)Termination phase: shuffling
% 5.38/2.02
% 5.38/2.02 % (10624)Memory used [KB]: 1535
% 5.38/2.02 % (10624)Time elapsed: 0.003 s
% 5.38/2.02 % (10624)Instructions burned: 7 (million)
% 5.38/2.02 % (10624)------------------------------
% 5.38/2.02 % (10624)------------------------------
% 5.38/2.02 % (10623)Instruction limit reached!
% 5.38/2.02 % (10623)------------------------------
% 5.38/2.02 % (10623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.38/2.02 % (10623)Termination reason: Unknown
% 5.38/2.02 % (10623)Termination phase: shuffling
% 5.38/2.02
% 5.38/2.02 % (10623)Memory used [KB]: 2302
% 5.38/2.02 % (10623)Time elapsed: 0.013 s
% 5.38/2.02 % (10623)Instructions burned: 44 (million)
% 5.38/2.02 % (10623)------------------------------
% 5.38/2.02 % (10623)------------------------------
% 5.38/2.02 % (10625)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/150Mi)
% 5.38/2.03 % (10626)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/343Mi)
% 5.38/2.03 % (10627)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/109Mi)
% 5.38/2.03 % (10628)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_10235 for (2996ds/253Mi)
% 5.38/2.06 % (10627)Instruction limit reached!
% 5.38/2.06 % (10627)------------------------------
% 5.38/2.06 % (10627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.38/2.06 % (10627)Termination reason: Unknown
% 5.38/2.06 % (10627)Termination phase: Property scanning
% 5.38/2.06
% 5.38/2.06 % (10627)Memory used [KB]: 2558
% 5.38/2.06 % (10627)Time elapsed: 0.033 s
% 5.38/2.06 % (10627)Instructions burned: 111 (million)
% 5.38/2.06 % (10627)------------------------------
% 5.38/2.06 % (10627)------------------------------
% 5.38/2.07 % (10625)Instruction limit reached!
% 5.38/2.07 % (10625)------------------------------
% 5.38/2.07 % (10625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.38/2.07 % (10625)Termination reason: Unknown
% 5.38/2.07 % (10625)Termination phase: Saturation
% 5.38/2.07
% 5.38/2.07 % (10625)Memory used [KB]: 7291
% 5.38/2.07 % (10625)Time elapsed: 0.044 s
% 5.38/2.07 % (10625)Instructions burned: 152 (million)
% 5.38/2.07 % (10625)------------------------------
% 5.38/2.07 % (10625)------------------------------
% 5.38/2.07 % (10629)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_10235 for (2995ds/140Mi)
% 5.38/2.08 % (10630)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_10235 for (2995ds/614Mi)
% 5.38/2.08 % (10615)Instruction limit reached!
% 5.38/2.08 % (10615)------------------------------
% 5.38/2.08 % (10615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.38/2.08 % (10615)Termination reason: Unknown
% 5.38/2.08 % (10615)Termination phase: Saturation
% 5.38/2.08
% 5.38/2.08 % (10615)Memory used [KB]: 3837
% 5.38/2.08 % (10615)Time elapsed: 0.131 s
% 5.38/2.08 % (10615)Instructions burned: 433 (million)
% 5.38/2.08 % (10615)------------------------------
% 5.38/2.08 % (10615)------------------------------
% 5.38/2.09 % (10631)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_10235 for (2995ds/202Mi)
% 5.38/2.11 % (10628)Instruction limit reached!
% 5.38/2.11 % (10628)------------------------------
% 5.38/2.11 % (10628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.38/2.11 % (10628)Termination reason: Unknown
% 5.38/2.11 % (10628)Termination phase: Saturation
% 5.38/2.11
% 5.38/2.11 % (10628)Memory used [KB]: 8059
% 5.38/2.11 % (10628)Time elapsed: 0.076 s
% 5.38/2.11 % (10628)Instructions burned: 255 (million)
% 5.38/2.11 % (10628)------------------------------
% 5.38/2.11 % (10628)------------------------------
% 5.38/2.11 % (10619)Instruction limit reached!
% 5.38/2.11 % (10619)------------------------------
% 5.38/2.11 % (10619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.38/2.11 % (10619)Termination reason: Unknown
% 5.38/2.11 % (10619)Termination phase: Saturation
% 5.38/2.11
% 5.38/2.11 % (10619)Memory used [KB]: 7931
% 5.38/2.11 % (10619)Time elapsed: 0.125 s
% 5.38/2.11 % (10619)Instructions burned: 453 (million)
% 5.38/2.11 % (10619)------------------------------
% 5.38/2.11 % (10619)------------------------------
% 5.94/2.11 % (10629)Instruction limit reached!
% 5.94/2.11 % (10629)------------------------------
% 5.94/2.11 % (10629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.11 % (10629)Termination reason: Unknown
% 5.94/2.11 % (10629)Termination phase: Saturation
% 5.94/2.11
% 5.94/2.11 % (10629)Memory used [KB]: 7291
% 5.94/2.11 % (10629)Time elapsed: 0.044 s
% 5.94/2.11 % (10629)Instructions burned: 140 (million)
% 5.94/2.11 % (10629)------------------------------
% 5.94/2.11 % (10629)------------------------------
% 5.94/2.12 % (10632)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_10235 for (2995ds/339Mi)
% 5.94/2.12 % (10633)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_10235 for (2995ds/283Mi)
% 5.94/2.12 % (10634)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_10235 for (2995ds/134Mi)
% 5.94/2.13 % (10626)Instruction limit reached!
% 5.94/2.13 % (10626)------------------------------
% 5.94/2.13 % (10626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.13 % (10626)Termination reason: Unknown
% 5.94/2.13 % (10626)Termination phase: Saturation
% 5.94/2.13
% 5.94/2.13 % (10626)Memory used [KB]: 8443
% 5.94/2.13 % (10626)Time elapsed: 0.106 s
% 5.94/2.13 % (10626)Instructions burned: 345 (million)
% 5.94/2.13 % (10626)------------------------------
% 5.94/2.13 % (10626)------------------------------
% 5.94/2.14 % (10631)Refutation not found, incomplete strategy
% 5.94/2.14 % (10631)------------------------------
% 5.94/2.14 % (10631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.14 % (10631)Termination reason: Refutation not found, incomplete strategy
% 5.94/2.14
% 5.94/2.14
% 5.94/2.14 % (10631)Memory used [KB]: 7675
% 5.94/2.14 % (10631)Time elapsed: 0.051 s
% 5.94/2.14 % (10631)Instructions burned: 167 (million)
% 5.94/2.14 % (10631)------------------------------
% 5.94/2.14 % (10631)------------------------------
% 5.94/2.14 % (10635)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_10235 for (2994ds/298Mi)
% 5.94/2.15 % (10636)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_10235 for (2994ds/192Mi)
% 5.94/2.16 % (10634)Instruction limit reached!
% 5.94/2.16 % (10634)------------------------------
% 5.94/2.16 % (10634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.16 % (10634)Termination reason: Unknown
% 5.94/2.16 % (10634)Termination phase: Saturation
% 5.94/2.16
% 5.94/2.16 % (10634)Memory used [KB]: 7164
% 5.94/2.16 % (10634)Time elapsed: 0.040 s
% 5.94/2.16 % (10634)Instructions burned: 134 (million)
% 5.94/2.16 % (10634)------------------------------
% 5.94/2.16 % (10634)------------------------------
% 5.94/2.17 % (10637)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_10235 for (2994ds/258Mi)
% 6.31/2.20 % (10633)Instruction limit reached!
% 6.31/2.20 % (10633)------------------------------
% 6.31/2.20 % (10633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.20 % (10633)Termination reason: Unknown
% 6.31/2.20 % (10633)Termination phase: Saturation
% 6.31/2.20
% 6.31/2.20 % (10633)Memory used [KB]: 7675
% 6.31/2.20 % (10633)Time elapsed: 0.084 s
% 6.31/2.20 % (10633)Instructions burned: 285 (million)
% 6.31/2.20 % (10633)------------------------------
% 6.31/2.20 % (10633)------------------------------
% 6.31/2.21 % (10636)Instruction limit reached!
% 6.31/2.21 % (10636)------------------------------
% 6.31/2.21 % (10636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.21 % (10636)Termination reason: Unknown
% 6.31/2.21 % (10636)Termination phase: Saturation
% 6.31/2.21
% 6.31/2.21 % (10636)Memory used [KB]: 3582
% 6.31/2.21 % (10636)Time elapsed: 0.058 s
% 6.31/2.21 % (10636)Instructions burned: 193 (million)
% 6.31/2.21 % (10636)------------------------------
% 6.31/2.21 % (10636)------------------------------
% 6.31/2.21 % (10638)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_10235 for (2994ds/90Mi)
% 6.31/2.21 % (10632)Instruction limit reached!
% 6.31/2.21 % (10632)------------------------------
% 6.31/2.21 % (10632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.21 % (10632)Termination reason: Unknown
% 6.31/2.21 % (10632)Termination phase: Saturation
% 6.31/2.21
% 6.31/2.21 % (10632)Memory used [KB]: 7803
% 6.31/2.21 % (10632)Time elapsed: 0.099 s
% 6.31/2.21 % (10632)Instructions burned: 341 (million)
% 6.31/2.21 % (10632)------------------------------
% 6.31/2.21 % (10632)------------------------------
% 6.31/2.22 % (10639)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_10235 for (2994ds/231Mi)
% 6.31/2.22 % (10635)Instruction limit reached!
% 6.31/2.22 % (10635)------------------------------
% 6.31/2.22 % (10635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.22 % (10635)Termination reason: Unknown
% 6.31/2.22 % (10635)Termination phase: Saturation
% 6.31/2.22
% 6.31/2.22 % (10635)Memory used [KB]: 7547
% 6.31/2.22 % (10635)Time elapsed: 0.082 s
% 6.31/2.22 % (10635)Instructions burned: 299 (million)
% 6.31/2.22 % (10635)------------------------------
% 6.31/2.22 % (10635)------------------------------
% 6.31/2.22 % (10640)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_10235 for (2994ds/458Mi)
% 6.31/2.23 % (10642)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_10235 for (2994ds/31Mi)
% 6.31/2.24 % (10638)Instruction limit reached!
% 6.31/2.24 % (10638)------------------------------
% 6.31/2.24 % (10638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.24 % (10638)Termination reason: Unknown
% 6.31/2.24 % (10638)Termination phase: Property scanning
% 6.31/2.24
% 6.31/2.24 % (10638)Memory used [KB]: 2558
% 6.31/2.24 % (10638)Time elapsed: 0.028 s
% 6.31/2.24 % (10638)Instructions burned: 92 (million)
% 6.31/2.24 % (10638)------------------------------
% 6.31/2.24 % (10638)------------------------------
% 6.31/2.24 % (10642)Instruction limit reached!
% 6.31/2.24 % (10642)------------------------------
% 6.31/2.24 % (10642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.24 % (10642)Termination reason: Unknown
% 6.31/2.24 % (10642)Termination phase: shuffling
% 6.31/2.24
% 6.31/2.24 % (10642)Memory used [KB]: 2046
% 6.31/2.24 % (10642)Time elapsed: 0.011 s
% 6.31/2.24 % (10642)Instructions burned: 31 (million)
% 6.31/2.24 % (10642)------------------------------
% 6.31/2.24 % (10642)------------------------------
% 6.31/2.24 % (10637)Instruction limit reached!
% 6.31/2.24 % (10637)------------------------------
% 6.31/2.24 % (10637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.24 % (10637)Termination reason: Unknown
% 6.31/2.24 % (10637)Termination phase: Saturation
% 6.31/2.24
% 6.31/2.24 % (10637)Memory used [KB]: 3198
% 6.31/2.24 % (10637)Time elapsed: 0.073 s
% 6.31/2.24 % (10637)Instructions burned: 260 (million)
% 6.31/2.24 % (10637)------------------------------
% 6.31/2.24 % (10637)------------------------------
% 6.31/2.24 % (10643)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_10235 for (2993ds/297Mi)
% 6.31/2.25 % (10630)Instruction limit reached!
% 6.31/2.25 % (10630)------------------------------
% 6.31/2.25 % (10630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.25 % (10630)Termination reason: Unknown
% 6.31/2.25 % (10630)Termination phase: Saturation
% 6.31/2.25
% 6.31/2.25 % (10630)Memory used [KB]: 8827
% 6.31/2.25 % (10630)Time elapsed: 0.177 s
% 6.31/2.25 % (10630)Instructions burned: 614 (million)
% 6.31/2.25 % (10630)------------------------------
% 6.31/2.25 % (10630)------------------------------
% 6.31/2.25 % (10644)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_10235 for (2993ds/987Mi)
% 6.31/2.25 % (10645)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_10235 for (2993ds/182Mi)
% 6.31/2.26 % (10646)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_10235 for (2993ds/182Mi)
% 6.31/2.27 % (10612)Instruction limit reached!
% 6.31/2.27 % (10612)------------------------------
% 6.31/2.27 % (10612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.27 % (10612)Termination reason: Unknown
% 6.31/2.27 % (10612)Termination phase: Saturation
% 6.31/2.27
% 6.31/2.27 % (10612)Memory used [KB]: 8443
% 6.31/2.27 % (10612)Time elapsed: 0.331 s
% 6.31/2.27 % (10612)Instructions burned: 1088 (million)
% 6.31/2.27 % (10612)------------------------------
% 6.31/2.27 % (10612)------------------------------
% 6.31/2.28 % (10647)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_10235 for (2993ds/154Mi)
% 6.31/2.28 % (10639)Instruction limit reached!
% 6.31/2.28 % (10639)------------------------------
% 6.31/2.28 % (10639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.28 % (10639)Termination reason: Unknown
% 6.31/2.28 % (10639)Termination phase: Saturation
% 6.31/2.28
% 6.31/2.28 % (10639)Memory used [KB]: 7291
% 6.31/2.28 % (10639)Time elapsed: 0.061 s
% 6.31/2.28 % (10639)Instructions burned: 231 (million)
% 6.31/2.28 % (10639)------------------------------
% 6.31/2.28 % (10639)------------------------------
% 6.31/2.29 % (10648)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_10235 for (2993ds/79Mi)
% 7.14/2.30 % (10645)Instruction limit reached!
% 7.14/2.30 % (10645)------------------------------
% 7.14/2.30 % (10645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.30 % (10645)Termination reason: Unknown
% 7.14/2.30 % (10645)Termination phase: Saturation
% 7.14/2.30
% 7.14/2.30 % (10645)Memory used [KB]: 7164
% 7.14/2.30 % (10645)Time elapsed: 0.051 s
% 7.14/2.30 % (10645)Instructions burned: 185 (million)
% 7.14/2.30 % (10645)------------------------------
% 7.14/2.30 % (10645)------------------------------
% 7.14/2.31 % (10648)Instruction limit reached!
% 7.14/2.31 % (10648)------------------------------
% 7.14/2.31 % (10648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.31 % (10648)Termination reason: Unknown
% 7.14/2.31 % (10648)Termination phase: Property scanning
% 7.14/2.31
% 7.14/2.31 % (10648)Memory used [KB]: 2686
% 7.14/2.31 % (10648)Time elapsed: 0.026 s
% 7.14/2.31 % (10648)Instructions burned: 82 (million)
% 7.14/2.31 % (10648)------------------------------
% 7.14/2.31 % (10648)------------------------------
% 7.14/2.31 % (10649)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_10235 for (2993ds/216Mi)
% 7.14/2.32 % (10646)Instruction limit reached!
% 7.14/2.32 % (10646)------------------------------
% 7.14/2.32 % (10646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.32 % (10646)Termination reason: Unknown
% 7.14/2.32 % (10646)Termination phase: Saturation
% 7.14/2.32
% 7.14/2.32 % (10646)Memory used [KB]: 7419
% 7.14/2.32 % (10646)Time elapsed: 0.078 s
% 7.14/2.32 % (10646)Instructions burned: 183 (million)
% 7.14/2.32 % (10646)------------------------------
% 7.14/2.32 % (10646)------------------------------
% 7.14/2.32 % (10647)Instruction limit reached!
% 7.14/2.32 % (10647)------------------------------
% 7.14/2.32 % (10647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.32 % (10647)Termination reason: Unknown
% 7.14/2.32 % (10647)Termination phase: Property scanning
% 7.14/2.32
% 7.14/2.32 % (10647)Memory used [KB]: 2814
% 7.14/2.32 % (10647)Time elapsed: 0.043 s
% 7.14/2.32 % (10647)Instructions burned: 156 (million)
% 7.14/2.32 % (10647)------------------------------
% 7.14/2.32 % (10647)------------------------------
% 7.14/2.32 % (10650)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_10235 for (2993ds/114Mi)
% 7.14/2.33 % (10651)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/922Mi)
% 7.14/2.33 % (10652)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/182Mi)
% 7.14/2.33 % (10643)Instruction limit reached!
% 7.14/2.33 % (10643)------------------------------
% 7.14/2.33 % (10643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.33 % (10643)Termination reason: Unknown
% 7.14/2.33 % (10643)Termination phase: Saturation
% 7.14/2.33
% 7.14/2.33 % (10643)Memory used [KB]: 7675
% 7.14/2.33 % (10643)Time elapsed: 0.088 s
% 7.14/2.33 % (10643)Instructions burned: 299 (million)
% 7.14/2.33 % (10643)------------------------------
% 7.14/2.33 % (10643)------------------------------
% 7.14/2.34 % (10653)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/164Mi)
% 7.14/2.36 % (10650)Instruction limit reached!
% 7.14/2.36 % (10650)------------------------------
% 7.14/2.36 % (10650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.36 % (10650)Termination reason: Unknown
% 7.14/2.36 % (10650)Termination phase: Property scanning
% 7.14/2.36
% 7.14/2.36 % (10650)Memory used [KB]: 2686
% 7.14/2.36 % (10650)Time elapsed: 0.036 s
% 7.14/2.36 % (10650)Instructions burned: 115 (million)
% 7.14/2.36 % (10650)------------------------------
% 7.14/2.36 % (10650)------------------------------
% 7.14/2.36 % (10640)Instruction limit reached!
% 7.14/2.36 % (10640)------------------------------
% 7.14/2.36 % (10640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.36 % (10640)Termination reason: Unknown
% 7.14/2.36 % (10640)Termination phase: Saturation
% 7.14/2.36
% 7.14/2.36 % (10640)Memory used [KB]: 8443
% 7.14/2.36 % (10640)Time elapsed: 0.140 s
% 7.14/2.36 % (10640)Instructions burned: 460 (million)
% 7.14/2.36 % (10640)------------------------------
% 7.14/2.36 % (10640)------------------------------
% 7.14/2.37 % (10654)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/50Mi)
% 7.14/2.37 % (10655)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/368Mi)
% 7.14/2.37 % (10649)Instruction limit reached!
% 7.14/2.37 % (10649)------------------------------
% 7.14/2.37 % (10649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.37 % (10649)Termination reason: Unknown
% 7.14/2.37 % (10649)Termination phase: Saturation
% 7.14/2.37
% 7.14/2.37 % (10649)Memory used [KB]: 7547
% 7.14/2.37 % (10649)Time elapsed: 0.063 s
% 7.14/2.37 % (10649)Instructions burned: 218 (million)
% 7.14/2.37 % (10649)------------------------------
% 7.14/2.37 % (10649)------------------------------
% 7.14/2.38 % (10652)Instruction limit reached!
% 7.14/2.38 % (10652)------------------------------
% 7.14/2.38 % (10652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.38 % (10652)Termination reason: Unknown
% 7.14/2.38 % (10652)Termination phase: Saturation
% 7.14/2.38
% 7.14/2.38 % (10652)Memory used [KB]: 7291
% 7.14/2.38 % (10652)Time elapsed: 0.051 s
% 7.14/2.38 % (10652)Instructions burned: 182 (million)
% 7.14/2.38 % (10652)------------------------------
% 7.14/2.38 % (10652)------------------------------
% 7.14/2.38 % (10654)Instruction limit reached!
% 7.14/2.38 % (10654)------------------------------
% 7.14/2.38 % (10654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.38 % (10654)Termination reason: Unknown
% 7.14/2.38 % (10654)Termination phase: Property scanning
% 7.14/2.38
% 7.14/2.38 % (10654)Memory used [KB]: 2430
% 7.14/2.38 % (10654)Time elapsed: 0.016 s
% 7.14/2.38 % (10654)Instructions burned: 53 (million)
% 7.14/2.38 % (10654)------------------------------
% 7.14/2.38 % (10654)------------------------------
% 7.14/2.38 % (10656)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/1021Mi)
% 7.14/2.39 % (10657)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/267Mi)
% 7.14/2.39 % (10653)Instruction limit reached!
% 7.14/2.39 % (10653)------------------------------
% 7.14/2.39 % (10653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.39 % (10653)Termination reason: Unknown
% 7.14/2.39 % (10653)Termination phase: Saturation
% 7.14/2.39
% 7.14/2.39 % (10653)Memory used [KB]: 2814
% 7.14/2.39 % (10653)Time elapsed: 0.048 s
% 7.14/2.39 % (10653)Instructions burned: 167 (million)
% 7.14/2.39 % (10653)------------------------------
% 7.14/2.39 % (10653)------------------------------
% 7.14/2.39 % (10658)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/204Mi)
% 7.85/2.40 % (10659)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/26Mi)
% 7.85/2.41 % (10659)Instruction limit reached!
% 7.85/2.41 % (10659)------------------------------
% 7.85/2.41 % (10659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.41 % (10659)Termination reason: Unknown
% 7.85/2.41 % (10659)Termination phase: shuffling
% 7.85/2.41
% 7.85/2.41 % (10659)Memory used [KB]: 2046
% 7.85/2.41 % (10659)Time elapsed: 0.009 s
% 7.85/2.41 % (10659)Instructions burned: 29 (million)
% 7.85/2.41 % (10659)------------------------------
% 7.85/2.41 % (10659)------------------------------
% 7.85/2.42 % (10660)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_10235 for (2992ds/53Mi)
% 7.85/2.43 % (10660)Instruction limit reached!
% 7.85/2.43 % (10660)------------------------------
% 7.85/2.43 % (10660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.43 % (10660)Termination reason: Unknown
% 7.85/2.43 % (10660)Termination phase: Property scanning
% 7.85/2.43
% 7.85/2.43 % (10660)Memory used [KB]: 2430
% 7.85/2.43 % (10660)Time elapsed: 0.017 s
% 7.85/2.43 % (10660)Instructions burned: 54 (million)
% 7.85/2.43 % (10660)------------------------------
% 7.85/2.43 % (10660)------------------------------
% 7.85/2.44 % (10661)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_10235 for (2991ds/4436Mi)
% 7.85/2.45 % (10658)Instruction limit reached!
% 7.85/2.45 % (10658)------------------------------
% 7.85/2.45 % (10658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.45 % (10658)Termination reason: Unknown
% 7.85/2.45 % (10658)Termination phase: Saturation
% 7.85/2.45
% 7.85/2.45 % (10658)Memory used [KB]: 7419
% 7.85/2.45 % (10658)Time elapsed: 0.063 s
% 7.85/2.45 % (10658)Instructions burned: 204 (million)
% 7.85/2.45 % (10658)------------------------------
% 7.85/2.45 % (10658)------------------------------
% 7.85/2.46 % (10662)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_10235 for (2991ds/1539Mi)
% 7.85/2.46 % (10657)Instruction limit reached!
% 7.85/2.46 % (10657)------------------------------
% 7.85/2.46 % (10657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.46 % (10657)Termination reason: Unknown
% 7.85/2.46 % (10657)Termination phase: Saturation
% 7.85/2.46
% 7.85/2.46 % (10657)Memory used [KB]: 7547
% 7.85/2.46 % (10657)Time elapsed: 0.078 s
% 7.85/2.46 % (10657)Instructions burned: 267 (million)
% 7.85/2.46 % (10657)------------------------------
% 7.85/2.46 % (10657)------------------------------
% 7.85/2.47 % (10663)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_10235 for (2991ds/408Mi)
% 7.85/2.49 % (10655)Instruction limit reached!
% 7.85/2.49 % (10655)------------------------------
% 7.85/2.49 % (10655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.49 % (10655)Termination reason: Unknown
% 7.85/2.49 % (10655)Termination phase: Saturation
% 7.85/2.49
% 7.85/2.49 % (10655)Memory used [KB]: 8315
% 7.85/2.49 % (10655)Time elapsed: 0.116 s
% 7.85/2.49 % (10655)Instructions burned: 369 (million)
% 7.85/2.49 % (10655)------------------------------
% 7.85/2.49 % (10655)------------------------------
% 8.17/2.50 % (10664)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_10235 for (2991ds/5205Mi)
% 8.17/2.55 % (10644)Instruction limit reached!
% 8.17/2.55 % (10644)------------------------------
% 8.17/2.55 % (10644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.17/2.55 % (10644)Termination reason: Unknown
% 8.17/2.55 % (10644)Termination phase: Saturation
% 8.17/2.55
% 8.17/2.55 % (10644)Memory used [KB]: 9850
% 8.17/2.55 % (10644)Time elapsed: 0.321 s
% 8.17/2.55 % (10644)Instructions burned: 987 (million)
% 8.17/2.55 % (10644)------------------------------
% 8.17/2.55 % (10644)------------------------------
% 8.17/2.56 % (10665)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_10235 for (2990ds/1913Mi)
% 8.47/2.60 % (10663)Instruction limit reached!
% 8.47/2.60 % (10663)------------------------------
% 8.47/2.60 % (10663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.47/2.60 % (10663)Termination reason: Unknown
% 8.47/2.60 % (10663)Termination phase: Saturation
% 8.47/2.60
% 8.47/2.60 % (10663)Memory used [KB]: 8571
% 8.47/2.60 % (10663)Time elapsed: 0.125 s
% 8.47/2.60 % (10663)Instructions burned: 409 (million)
% 8.47/2.60 % (10663)------------------------------
% 8.47/2.60 % (10663)------------------------------
% 8.47/2.61 % (10666)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_10235 for (2990ds/4350Mi)
% 8.47/2.62 % (10651)Instruction limit reached!
% 8.47/2.62 % (10651)------------------------------
% 8.47/2.62 % (10651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.47/2.62 % (10651)Termination reason: Unknown
% 8.47/2.62 % (10651)Termination phase: Saturation
% 8.47/2.62
% 8.47/2.62 % (10651)Memory used [KB]: 8315
% 8.47/2.62 % (10651)Time elapsed: 0.292 s
% 8.47/2.62 % (10651)Instructions burned: 924 (million)
% 8.47/2.62 % (10651)------------------------------
% 8.47/2.62 % (10651)------------------------------
% 8.47/2.63 % (10667)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_10235 for (2990ds/68Mi)
% 8.47/2.65 % (10667)Instruction limit reached!
% 8.47/2.65 % (10667)------------------------------
% 8.47/2.65 % (10667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.47/2.65 % (10667)Termination reason: Unknown
% 8.47/2.65 % (10667)Termination phase: Preprocessing 3
% 8.47/2.65
% 8.47/2.65 % (10667)Memory used [KB]: 2302
% 8.47/2.65 % (10667)Time elapsed: 0.023 s
% 8.47/2.65 % (10667)Instructions burned: 68 (million)
% 8.47/2.65 % (10667)------------------------------
% 8.47/2.65 % (10667)------------------------------
% 8.47/2.66 % (10668)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_10235 for (2989ds/358Mi)
% 8.47/2.69 % (10656)Instruction limit reached!
% 8.47/2.69 % (10656)------------------------------
% 8.47/2.69 % (10656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.47/2.69 % (10656)Termination reason: Unknown
% 8.47/2.69 % (10656)Termination phase: Saturation
% 8.47/2.69
% 8.47/2.69 % (10656)Memory used [KB]: 8827
% 8.47/2.69 % (10656)Time elapsed: 0.309 s
% 8.47/2.69 % (10656)Instructions burned: 1022 (million)
% 8.47/2.69 % (10656)------------------------------
% 8.47/2.69 % (10656)------------------------------
% 9.26/2.70 % (10669)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_10235 for (2989ds/31Mi)
% 9.26/2.71 % (10669)Instruction limit reached!
% 9.26/2.71 % (10669)------------------------------
% 9.26/2.71 % (10669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/2.71 % (10669)Termination reason: Unknown
% 9.26/2.71 % (10669)Termination phase: shuffling
% 9.26/2.71
% 9.26/2.71 % (10669)Memory used [KB]: 2046
% 9.26/2.71 % (10669)Time elapsed: 0.012 s
% 9.26/2.71 % (10669)Instructions burned: 33 (million)
% 9.26/2.71 % (10669)------------------------------
% 9.26/2.71 % (10669)------------------------------
% 9.26/2.72 % (10670)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_10235 for (2989ds/279Mi)
% 9.26/2.77 % (10668)Instruction limit reached!
% 9.26/2.77 % (10668)------------------------------
% 9.26/2.77 % (10668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/2.77 % (10668)Termination reason: Unknown
% 9.26/2.77 % (10668)Termination phase: Saturation
% 9.26/2.77
% 9.26/2.77 % (10668)Memory used [KB]: 7931
% 9.26/2.77 % (10668)Time elapsed: 0.111 s
% 9.26/2.77 % (10668)Instructions burned: 360 (million)
% 9.26/2.77 % (10668)------------------------------
% 9.26/2.77 % (10668)------------------------------
% 9.26/2.78 % (10671)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_10235 for (2988ds/258Mi)
% 9.40/2.80 % (10670)Instruction limit reached!
% 9.40/2.80 % (10670)------------------------------
% 9.40/2.80 % (10670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.40/2.80 % (10670)Termination reason: Unknown
% 9.40/2.80 % (10670)Termination phase: Saturation
% 9.40/2.80
% 9.40/2.80 % (10670)Memory used [KB]: 7803
% 9.40/2.80 % (10670)Time elapsed: 0.079 s
% 9.40/2.80 % (10670)Instructions burned: 280 (million)
% 9.40/2.80 % (10670)------------------------------
% 9.40/2.80 % (10670)------------------------------
% 9.40/2.81 % (10672)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_10235 for (2988ds/26Mi)
% 9.40/2.82 % (10672)Instruction limit reached!
% 9.40/2.82 % (10672)------------------------------
% 9.40/2.82 % (10672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.40/2.82 % (10672)Termination reason: Unknown
% 9.40/2.82 % (10672)Termination phase: shuffling
% 9.40/2.82
% 9.40/2.82 % (10672)Memory used [KB]: 2046
% 9.40/2.82 % (10672)Time elapsed: 0.009 s
% 9.40/2.82 % (10672)Instructions burned: 28 (million)
% 9.40/2.82 % (10672)------------------------------
% 9.40/2.82 % (10672)------------------------------
% 9.40/2.83 % (10673)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_10235 for (2988ds/995Mi)
% 9.40/2.85 % (10671)Instruction limit reached!
% 9.40/2.85 % (10671)------------------------------
% 9.40/2.85 % (10671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.40/2.85 % (10671)Termination reason: Unknown
% 9.40/2.85 % (10671)Termination phase: Saturation
% 9.40/2.85
% 9.40/2.85 % (10671)Memory used [KB]: 7803
% 9.40/2.85 % (10671)Time elapsed: 0.078 s
% 9.40/2.85 % (10671)Instructions burned: 259 (million)
% 9.40/2.85 % (10671)------------------------------
% 9.40/2.85 % (10671)------------------------------
% 9.40/2.86 % (10674)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_10235 for (2987ds/373Mi)
% 9.59/2.93 % (10662)Instruction limit reached!
% 9.59/2.93 % (10662)------------------------------
% 9.59/2.93 % (10662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.93 % (10662)Termination reason: Unknown
% 9.59/2.93 % (10662)Termination phase: Saturation
% 9.59/2.93
% 9.59/2.93 % (10662)Memory used [KB]: 11513
% 9.59/2.93 % (10662)Time elapsed: 0.468 s
% 9.59/2.93 % (10662)Instructions burned: 1541 (million)
% 9.59/2.93 % (10662)------------------------------
% 9.59/2.93 % (10662)------------------------------
% 9.59/2.94 % (10675)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_10235 for (2986ds/253Mi)
% 9.59/2.98 % (10674)Instruction limit reached!
% 9.59/2.98 % (10674)------------------------------
% 9.59/2.98 % (10674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.98 % (10674)Termination reason: Unknown
% 9.59/2.98 % (10674)Termination phase: Saturation
% 9.59/2.98
% 9.59/2.98 % (10674)Memory used [KB]: 8059
% 9.59/2.98 % (10674)Time elapsed: 0.113 s
% 9.59/2.98 % (10674)Instructions burned: 374 (million)
% 9.59/2.98 % (10674)------------------------------
% 9.59/2.98 % (10674)------------------------------
% 9.59/2.99 % (10676)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_10235 for (2986ds/832Mi)
% 9.59/3.01 % (10675)Instruction limit reached!
% 9.59/3.01 % (10675)------------------------------
% 9.59/3.01 % (10675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/3.01 % (10675)Termination reason: Unknown
% 9.59/3.01 % (10675)Termination phase: Saturation
% 9.59/3.01
% 9.59/3.01 % (10675)Memory used [KB]: 7547
% 9.59/3.01 % (10675)Time elapsed: 0.070 s
% 9.59/3.01 % (10675)Instructions burned: 255 (million)
% 9.59/3.01 % (10675)------------------------------
% 9.59/3.01 % (10675)------------------------------
% 12.41/3.02 % (10677)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_10235 for (2986ds/668Mi)
% 12.41/3.04 % (10676)Refutation not found, incomplete strategy
% 12.41/3.04 % (10676)------------------------------
% 12.41/3.04 % (10676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.41/3.04 % (10676)Termination reason: Refutation not found, incomplete strategy
% 12.41/3.04
% 12.41/3.04
% 12.41/3.04 % (10676)Memory used [KB]: 8059
% 12.41/3.04 % (10676)Time elapsed: 0.059 s
% 12.41/3.04 % (10676)Instructions burned: 197 (million)
% 12.41/3.04 % (10676)------------------------------
% 12.41/3.04 % (10676)------------------------------
% 12.41/3.05 % (10678)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_10235 for (2985ds/40Mi)
% 12.41/3.07 % (10678)Instruction limit reached!
% 12.41/3.07 % (10678)------------------------------
% 12.41/3.07 % (10678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.41/3.07 % (10678)Termination reason: Unknown
% 12.41/3.07 % (10678)Termination phase: shuffling
% 12.41/3.07
% 12.41/3.07 % (10678)Memory used [KB]: 2302
% 12.41/3.07 % (10678)Time elapsed: 0.013 s
% 12.41/3.07 % (10678)Instructions burned: 43 (million)
% 12.41/3.07 % (10678)------------------------------
% 12.41/3.07 % (10678)------------------------------
% 12.41/3.07 % (10679)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_10235 for (2985ds/294Mi)
% 12.99/3.11 % (10673)Instruction limit reached!
% 12.99/3.11 % (10673)------------------------------
% 12.99/3.11 % (10673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.11 % (10673)Termination reason: Unknown
% 12.99/3.11 % (10673)Termination phase: Saturation
% 12.99/3.11
% 12.99/3.11 % (10673)Memory used [KB]: 8827
% 12.99/3.11 % (10673)Time elapsed: 0.286 s
% 12.99/3.11 % (10673)Instructions burned: 997 (million)
% 12.99/3.11 % (10673)------------------------------
% 12.99/3.11 % (10673)------------------------------
% 12.99/3.12 % (10680)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_10235 for (2985ds/187Mi)
% 12.99/3.14 % (10665)Instruction limit reached!
% 12.99/3.14 % (10665)------------------------------
% 12.99/3.14 % (10665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.14 % (10665)Termination reason: Unknown
% 12.99/3.14 % (10665)Termination phase: Saturation
% 12.99/3.14
% 12.99/3.14 % (10665)Memory used [KB]: 4349
% 12.99/3.14 % (10665)Time elapsed: 0.583 s
% 12.99/3.14 % (10665)Instructions burned: 1914 (million)
% 12.99/3.14 % (10665)------------------------------
% 12.99/3.14 % (10665)------------------------------
% 12.99/3.15 % (10681)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_10235 for (2984ds/371Mi)
% 12.99/3.16 % (10679)Instruction limit reached!
% 12.99/3.16 % (10679)------------------------------
% 12.99/3.16 % (10679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.16 % (10679)Termination reason: Unknown
% 12.99/3.16 % (10679)Termination phase: Saturation
% 12.99/3.16
% 12.99/3.16 % (10679)Memory used [KB]: 7419
% 12.99/3.16 % (10679)Time elapsed: 0.082 s
% 12.99/3.16 % (10679)Instructions burned: 294 (million)
% 12.99/3.16 % (10679)------------------------------
% 12.99/3.16 % (10679)------------------------------
% 12.99/3.17 % (10682)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_10235 for (2984ds/1827Mi)
% 12.99/3.18 % (10680)Instruction limit reached!
% 12.99/3.18 % (10680)------------------------------
% 12.99/3.18 % (10680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.18 % (10680)Termination reason: Unknown
% 12.99/3.18 % (10680)Termination phase: Saturation
% 12.99/3.18
% 12.99/3.18 % (10680)Memory used [KB]: 7547
% 12.99/3.18 % (10680)Time elapsed: 0.055 s
% 12.99/3.18 % (10680)Instructions burned: 187 (million)
% 12.99/3.18 % (10680)------------------------------
% 12.99/3.18 % (10680)------------------------------
% 12.99/3.18 % (10683)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_10235 for (2984ds/70Mi)
% 13.46/3.20 % (10683)Instruction limit reached!
% 13.46/3.20 % (10683)------------------------------
% 13.46/3.20 % (10683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.20 % (10683)Termination reason: Unknown
% 13.46/3.20 % (10683)Termination phase: Property scanning
% 13.46/3.20
% 13.46/3.20 % (10683)Memory used [KB]: 2430
% 13.46/3.20 % (10683)Time elapsed: 0.020 s
% 13.46/3.20 % (10683)Instructions burned: 72 (million)
% 13.46/3.20 % (10683)------------------------------
% 13.46/3.20 % (10683)------------------------------
% 13.46/3.21 % (10677)Instruction limit reached!
% 13.46/3.21 % (10677)------------------------------
% 13.46/3.21 % (10677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.21 % (10677)Termination reason: Unknown
% 13.46/3.21 % (10677)Termination phase: Saturation
% 13.46/3.21
% 13.46/3.21 % (10677)Memory used [KB]: 13176
% 13.46/3.21 % (10677)Time elapsed: 0.190 s
% 13.46/3.21 % (10677)Instructions burned: 668 (million)
% 13.46/3.21 % (10677)------------------------------
% 13.46/3.21 % (10677)------------------------------
% 13.46/3.21 % (10684)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_10235 for (2984ds/316Mi)
% 13.46/3.22 % (10685)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_10235 for (2984ds/932Mi)
% 13.46/3.27 % (10681)Instruction limit reached!
% 13.46/3.27 % (10681)------------------------------
% 13.46/3.27 % (10681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.27 % (10681)Termination reason: Unknown
% 13.46/3.27 % (10681)Termination phase: Saturation
% 13.46/3.27
% 13.46/3.27 % (10681)Memory used [KB]: 8315
% 13.46/3.27 % (10681)Time elapsed: 0.116 s
% 13.46/3.27 % (10681)Instructions burned: 371 (million)
% 13.46/3.27 % (10681)------------------------------
% 13.46/3.27 % (10681)------------------------------
% 13.46/3.28 % (10686)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_10235 for (2983ds/4714Mi)
% 14.11/3.30 % (10684)Instruction limit reached!
% 14.11/3.30 % (10684)------------------------------
% 14.11/3.30 % (10684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.11/3.30 % (10684)Termination reason: Unknown
% 14.11/3.30 % (10684)Termination phase: Saturation
% 14.11/3.30
% 14.11/3.30 % (10684)Memory used [KB]: 8059
% 14.11/3.30 % (10684)Time elapsed: 0.086 s
% 14.11/3.30 % (10684)Instructions burned: 319 (million)
% 14.11/3.30 % (10684)------------------------------
% 14.11/3.30 % (10684)------------------------------
% 14.11/3.31 % (10687)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_10235 for (2983ds/8250Mi)
% 14.50/3.48 % (10685)Instruction limit reached!
% 14.50/3.48 % (10685)------------------------------
% 14.50/3.48 % (10685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.50/3.48 % (10685)Termination reason: Unknown
% 14.50/3.48 % (10685)Termination phase: Saturation
% 14.50/3.48
% 14.50/3.48 % (10685)Memory used [KB]: 11385
% 14.50/3.48 % (10685)Time elapsed: 0.268 s
% 14.50/3.48 % (10685)Instructions burned: 933 (million)
% 14.50/3.48 % (10685)------------------------------
% 14.50/3.48 % (10685)------------------------------
% 14.50/3.49 % (10688)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_10235 for (2981ds/770Mi)
% 15.67/3.71 % (10688)Instruction limit reached!
% 15.67/3.71 % (10688)------------------------------
% 15.67/3.71 % (10688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.67/3.71 % (10688)Termination reason: Unknown
% 15.67/3.71 % (10688)Termination phase: Saturation
% 15.67/3.71
% 15.67/3.71 % (10688)Memory used [KB]: 8059
% 15.67/3.71 % (10688)Time elapsed: 0.221 s
% 15.67/3.71 % (10688)Instructions burned: 771 (million)
% 15.67/3.71 % (10688)------------------------------
% 15.67/3.71 % (10688)------------------------------
% 15.67/3.72 % (10689)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_10235 for (2979ds/794Mi)
% 15.67/3.73 % (10682)Instruction limit reached!
% 15.67/3.73 % (10682)------------------------------
% 15.67/3.73 % (10682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.67/3.73 % (10682)Termination reason: Unknown
% 15.67/3.73 % (10682)Termination phase: Saturation
% 15.67/3.73
% 15.67/3.73 % (10682)Memory used [KB]: 11129
% 15.67/3.73 % (10682)Time elapsed: 0.564 s
% 15.67/3.73 % (10682)Instructions burned: 1829 (million)
% 15.67/3.73 % (10682)------------------------------
% 15.67/3.73 % (10682)------------------------------
% 15.67/3.73 % (10661)Instruction limit reached!
% 15.67/3.73 % (10661)------------------------------
% 15.67/3.73 % (10661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.67/3.73 % (10661)Termination reason: Unknown
% 15.67/3.73 % (10661)Termination phase: Saturation
% 15.67/3.73
% 15.67/3.73 % (10661)Memory used [KB]: 12792
% 15.67/3.73 % (10661)Time elapsed: 1.290 s
% 15.67/3.73 % (10661)Instructions burned: 4437 (million)
% 15.67/3.73 % (10661)------------------------------
% 15.67/3.73 % (10661)------------------------------
% 15.67/3.74 % (10690)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_10235 for (2978ds/464Mi)
% 15.67/3.74 % (10691)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_10235 for (2978ds/1376Mi)
% 16.73/3.88 % (10690)Instruction limit reached!
% 16.73/3.88 % (10690)------------------------------
% 16.73/3.88 % (10690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/3.88 % (10690)Termination reason: Unknown
% 16.73/3.88 % (10690)Termination phase: Saturation
% 16.73/3.88
% 16.73/3.88 % (10690)Memory used [KB]: 7931
% 16.73/3.88 % (10690)Time elapsed: 0.145 s
% 16.73/3.88 % (10690)Instructions burned: 466 (million)
% 16.73/3.88 % (10690)------------------------------
% 16.73/3.88 % (10690)------------------------------
% 16.73/3.89 % (10666)Instruction limit reached!
% 16.73/3.89 % (10666)------------------------------
% 16.73/3.89 % (10666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.73/3.89 % (10666)Termination reason: Unknown
% 16.73/3.89 % (10666)Termination phase: Saturation
% 16.73/3.89
% 16.73/3.89 % (10666)Memory used [KB]: 12665
% 16.73/3.89 % (10666)Time elapsed: 1.285 s
% 16.73/3.89 % (10666)Instructions burned: 4351 (million)
% 16.73/3.89 % (10666)------------------------------
% 16.73/3.89 % (10666)------------------------------
% 16.73/3.89 % (10692)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_10235 for (2977ds/906Mi)
% 17.08/3.90 % (10693)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_10235 for (2977ds/434Mi)
% 17.08/3.96 % (10689)Instruction limit reached!
% 17.08/3.96 % (10689)------------------------------
% 17.08/3.96 % (10689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.08/3.96 % (10689)Termination reason: Unknown
% 17.08/3.96 % (10689)Termination phase: Saturation
% 17.08/3.96
% 17.08/3.96 % (10689)Memory used [KB]: 5373
% 17.08/3.96 % (10689)Time elapsed: 0.242 s
% 17.08/3.96 % (10689)Instructions burned: 794 (million)
% 17.08/3.96 % (10689)------------------------------
% 17.08/3.96 % (10689)------------------------------
% 17.08/3.97 % (10694)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_10235 for (2976ds/865Mi)
% 19.42/4.03 % (10664)Instruction limit reached!
% 19.42/4.03 % (10664)------------------------------
% 19.42/4.03 % (10664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.42/4.03 % (10664)Termination reason: Unknown
% 19.42/4.03 % (10664)Termination phase: Saturation
% 19.42/4.03
% 19.42/4.03 % (10664)Memory used [KB]: 14456
% 19.42/4.03 % (10664)Time elapsed: 1.530 s
% 19.42/4.03 % (10664)Instructions burned: 5206 (million)
% 19.42/4.03 % (10664)------------------------------
% 19.42/4.03 % (10664)------------------------------
% 19.42/4.03 % (10693)Instruction limit reached!
% 19.42/4.03 % (10693)------------------------------
% 19.42/4.03 % (10693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.42/4.03 % (10693)Termination reason: Unknown
% 19.42/4.03 % (10693)Termination phase: Saturation
% 19.42/4.03
% 19.42/4.03 % (10693)Memory used [KB]: 8187
% 19.42/4.03 % (10693)Time elapsed: 0.128 s
% 19.42/4.03 % (10693)Instructions burned: 435 (million)
% 19.42/4.03 % (10693)------------------------------
% 19.42/4.03 % (10693)------------------------------
% 19.42/4.04 % (10695)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_10235 for (2976ds/593Mi)
% 19.42/4.04 % (10696)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_10235 for (2976ds/443Mi)
% 19.98/4.16 % (10691)Instruction limit reached!
% 19.98/4.16 % (10691)------------------------------
% 19.98/4.16 % (10691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.98/4.16 % (10691)Termination reason: Unknown
% 19.98/4.16 % (10691)Termination phase: Saturation
% 19.98/4.16
% 19.98/4.16 % (10691)Memory used [KB]: 13816
% 19.98/4.16 % (10691)Time elapsed: 0.423 s
% 19.98/4.16 % (10691)Instructions burned: 1378 (million)
% 19.98/4.16 % (10691)------------------------------
% 19.98/4.16 % (10691)------------------------------
% 19.98/4.17 % (10697)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_10235 for (2974ds/594Mi)
% 19.98/4.18 % (10696)Instruction limit reached!
% 19.98/4.18 % (10696)------------------------------
% 19.98/4.18 % (10696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.98/4.18 % (10696)Termination reason: Unknown
% 19.98/4.18 % (10696)Termination phase: Saturation
% 19.98/4.18
% 19.98/4.18 % (10696)Memory used [KB]: 8059
% 19.98/4.18 % (10696)Time elapsed: 0.144 s
% 19.98/4.18 % (10696)Instructions burned: 445 (million)
% 19.98/4.18 % (10696)------------------------------
% 19.98/4.18 % (10696)------------------------------
% 19.98/4.19 % (10698)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_10235 for (2974ds/327Mi)
% 20.52/4.20 % (10695)Instruction limit reached!
% 20.52/4.20 % (10695)------------------------------
% 20.52/4.20 % (10695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.20 % (10695)Termination reason: Unknown
% 20.52/4.20 % (10695)Termination phase: Saturation
% 20.52/4.20
% 20.52/4.20 % (10695)Memory used [KB]: 9210
% 20.52/4.20 % (10695)Time elapsed: 0.170 s
% 20.52/4.20 % (10695)Instructions burned: 594 (million)
% 20.52/4.20 % (10695)------------------------------
% 20.52/4.20 % (10695)------------------------------
% 20.52/4.21 % (10692)Instruction limit reached!
% 20.52/4.21 % (10692)------------------------------
% 20.52/4.21 % (10692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.21 % (10692)Termination reason: Unknown
% 20.52/4.21 % (10692)Termination phase: Saturation
% 20.52/4.21
% 20.52/4.21 % (10692)Memory used [KB]: 12792
% 20.52/4.21 % (10692)Time elapsed: 0.316 s
% 20.52/4.21 % (10692)Instructions burned: 908 (million)
% 20.52/4.21 % (10692)------------------------------
% 20.52/4.21 % (10692)------------------------------
% 20.52/4.21 % (10699)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_10235 for (2974ds/5411Mi)
% 20.52/4.22 % (10700)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_10235 for (2974ds/1762Mi)
% 20.52/4.23 % (10694)Instruction limit reached!
% 20.52/4.23 % (10694)------------------------------
% 20.52/4.23 % (10694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.23 % (10694)Termination reason: Unknown
% 20.52/4.23 % (10694)Termination phase: Saturation
% 20.52/4.23
% 20.52/4.23 % (10694)Memory used [KB]: 9338
% 20.52/4.23 % (10694)Time elapsed: 0.261 s
% 20.52/4.23 % (10694)Instructions burned: 866 (million)
% 20.52/4.23 % (10694)------------------------------
% 20.52/4.23 % (10694)------------------------------
% 20.52/4.24 % (10701)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_10235 for (2973ds/96Mi)
% 20.52/4.25 % (10699)Refutation not found, incomplete strategy
% 20.52/4.25 % (10699)------------------------------
% 20.52/4.25 % (10699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.25 % (10699)Termination reason: Refutation not found, incomplete strategy
% 20.52/4.25
% 20.52/4.25
% 20.52/4.25 % (10699)Memory used [KB]: 7419
% 20.52/4.25 % (10699)Time elapsed: 0.036 s
% 20.52/4.25 % (10699)Instructions burned: 117 (million)
% 20.52/4.25 % (10699)------------------------------
% 20.52/4.25 % (10699)------------------------------
% 20.52/4.26 % (10702)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_10235 for (2973ds/503Mi)
% 20.52/4.27 % (10701)Instruction limit reached!
% 20.52/4.27 % (10701)------------------------------
% 20.52/4.27 % (10701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.27 % (10701)Termination reason: Unknown
% 20.52/4.27 % (10701)Termination phase: Preprocessing 3
% 20.52/4.27
% 20.52/4.27 % (10701)Memory used [KB]: 2558
% 20.52/4.27 % (10701)Time elapsed: 0.027 s
% 20.52/4.27 % (10701)Instructions burned: 96 (million)
% 20.52/4.27 % (10701)------------------------------
% 20.52/4.27 % (10701)------------------------------
% 20.52/4.28 % (10703)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_10235 for (2973ds/90Mi)
% 20.52/4.29 % (10698)Instruction limit reached!
% 20.52/4.29 % (10698)------------------------------
% 20.52/4.29 % (10698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.29 % (10698)Termination reason: Unknown
% 20.52/4.29 % (10698)Termination phase: Saturation
% 20.52/4.29
% 20.52/4.29 % (10698)Memory used [KB]: 8059
% 20.52/4.29 % (10698)Time elapsed: 0.100 s
% 20.52/4.29 % (10698)Instructions burned: 328 (million)
% 20.52/4.29 % (10698)------------------------------
% 20.52/4.29 % (10698)------------------------------
% 21.17/4.30 % (10704)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_10235 for (2973ds/593Mi)
% 21.17/4.31 % (10703)Instruction limit reached!
% 21.17/4.31 % (10703)------------------------------
% 21.17/4.31 % (10703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.31 % (10703)Termination reason: Unknown
% 21.17/4.31 % (10703)Termination phase: Property scanning
% 21.17/4.31
% 21.17/4.31 % (10703)Memory used [KB]: 2558
% 21.17/4.31 % (10703)Time elapsed: 0.028 s
% 21.17/4.31 % (10703)Instructions burned: 93 (million)
% 21.17/4.31 % (10703)------------------------------
% 21.17/4.31 % (10703)------------------------------
% 21.17/4.31 % (10705)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_10235 for (2973ds/1512Mi)
% 21.17/4.35 % (10697)Instruction limit reached!
% 21.17/4.35 % (10697)------------------------------
% 21.17/4.35 % (10697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.35 % (10697)Termination reason: Unknown
% 21.17/4.35 % (10697)Termination phase: Saturation
% 21.17/4.35
% 21.17/4.35 % (10697)Memory used [KB]: 8059
% 21.17/4.35 % (10697)Time elapsed: 0.183 s
% 21.17/4.35 % (10697)Instructions burned: 596 (million)
% 21.17/4.35 % (10697)------------------------------
% 21.17/4.35 % (10697)------------------------------
% 21.17/4.36 % (10706)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_10235 for (2972ds/569Mi)
% 21.17/4.37 % (10705)Refutation not found, incomplete strategy
% 21.17/4.37 % (10705)------------------------------
% 21.17/4.37 % (10705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.37 % (10705)Termination reason: Refutation not found, incomplete strategy
% 21.17/4.37
% 21.17/4.37
% 21.17/4.37 % (10705)Memory used [KB]: 8059
% 21.17/4.37 % (10705)Time elapsed: 0.059 s
% 21.17/4.37 % (10705)Instructions burned: 198 (million)
% 21.17/4.37 % (10705)------------------------------
% 21.17/4.37 % (10705)------------------------------
% 21.17/4.38 % (10707)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_10235 for (2972ds/501Mi)
% 21.66/4.41 % (10702)Instruction limit reached!
% 21.66/4.41 % (10702)------------------------------
% 21.66/4.41 % (10702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.66/4.41 % (10702)Termination reason: Unknown
% 21.66/4.41 % (10702)Termination phase: Saturation
% 21.66/4.41
% 21.66/4.41 % (10702)Memory used [KB]: 8699
% 21.66/4.41 % (10702)Time elapsed: 0.149 s
% 21.66/4.41 % (10702)Instructions burned: 505 (million)
% 21.66/4.41 % (10702)------------------------------
% 21.66/4.41 % (10702)------------------------------
% 21.66/4.42 % (10708)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_10235 for (2972ds/562Mi)
% 21.66/4.48 % (10704)Instruction limit reached!
% 21.66/4.48 % (10704)------------------------------
% 21.66/4.48 % (10704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.66/4.48 % (10704)Termination reason: Unknown
% 21.66/4.48 % (10704)Termination phase: Saturation
% 21.66/4.48
% 21.66/4.48 % (10704)Memory used [KB]: 8699
% 21.66/4.48 % (10704)Time elapsed: 0.179 s
% 21.66/4.48 % (10704)Instructions burned: 595 (million)
% 21.66/4.48 % (10704)------------------------------
% 21.66/4.48 % (10704)------------------------------
% 21.66/4.49 % (10709)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_10235 for (2971ds/406Mi)
% 22.20/4.52 % (10706)Instruction limit reached!
% 22.20/4.52 % (10706)------------------------------
% 22.20/4.52 % (10706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.52 % (10706)Termination reason: Unknown
% 22.20/4.52 % (10706)Termination phase: Saturation
% 22.20/4.52
% 22.20/4.52 % (10706)Memory used [KB]: 8699
% 22.20/4.52 % (10706)Time elapsed: 0.159 s
% 22.20/4.52 % (10706)Instructions burned: 569 (million)
% 22.20/4.52 % (10706)------------------------------
% 22.20/4.52 % (10706)------------------------------
% 22.20/4.53 % (10707)Instruction limit reached!
% 22.20/4.53 % (10707)------------------------------
% 22.20/4.53 % (10707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.53 % (10707)Termination reason: Unknown
% 22.20/4.53 % (10707)Termination phase: Saturation
% 22.20/4.53
% 22.20/4.53 % (10707)Memory used [KB]: 9083
% 22.20/4.53 % (10707)Time elapsed: 0.166 s
% 22.20/4.53 % (10707)Instructions burned: 503 (million)
% 22.20/4.53 % (10707)------------------------------
% 22.20/4.53 % (10707)------------------------------
% 22.20/4.53 % (10710)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_10235 for (2971ds/582Mi)
% 22.20/4.54 % (10711)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_10235 for (2971ds/456Mi)
% 22.20/4.56 % (10686)Instruction limit reached!
% 22.20/4.56 % (10686)------------------------------
% 22.20/4.56 % (10686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.56 % (10686)Termination reason: Unknown
% 22.20/4.56 % (10686)Termination phase: Saturation
% 22.20/4.56
% 22.20/4.56 % (10686)Memory used [KB]: 26609
% 22.20/4.56 % (10686)Time elapsed: 1.282 s
% 22.20/4.56 % (10686)Instructions burned: 4716 (million)
% 22.20/4.56 % (10686)------------------------------
% 22.20/4.56 % (10686)------------------------------
% 22.20/4.57 % (10712)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_10235 for (2970ds/393Mi)
% 22.20/4.58 % (10708)Instruction limit reached!
% 22.20/4.58 % (10708)------------------------------
% 22.20/4.58 % (10708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.58 % (10708)Termination reason: Unknown
% 22.20/4.58 % (10708)Termination phase: Saturation
% 22.20/4.58
% 22.20/4.58 % (10708)Memory used [KB]: 8955
% 22.20/4.58 % (10708)Time elapsed: 0.164 s
% 22.20/4.58 % (10708)Instructions burned: 564 (million)
% 22.20/4.58 % (10708)------------------------------
% 22.20/4.58 % (10708)------------------------------
% 22.20/4.59 % (10713)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_10235 for (2970ds/1335Mi)
% 22.87/4.61 % (10709)Instruction limit reached!
% 22.87/4.61 % (10709)------------------------------
% 22.87/4.61 % (10709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.87/4.61 % (10709)Termination reason: Unknown
% 22.87/4.61 % (10709)Termination phase: Saturation
% 22.87/4.61
% 22.87/4.61 % (10709)Memory used [KB]: 8571
% 22.87/4.61 % (10709)Time elapsed: 0.123 s
% 22.87/4.61 % (10709)Instructions burned: 406 (million)
% 22.87/4.61 % (10709)------------------------------
% 22.87/4.61 % (10709)------------------------------
% 22.87/4.62 % (10714)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_10235 for (2970ds/3373Mi)
% 22.87/4.67 % (10711)Instruction limit reached!
% 22.87/4.67 % (10711)------------------------------
% 22.87/4.67 % (10711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.87/4.67 % (10711)Termination reason: Unknown
% 22.87/4.67 % (10711)Termination phase: Saturation
% 22.87/4.67
% 22.87/4.67 % (10711)Memory used [KB]: 8699
% 22.87/4.67 % (10711)Time elapsed: 0.139 s
% 22.87/4.67 % (10711)Instructions burned: 459 (million)
% 22.87/4.67 % (10711)------------------------------
% 22.87/4.67 % (10711)------------------------------
% 22.87/4.68 % (10712)Instruction limit reached!
% 22.87/4.68 % (10712)------------------------------
% 22.87/4.68 % (10712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.87/4.68 % (10712)Termination reason: Unknown
% 22.87/4.68 % (10712)Termination phase: Saturation
% 22.87/4.68
% 22.87/4.68 % (10712)Memory used [KB]: 7803
% 22.87/4.68 % (10712)Time elapsed: 0.111 s
% 22.87/4.68 % (10712)Instructions burned: 394 (million)
% 22.87/4.68 % (10712)------------------------------
% 22.87/4.68 % (10712)------------------------------
% 22.87/4.69 % (10715)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_10235 for (2969ds/474Mi)
% 22.87/4.69 % (10716)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_10235 for (2969ds/157Mi)
% 23.37/4.72 % (10710)Instruction limit reached!
% 23.37/4.72 % (10710)------------------------------
% 23.37/4.72 % (10710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.37/4.72 % (10710)Termination reason: Unknown
% 23.37/4.72 % (10710)Termination phase: Saturation
% 23.37/4.72
% 23.37/4.72 % (10710)Memory used [KB]: 9466
% 23.37/4.72 % (10710)Time elapsed: 0.211 s
% 23.37/4.72 % (10710)Instructions burned: 584 (million)
% 23.37/4.72 % (10710)------------------------------
% 23.37/4.72 % (10710)------------------------------
% 23.37/4.73 % (10717)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_10235 for (2968ds/590Mi)
% 23.37/4.73 % (10716)Instruction limit reached!
% 23.37/4.73 % (10716)------------------------------
% 23.37/4.73 % (10716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.37/4.73 % (10716)Termination reason: Unknown
% 23.37/4.73 % (10716)Termination phase: Property scanning
% 23.37/4.73
% 23.37/4.73 % (10716)Memory used [KB]: 2814
% 23.37/4.73 % (10716)Time elapsed: 0.046 s
% 23.37/4.73 % (10716)Instructions burned: 160 (million)
% 23.37/4.73 % (10716)------------------------------
% 23.37/4.73 % (10716)------------------------------
% 23.37/4.74 % (10700)Instruction limit reached!
% 23.37/4.74 % (10700)------------------------------
% 23.37/4.74 % (10700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.37/4.74 % (10700)Termination reason: Unknown
% 23.37/4.74 % (10700)Termination phase: Saturation
% 23.37/4.74
% 23.37/4.74 % (10700)Memory used [KB]: 11897
% 23.37/4.74 % (10700)Time elapsed: 0.525 s
% 23.37/4.74 % (10700)Instructions burned: 1762 (million)
% 23.37/4.74 % (10700)------------------------------
% 23.37/4.74 % (10700)------------------------------
% 23.37/4.74 % (10718)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_10235 for (2968ds/104Mi)
% 23.37/4.75 % (10719)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_10235 for (2968ds/414Mi)
% 23.37/4.77 % (10718)Instruction limit reached!
% 23.37/4.77 % (10718)------------------------------
% 23.37/4.77 % (10718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.37/4.77 % (10718)Termination reason: Unknown
% 23.37/4.77 % (10718)Termination phase: Property scanning
% 23.37/4.77
% 23.37/4.77 % (10718)Memory used [KB]: 2686
% 23.37/4.77 % (10718)Time elapsed: 0.032 s
% 23.37/4.77 % (10718)Instructions burned: 106 (million)
% 23.37/4.77 % (10718)------------------------------
% 23.37/4.77 % (10718)------------------------------
% 23.37/4.78 % (10720)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_10235 for (2968ds/715Mi)
% 24.29/4.83 % (10715)Instruction limit reached!
% 24.29/4.83 % (10715)------------------------------
% 24.29/4.83 % (10715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.29/4.83 % (10715)Termination reason: Unknown
% 24.29/4.83 % (10715)Termination phase: Saturation
% 24.29/4.83
% 24.29/4.83 % (10715)Memory used [KB]: 8571
% 24.29/4.83 % (10715)Time elapsed: 0.146 s
% 24.29/4.83 % (10715)Instructions burned: 474 (million)
% 24.29/4.83 % (10715)------------------------------
% 24.29/4.83 % (10715)------------------------------
% 24.29/4.84 % (10721)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_10235 for (2967ds/961Mi)
% 24.29/4.86 % (10719)Instruction limit reached!
% 24.29/4.86 % (10719)------------------------------
% 24.29/4.86 % (10719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.29/4.86 % (10719)Termination reason: Unknown
% 24.29/4.86 % (10719)Termination phase: Saturation
% 24.29/4.86
% 24.29/4.86 % (10719)Memory used [KB]: 7803
% 24.29/4.86 % (10719)Time elapsed: 0.115 s
% 24.29/4.86 % (10719)Instructions burned: 414 (million)
% 24.29/4.86 % (10719)------------------------------
% 24.29/4.86 % (10719)------------------------------
% 24.29/4.87 % (10722)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_10235 for (2967ds/1213Mi)
% 24.68/4.90 % (10717)Instruction limit reached!
% 24.68/4.90 % (10717)------------------------------
% 24.68/4.90 % (10717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.68/4.90 % (10717)Termination reason: Unknown
% 24.68/4.90 % (10717)Termination phase: Saturation
% 24.68/4.90
% 24.68/4.90 % (10717)Memory used [KB]: 8571
% 24.68/4.90 % (10717)Time elapsed: 0.172 s
% 24.68/4.90 % (10717)Instructions burned: 591 (million)
% 24.68/4.90 % (10717)------------------------------
% 24.68/4.90 % (10717)------------------------------
% 24.68/4.91 % (10723)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_10235 for (2967ds/1979Mi)
% 24.68/4.98 % (10713)Refutation not found, non-redundant clauses discarded% (10713)------------------------------
% 24.68/4.98 % (10713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.68/4.98 % (10713)Termination reason: Refutation not found, non-redundant clauses discarded
% 24.68/4.98
% 24.68/4.98 % (10713)Memory used [KB]: 9722
% 24.68/4.98 % (10713)Time elapsed: 0.412 s
% 24.68/4.98 % (10713)Instructions burned: 1299 (million)
% 24.68/4.98 % (10713)------------------------------
% 24.68/4.98 % (10713)------------------------------
% 24.68/4.99 % (10724)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_10235 for (2966ds/481Mi)
% 24.68/5.00 % (10720)Instruction limit reached!
% 24.68/5.00 % (10720)------------------------------
% 24.68/5.00 % (10720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.68/5.00 % (10720)Termination reason: Unknown
% 24.68/5.00 % (10720)Termination phase: Saturation
% 24.68/5.00
% 24.68/5.00 % (10720)Memory used [KB]: 4477
% 24.68/5.00 % (10720)Time elapsed: 0.221 s
% 24.68/5.00 % (10720)Instructions burned: 715 (million)
% 24.68/5.00 % (10720)------------------------------
% 24.68/5.00 % (10720)------------------------------
% 26.43/5.01 % (10725)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_10235 for (2966ds/783Mi)
% 27.06/5.13 % (10721)Instruction limit reached!
% 27.06/5.13 % (10721)------------------------------
% 27.06/5.13 % (10721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.06/5.13 % (10721)Termination reason: Unknown
% 27.06/5.13 % (10721)Termination phase: Saturation
% 27.06/5.13
% 27.06/5.13 % (10721)Memory used [KB]: 8315
% 27.06/5.13 % (10721)Time elapsed: 0.293 s
% 27.06/5.13 % (10721)Instructions burned: 962 (million)
% 27.06/5.13 % (10721)------------------------------
% 27.06/5.13 % (10721)------------------------------
% 27.06/5.13 % (10724)Instruction limit reached!
% 27.06/5.13 % (10724)------------------------------
% 27.06/5.13 % (10724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.06/5.13 % (10724)Termination reason: Unknown
% 27.06/5.13 % (10724)Termination phase: Saturation
% 27.06/5.13
% 27.06/5.13 % (10724)Memory used [KB]: 7931
% 27.06/5.13 % (10724)Time elapsed: 0.145 s
% 27.06/5.13 % (10724)Instructions burned: 483 (million)
% 27.06/5.13 % (10724)------------------------------
% 27.06/5.13 % (10724)------------------------------
% 27.06/5.14 % (10726)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_10235 for (2964ds/432Mi)
% 27.06/5.14 % (10727)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_10235 for (2964ds/1670Mi)
% 27.44/5.25 % (10722)Instruction limit reached!
% 27.44/5.25 % (10722)------------------------------
% 27.44/5.25 % (10722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.44/5.25 % (10722)Termination reason: Unknown
% 27.44/5.25 % (10722)Termination phase: Saturation
% 27.44/5.25
% 27.44/5.25 % (10722)Memory used [KB]: 9210
% 27.44/5.25 % (10722)Time elapsed: 0.376 s
% 27.44/5.25 % (10722)Instructions burned: 1215 (million)
% 27.44/5.25 % (10722)------------------------------
% 27.44/5.25 % (10722)------------------------------
% 27.44/5.25 % (10725)Instruction limit reached!
% 27.44/5.25 % (10725)------------------------------
% 27.44/5.25 % (10725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.44/5.25 % (10725)Termination reason: Unknown
% 27.44/5.25 % (10725)Termination phase: Saturation
% 27.44/5.25
% 27.44/5.25 % (10725)Memory used [KB]: 8571
% 27.44/5.25 % (10725)Time elapsed: 0.239 s
% 27.44/5.25 % (10725)Instructions burned: 785 (million)
% 27.44/5.25 % (10725)------------------------------
% 27.44/5.25 % (10725)------------------------------
% 27.44/5.26 % (10728)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_10235 for (2963ds/90Mi)
% 27.44/5.26 % (10729)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_10235 for (2963ds/346Mi)
% 27.44/5.27 % (10726)Instruction limit reached!
% 27.44/5.27 % (10726)------------------------------
% 27.44/5.27 % (10726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.44/5.27 % (10726)Termination reason: Unknown
% 27.44/5.27 % (10726)Termination phase: Saturation
% 27.44/5.27
% 27.44/5.27 % (10726)Memory used [KB]: 7803
% 27.44/5.27 % (10726)Time elapsed: 0.130 s
% 27.44/5.27 % (10726)Instructions burned: 432 (million)
% 27.44/5.27 % (10726)------------------------------
% 27.44/5.27 % (10726)------------------------------
% 27.44/5.28 % (10730)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_10235 for (2963ds/401Mi)
% 27.44/5.29 % (10728)Instruction limit reached!
% 27.44/5.29 % (10728)------------------------------
% 27.44/5.29 % (10728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.44/5.29 % (10728)Termination reason: Unknown
% 27.44/5.29 % (10728)Termination phase: Property scanning
% 27.44/5.29
% 27.44/5.29 % (10728)Memory used [KB]: 2558
% 27.44/5.29 % (10728)Time elapsed: 0.029 s
% 27.44/5.29 % (10728)Instructions burned: 93 (million)
% 27.44/5.29 % (10728)------------------------------
% 27.44/5.29 % (10728)------------------------------
% 28.22/5.30 % (10731)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_10235 for (2963ds/6454Mi)
% 28.22/5.37 % (10729)Instruction limit reached!
% 28.22/5.37 % (10729)------------------------------
% 28.22/5.37 % (10729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.22/5.37 % (10729)Termination reason: Unknown
% 28.22/5.37 % (10729)Termination phase: Saturation
% 28.22/5.37
% 28.22/5.37 % (10729)Memory used [KB]: 7803
% 28.22/5.37 % (10729)Time elapsed: 0.107 s
% 28.22/5.37 % (10729)Instructions burned: 346 (million)
% 28.22/5.37 % (10729)------------------------------
% 28.22/5.37 % (10729)------------------------------
% 28.22/5.38 % (10732)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_10235 for (2962ds/283Mi)
% 28.22/5.39 % (10730)Instruction limit reached!
% 28.22/5.39 % (10730)------------------------------
% 28.22/5.39 % (10730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.22/5.39 % (10730)Termination reason: Unknown
% 28.22/5.39 % (10730)Termination phase: Saturation
% 28.22/5.39
% 28.22/5.39 % (10730)Memory used [KB]: 8699
% 28.22/5.39 % (10730)Time elapsed: 0.114 s
% 28.22/5.39 % (10730)Instructions burned: 402 (million)
% 28.22/5.39 % (10730)------------------------------
% 28.22/5.39 % (10730)------------------------------
% 28.76/5.40 % (10733)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_10235 for (2962ds/865Mi)
% 28.76/5.47 % (10732)Instruction limit reached!
% 28.76/5.47 % (10732)------------------------------
% 28.76/5.47 % (10732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.76/5.47 % (10732)Termination reason: Unknown
% 28.76/5.47 % (10732)Termination phase: Saturation
% 28.76/5.47
% 28.76/5.47 % (10732)Memory used [KB]: 7931
% 28.76/5.47 % (10732)Time elapsed: 0.091 s
% 28.76/5.47 % (10732)Instructions burned: 283 (million)
% 28.76/5.47 % (10732)------------------------------
% 28.76/5.47 % (10732)------------------------------
% 28.76/5.48 % (10734)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_10235 for (2961ds/4528Mi)
% 29.16/5.50 % (10734)Refutation not found, incomplete strategy
% 29.16/5.50 % (10734)------------------------------
% 29.16/5.50 % (10734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.16/5.50 % (10734)Termination reason: Refutation not found, incomplete strategy
% 29.16/5.50
% 29.16/5.50
% 29.16/5.50 % (10734)Memory used [KB]: 2686
% 29.16/5.50 % (10734)Time elapsed: 0.029 s
% 29.16/5.50 % (10734)Instructions burned: 91 (million)
% 29.16/5.50 % (10734)------------------------------
% 29.16/5.50 % (10734)------------------------------
% 29.16/5.50 % (10723)Instruction limit reached!
% 29.16/5.50 % (10723)------------------------------
% 29.16/5.50 % (10723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.16/5.50 % (10723)Termination reason: Unknown
% 29.16/5.50 % (10723)Termination phase: Saturation
% 29.16/5.50
% 29.16/5.50 % (10723)Memory used [KB]: 8443
% 29.16/5.50 % (10723)Time elapsed: 0.597 s
% 29.16/5.50 % (10723)Instructions burned: 1980 (million)
% 29.16/5.50 % (10723)------------------------------
% 29.16/5.50 % (10723)------------------------------
% 29.16/5.51 % (10735)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_10235 for (2961ds/1001Mi)
% 29.16/5.51 % (10736)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_10235 for (2961ds/102Mi)
% 29.16/5.54 % (10736)Instruction limit reached!
% 29.16/5.54 % (10736)------------------------------
% 29.16/5.54 % (10736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.16/5.54 % (10736)Termination reason: Unknown
% 29.16/5.54 % (10736)Termination phase: Preprocessing 3
% 29.16/5.54
% 29.16/5.54 % (10736)Memory used [KB]: 2814
% 29.16/5.54 % (10736)Time elapsed: 0.029 s
% 29.16/5.54 % (10736)Instructions burned: 102 (million)
% 29.16/5.54 % (10736)------------------------------
% 29.16/5.54 % (10736)------------------------------
% 29.16/5.55 % (10737)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_10235 for (2960ds/952Mi)
% 29.45/5.60 % (10714)Instruction limit reached!
% 29.45/5.60 % (10714)------------------------------
% 29.45/5.60 % (10714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.45/5.60 % (10714)Termination reason: Unknown
% 29.45/5.60 % (10714)Termination phase: Saturation
% 29.45/5.60
% 29.45/5.60 % (10714)Memory used [KB]: 14072
% 29.45/5.60 % (10714)Time elapsed: 1.011 s
% 29.45/5.60 % (10714)Instructions burned: 3374 (million)
% 29.45/5.60 % (10714)------------------------------
% 29.45/5.60 % (10714)------------------------------
% 29.45/5.61 % (10738)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_10235 for (2960ds/578Mi)
% 29.45/5.63 % (10727)Instruction limit reached!
% 29.45/5.63 % (10727)------------------------------
% 29.45/5.63 % (10727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.45/5.63 % (10727)Termination reason: Unknown
% 29.45/5.63 % (10727)Termination phase: Saturation
% 29.45/5.63
% 29.45/5.63 % (10727)Memory used [KB]: 9978
% 29.45/5.63 % (10727)Time elapsed: 0.492 s
% 29.45/5.63 % (10727)Instructions burned: 1671 (million)
% 29.45/5.63 % (10727)------------------------------
% 29.45/5.63 % (10727)------------------------------
% 29.45/5.64 % (10739)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_10235 for (2959ds/643Mi)
% 29.45/5.67 % (10733)Instruction limit reached!
% 29.45/5.67 % (10733)------------------------------
% 29.45/5.67 % (10733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.45/5.67 % (10733)Termination reason: Unknown
% 29.45/5.67 % (10733)Termination phase: Saturation
% 29.45/5.67
% 29.45/5.67 % (10733)Memory used [KB]: 9850
% 29.45/5.67 % (10733)Time elapsed: 0.266 s
% 29.45/5.67 % (10733)Instructions burned: 867 (million)
% 29.45/5.67 % (10733)------------------------------
% 29.45/5.67 % (10733)------------------------------
% 29.45/5.68 % (10740)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_10235 for (2959ds/865Mi)
% 30.34/5.76 % (10687)Instruction limit reached!
% 30.34/5.76 % (10687)------------------------------
% 30.34/5.76 % (10687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.34/5.76 % (10687)Termination reason: Unknown
% 30.34/5.76 % (10687)Termination phase: Saturation
% 30.34/5.76
% 30.34/5.76 % (10687)Memory used [KB]: 15223
% 30.34/5.76 % (10687)Time elapsed: 2.452 s
% 30.34/5.76 % (10687)Instructions burned: 8252 (million)
% 30.34/5.76 % (10687)------------------------------
% 30.34/5.76 % (10687)------------------------------
% 30.34/5.77 % (10741)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_10235 for (2958ds/1174Mi)
% 30.34/5.78 % (10738)Instruction limit reached!
% 30.34/5.78 % (10738)------------------------------
% 30.34/5.78 % (10738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.34/5.78 % (10738)Termination reason: Unknown
% 30.34/5.78 % (10738)Termination phase: Saturation
% 30.34/5.78
% 30.34/5.78 % (10738)Memory used [KB]: 9210
% 30.34/5.78 % (10738)Time elapsed: 0.168 s
% 30.34/5.78 % (10738)Instructions burned: 578 (million)
% 30.34/5.78 % (10738)------------------------------
% 30.34/5.78 % (10738)------------------------------
% 30.34/5.79 % (10742)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_10235 for (2958ds/644Mi)
% 30.60/5.82 % (10739)Instruction limit reached!
% 30.60/5.82 % (10739)------------------------------
% 30.60/5.82 % (10739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.60/5.82 % (10739)Termination reason: Unknown
% 30.60/5.82 % (10739)Termination phase: Saturation
% 30.60/5.82
% 30.60/5.82 % (10739)Memory used [KB]: 9594
% 30.60/5.82 % (10739)Time elapsed: 0.183 s
% 30.60/5.82 % (10739)Instructions burned: 643 (million)
% 30.60/5.82 % (10739)------------------------------
% 30.60/5.82 % (10739)------------------------------
% 30.60/5.82 % (10735)Instruction limit reached!
% 30.60/5.82 % (10735)------------------------------
% 30.60/5.82 % (10735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.60/5.82 % (10735)Termination reason: Unknown
% 30.60/5.82 % (10735)Termination phase: Saturation
% 30.60/5.82
% 30.60/5.82 % (10735)Memory used [KB]: 9466
% 30.60/5.82 % (10735)Time elapsed: 0.311 s
% 30.60/5.82 % (10735)Instructions burned: 1002 (million)
% 30.60/5.82 % (10735)------------------------------
% 30.60/5.82 % (10735)------------------------------
% 30.60/5.83 % (10743)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_10235 for (2958ds/1201Mi)
% 30.60/5.83 % (10744)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_10235 for (2958ds/1046Mi)
% 30.60/5.84 % (10737)Instruction limit reached!
% 30.60/5.84 % (10737)------------------------------
% 30.60/5.84 % (10737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.60/5.84 % (10737)Termination reason: Unknown
% 30.60/5.84 % (10737)Termination phase: Saturation
% 30.60/5.84
% 30.60/5.84 % (10737)Memory used [KB]: 8827
% 30.60/5.84 % (10737)Time elapsed: 0.291 s
% 30.60/5.84 % (10737)Instructions burned: 954 (million)
% 30.60/5.84 % (10737)------------------------------
% 30.60/5.84 % (10737)------------------------------
% 30.60/5.85 % (10745)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_10235 for (2957ds/222Mi)
% 31.42/5.91 % (10745)Instruction limit reached!
% 31.42/5.91 % (10745)------------------------------
% 31.42/5.91 % (10745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.42/5.91 % (10745)Termination reason: Unknown
% 31.42/5.91 % (10745)Termination phase: Saturation
% 31.42/5.91
% 31.42/5.91 % (10745)Memory used [KB]: 7419
% 31.42/5.91 % (10745)Time elapsed: 0.061 s
% 31.42/5.91 % (10745)Instructions burned: 224 (million)
% 31.42/5.91 % (10745)------------------------------
% 31.42/5.91 % (10745)------------------------------
% 31.42/5.92 % (10746)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_10235 for (2957ds/68Mi)
% 31.42/5.94 % (10740)Instruction limit reached!
% 31.42/5.94 % (10740)------------------------------
% 31.42/5.94 % (10740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.42/5.94 % (10740)Termination reason: Unknown
% 31.42/5.94 % (10740)Termination phase: Saturation
% 31.42/5.94
% 31.42/5.94 % (10740)Memory used [KB]: 9850
% 31.42/5.94 % (10740)Time elapsed: 0.265 s
% 31.42/5.94 % (10740)Instructions burned: 865 (million)
% 31.42/5.94 % (10740)------------------------------
% 31.42/5.94 % (10740)------------------------------
% 31.42/5.94 % (10746)Instruction limit reached!
% 31.42/5.94 % (10746)------------------------------
% 31.42/5.94 % (10746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.42/5.94 % (10746)Termination reason: Unknown
% 31.42/5.94 % (10746)Termination phase: Preprocessing 3
% 31.42/5.94
% 31.42/5.94 % (10746)Memory used [KB]: 2302
% 31.42/5.94 % (10746)Time elapsed: 0.023 s
% 31.42/5.94 % (10746)Instructions burned: 68 (million)
% 31.42/5.94 % (10746)------------------------------
% 31.42/5.94 % (10746)------------------------------
% 31.42/5.95 % (10747)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_10235 for (2956ds/454Mi)
% 31.42/5.95 % (10748)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_10235 for (2956ds/360Mi)
% 31.42/5.99 % (10742)Instruction limit reached!
% 31.42/5.99 % (10742)------------------------------
% 31.42/5.99 % (10742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.42/5.99 % (10742)Termination reason: Unknown
% 31.42/5.99 % (10742)Termination phase: Saturation
% 31.42/5.99
% 31.42/5.99 % (10742)Memory used [KB]: 9850
% 31.42/5.99 % (10742)Time elapsed: 0.197 s
% 31.42/5.99 % (10742)Instructions burned: 644 (million)
% 31.42/5.99 % (10742)------------------------------
% 31.42/5.99 % (10742)------------------------------
% 31.42/6.00 % (10749)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_10235 for (2956ds/157Mi)
% 33.44/6.04 % (10749)Instruction limit reached!
% 33.44/6.04 % (10749)------------------------------
% 33.44/6.04 % (10749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.44/6.04 % (10749)Termination reason: Unknown
% 33.44/6.04 % (10749)Termination phase: Property scanning
% 33.44/6.04
% 33.44/6.04 % (10749)Memory used [KB]: 2814
% 33.44/6.04 % (10749)Time elapsed: 0.046 s
% 33.44/6.04 % (10749)Instructions burned: 160 (million)
% 33.44/6.04 % (10749)------------------------------
% 33.44/6.04 % (10749)------------------------------
% 33.44/6.05 % (10750)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_10235 for (2955ds/5061Mi)
% 33.44/6.05 % (10748)Instruction limit reached!
% 33.44/6.05 % (10748)------------------------------
% 33.44/6.05 % (10748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.44/6.05 % (10748)Termination reason: Unknown
% 33.44/6.05 % (10748)Termination phase: Saturation
% 33.44/6.05
% 33.44/6.05 % (10748)Memory used [KB]: 8443
% 33.44/6.05 % (10748)Time elapsed: 0.100 s
% 33.44/6.05 % (10748)Instructions burned: 360 (million)
% 33.44/6.05 % (10748)------------------------------
% 33.44/6.05 % (10748)------------------------------
% 33.44/6.06 % (10751)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_10235 for (2955ds/2401Mi)
% 33.44/6.08 % (10747)Instruction limit reached!
% 33.44/6.08 % (10747)------------------------------
% 33.44/6.08 % (10747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.44/6.08 % (10747)Termination reason: Unknown
% 33.44/6.08 % (10747)Termination phase: Saturation
% 33.44/6.08
% 33.44/6.08 % (10747)Memory used [KB]: 13176
% 33.44/6.08 % (10747)Time elapsed: 0.132 s
% 33.44/6.08 % (10747)Instructions burned: 455 (million)
% 33.44/6.08 % (10747)------------------------------
% 33.44/6.08 % (10747)------------------------------
% 33.44/6.09 % (10752)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_10235 for (2955ds/5798Mi)
% 34.01/6.14 % (10741)Instruction limit reached!
% 34.01/6.14 % (10741)------------------------------
% 34.01/6.14 % (10741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.01/6.14 % (10741)Termination reason: Unknown
% 34.01/6.14 % (10741)Termination phase: Saturation
% 34.01/6.14
% 34.01/6.14 % (10741)Memory used [KB]: 10234
% 34.01/6.14 % (10741)Time elapsed: 0.368 s
% 34.01/6.14 % (10741)Instructions burned: 1175 (million)
% 34.01/6.14 % (10741)------------------------------
% 34.01/6.14 % (10741)------------------------------
% 34.01/6.14 % (10744)Instruction limit reached!
% 34.01/6.14 % (10744)------------------------------
% 34.01/6.14 % (10744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.01/6.14 % (10744)Termination reason: Unknown
% 34.01/6.14 % (10744)Termination phase: Saturation
% 34.01/6.14
% 34.01/6.14 % (10744)Memory used [KB]: 7803
% 34.01/6.14 % (10744)Time elapsed: 0.310 s
% 34.01/6.14 % (10744)Instructions burned: 1046 (million)
% 34.01/6.14 % (10744)------------------------------
% 34.01/6.14 % (10744)------------------------------
% 34.01/6.15 % (10753)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_10235 for (2954ds/346Mi)
% 34.01/6.15 % (10754)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_10235 for (2954ds/1321Mi)
% 34.01/6.19 % (10743)Instruction limit reached!
% 34.01/6.19 % (10743)------------------------------
% 34.01/6.19 % (10743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.01/6.19 % (10743)Termination reason: Unknown
% 34.01/6.19 % (10743)Termination phase: Saturation
% 34.01/6.19
% 34.01/6.19 % (10743)Memory used [KB]: 9594
% 34.01/6.19 % (10743)Time elapsed: 0.362 s
% 34.01/6.19 % (10743)Instructions burned: 1202 (million)
% 34.01/6.19 % (10743)------------------------------
% 34.01/6.19 % (10743)------------------------------
% 34.27/6.20 % (10755)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_10235 for (2954ds/1312Mi)
% 34.27/6.25 % (10753)Instruction limit reached!
% 34.27/6.25 % (10753)------------------------------
% 34.27/6.25 % (10753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.27/6.25 % (10753)Termination reason: Unknown
% 34.27/6.25 % (10753)Termination phase: Saturation
% 34.27/6.25
% 34.27/6.25 % (10753)Memory used [KB]: 7803
% 34.27/6.25 % (10753)Time elapsed: 0.107 s
% 34.27/6.25 % (10753)Instructions burned: 348 (million)
% 34.27/6.25 % (10753)------------------------------
% 34.27/6.25 % (10753)------------------------------
% 34.27/6.26 % (10756)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_10235 for (2953ds/672Mi)
% 34.27/6.28 % (10754)Refutation not found, incomplete strategy
% 34.27/6.28 % (10754)------------------------------
% 34.27/6.28 % (10754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.27/6.28 % (10754)Termination reason: Refutation not found, incomplete strategy
% 34.27/6.28
% 34.27/6.28
% 34.27/6.28 % (10754)Memory used [KB]: 4221
% 34.27/6.28 % (10754)Time elapsed: 0.127 s
% 34.27/6.28 % (10754)Instructions burned: 417 (million)
% 34.27/6.28 % (10754)------------------------------
% 34.27/6.28 % (10754)------------------------------
% 34.27/6.29 % (10757)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_10235 for (2953ds/1897Mi)
% 34.71/6.47 % (10756)Instruction limit reached!
% 34.71/6.47 % (10756)------------------------------
% 34.71/6.47 % (10756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.71/6.47 % (10756)Termination reason: Unknown
% 34.71/6.47 % (10756)Termination phase: Saturation
% 34.71/6.47
% 34.71/6.47 % (10756)Memory used [KB]: 8955
% 34.71/6.47 % (10756)Time elapsed: 0.206 s
% 34.71/6.47 % (10756)Instructions burned: 673 (million)
% 34.71/6.47 % (10756)------------------------------
% 34.71/6.47 % (10756)------------------------------
% 34.71/6.48 % (10758)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_10235 for (2951ds/1202Mi)
% 35.03/6.59 % (10755)Instruction limit reached!
% 35.03/6.59 % (10755)------------------------------
% 35.03/6.59 % (10755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.03/6.59 % (10755)Termination reason: Unknown
% 35.03/6.59 % (10755)Termination phase: Saturation
% 35.03/6.59
% 35.03/6.59 % (10755)Memory used [KB]: 9722
% 35.03/6.59 % (10755)Time elapsed: 0.391 s
% 35.03/6.59 % (10755)Instructions burned: 1312 (million)
% 35.03/6.59 % (10755)------------------------------
% 35.03/6.59 % (10755)------------------------------
% 35.53/6.60 % (10759)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_10235 for (2950ds/1493Mi)
% 35.73/6.80 % (10751)Instruction limit reached!
% 35.73/6.80 % (10751)------------------------------
% 35.73/6.80 % (10751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.73/6.80 % (10751)Termination reason: Unknown
% 35.73/6.80 % (10751)Termination phase: Saturation
% 35.73/6.80
% 35.73/6.80 % (10751)Memory used [KB]: 10362
% 35.73/6.80 % (10751)Time elapsed: 0.744 s
% 35.73/6.80 % (10751)Instructions burned: 2403 (million)
% 35.73/6.80 % (10751)------------------------------
% 35.73/6.80 % (10751)------------------------------
% 35.73/6.81 % (10760)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_10235 for (2948ds/7679Mi)
% 35.73/6.84 % (10758)Instruction limit reached!
% 35.73/6.84 % (10758)------------------------------
% 35.73/6.84 % (10758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.73/6.84 % (10758)Termination reason: Unknown
% 35.73/6.84 % (10758)Termination phase: Saturation
% 35.73/6.84
% 35.73/6.84 % (10758)Memory used [KB]: 4989
% 35.73/6.84 % (10758)Time elapsed: 0.361 s
% 35.73/6.84 % (10758)Instructions burned: 1205 (million)
% 35.73/6.84 % (10758)------------------------------
% 35.73/6.84 % (10758)------------------------------
% 35.73/6.85 % (10761)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_10235 for (2947ds/340Mi)
% 35.73/6.87 % (10757)Instruction limit reached!
% 35.73/6.87 % (10757)------------------------------
% 35.73/6.87 % (10757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.73/6.87 % (10757)Termination reason: Unknown
% 35.73/6.87 % (10757)Termination phase: Saturation
% 35.73/6.87
% 35.73/6.87 % (10757)Memory used [KB]: 11257
% 35.73/6.87 % (10757)Time elapsed: 0.582 s
% 35.73/6.87 % (10757)Instructions burned: 1899 (million)
% 35.73/6.87 % (10757)------------------------------
% 35.73/6.87 % (10757)------------------------------
% 35.73/6.88 % (10762)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_10235 for (2947ds/3672Mi)
% 37.55/6.95 % (10761)Instruction limit reached!
% 37.55/6.95 % (10761)------------------------------
% 37.55/6.95 % (10761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.55/6.95 % (10761)Termination reason: Unknown
% 37.55/6.95 % (10761)Termination phase: Saturation
% 37.55/6.95
% 37.55/6.95 % (10761)Memory used [KB]: 8827
% 37.55/6.95 % (10761)Time elapsed: 0.101 s
% 37.55/6.95 % (10761)Instructions burned: 343 (million)
% 37.55/6.95 % (10761)------------------------------
% 37.55/6.95 % (10761)------------------------------
% 37.55/6.96 % (10763)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_10235 for (2946ds/1535Mi)
% 37.55/7.00 % (10759)Instruction limit reached!
% 37.55/7.00 % (10759)------------------------------
% 37.55/7.00 % (10759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.55/7.00 % (10759)Termination reason: Unknown
% 37.55/7.00 % (10759)Termination phase: Saturation
% 37.55/7.00
% 37.55/7.00 % (10759)Memory used [KB]: 9210
% 37.55/7.00 % (10759)Time elapsed: 0.402 s
% 37.55/7.00 % (10759)Instructions burned: 1494 (million)
% 37.55/7.00 % (10759)------------------------------
% 37.55/7.00 % (10759)------------------------------
% 40.44/7.01 % (10764)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_10235 for (2946ds/4637Mi)
% 41.56/7.27 % (10731)Refutation not found, non-redundant clauses discarded% (10731)------------------------------
% 41.56/7.27 % (10731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.56/7.27 % (10731)Termination reason: Refutation not found, non-redundant clauses discarded
% 41.56/7.27
% 41.56/7.27 % (10731)Memory used [KB]: 11513
% 41.56/7.27 % (10731)Time elapsed: 1.972 s
% 41.56/7.27 % (10731)Instructions burned: 6358 (million)
% 41.56/7.27 % (10731)------------------------------
% 41.56/7.27 % (10731)------------------------------
% 41.56/7.28 % (10765)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_10235 for (2943ds/3174Mi)
% 42.65/7.41 % (10763)Instruction limit reached!
% 42.65/7.41 % (10763)------------------------------
% 42.65/7.41 % (10763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.65/7.41 % (10763)Termination reason: Unknown
% 42.65/7.41 % (10763)Termination phase: Saturation
% 42.65/7.41
% 42.65/7.41 % (10763)Memory used [KB]: 12537
% 42.65/7.41 % (10763)Time elapsed: 0.451 s
% 42.65/7.41 % (10763)Instructions burned: 1536 (million)
% 42.65/7.41 % (10763)------------------------------
% 42.65/7.41 % (10763)------------------------------
% 42.65/7.42 % (10766)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_10235 for (2942ds/307Mi)
% 43.06/7.50 % (10766)Instruction limit reached!
% 43.06/7.50 % (10766)------------------------------
% 43.06/7.50 % (10766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.06/7.50 % (10766)Termination reason: Unknown
% 43.06/7.50 % (10766)Termination phase: Saturation
% 43.06/7.50
% 43.06/7.50 % (10766)Memory used [KB]: 7547
% 43.06/7.50 % (10766)Time elapsed: 0.084 s
% 43.06/7.50 % (10766)Instructions burned: 308 (million)
% 43.06/7.50 % (10766)------------------------------
% 43.06/7.50 % (10766)------------------------------
% 43.06/7.51 % (10767)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_10235 for (2941ds/3619Mi)
% 43.06/7.56 % (10767)Refutation not found, incomplete strategy
% 43.06/7.56 % (10767)------------------------------
% 43.06/7.56 % (10767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.06/7.56 % (10767)Termination reason: Refutation not found, incomplete strategy
% 43.06/7.56
% 43.06/7.56
% 43.06/7.56 % (10767)Memory used [KB]: 7803
% 43.06/7.56 % (10767)Time elapsed: 0.052 s
% 43.06/7.56 % (10767)Instructions burned: 173 (million)
% 43.06/7.56 % (10767)------------------------------
% 43.06/7.56 % (10767)------------------------------
% 43.06/7.57 % (10768)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_10235 for (2940ds/2325Mi)
% 43.06/7.57 % (10750)Instruction limit reached!
% 43.06/7.57 % (10750)------------------------------
% 43.06/7.57 % (10750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.06/7.57 % (10750)Termination reason: Unknown
% 43.06/7.57 % (10750)Termination phase: Saturation
% 43.06/7.57
% 43.06/7.57 % (10750)Memory used [KB]: 16886
% 43.06/7.57 % (10750)Time elapsed: 1.524 s
% 43.06/7.57 % (10750)Instructions burned: 5061 (million)
% 43.06/7.57 % (10750)------------------------------
% 43.06/7.57 % (10750)------------------------------
% 43.06/7.58 % (10769)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_10235 for (2940ds/2341Mi)
% 44.21/7.85 % (10752)Instruction limit reached!
% 44.21/7.85 % (10752)------------------------------
% 44.21/7.85 % (10752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.21/7.85 % (10752)Termination reason: Unknown
% 44.21/7.85 % (10752)Termination phase: Saturation
% 44.21/7.85
% 44.21/7.85 % (10752)Memory used [KB]: 13688
% 44.21/7.85 % (10752)Time elapsed: 1.760 s
% 44.21/7.85 % (10752)Instructions burned: 5799 (million)
% 44.21/7.85 % (10752)------------------------------
% 44.21/7.85 % (10752)------------------------------
% 44.21/7.86 % (10770)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_10235 for (2937ds/7257Mi)
% 44.21/7.89 % (10768)Refutation not found, non-redundant clauses discarded% (10768)------------------------------
% 44.21/7.89 % (10768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.21/7.89 % (10768)Termination reason: Refutation not found, non-redundant clauses discarded
% 44.21/7.89
% 44.21/7.89 % (10768)Memory used [KB]: 9594
% 44.21/7.89 % (10768)Time elapsed: 0.343 s
% 44.21/7.89 % (10768)Instructions burned: 1085 (million)
% 44.21/7.89 % (10768)------------------------------
% 44.21/7.89 % (10768)------------------------------
% 44.79/7.90 % (10771)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_10235 for (2937ds/3710Mi)
% 44.79/7.95 % (10762)Instruction limit reached!
% 44.79/7.95 % (10762)------------------------------
% 44.79/7.95 % (10762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.79/7.95 % (10762)Termination reason: Unknown
% 44.79/7.95 % (10762)Termination phase: Saturation
% 44.79/7.95
% 44.79/7.95 % (10762)Memory used [KB]: 11641
% 44.79/7.95 % (10762)Time elapsed: 1.070 s
% 44.79/7.95 % (10762)Instructions burned: 3674 (million)
% 44.79/7.95 % (10762)------------------------------
% 44.79/7.95 % (10762)------------------------------
% 44.79/7.96 % (10772)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_10235 for (2936ds/326Mi)
% 47.44/8.05 % (10772)Instruction limit reached!
% 47.44/8.05 % (10772)------------------------------
% 47.44/8.05 % (10772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.44/8.05 % (10772)Termination reason: Unknown
% 47.44/8.05 % (10772)Termination phase: Saturation
% 47.44/8.05
% 47.44/8.05 % (10772)Memory used [KB]: 7291
% 47.44/8.05 % (10772)Time elapsed: 0.119 s
% 47.44/8.05 % (10772)Instructions burned: 326 (million)
% 47.44/8.05 % (10772)------------------------------
% 47.44/8.05 % (10772)------------------------------
% 47.44/8.06 % (10773)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_10235 for (2935ds/1100Mi)
% 48.63/8.23 % (10765)Instruction limit reached!
% 48.63/8.23 % (10765)------------------------------
% 48.63/8.23 % (10765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.63/8.23 % (10765)Termination reason: Unknown
% 48.63/8.23 % (10765)Termination phase: Saturation
% 48.63/8.23
% 48.63/8.23 % (10765)Memory used [KB]: 14200
% 48.63/8.23 % (10765)Time elapsed: 0.949 s
% 48.63/8.23 % (10765)Instructions burned: 3175 (million)
% 48.63/8.23 % (10765)------------------------------
% 48.63/8.23 % (10765)------------------------------
% 48.63/8.24 % (10774)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_10235 for (2934ds/406Mi)
% 48.63/8.27 % (10769)Instruction limit reached!
% 48.63/8.27 % (10769)------------------------------
% 48.63/8.27 % (10769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.63/8.27 % (10769)Termination reason: Unknown
% 48.63/8.27 % (10769)Termination phase: Saturation
% 48.63/8.27
% 48.63/8.27 % (10769)Memory used [KB]: 9850
% 48.63/8.27 % (10769)Time elapsed: 0.707 s
% 48.63/8.27 % (10769)Instructions burned: 2341 (million)
% 48.63/8.27 % (10769)------------------------------
% 48.63/8.27 % (10769)------------------------------
% 48.63/8.28 % (10775)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_10235 for (2933ds/1871Mi)
% 49.14/8.36 % (10774)Instruction limit reached!
% 49.14/8.36 % (10774)------------------------------
% 49.14/8.36 % (10774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.14/8.36 % (10774)Termination reason: Unknown
% 49.14/8.36 % (10774)Termination phase: Saturation
% 49.14/8.36
% 49.14/8.36 % (10774)Memory used [KB]: 8443
% 49.14/8.36 % (10774)Time elapsed: 0.122 s
% 49.14/8.36 % (10774)Instructions burned: 407 (million)
% 49.14/8.36 % (10774)------------------------------
% 49.14/8.36 % (10774)------------------------------
% 49.14/8.37 % (10776)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_10235 for (2932ds/1194Mi)
% 49.14/8.39 % (10773)Instruction limit reached!
% 49.14/8.39 % (10773)------------------------------
% 49.14/8.39 % (10773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.14/8.39 % (10773)Termination reason: Unknown
% 49.14/8.39 % (10773)Termination phase: Saturation
% 49.14/8.39
% 49.14/8.39 % (10773)Memory used [KB]: 9978
% 49.14/8.39 % (10773)Time elapsed: 0.330 s
% 49.14/8.39 % (10773)Instructions burned: 1102 (million)
% 49.14/8.39 % (10773)------------------------------
% 49.14/8.39 % (10773)------------------------------
% 50.01/8.40 % (10777)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_10235 for (2932ds/474Mi)
% 50.01/8.41 % (10764)Instruction limit reached!
% 50.01/8.41 % (10764)------------------------------
% 50.01/8.41 % (10764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.01/8.41 % (10764)Termination reason: Unknown
% 50.01/8.41 % (10764)Termination phase: Saturation
% 50.01/8.41
% 50.01/8.41 % (10764)Memory used [KB]: 13816
% 50.01/8.41 % (10764)Time elapsed: 1.401 s
% 50.01/8.41 % (10764)Instructions burned: 4638 (million)
% 50.01/8.41 % (10764)------------------------------
% 50.01/8.41 % (10764)------------------------------
% 50.01/8.42 % (10778)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_10235 for (2931ds/3115Mi)
% 50.34/8.55 % (10777)Instruction limit reached!
% 50.34/8.55 % (10777)------------------------------
% 50.34/8.55 % (10777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.34/8.55 % (10777)Termination reason: Unknown
% 50.34/8.55 % (10777)Termination phase: Saturation
% 50.34/8.55
% 50.34/8.55 % (10777)Memory used [KB]: 8571
% 50.34/8.55 % (10777)Time elapsed: 0.144 s
% 50.34/8.55 % (10777)Instructions burned: 476 (million)
% 50.34/8.55 % (10777)------------------------------
% 50.34/8.55 % (10777)------------------------------
% 50.34/8.56 % (10779)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_10235 for (2930ds/831Mi)
% 51.10/8.72 % (10776)Instruction limit reached!
% 51.10/8.72 % (10776)------------------------------
% 51.10/8.72 % (10776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.10/8.72 % (10776)Termination reason: Unknown
% 51.10/8.72 % (10776)Termination phase: Saturation
% 51.10/8.72
% 51.10/8.72 % (10776)Memory used [KB]: 8827
% 51.10/8.72 % (10776)Time elapsed: 0.376 s
% 51.10/8.72 % (10776)Instructions burned: 1196 (million)
% 51.10/8.72 % (10776)------------------------------
% 51.10/8.72 % (10776)------------------------------
% 51.10/8.73 % (10780)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_10235 for (2928ds/1188Mi)
% 51.75/8.80 % (10779)Instruction limit reached!
% 51.75/8.80 % (10779)------------------------------
% 51.75/8.80 % (10779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.75/8.80 % (10779)Termination reason: Unknown
% 51.75/8.80 % (10779)Termination phase: Saturation
% 51.75/8.80
% 51.75/8.80 % (10779)Memory used [KB]: 9978
% 51.75/8.80 % (10779)Time elapsed: 0.247 s
% 51.75/8.80 % (10779)Instructions burned: 831 (million)
% 51.75/8.80 % (10779)------------------------------
% 51.75/8.80 % (10779)------------------------------
% 51.75/8.81 % (10781)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_10235 for (2928ds/2868Mi)
% 51.75/8.84 % (10775)Instruction limit reached!
% 51.75/8.84 % (10775)------------------------------
% 51.75/8.84 % (10775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.75/8.84 % (10775)Termination reason: Unknown
% 51.75/8.84 % (10775)Termination phase: Saturation
% 51.75/8.84
% 51.75/8.84 % (10775)Memory used [KB]: 13304
% 51.75/8.84 % (10775)Time elapsed: 0.589 s
% 51.75/8.84 % (10775)Instructions burned: 1872 (million)
% 51.75/8.84 % (10775)------------------------------
% 51.75/8.84 % (10775)------------------------------
% 51.75/8.85 % (10782)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_10235 for (2927ds/1516Mi)
% 52.88/8.98 % (10771)Instruction limit reached!
% 52.88/8.98 % (10771)------------------------------
% 52.88/8.98 % (10771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.88/8.98 % (10771)Termination reason: Unknown
% 52.88/8.98 % (10771)Termination phase: Saturation
% 52.88/8.98
% 52.88/8.98 % (10771)Memory used [KB]: 20980
% 52.88/8.98 % (10771)Time elapsed: 1.106 s
% 52.88/8.98 % (10771)Instructions burned: 3711 (million)
% 52.88/8.98 % (10771)------------------------------
% 52.88/8.98 % (10771)------------------------------
% 52.88/8.99 % (10783)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_10235 for (2926ds/2321Mi)
% 54.46/9.08 % (10760)Instruction limit reached!
% 54.46/9.08 % (10760)------------------------------
% 54.46/9.08 % (10760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.46/9.08 % (10760)Termination reason: Unknown
% 54.46/9.08 % (10760)Termination phase: Saturation
% 54.46/9.08
% 54.46/9.08 % (10760)Memory used [KB]: 14711
% 54.46/9.08 % (10760)Time elapsed: 2.267 s
% 54.46/9.08 % (10760)Instructions burned: 7682 (million)
% 54.46/9.08 % (10760)------------------------------
% 54.46/9.08 % (10760)------------------------------
% 54.46/9.09 % (10784)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_10235 for (2925ds/2812Mi)
% 54.46/9.10 % (10780)Instruction limit reached!
% 54.46/9.10 % (10780)------------------------------
% 54.46/9.10 % (10780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.46/9.10 % (10780)Termination reason: Unknown
% 54.46/9.10 % (10780)Termination phase: Saturation
% 54.46/9.10
% 54.46/9.10 % (10780)Memory used [KB]: 9978
% 54.46/9.10 % (10780)Time elapsed: 0.368 s
% 54.46/9.10 % (10780)Instructions burned: 1190 (million)
% 54.46/9.10 % (10780)------------------------------
% 54.46/9.10 % (10780)------------------------------
% 54.46/9.11 % (10785)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_10235 for (2925ds/4604Mi)
% 56.04/9.31 % (10782)Instruction limit reached!
% 56.04/9.31 % (10782)------------------------------
% 56.04/9.31 % (10782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.04/9.31 % (10782)Termination reason: Unknown
% 56.04/9.31 % (10782)Termination phase: Saturation
% 56.04/9.31
% 56.04/9.31 % (10782)Memory used [KB]: 9722
% 56.04/9.31 % (10782)Time elapsed: 0.458 s
% 56.04/9.31 % (10782)Instructions burned: 1518 (million)
% 56.04/9.31 % (10782)------------------------------
% 56.04/9.31 % (10782)------------------------------
% 56.04/9.32 % (10786)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_10235 for (2923ds/2678Mi)
% 56.04/9.35 % (10778)Instruction limit reached!
% 56.04/9.35 % (10778)------------------------------
% 56.04/9.35 % (10778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.04/9.35 % (10778)Termination reason: Unknown
% 56.04/9.35 % (10778)Termination phase: Saturation
% 56.04/9.35
% 56.04/9.35 % (10778)Memory used [KB]: 12792
% 56.04/9.35 % (10778)Time elapsed: 0.924 s
% 56.04/9.35 % (10778)Instructions burned: 3117 (million)
% 56.04/9.35 % (10778)------------------------------
% 56.04/9.35 % (10778)------------------------------
% 56.04/9.36 % (10787)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_10235 for (2922ds/643Mi)
% 56.75/9.53 % (10783)Refutation not found, non-redundant clauses discarded% (10783)------------------------------
% 56.75/9.53 % (10783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.75/9.53 % (10783)Termination reason: Refutation not found, non-redundant clauses discarded
% 56.75/9.53
% 56.75/9.53 % (10783)Memory used [KB]: 11897
% 56.75/9.53 % (10783)Time elapsed: 0.540 s
% 56.75/9.53 % (10783)Instructions burned: 1924 (million)
% 56.75/9.53 % (10783)------------------------------
% 56.75/9.53 % (10783)------------------------------
% 56.75/9.54 % (10787)Instruction limit reached!
% 56.75/9.54 % (10787)------------------------------
% 56.75/9.54 % (10787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.75/9.54 % (10787)Termination reason: Unknown
% 56.75/9.54 % (10787)Termination phase: Saturation
% 56.75/9.54
% 56.75/9.54 % (10787)Memory used [KB]: 9594
% 56.75/9.54 % (10787)Time elapsed: 0.179 s
% 56.75/9.54 % (10787)Instructions burned: 644 (million)
% 56.75/9.54 % (10787)------------------------------
% 56.75/9.54 % (10787)------------------------------
% 56.75/9.54 % (10788)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_10235 for (2920ds/458Mi)
% 56.75/9.55 % (10789)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_10235 for (2920ds/2546Mi)
% 56.75/9.55 % (10781)Instruction limit reached!
% 56.75/9.55 % (10781)------------------------------
% 56.75/9.55 % (10781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.75/9.55 % (10781)Termination reason: Unknown
% 56.75/9.55 % (10781)Termination phase: Saturation
% 56.75/9.55
% 56.75/9.55 % (10781)Memory used [KB]: 13944
% 56.75/9.55 % (10781)Time elapsed: 0.743 s
% 56.75/9.55 % (10781)Instructions burned: 2870 (million)
% 56.75/9.55 % (10781)------------------------------
% 56.75/9.55 % (10781)------------------------------
% 56.75/9.56 % (10790)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_10235 for (2920ds/1432Mi)
% 57.15/9.67 % (10788)Instruction limit reached!
% 57.15/9.67 % (10788)------------------------------
% 57.15/9.67 % (10788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.15/9.67 % (10788)Termination reason: Unknown
% 57.15/9.67 % (10788)Termination phase: Saturation
% 57.15/9.67
% 57.15/9.67 % (10788)Memory used [KB]: 7675
% 57.15/9.67 % (10788)Time elapsed: 0.129 s
% 57.15/9.67 % (10788)Instructions burned: 461 (million)
% 57.15/9.67 % (10788)------------------------------
% 57.15/9.67 % (10788)------------------------------
% 57.15/9.68 % (10791)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_10235 for (2919ds/386Mi)
% 57.39/9.79 % (10791)Instruction limit reached!
% 57.39/9.79 % (10791)------------------------------
% 57.39/9.79 % (10791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.39/9.79 % (10791)Termination reason: Unknown
% 57.39/9.79 % (10791)Termination phase: Saturation
% 57.39/9.79
% 57.39/9.79 % (10791)Memory used [KB]: 8699
% 57.39/9.79 % (10791)Time elapsed: 0.106 s
% 57.39/9.79 % (10791)Instructions burned: 388 (million)
% 57.39/9.79 % (10791)------------------------------
% 57.39/9.79 % (10791)------------------------------
% 57.60/9.80 % (10792)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_10235 for (2918ds/360Mi)
% 57.60/9.82 % (10770)Instruction limit reached!
% 57.60/9.82 % (10770)------------------------------
% 57.60/9.82 % (10770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.60/9.82 % (10770)Termination reason: Unknown
% 57.60/9.82 % (10770)Termination phase: Saturation
% 57.60/9.82
% 57.60/9.82 % (10770)Memory used [KB]: 18549
% 57.60/9.82 % (10770)Time elapsed: 1.980 s
% 57.60/9.82 % (10770)Instructions burned: 7260 (million)
% 57.60/9.82 % (10770)------------------------------
% 57.60/9.82 % (10770)------------------------------
% 57.60/9.83 % (10793)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_10235 for (2918ds/5446Mi)
% 57.60/9.89 % (10792)Instruction limit reached!
% 57.60/9.89 % (10792)------------------------------
% 57.60/9.89 % (10792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.60/9.89 % (10792)Termination reason: Unknown
% 57.60/9.89 % (10792)Termination phase: Saturation
% 57.60/9.89
% 57.60/9.89 % (10792)Memory used [KB]: 7803
% 57.60/9.89 % (10792)Time elapsed: 0.098 s
% 57.60/9.89 % (10792)Instructions burned: 360 (million)
% 57.60/9.89 % (10792)------------------------------
% 57.60/9.89 % (10792)------------------------------
% 57.75/9.90 % (10794)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_10235 for (2917ds/2573Mi)
% 57.75/9.96 % (10784)Instruction limit reached!
% 57.75/9.96 % (10784)------------------------------
% 57.75/9.96 % (10784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.75/9.96 % (10784)Termination reason: Unknown
% 57.75/9.96 % (10784)Termination phase: Saturation
% 57.75/9.96
% 57.75/9.96 % (10784)Memory used [KB]: 11385
% 57.75/9.96 % (10784)Time elapsed: 0.866 s
% 57.75/9.96 % (10784)Instructions burned: 2814 (million)
% 57.75/9.96 % (10784)------------------------------
% 57.75/9.96 % (10784)------------------------------
% 57.75/9.97 % (10795)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_10235 for (2916ds/2655Mi)
% 57.75/9.98 % (10790)Instruction limit reached!
% 57.75/9.98 % (10790)------------------------------
% 57.75/9.98 % (10790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.75/9.98 % (10790)Termination reason: Unknown
% 57.75/9.98 % (10790)Termination phase: Saturation
% 57.75/9.98
% 57.75/9.98 % (10790)Memory used [KB]: 12281
% 57.75/9.98 % (10790)Time elapsed: 0.422 s
% 57.75/9.98 % (10790)Instructions burned: 1432 (million)
% 57.75/9.98 % (10790)------------------------------
% 57.75/9.98 % (10790)------------------------------
% 57.75/9.99 % (10796)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_10235 for (2916ds/2781Mi)
% 61.46/10.09 % (10786)Instruction limit reached!
% 61.46/10.09 % (10786)------------------------------
% 61.46/10.09 % (10786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.46/10.09 % (10786)Termination reason: Unknown
% 61.46/10.09 % (10786)Termination phase: Saturation
% 61.46/10.09
% 61.46/10.09 % (10786)Memory used [KB]: 12153
% 61.46/10.09 % (10786)Time elapsed: 0.776 s
% 61.46/10.09 % (10786)Instructions burned: 2678 (million)
% 61.46/10.09 % (10786)------------------------------
% 61.46/10.09 % (10786)------------------------------
% 61.46/10.10 % (10797)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_10235 for (2915ds/307Mi)
% 62.18/10.19 % (10797)Instruction limit reached!
% 62.18/10.19 % (10797)------------------------------
% 62.18/10.19 % (10797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.18/10.19 % (10797)Termination reason: Unknown
% 62.18/10.19 % (10797)Termination phase: Saturation
% 62.18/10.19
% 62.18/10.19 % (10797)Memory used [KB]: 7675
% 62.18/10.19 % (10797)Time elapsed: 0.084 s
% 62.18/10.19 % (10797)Instructions burned: 308 (million)
% 62.18/10.19 % (10797)------------------------------
% 62.18/10.19 % (10797)------------------------------
% 62.76/10.20 % (10798)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_10235 for (2914ds/1548Mi)
% 63.36/10.33 % (10789)Instruction limit reached!
% 63.36/10.33 % (10789)------------------------------
% 63.36/10.33 % (10789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.36/10.33 % (10789)Termination reason: Unknown
% 63.36/10.33 % (10789)Termination phase: Saturation
% 63.36/10.33
% 63.36/10.33 % (10789)Memory used [KB]: 12025
% 63.36/10.33 % (10789)Time elapsed: 0.786 s
% 63.36/10.33 % (10789)Instructions burned: 2547 (million)
% 63.36/10.33 % (10789)------------------------------
% 63.36/10.33 % (10789)------------------------------
% 63.36/10.34 % (10799)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_10235 for (2912ds/5214Mi)
% 63.91/10.47 % (10785)Instruction limit reached!
% 63.91/10.47 % (10785)------------------------------
% 63.91/10.47 % (10785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.91/10.47 % (10785)Termination reason: Unknown
% 63.91/10.47 % (10785)Termination phase: Saturation
% 63.91/10.47
% 63.91/10.47 % (10785)Memory used [KB]: 14200
% 63.91/10.47 % (10785)Time elapsed: 1.360 s
% 63.91/10.47 % (10785)Instructions burned: 4605 (million)
% 63.91/10.47 % (10785)------------------------------
% 63.91/10.47 % (10785)------------------------------
% 63.91/10.48 % (10800)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_10235 for (2911ds/3201Mi)
% 64.79/10.65 % (10798)Instruction limit reached!
% 64.79/10.65 % (10798)------------------------------
% 64.79/10.65 % (10798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.79/10.65 % (10798)Termination reason: Unknown
% 64.79/10.65 % (10798)Termination phase: Saturation
% 64.79/10.65
% 64.79/10.65 % (10798)Memory used [KB]: 9850
% 64.79/10.65 % (10798)Time elapsed: 0.452 s
% 64.79/10.65 % (10798)Instructions burned: 1551 (million)
% 64.79/10.65 % (10798)------------------------------
% 64.79/10.65 % (10798)------------------------------
% 64.79/10.66 % (10801)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_10235 for (2909ds/454Mi)
% 64.79/10.67 % (10794)Instruction limit reached!
% 64.79/10.67 % (10794)------------------------------
% 64.79/10.67 % (10794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.79/10.67 % (10794)Termination reason: Unknown
% 64.79/10.67 % (10794)Termination phase: Saturation
% 64.79/10.67
% 64.79/10.67 % (10794)Memory used [KB]: 15735
% 64.79/10.67 % (10794)Time elapsed: 0.767 s
% 64.79/10.67 % (10794)Instructions burned: 2573 (million)
% 64.79/10.67 % (10794)------------------------------
% 64.79/10.67 % (10794)------------------------------
% 64.79/10.68 % (10802)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_10235 for (2909ds/3049Mi)
% 65.63/10.75 % (10795)Instruction limit reached!
% 65.63/10.75 % (10795)------------------------------
% 65.63/10.75 % (10795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.63/10.75 % (10795)Termination reason: Unknown
% 65.63/10.75 % (10795)Termination phase: Saturation
% 65.63/10.75
% 65.63/10.75 % (10795)Memory used [KB]: 15479
% 65.63/10.75 % (10795)Time elapsed: 0.784 s
% 65.63/10.75 % (10795)Instructions burned: 2655 (million)
% 65.63/10.75 % (10795)------------------------------
% 65.63/10.75 % (10795)------------------------------
% 65.63/10.76 % (10803)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_10235 for (2908ds/7311Mi)
% 65.63/10.78 % (10801)Instruction limit reached!
% 65.63/10.78 % (10801)------------------------------
% 65.63/10.78 % (10801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.63/10.78 % (10801)Termination reason: Unknown
% 65.63/10.78 % (10801)Termination phase: Saturation
% 65.63/10.78
% 65.63/10.78 % (10801)Memory used [KB]: 13048
% 65.63/10.78 % (10801)Time elapsed: 0.126 s
% 65.63/10.78 % (10801)Instructions burned: 457 (million)
% 65.63/10.78 % (10801)------------------------------
% 65.63/10.78 % (10801)------------------------------
% 65.63/10.79 % (10804)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_10235 for (2908ds/6804Mi)
% 66.03/10.85 % (10796)Instruction limit reached!
% 66.03/10.85 % (10796)------------------------------
% 66.03/10.85 % (10796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.03/10.85 % (10796)Termination reason: Unknown
% 66.03/10.85 % (10796)Termination phase: Saturation
% 66.03/10.85
% 66.03/10.85 % (10796)Memory used [KB]: 4989
% 66.03/10.85 % (10796)Time elapsed: 0.852 s
% 66.03/10.85 % (10796)Instructions burned: 2782 (million)
% 66.03/10.85 % (10796)------------------------------
% 66.03/10.85 % (10796)------------------------------
% 66.03/10.85 % (10804)Refutation not found, incomplete strategy
% 66.03/10.85 % (10804)------------------------------
% 66.03/10.85 % (10804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.03/10.85 % (10804)Termination reason: Refutation not found, incomplete strategy
% 66.03/10.85
% 66.03/10.85
% 66.03/10.85 % (10804)Memory used [KB]: 8059
% 66.03/10.85 % (10804)Time elapsed: 0.058 s
% 66.03/10.85 % (10804)Instructions burned: 196 (million)
% 66.03/10.85 % (10804)------------------------------
% 66.03/10.85 % (10804)------------------------------
% 66.03/10.85 % (10805)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_10235 for (2907ds/1683Mi)
% 66.03/10.86 % (10806)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_10235 for (2907ds/4688Mi)
% 70.48/11.37 % (10805)Instruction limit reached!
% 70.48/11.37 % (10805)------------------------------
% 70.48/11.37 % (10805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.48/11.37 % (10805)Termination reason: Unknown
% 70.48/11.37 % (10805)Termination phase: Saturation
% 70.48/11.37
% 70.48/11.37 % (10805)Memory used [KB]: 10874
% 70.48/11.37 % (10805)Time elapsed: 0.521 s
% 70.48/11.37 % (10805)Instructions burned: 1684 (million)
% 70.48/11.37 % (10805)------------------------------
% 70.48/11.37 % (10805)------------------------------
% 70.48/11.38 % (10807)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_10235 for (2902ds/2207Mi)
% 71.17/11.42 % (10800)Instruction limit reached!
% 71.17/11.42 % (10800)------------------------------
% 71.17/11.42 % (10800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.17/11.42 % (10800)Termination reason: Unknown
% 71.17/11.42 % (10800)Termination phase: Saturation
% 71.17/11.42
% 71.17/11.42 % (10800)Memory used [KB]: 12409
% 71.17/11.42 % (10800)Time elapsed: 0.949 s
% 71.17/11.42 % (10800)Instructions burned: 3202 (million)
% 71.17/11.42 % (10800)------------------------------
% 71.17/11.42 % (10800)------------------------------
% 71.17/11.43 % (10808)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_10235 for (2902ds/8216Mi)
% 71.70/11.50 % (10793)Instruction limit reached!
% 71.70/11.50 % (10793)------------------------------
% 71.70/11.50 % (10793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.70/11.50 % (10793)Termination reason: Unknown
% 71.70/11.50 % (10793)Termination phase: Saturation
% 71.70/11.50
% 71.70/11.50 % (10793)Memory used [KB]: 14583
% 71.70/11.50 % (10793)Time elapsed: 1.671 s
% 71.70/11.50 % (10793)Instructions burned: 5447 (million)
% 71.70/11.50 % (10793)------------------------------
% 71.70/11.50 % (10793)------------------------------
% 71.70/11.51 % (10809)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_10235 for (2901ds/430Mi)
% 71.70/11.57 % (10802)Instruction limit reached!
% 71.70/11.57 % (10802)------------------------------
% 71.70/11.57 % (10802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.70/11.57 % (10802)Termination reason: Unknown
% 71.70/11.57 % (10802)Termination phase: Saturation
% 71.70/11.57
% 71.70/11.57 % (10802)Memory used [KB]: 9338
% 71.70/11.57 % (10802)Time elapsed: 0.895 s
% 71.70/11.57 % (10802)Instructions burned: 3050 (million)
% 71.70/11.57 % (10802)------------------------------
% 71.70/11.57 % (10802)------------------------------
% 71.70/11.58 % (10810)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_10235 for (2900ds/2012Mi)
% 72.10/11.63 % (10809)Instruction limit reached!
% 72.10/11.63 % (10809)------------------------------
% 72.10/11.63 % (10809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.10/11.63 % (10809)Termination reason: Unknown
% 72.10/11.63 % (10809)Termination phase: Saturation
% 72.10/11.63
% 72.10/11.63 % (10809)Memory used [KB]: 7931
% 72.10/11.63 % (10809)Time elapsed: 0.119 s
% 72.10/11.63 % (10809)Instructions burned: 431 (million)
% 72.10/11.63 % (10809)------------------------------
% 72.10/11.63 % (10809)------------------------------
% 72.10/11.64 % (10811)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_10235 for (2899ds/631Mi)
% 72.84/11.83 % (10811)Instruction limit reached!
% 72.84/11.83 % (10811)------------------------------
% 72.84/11.83 % (10811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.84/11.83 % (10811)Termination reason: Unknown
% 72.84/11.83 % (10811)Termination phase: Saturation
% 72.84/11.83
% 72.84/11.83 % (10811)Memory used [KB]: 9850
% 72.84/11.83 % (10811)Time elapsed: 0.190 s
% 72.84/11.83 % (10811)Instructions burned: 633 (million)
% 72.84/11.83 % (10811)------------------------------
% 72.84/11.83 % (10811)------------------------------
% 72.84/11.84 % (10812)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_10235 for (2897ds/8785Mi)
% 73.34/11.92 % (10799)Instruction limit reached!
% 73.34/11.92 % (10799)------------------------------
% 73.34/11.92 % (10799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.34/11.92 % (10799)Termination reason: Unknown
% 73.34/11.92 % (10799)Termination phase: Saturation
% 73.34/11.92
% 73.34/11.92 % (10799)Memory used [KB]: 17142
% 73.34/11.92 % (10799)Time elapsed: 1.577 s
% 73.34/11.92 % (10799)Instructions burned: 5216 (million)
% 73.34/11.92 % (10799)------------------------------
% 73.34/11.92 % (10799)------------------------------
% 73.34/11.93 % (10813)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_10235 for (2896ds/739Mi)
% 75.46/12.06 % (10807)Instruction limit reached!
% 75.46/12.06 % (10807)------------------------------
% 75.46/12.06 % (10807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.46/12.06 % (10807)Termination reason: Unknown
% 75.46/12.06 % (10807)Termination phase: Saturation
% 75.46/12.06
% 75.46/12.06 % (10807)Memory used [KB]: 10746
% 75.46/12.06 % (10807)Time elapsed: 0.676 s
% 75.46/12.06 % (10807)Instructions burned: 2209 (million)
% 75.46/12.06 % (10807)------------------------------
% 75.46/12.06 % (10807)------------------------------
% 75.46/12.07 % (10814)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_10235 for (2895ds/5473Mi)
% 76.13/12.15 % (10813)Instruction limit reached!
% 76.13/12.15 % (10813)------------------------------
% 76.13/12.15 % (10813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.13/12.15 % (10813)Termination reason: Unknown
% 76.13/12.15 % (10813)Termination phase: Saturation
% 76.13/12.15
% 76.13/12.15 % (10813)Memory used [KB]: 8955
% 76.13/12.15 % (10813)Time elapsed: 0.225 s
% 76.13/12.15 % (10813)Instructions burned: 741 (million)
% 76.13/12.15 % (10813)------------------------------
% 76.13/12.15 % (10813)------------------------------
% 76.13/12.16 % (10815)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_10235 for (2894ds/43570Mi)
% 76.13/12.18 % (10810)Instruction limit reached!
% 76.13/12.18 % (10810)------------------------------
% 76.13/12.18 % (10810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.13/12.18 % (10810)Termination reason: Unknown
% 76.13/12.18 % (10810)Termination phase: Saturation
% 76.13/12.18
% 76.13/12.18 % (10810)Memory used [KB]: 23155
% 76.13/12.18 % (10810)Time elapsed: 0.594 s
% 76.13/12.18 % (10810)Instructions burned: 2014 (million)
% 76.13/12.18 % (10810)------------------------------
% 76.13/12.18 % (10810)------------------------------
% 76.13/12.19 % (10816)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_10235 for (2894ds/8382Mi)
% 76.13/12.20 % (10815)Refutation not found, incomplete strategy
% 76.13/12.20 % (10815)------------------------------
% 76.13/12.20 % (10815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.13/12.20 % (10815)Termination reason: Refutation not found, incomplete strategy
% 76.13/12.20
% 76.13/12.20
% 76.13/12.20 % (10815)Memory used [KB]: 7419
% 76.13/12.20 % (10815)Time elapsed: 0.036 s
% 76.13/12.20 % (10815)Instructions burned: 118 (million)
% 76.13/12.20 % (10815)------------------------------
% 76.13/12.20 % (10815)------------------------------
% 76.60/12.21 % (10817)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_10235 for (2894ds/407Mi)
% 76.60/12.23 % (10806)Instruction limit reached!
% 76.60/12.23 % (10806)------------------------------
% 76.60/12.23 % (10806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.60/12.23 % (10806)Termination reason: Unknown
% 76.60/12.23 % (10806)Termination phase: Saturation
% 76.60/12.23
% 76.60/12.23 % (10806)Memory used [KB]: 8315
% 76.60/12.23 % (10806)Time elapsed: 1.376 s
% 76.60/12.23 % (10806)Instructions burned: 4689 (million)
% 76.60/12.23 % (10806)------------------------------
% 76.60/12.23 % (10806)------------------------------
% 76.60/12.24 % (10818)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_10235 for (2893ds/2971Mi)
% 76.98/12.32 % (10817)Instruction limit reached!
% 76.98/12.32 % (10817)------------------------------
% 76.98/12.32 % (10817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.98/12.32 % (10817)Termination reason: Unknown
% 76.98/12.32 % (10817)Termination phase: Saturation
% 76.98/12.32
% 76.98/12.32 % (10817)Memory used [KB]: 7931
% 76.98/12.32 % (10817)Time elapsed: 0.114 s
% 76.98/12.32 % (10817)Instructions burned: 409 (million)
% 76.98/12.32 % (10817)------------------------------
% 76.98/12.32 % (10817)------------------------------
% 76.98/12.33 % (10819)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_10235 for (2892ds/9822Mi)
% 77.42/12.45 % (10819)Refutation not found, incomplete strategy
% 77.42/12.45 % (10819)------------------------------
% 77.42/12.45 % (10819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.42/12.45 % (10819)Termination reason: Refutation not found, incomplete strategy
% 77.42/12.45
% 77.42/12.45
% 77.42/12.45 % (10819)Memory used [KB]: 8827
% 77.42/12.45 % (10819)Time elapsed: 0.126 s
% 77.42/12.45 % (10819)Instructions burned: 430 (million)
% 77.42/12.45 % (10819)------------------------------
% 77.42/12.45 % (10819)------------------------------
% 77.42/12.46 % (10820)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_10235 for (2891ds/8425Mi)
% 79.06/12.96 % (10803)Instruction limit reached!
% 79.06/12.96 % (10803)------------------------------
% 79.06/12.96 % (10803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.06/12.96 % (10803)Termination reason: Unknown
% 79.06/12.96 % (10803)Termination phase: Saturation
% 79.06/12.96
% 79.06/12.96 % (10803)Memory used [KB]: 17782
% 79.06/12.96 % (10803)Time elapsed: 2.205 s
% 79.06/12.96 % (10803)Instructions burned: 7313 (million)
% 79.06/12.96 % (10803)------------------------------
% 79.06/12.96 % (10803)------------------------------
% 79.06/12.97 % (10821)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_10235 for (2886ds/3107Mi)
% 82.48/13.03 % (10818)Instruction limit reached!
% 82.48/13.03 % (10818)------------------------------
% 82.48/13.03 % (10818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.48/13.03 % (10818)Termination reason: Unknown
% 82.48/13.03 % (10818)Termination phase: Saturation
% 82.48/13.03
% 82.48/13.03 % (10818)Memory used [KB]: 13944
% 82.48/13.03 % (10818)Time elapsed: 0.785 s
% 82.48/13.03 % (10818)Instructions burned: 2974 (million)
% 82.48/13.03 % (10818)------------------------------
% 82.48/13.03 % (10818)------------------------------
% 82.48/13.04 % (10822)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_10235 for (2885ds/7967Mi)
% 86.02/13.69 % (10814)Instruction limit reached!
% 86.02/13.69 % (10814)------------------------------
% 86.02/13.69 % (10814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.02/13.69 % (10814)Termination reason: Unknown
% 86.02/13.69 % (10814)Termination phase: Saturation
% 86.02/13.69
% 86.02/13.69 % (10814)Memory used [KB]: 8571
% 86.02/13.69 % (10814)Time elapsed: 1.625 s
% 86.02/13.69 % (10814)Instructions burned: 5473 (million)
% 86.02/13.69 % (10814)------------------------------
% 86.02/13.69 % (10814)------------------------------
% 86.63/13.70 % (10823)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_10235 for (2879ds/3629Mi)
% 87.14/13.89 % (10821)Instruction limit reached!
% 87.14/13.89 % (10821)------------------------------
% 87.14/13.89 % (10821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.14/13.89 % (10821)Termination reason: Unknown
% 87.14/13.89 % (10821)Termination phase: Saturation
% 87.14/13.89
% 87.14/13.89 % (10821)Memory used [KB]: 11897
% 87.14/13.89 % (10821)Time elapsed: 0.922 s
% 87.14/13.89 % (10821)Instructions burned: 3110 (million)
% 87.14/13.89 % (10821)------------------------------
% 87.14/13.89 % (10821)------------------------------
% 87.64/13.90 % (10824)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_10235 for (2877ds/939Mi)
% 87.64/13.92 % (10808)Instruction limit reached!
% 87.64/13.92 % (10808)------------------------------
% 87.64/13.92 % (10808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.64/13.92 % (10808)Termination reason: Unknown
% 87.64/13.92 % (10808)Termination phase: Saturation
% 87.64/13.92
% 87.64/13.92 % (10808)Memory used [KB]: 15479
% 87.64/13.92 % (10808)Time elapsed: 2.487 s
% 87.64/13.92 % (10808)Instructions burned: 8218 (million)
% 87.64/13.92 % (10808)------------------------------
% 87.64/13.92 % (10808)------------------------------
% 87.64/13.93 % (10825)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_10235 for (2876ds/1188Mi)
% 90.20/14.18 % (10824)Instruction limit reached!
% 90.20/14.18 % (10824)------------------------------
% 90.20/14.18 % (10824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.20/14.18 % (10824)Termination reason: Unknown
% 90.20/14.18 % (10824)Termination phase: Saturation
% 90.20/14.18
% 90.20/14.18 % (10824)Memory used [KB]: 8827
% 90.20/14.18 % (10824)Time elapsed: 0.277 s
% 90.20/14.18 % (10824)Instructions burned: 939 (million)
% 90.20/14.18 % (10824)------------------------------
% 90.20/14.18 % (10824)------------------------------
% 90.20/14.19 % (10826)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_10235 for (2874ds/3205Mi)
% 90.77/14.29 % (10825)Instruction limit reached!
% 90.77/14.29 % (10825)------------------------------
% 90.77/14.29 % (10825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.77/14.29 % (10825)Termination reason: Unknown
% 90.77/14.29 % (10825)Termination phase: Saturation
% 90.77/14.29
% 90.77/14.29 % (10825)Memory used [KB]: 9978
% 90.77/14.29 % (10825)Time elapsed: 0.362 s
% 90.77/14.29 % (10825)Instructions burned: 1189 (million)
% 90.77/14.29 % (10825)------------------------------
% 90.77/14.29 % (10825)------------------------------
% 91.40/14.30 % (10827)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_10235 for (2873ds/865Mi)
% 92.40/14.51 % (10822)Refutation not found, non-redundant clauses discarded% (10822)------------------------------
% 92.40/14.51 % (10822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.40/14.51 % (10822)Termination reason: Refutation not found, non-redundant clauses discarded
% 92.40/14.51
% 92.40/14.51 % (10822)Memory used [KB]: 18549
% 92.40/14.51 % (10822)Time elapsed: 1.469 s
% 92.40/14.51 % (10822)Instructions burned: 5295 (million)
% 92.40/14.51 % (10822)------------------------------
% 92.40/14.51 % (10822)------------------------------
% 92.40/14.52 % (10812)Instruction limit reached!
% 92.40/14.52 % (10812)------------------------------
% 92.40/14.52 % (10812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.40/14.52 % (10812)Termination reason: Unknown
% 92.40/14.52 % (10812)Termination phase: Saturation
% 92.40/14.52
% 92.40/14.52 % (10812)Memory used [KB]: 18293
% 92.40/14.52 % (10812)Time elapsed: 2.681 s
% 92.40/14.52 % (10812)Instructions burned: 8786 (million)
% 92.40/14.52 % (10812)------------------------------
% 92.40/14.52 % (10812)------------------------------
% 92.40/14.52 % (10830)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_10235 for (2871ds/7469Mi)
% 92.40/14.53 % (10831)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_10235 for (2871ds/4165Mi)
% 92.40/14.56 % (10827)Instruction limit reached!
% 92.40/14.56 % (10827)------------------------------
% 92.40/14.56 % (10827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.40/14.56 % (10827)Termination reason: Unknown
% 92.40/14.56 % (10827)Termination phase: Saturation
% 92.40/14.56
% 92.40/14.56 % (10827)Memory used [KB]: 10106
% 92.40/14.56 % (10827)Time elapsed: 0.263 s
% 92.40/14.56 % (10827)Instructions burned: 865 (million)
% 92.40/14.56 % (10827)------------------------------
% 92.40/14.56 % (10827)------------------------------
% 92.40/14.57 % (10848)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_10235 for (2870ds/13468Mi)
% 93.03/14.67 % (10816)Instruction limit reached!
% 93.03/14.67 % (10816)------------------------------
% 93.03/14.67 % (10816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.03/14.67 % (10816)Termination reason: Unknown
% 93.03/14.67 % (10816)Termination phase: Saturation
% 93.03/14.67
% 93.03/14.67 % (10816)Memory used [KB]: 26609
% 93.03/14.67 % (10816)Time elapsed: 2.482 s
% 93.03/14.67 % (10816)Instructions burned: 8384 (million)
% 93.03/14.67 % (10816)------------------------------
% 93.03/14.67 % (10816)------------------------------
% 93.03/14.68 % (10934)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_10235 for (2869ds/2635Mi)
% 93.31/14.77 % (10823)Instruction limit reached!
% 93.31/14.77 % (10823)------------------------------
% 93.31/14.77 % (10823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.31/14.77 % (10823)Termination reason: Unknown
% 93.31/14.77 % (10823)Termination phase: Saturation
% 93.31/14.77
% 93.31/14.77 % (10823)Memory used [KB]: 11897
% 93.31/14.77 % (10823)Time elapsed: 1.068 s
% 93.31/14.77 % (10823)Instructions burned: 3629 (million)
% 93.31/14.77 % (10823)------------------------------
% 93.31/14.77 % (10823)------------------------------
% 93.31/14.78 % (10946)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_10235 for (2868ds/631Mi)
% 93.60/14.92 % (10820)Instruction limit reached!
% 93.60/14.92 % (10820)------------------------------
% 93.60/14.92 % (10820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.60/14.92 % (10820)Termination reason: Unknown
% 93.60/14.92 % (10820)Termination phase: Saturation
% 93.60/14.92
% 93.60/14.92 % (10820)Memory used [KB]: 17398
% 93.60/14.92 % (10820)Time elapsed: 2.456 s
% 93.60/14.92 % (10820)Instructions burned: 8426 (million)
% 93.60/14.92 % (10820)------------------------------
% 93.60/14.92 % (10820)------------------------------
% 93.60/14.93 % (11030)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_10235 for (2867ds/15557Mi)
% 93.60/14.96 % (10946)Instruction limit reached!
% 93.60/14.96 % (10946)------------------------------
% 93.60/14.96 % (10946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.60/14.96 % (10946)Termination reason: Unknown
% 93.60/14.96 % (10946)Termination phase: Saturation
% 93.60/14.96
% 93.60/14.96 % (10946)Memory used [KB]: 9722
% 93.60/14.96 % (10946)Time elapsed: 0.179 s
% 93.60/14.96 % (10946)Instructions burned: 632 (million)
% 93.60/14.96 % (10946)------------------------------
% 93.60/14.96 % (10946)------------------------------
% 93.60/14.97 % (11064)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_10235 for (2866ds/2142Mi)
% 97.80/15.21 % (10826)Instruction limit reached!
% 97.80/15.21 % (10826)------------------------------
% 97.80/15.21 % (10826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.80/15.21 % (10826)Termination reason: Unknown
% 97.80/15.21 % (10826)Termination phase: Saturation
% 97.80/15.21
% 97.80/15.21 % (10826)Memory used [KB]: 11769
% 97.80/15.21 % (10826)Time elapsed: 1.017 s
% 97.80/15.21 % (10826)Instructions burned: 3206 (million)
% 97.80/15.21 % (10826)------------------------------
% 97.80/15.21 % (10826)------------------------------
% 97.80/15.22 % (11204)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_10235 for (2864ds/5624Mi)
% 100.22/15.63 % (10934)Instruction limit reached!
% 100.22/15.63 % (10934)------------------------------
% 100.22/15.63 % (10934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.22/15.63 % (10934)Termination reason: Unknown
% 100.22/15.63 % (10934)Termination phase: Saturation
% 100.22/15.63
% 100.22/15.63 % (10934)Memory used [KB]: 12537
% 100.22/15.63 % (10934)Time elapsed: 0.953 s
% 100.22/15.63 % (10934)Instructions burned: 2636 (million)
% 100.22/15.63 % (10934)------------------------------
% 100.22/15.63 % (10934)------------------------------
% 100.22/15.65 % (11212)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_10235 for (2859ds/1665Mi)
% 101.26/15.81 % (11064)Instruction limit reached!
% 101.26/15.81 % (11064)------------------------------
% 101.26/15.81 % (11064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.26/15.81 % (11064)Termination reason: Unknown
% 101.26/15.81 % (11064)Termination phase: Saturation
% 101.26/15.81
% 101.26/15.81 % (11064)Memory used [KB]: 9722
% 101.26/15.81 % (11064)Time elapsed: 0.844 s
% 101.26/15.81 % (11064)Instructions burned: 2145 (million)
% 101.26/15.81 % (11064)------------------------------
% 101.26/15.81 % (11064)------------------------------
% 101.26/15.82 % (11213)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_10235 for (2858ds/64912Mi)
% 103.47/16.06 % (10831)Instruction limit reached!
% 103.47/16.06 % (10831)------------------------------
% 103.47/16.06 % (10831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.47/16.06 % (10831)Termination reason: Unknown
% 103.47/16.06 % (10831)Termination phase: Saturation
% 103.47/16.06
% 103.47/16.06 % (10831)Memory used [KB]: 23155
% 103.47/16.06 % (10831)Time elapsed: 1.536 s
% 103.47/16.06 % (10831)Instructions burned: 4165 (million)
% 103.47/16.06 % (10831)------------------------------
% 103.47/16.06 % (10831)------------------------------
% 103.47/16.08 % (11214)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_10235 for (2855ds/7801Mi)
% 104.13/16.14 % (11212)Instruction limit reached!
% 104.13/16.14 % (11212)------------------------------
% 104.13/16.14 % (11212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.13/16.14 % (11212)Termination reason: Unknown
% 104.13/16.14 % (11212)Termination phase: Saturation
% 104.13/16.14
% 104.13/16.14 % (11212)Memory used [KB]: 10106
% 104.13/16.14 % (11212)Time elapsed: 0.490 s
% 104.13/16.14 % (11212)Instructions burned: 1665 (million)
% 104.13/16.14 % (11212)------------------------------
% 104.13/16.14 % (11212)------------------------------
% 104.13/16.15 % (11215)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_10235 for (2854ds/15194Mi)
% 108.09/16.95 % (10830)Instruction limit reached!
% 108.09/16.95 % (10830)------------------------------
% 108.09/16.95 % (10830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.09/16.95 % (10830)Termination reason: Unknown
% 108.09/16.95 % (10830)Termination phase: Saturation
% 108.09/16.95
% 108.09/16.95 % (10830)Memory used [KB]: 12792
% 108.09/16.95 % (10830)Time elapsed: 2.435 s
% 108.09/16.95 % (10830)Instructions burned: 7470 (million)
% 108.09/16.95 % (10830)------------------------------
% 108.09/16.95 % (10830)------------------------------
% 108.09/16.96 % (11216)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on DTF2THF_10235 for (2846ds/6753Mi)
% 108.09/16.99 % (11204)Instruction limit reached!
% 108.09/16.99 % (11204)------------------------------
% 108.09/16.99 % (11204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.09/16.99 % (11204)Termination reason: Unknown
% 108.09/16.99 % (11204)Termination phase: Saturation
% 108.09/16.99
% 108.09/16.99 % (11204)Memory used [KB]: 13304
% 108.09/16.99 % (11204)Time elapsed: 1.768 s
% 108.09/16.99 % (11204)Instructions burned: 5626 (million)
% 108.09/16.99 % (11204)------------------------------
% 108.09/16.99 % (11204)------------------------------
% 108.09/17.00 % (11217)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_10235 for (2846ds/1003Mi)
% 110.43/17.02 % (11216)Refutation not found, incomplete strategy
% 110.43/17.02 % (11216)------------------------------
% 110.43/17.02 % (11216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 110.43/17.02 % (11216)Termination reason: Refutation not found, incomplete strategy
% 110.43/17.02
% 110.43/17.02
% 110.43/17.02 % (11216)Memory used [KB]: 8059
% 110.43/17.02 % (11216)Time elapsed: 0.061 s
% 110.43/17.02 % (11216)Instructions burned: 197 (million)
% 110.43/17.02 % (11216)------------------------------
% 110.43/17.02 % (11216)------------------------------
% 110.43/17.03 % (11218)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_10235 for (2846ds/13018Mi)
% 111.58/17.28 % (11217)Instruction limit reached!
% 111.58/17.28 % (11217)------------------------------
% 111.58/17.28 % (11217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 111.58/17.28 % (11217)Termination reason: Unknown
% 111.58/17.28 % (11217)Termination phase: Saturation
% 111.58/17.28
% 111.58/17.28 % (11217)Memory used [KB]: 8699
% 111.58/17.28 % (11217)Time elapsed: 0.286 s
% 111.58/17.28 % (11217)Instructions burned: 1003 (million)
% 111.58/17.28 % (11217)------------------------------
% 111.58/17.28 % (11217)------------------------------
% 111.58/17.29 % (11219)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_10235 for (2843ds/1267Mi)
% 113.66/17.67 % (11219)Instruction limit reached!
% 113.66/17.67 % (11219)------------------------------
% 113.66/17.67 % (11219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.66/17.67 % (11219)Termination reason: Unknown
% 113.66/17.67 % (11219)Termination phase: Saturation
% 113.66/17.67
% 113.66/17.67 % (11219)Memory used [KB]: 8699
% 113.66/17.67 % (11219)Time elapsed: 0.376 s
% 113.66/17.67 % (11219)Instructions burned: 1269 (million)
% 113.66/17.67 % (11219)------------------------------
% 113.66/17.67 % (11219)------------------------------
% 113.66/17.68 % (11220)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on DTF2THF_10235 for (2839ds/2570Mi)
% 120.09/18.47 % (11220)Instruction limit reached!
% 120.09/18.47 % (11220)------------------------------
% 120.09/18.47 % (11220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.09/18.47 % (11220)Termination reason: Unknown
% 120.09/18.47 % (11220)Termination phase: Saturation
% 120.09/18.47
% 120.09/18.47 % (11220)Memory used [KB]: 15095
% 120.09/18.47 % (11220)Time elapsed: 0.788 s
% 120.09/18.47 % (11220)Instructions burned: 2572 (million)
% 120.09/18.47 % (11220)------------------------------
% 120.09/18.47 % (11220)------------------------------
% 120.09/18.48 % (11221)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_10235 for (2831ds/13163Mi)
% 120.09/18.48 % (11214)Instruction limit reached!
% 120.09/18.48 % (11214)------------------------------
% 120.09/18.48 % (11214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.09/18.48 % (11214)Termination reason: Unknown
% 120.09/18.48 % (11214)Termination phase: Saturation
% 120.09/18.48
% 120.09/18.48 % (11214)Memory used [KB]: 19317
% 120.09/18.48 % (11214)Time elapsed: 2.405 s
% 120.09/18.48 % (11214)Instructions burned: 7803 (million)
% 120.09/18.48 % (11214)------------------------------
% 120.09/18.48 % (11214)------------------------------
% 120.09/18.49 % (11222)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_10235 for (2831ds/5087Mi)
% 122.28/18.83 % (10848)Instruction limit reached!
% 122.28/18.83 % (10848)------------------------------
% 122.28/18.83 % (10848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 122.28/18.83 % (10848)Termination reason: Unknown
% 122.28/18.83 % (10848)Termination phase: Saturation
% 122.28/18.83
% 122.28/18.83 % (10848)Memory used [KB]: 16886
% 122.28/18.83 % (10848)Time elapsed: 4.260 s
% 122.28/18.83 % (10848)Instructions burned: 13469 (million)
% 122.28/18.83 % (10848)------------------------------
% 122.28/18.83 % (10848)------------------------------
% 122.28/18.84 % (11223)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_10235 for (2828ds/10380Mi)
% 127.75/19.59 % (11030)Instruction limit reached!
% 127.75/19.59 % (11030)------------------------------
% 127.75/19.59 % (11030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.75/19.59 % (11030)Termination reason: Unknown
% 127.75/19.59 % (11030)Termination phase: Saturation
% 127.75/19.59
% 127.75/19.59 % (11030)Memory used [KB]: 33389
% 127.75/19.59 % (11030)Time elapsed: 4.661 s
% 127.75/19.59 % (11030)Instructions burned: 15557 (million)
% 127.75/19.59 % (11030)------------------------------
% 127.75/19.59 % (11030)------------------------------
% 128.49/19.60 % (11224)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_10235 for (2820ds/4218Mi)
% 129.09/19.77 % (11222)First to succeed.
% 129.09/19.78 % (11222)Refutation found. Thanks to Tanya!
% 129.09/19.78 % SZS status Theorem for DTF2THF_10235
% 129.09/19.78 % SZS output start Proof for DTF2THF_10235
% 129.09/19.78 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 129.09/19.78 thf(type_def_7, type, tree: ($tType) > $tType).
% 129.09/19.78 thf(type_def_8, type, list: ($tType) > $tType).
% 129.09/19.78 thf(type_def_9, type, multiset: ($tType) > $tType).
% 129.09/19.78 thf(type_def_10, type, set: ($tType) > $tType).
% 129.09/19.78 thf(type_def_11, type, a: $tType).
% 129.09/19.78 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 129.09/19.78 thf(func_def_1, type, multiset: ($tType) > $tType).
% 129.09/19.78 thf(func_def_2, type, list: ($tType) > $tType).
% 129.09/19.78 thf(func_def_3, type, tree: ($tType) > $tType).
% 129.09/19.78 thf(func_def_4, type, set: ($tType) > $tType).
% 129.09/19.78 thf(func_def_5, type, a: $tType).
% 129.09/19.78 thf(func_def_6, type, type: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_7, type, preorder: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_8, type, zero: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_9, type, neg_numeral: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_10, type, group_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_11, type, monoid_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_12, type, linorder: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_13, type, semigroup_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_14, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_15, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_16, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_17, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_18, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_19, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_20, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_21, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_22, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_23, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_24, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_25, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_26, type, semiri456707255roduct: !>[X0: $tType]:($o)).
% 129.09/19.78 thf(func_def_27, type, unique455577585es_aux: !>[X0: $tType]:(product_prod @ X0 @ X0 > $o)).
% 129.09/19.78 thf(func_def_28, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 129.09/19.78 thf(func_def_29, type, zero_zero: !>[X0: $tType]:(X0)).
% 129.09/19.78 thf(func_def_30, type, nO_MATCH: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 129.09/19.78 thf(func_def_31, type, heapIm818251801eapify: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_32, type, heapIm721255937_empty: !>[X0: $tType]:(tree @ X0 > $o)).
% 129.09/19.78 thf(func_def_33, type, heapIm874063447f_list: !>[X0: $tType]:(list @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_34, type, heapIm1542349758ve_max: !>[X0: $tType]:(tree @ X0 > product_prod @ X0 @ tree @ X0)).
% 129.09/19.78 thf(func_def_35, type, heapIm1271749598e_left: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_36, type, heapIm1912108042t_tree: !>[X0: $tType]:(list @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_37, type, heapIm970386777veLeaf: !>[X0: $tType]:(tree @ X0 > product_prod @ X0 @ tree @ X0)).
% 129.09/19.78 thf(func_def_38, type, heapIm1434396069_right: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_39, type, heapIm748920189ftDown: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_40, type, heap: !>[X0: $tType, X1: $tType]:(X0 > (X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > tree @ X1) > (X0 > product_prod @ X1 @ X0) > $o)).
% 129.09/19.78 thf(func_def_41, type, heap_axioms: !>[X0: $tType, X1: $tType]:((X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > tree @ X1) > (X0 > product_prod @ X1 @ X0) > $o)).
% 129.09/19.78 thf(func_def_42, type, e: !>[X0: $tType]:(tree @ X0)).
% 129.09/19.78 thf(func_def_43, type, t: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_44, type, in_tree: !>[X0: $tType]:(X0 > tree @ X0 > $o)).
% 129.09/19.78 thf(func_def_45, type, is_heap: !>[X0: $tType]:(tree @ X0 > $o)).
% 129.09/19.78 thf(func_def_46, type, multiset2: !>[X0: $tType]:(tree @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_47, type, val: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_48, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 129.09/19.78 thf(func_def_49, type, lattic929149872er_Max: !>[X0: $tType]:(set @ X0 > X0)).
% 129.09/19.78 thf(func_def_50, type, add_mset: !>[X0: $tType]:(X0 > multiset @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_51, type, comm_monoid_sum_mset: !>[X0: $tType]:((X0 > X0 > X0) > X0 > multiset @ X0 > X0)).
% 129.09/19.78 thf(func_def_52, type, is_empty: !>[X0: $tType]:(multiset @ X0 > $o)).
% 129.09/19.78 thf(func_def_53, type, mult: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0)).
% 129.09/19.78 thf(func_def_54, type, mult1: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0)).
% 129.09/19.78 thf(func_def_55, type, set_mset: !>[X0: $tType]:(multiset @ X0 > set @ X0)).
% 129.09/19.78 thf(func_def_56, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 129.09/19.78 thf(func_def_57, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 129.09/19.78 thf(func_def_58, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 129.09/19.78 thf(func_def_59, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 129.09/19.78 thf(func_def_60, type, product_fst: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 129.09/19.78 thf(func_def_61, type, product_snd: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 129.09/19.78 thf(func_def_62, type, product_swap: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > product_prod @ X1 @ X0)).
% 129.09/19.78 thf(func_def_63, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3)).
% 129.09/19.78 thf(func_def_64, type, irrefl: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 129.09/19.78 thf(func_def_65, type, trans: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 129.09/19.78 thf(func_def_66, type, collection: !>[X0: $tType, X1: $tType]:(X0 > (X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > $o)).
% 129.09/19.78 thf(func_def_67, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 129.09/19.78 thf(func_def_68, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 129.09/19.78 thf(func_def_69, type, l1: tree @ a).
% 129.09/19.78 thf(func_def_70, type, l2: tree @ a).
% 129.09/19.78 thf(func_def_71, type, r1: tree @ a).
% 129.09/19.78 thf(func_def_72, type, r2: tree @ a).
% 129.09/19.78 thf(func_def_73, type, t2: tree @ a).
% 129.09/19.78 thf(func_def_74, type, t3: tree @ a).
% 129.09/19.78 thf(func_def_75, type, t_a: tree @ a).
% 129.09/19.78 thf(func_def_76, type, v1: a).
% 129.09/19.78 thf(func_def_77, type, v2: a).
% 129.09/19.78 thf(func_def_78, type, v: a).
% 129.09/19.78 thf(func_def_79, type, v_a: a).
% 129.09/19.78 thf(func_def_80, type, v3: a).
% 129.09/19.78 thf(func_def_99, type, sP0: !>[X0: $tType]:((tree @ X0 > $o) > $o)).
% 129.09/19.78 thf(func_def_100, type, sP1: !>[X0: $tType]:((tree @ X0 > $o) > $o)).
% 129.09/19.78 thf(func_def_101, type, sP2: !>[X0: $tType]:((tree @ X0 > $o) > $o)).
% 129.09/19.78 thf(func_def_102, type, sP3: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > tree @ X0) > $o)).
% 129.09/19.78 thf(func_def_103, type, sP4: !>[X0: $tType, X1: $tType]:((X0 > multiset @ X1) > (X0 > $o) > (X0 > product_prod @ X1 @ X0) > $o)).
% 129.09/19.78 thf(func_def_104, type, sK5: !>[X0: $tType]:(multiset @ X0 > X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_105, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_106, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 129.09/19.78 thf(func_def_107, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 129.09/19.78 thf(func_def_108, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 129.09/19.78 thf(func_def_109, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 129.09/19.78 thf(func_def_110, type, sK11: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 129.09/19.78 thf(func_def_111, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 129.09/19.78 thf(func_def_112, type, sK13: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_113, type, sK14: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_114, type, sK15: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_115, type, sK16: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_116, type, sK17: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_117, type, sK18: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_118, type, sK19: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_119, type, sK20: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_120, type, sK21: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_121, type, sK22: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_122, type, sK23: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_123, type, sK24: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_124, type, sK25: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_125, type, sK26: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_126, type, sK27: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_127, type, sK28: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_128, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 129.09/19.78 thf(func_def_129, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 129.09/19.78 thf(func_def_130, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 129.09/19.78 thf(func_def_131, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 129.09/19.78 thf(func_def_132, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 129.09/19.78 thf(func_def_133, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 129.09/19.78 thf(func_def_134, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 129.09/19.78 thf(func_def_135, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 129.09/19.78 thf(func_def_136, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 129.09/19.78 thf(func_def_137, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 129.09/19.78 thf(func_def_138, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 129.09/19.78 thf(func_def_139, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 129.09/19.78 thf(func_def_140, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 129.09/19.78 thf(func_def_141, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_142, type, sK43: !>[X0: $tType]:(multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_143, type, sK44: !>[X0: $tType]:(multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_144, type, sK45: !>[X0: $tType]:(multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_145, type, sK46: !>[X0: $tType]:(X0 > multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_146, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 129.09/19.78 thf(func_def_147, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 129.09/19.78 thf(func_def_148, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 129.09/19.78 thf(func_def_149, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 129.09/19.78 thf(func_def_150, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 129.09/19.78 thf(func_def_151, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 129.09/19.78 thf(func_def_152, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_153, type, sK54: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > multiset @ X0 > X0 > X0)).
% 129.09/19.78 thf(func_def_154, type, sK55: !>[X0: $tType]:((multiset @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_155, type, sK56: !>[X0: $tType]:((multiset @ X0 > $o) > multiset @ X0)).
% 129.09/19.78 thf(func_def_156, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 129.09/19.78 thf(func_def_157, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 129.09/19.78 thf(func_def_158, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 129.09/19.78 thf(func_def_159, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 129.09/19.78 thf(func_def_160, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_161, type, sK62: !>[X0: $tType]:(multiset @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_162, type, sK63: !>[X0: $tType]:(multiset @ X0 > X0)).
% 129.09/19.78 thf(func_def_163, type, sK64: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_164, type, sK65: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_165, type, sK66: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_166, type, sK67: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_167, type, sK68: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_168, type, sK69: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_169, type, sK70: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_170, type, sK71: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_171, type, sK72: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_172, type, sK73: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_173, type, sK74: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_174, type, sK75: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_175, type, sK76: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_176, type, sK77: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_177, type, sK78: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_178, type, sK79: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_179, type, sK80: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_180, type, sK81: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_181, type, sK82: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_182, type, sK83: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_183, type, sK84: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_184, type, sK85: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_185, type, sK86: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_186, type, sK87: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_187, type, sK88: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 129.09/19.78 thf(func_def_188, type, sK89: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_189, type, sK90: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > multiset @ X0 > multiset @ X0 > X0)).
% 129.09/19.78 thf(func_def_190, type, sK91: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > multiset @ X0 > multiset @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_191, type, sK92: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > multiset @ X0 > multiset @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_192, type, sK93: !>[X0: $tType]:(multiset @ X0 > X0)).
% 129.09/19.78 thf(func_def_193, type, sK94: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 129.09/19.78 thf(func_def_194, type, sK95: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 129.09/19.78 thf(func_def_195, type, sK96: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > multiset @ X0 > multiset @ X0 > X0)).
% 129.09/19.78 thf(func_def_196, type, sK97: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_197, type, sK98: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_198, type, sK99: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_199, type, sK100: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_200, type, sK101: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_201, type, sK102: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_202, type, sK103: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_203, type, sK104: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_204, type, sK105: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_205, type, sK106: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_206, type, sK107: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_207, type, sK108: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_208, type, sK109: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_209, type, sK110: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_210, type, sK111: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_211, type, sK112: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_212, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 129.09/19.78 thf(func_def_213, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 129.09/19.78 thf(func_def_214, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_215, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 129.09/19.78 thf(func_def_216, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 129.09/19.78 thf(func_def_217, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 129.09/19.78 thf(func_def_218, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 129.09/19.78 thf(func_def_219, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 129.09/19.78 thf(func_def_220, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 129.09/19.78 thf(func_def_221, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 129.09/19.78 thf(func_def_222, type, sK123: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 129.09/19.78 thf(func_def_223, type, sK124: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 129.09/19.78 thf(func_def_224, type, sK125: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 129.09/19.78 thf(func_def_225, type, sK126: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_226, type, sK127: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 129.09/19.78 thf(func_def_227, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 129.09/19.78 thf(func_def_228, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 129.09/19.78 thf(func_def_229, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 129.09/19.78 thf(func_def_230, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 129.09/19.78 thf(func_def_231, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_232, type, sK133: !>[X0: $tType]:(multiset @ X0 > X0)).
% 129.09/19.78 thf(func_def_233, type, sK134: !>[X0: $tType]:(multiset @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_234, type, sK135: !>[X0: $tType]:((multiset @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_235, type, sK136: !>[X0: $tType]:((multiset @ X0 > $o) > multiset @ X0)).
% 129.09/19.78 thf(func_def_236, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 129.09/19.78 thf(func_def_237, type, sK138: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 129.09/19.78 thf(func_def_238, type, sK139: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 129.09/19.78 thf(func_def_239, type, sK140: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 129.09/19.78 thf(func_def_240, type, sK141: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 129.09/19.78 thf(func_def_241, type, sK142: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1)).
% 129.09/19.78 thf(func_def_242, type, sK143: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0)).
% 129.09/19.78 thf(func_def_243, type, sK144: !>[X0: $tType]:((multiset @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_244, type, sK145: !>[X0: $tType]:((multiset @ X0 > $o) > multiset @ X0)).
% 129.09/19.78 thf(func_def_245, type, sK146: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_246, type, sK147: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_247, type, sK148: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_248, type, sK149: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_249, type, sK150: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_250, type, sK151: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_251, type, sK152: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_252, type, sK153: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_253, type, sK154: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_254, type, sK155: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_255, type, sK156: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_256, type, sK157: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_257, type, sK158: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_258, type, sK159: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_259, type, sK160: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_260, type, sK161: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_261, type, sK162: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_262, type, sK163: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_263, type, sK164: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_264, type, sK165: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_265, type, sK166: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_266, type, sK167: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_267, type, sK168: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_268, type, sK169: !>[X0: $tType, X1: $tType]:((multiset @ X0 > multiset @ X1 > $o) > X1)).
% 129.09/19.78 thf(func_def_269, type, sK170: !>[X0: $tType, X1: $tType]:((multiset @ X0 > multiset @ X1 > $o) > multiset @ X0)).
% 129.09/19.78 thf(func_def_270, type, sK171: !>[X0: $tType, X1: $tType]:((multiset @ X0 > multiset @ X1 > $o) > multiset @ X1)).
% 129.09/19.78 thf(func_def_271, type, sK172: !>[X0: $tType, X1: $tType]:((multiset @ X0 > multiset @ X1 > $o) > X0)).
% 129.09/19.78 thf(func_def_272, type, sK173: !>[X0: $tType, X1: $tType]:((multiset @ X0 > multiset @ X1 > $o) > multiset @ X0)).
% 129.09/19.78 thf(func_def_273, type, sK174: !>[X0: $tType, X1: $tType]:((multiset @ X0 > multiset @ X1 > $o) > multiset @ X1)).
% 129.09/19.78 thf(func_def_274, type, sK175: !>[X0: $tType]:(multiset @ X0 > X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_275, type, sK176: !>[X0: $tType]:(tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_276, type, sK177: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_277, type, sK178: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_278, type, sK179: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 129.09/19.78 thf(func_def_279, type, sK180: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 129.09/19.78 thf(func_def_280, type, sK181: !>[X0: $tType, X1: $tType]:((X0 > multiset @ X1) > (X0 > $o) > (X0 > product_prod @ X1 @ X0) > X0)).
% 129.09/19.78 thf(func_def_281, type, sK182: !>[X0: $tType, X1: $tType]:((X0 > multiset @ X1) > (X0 > $o) > (X0 > product_prod @ X1 @ X0) > X1)).
% 129.09/19.78 thf(func_def_282, type, sK183: !>[X0: $tType, X1: $tType]:((X0 > multiset @ X1) > (X0 > $o) > (X0 > product_prod @ X1 @ X0) > X0)).
% 129.09/19.78 thf(func_def_283, type, sK184: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > tree @ X0) > X1)).
% 129.09/19.78 thf(func_def_284, type, sK185: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > tree @ X0) > X0)).
% 129.09/19.78 thf(func_def_285, type, sK186: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > tree @ X0) > X1)).
% 129.09/19.78 thf(func_def_286, type, sK187: !>[X0: $tType, X1: $tType]:((X1 > product_prod @ X0 @ X1) > (X1 > $o) > (X1 > tree @ X0) > X1)).
% 129.09/19.78 thf(func_def_287, type, sK188: !>[X0: $tType, X1: $tType]:((X1 > product_prod @ X0 @ X1) > (X1 > $o) > (X1 > tree @ X0) > X0)).
% 129.09/19.78 thf(func_def_288, type, sK189: !>[X0: $tType, X1: $tType]:((X1 > product_prod @ X0 @ X1) > (X1 > $o) > (X1 > tree @ X0) > X1)).
% 129.09/19.78 thf(func_def_289, type, sK190: !>[X0: $tType, X1: $tType]:((list @ X0 > X1) > (X1 > tree @ X0) > list @ X0)).
% 129.09/19.78 thf(func_def_290, type, sK191: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > tree @ X0) > X1)).
% 129.09/19.78 thf(func_def_291, type, sK192: !>[X0: $tType, X1: $tType]:((X1 > tree @ X0) > (X1 > multiset @ X0) > X1)).
% 129.09/19.78 thf(func_def_292, type, sK193: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_293, type, sK194: !>[X0: $tType]:(X0 > tree @ X0 > X0)).
% 129.09/19.78 thf(func_def_294, type, sK195: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 129.09/19.78 thf(func_def_295, type, sK196: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > multiset @ X0 > X0 > multiset @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_296, type, sK197: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > multiset @ X0 > X0 > multiset @ X0 > multiset @ X0)).
% 129.09/19.78 thf(func_def_298, type, sK199: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_299, type, sK200: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_300, type, sK201: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_301, type, sK202: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_302, type, sK203: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_303, type, sK204: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_304, type, sK205: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_305, type, sK206: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_306, type, sK207: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_307, type, sK208: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_308, type, sK209: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_309, type, sK210: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_310, type, sK211: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_311, type, sK212: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_312, type, sK213: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 129.09/19.78 thf(func_def_313, type, ph214: !>[X0: $tType]:(X0)).
% 129.09/19.78 thf(f7770,plain,(
% 129.09/19.78 $false),
% 129.09/19.78 inference(subsumption_resolution,[status(thm)],[f7769,f1153])).
% 129.09/19.78 thf(f1153,plain,(
% 129.09/19.78 (linorder @ a = $true)),
% 129.09/19.78 inference(cnf_transformation,[status(thm)],[f399])).
% 129.09/19.78 thf(f399,plain,(
% 129.09/19.78 (linorder @ a = $true)),
% 129.09/19.78 inference(fool_elimination,[status(thm)],[f398])).
% 129.09/19.78 thf(f398,plain,(
% 129.09/19.78 linorder @ a),
% 129.09/19.78 inference(rectify,[status(thm)],[f274])).
% 129.09/19.78 thf(f274,axiom,(
% 129.09/19.78 linorder @ a),
% 129.09/19.78 file('/export/starexec/sandbox/tmp/tmp.P5IR1jFQuE/DTF2THF_10235.p',tfree_0)).
% 129.09/19.78 thf(f7769,plain,(
% 129.09/19.78 (linorder @ a != $true)),
% 129.09/19.78 inference(subsumption_resolution,[status(thm)],[f7762,f1064])).
% 129.09/19.78 thf(f1064,plain,(
% 129.09/19.78 (v_a != (product_fst @ a @ tree @ a @ (heapIm970386777veLeaf @ a @ (t @ a @ v1 @ l1 @ r1))))),
% 129.09/19.78 inference(cnf_transformation,[status(thm)],[f712])).
% 129.09/19.78 thf(f712,plain,(
% 129.09/19.78 (v_a != (product_fst @ a @ tree @ a @ (heapIm970386777veLeaf @ a @ (t @ a @ v1 @ l1 @ r1))))),
% 129.09/19.78 inference(flattening,[status(thm)],[f276])).
% 129.09/19.78 thf(f276,negated_conjecture,(
% 129.09/19.78 ~(v_a = (product_fst @ a @ tree @ a @ (heapIm970386777veLeaf @ a @ (t @ a @ v1 @ l1 @ r1))))),
% 129.09/19.78 inference(negated_conjecture,[status(cth)],[f275])).
% 129.09/19.78 thf(f275,conjecture,(
% 129.09/19.78 (v_a = (product_fst @ a @ tree @ a @ (heapIm970386777veLeaf @ a @ (t @ a @ v1 @ l1 @ r1))))),
% 129.09/19.78 file('/export/starexec/sandbox/tmp/tmp.P5IR1jFQuE/DTF2THF_10235.p',conj_0)).
% 129.09/19.78 thf(f7762,plain,(
% 129.09/19.78 (v_a = (product_fst @ a @ tree @ a @ (heapIm970386777veLeaf @ a @ (t @ a @ v1 @ l1 @ r1)))) | (linorder @ a != $true)),
% 129.09/19.78 inference(superposition,[status(thm)],[f1877,f1793])).
% 129.09/19.78 thf(f1793,plain,(
% 129.09/19.78 (v_a = (product_fst @ a @ tree @ a @ (heapIm970386777veLeaf @ a @ (t @ a @ v3 @ (t @ a @ v1 @ l1 @ r1) @ (t @ a @ v2 @ l2 @ r2)))))),
% 129.09/19.78 inference(superposition,[status(thm)],[f1113,f1240])).
% 129.09/19.78 thf(f1240,plain,(
% 129.09/19.78 ((heapIm970386777veLeaf @ a @ (t @ a @ v3 @ (t @ a @ v1 @ l1 @ r1) @ (t @ a @ v2 @ l2 @ r2))) = (product_Pair @ a @ tree @ a @ v_a @ (t @ a @ v3 @ (product_snd @ a @ tree @ a @ (heapIm970386777veLeaf @ a @ (t @ a @ v1 @ l1 @ r1))) @ (t @ a @ v2 @ l2 @ r2))))),
% 129.09/19.78 inference(definition_unfolding,[status(thm)],[f1185,f1224])).
% 129.09/19.78 thf(f1224,plain,(
% 129.09/19.78 (t_a = (t @ a @ v3 @ (product_snd @ a @ tree @ a @ (heapIm970386777veLeaf @ a @ (t @ a @ v1 @ l1 @ r1))) @ (t @ a @ v2 @ l2 @ r2)))),
% 129.09/19.78 inference(cnf_transformation,[status(thm)],[f4])).
% 129.09/19.78 thf(f4,axiom,(
% 129.09/19.78 (t_a = (t @ a @ v3 @ (product_snd @ a @ tree @ a @ (heapIm970386777veLeaf @ a @ (t @ a @ v1 @ l1 @ r1))) @ (t @ a @ v2 @ l2 @ r2)))),
% 129.09/19.78 file('/export/starexec/sandbox/tmp/tmp.P5IR1jFQuE/DTF2THF_10235.p',fact_3__092_060open_062t_H_A_061_AT_Av_A_Isnd_A_IremoveLeaf_A_IT_Av1_Al1_Ar1_J_J_J_A_IT_Av2_Al2_Ar2_J_092_060close_062)).
% 129.09/19.78 thf(f1185,plain,(
% 129.09/19.78 ((product_Pair @ a @ tree @ a @ v_a @ t_a) = (heapIm970386777veLeaf @ a @ (t @ a @ v3 @ (t @ a @ v1 @ l1 @ r1) @ (t @ a @ v2 @ l2 @ r2))))),
% 129.09/19.78 inference(cnf_transformation,[status(thm)],[f1])).
% 129.09/19.78 thf(f1,axiom,(
% 129.09/19.78 ((product_Pair @ a @ tree @ a @ v_a @ t_a) = (heapIm970386777veLeaf @ a @ (t @ a @ v3 @ (t @ a @ v1 @ l1 @ r1) @ (t @ a @ v2 @ l2 @ r2))))),
% 129.09/19.78 file('/export/starexec/sandbox/tmp/tmp.P5IR1jFQuE/DTF2THF_10235.p',fact_0__C4__2_Oprems_C_I1_J)).
% 129.09/19.78 thf(f1113,plain,(
% 129.09/19.78 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0] : (((product_fst @ X1 @ X0 @ (product_Pair @ X1 @ X0 @ X2 @ X3)) = X2)) )),
% 129.09/19.78 inference(cnf_transformation,[status(thm)],[f737])).
% 129.09/19.78 thf(f737,plain,(
% 129.09/19.78 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0] : ((product_fst @ X1 @ X0 @ (product_Pair @ X1 @ X0 @ X2 @ X3)) = X2)),
% 129.09/19.78 inference(rectify,[status(thm)],[f14])).
% 129.09/19.78 thf(f14,axiom,(
% 129.09/19.78 ! [X1 : $tType,X0 : $tType,X26 : X0,X27 : X1] : ((product_fst @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X26 @ X27)) = X26)),
% 129.09/19.78 file('/export/starexec/sandbox/tmp/tmp.P5IR1jFQuE/DTF2THF_10235.p',fact_13_fst__conv)).
% 129.09/19.78 thf(f1877,plain,(
% 129.09/19.78 ( ! [X0 : $tType,X2 : tree @ X0,X3 : tree @ X0,X1 : X0,X6 : tree @ X0,X7 : tree @ X0,X4 : X0,X5 : X0] : (((product_fst @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X1 @ X2 @ X3))) = (product_fst @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X4 @ (t @ X0 @ X1 @ X2 @ X3) @ (t @ X0 @ X5 @ X6 @ X7))))) | (linorder @ X0 != $true)) )),
% 129.09/19.78 inference(superposition,[status(thm)],[f1113,f1112])).
% 129.09/19.78 thf(f1112,plain,(
% 129.09/19.78 ( ! [X0 : $tType,X2 : X0,X3 : tree @ X0,X1 : X0,X6 : tree @ X0,X7 : tree @ X0,X4 : tree @ X0,X5 : X0] : (((product_Pair @ X0 @ tree @ X0 @ (product_fst @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) @ (t @ X0 @ X1 @ (product_snd @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) @ (t @ X0 @ X5 @ X6 @ X7))) = (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X1 @ (t @ X0 @ X2 @ X3 @ X4) @ (t @ X0 @ X5 @ X6 @ X7)))) | (linorder @ X0 != $true)) )),
% 129.09/19.78 inference(cnf_transformation,[status(thm)],[f822])).
% 129.09/19.78 thf(f822,plain,(
% 129.09/19.78 ! [X0 : $tType] : ((linorder @ X0 != $true) | ! [X1 : X0,X2 : X0,X3 : tree @ X0,X4 : tree @ X0,X5 : X0,X6 : tree @ X0,X7 : tree @ X0] : ((product_Pair @ X0 @ tree @ X0 @ (product_fst @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) @ (t @ X0 @ X1 @ (product_snd @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) @ (t @ X0 @ X5 @ X6 @ X7))) = (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X1 @ (t @ X0 @ X2 @ X3 @ X4) @ (t @ X0 @ X5 @ X6 @ X7)))))),
% 129.09/19.78 inference(ennf_transformation,[status(thm)],[f295])).
% 129.09/19.78 thf(f295,plain,(
% 129.09/19.78 ! [X0 : $tType] : ((linorder @ X0 = $true) => ! [X1 : X0,X2 : X0,X3 : tree @ X0,X4 : tree @ X0,X5 : X0,X6 : tree @ X0,X7 : tree @ X0] : ((product_Pair @ X0 @ tree @ X0 @ (product_fst @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) @ (t @ X0 @ X1 @ (product_snd @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) @ (t @ X0 @ X5 @ X6 @ X7))) = (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X1 @ (t @ X0 @ X2 @ X3 @ X4) @ (t @ X0 @ X5 @ X6 @ X7)))))),
% 129.09/19.78 inference(fool_elimination,[status(thm)],[f294])).
% 129.09/19.78 thf(f294,plain,(
% 129.09/19.78 ! [X0 : $tType] : (linorder @ X0 => ! [X1 : X0,X2 : X0,X3 : tree @ X0,X4 : tree @ X0,X5 : X0,X6 : tree @ X0,X7 : tree @ X0] : ((product_Pair @ X0 @ tree @ X0 @ (product_fst @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) @ (t @ X0 @ X1 @ (product_snd @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) @ (t @ X0 @ X5 @ X6 @ X7))) = (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X1 @ (t @ X0 @ X2 @ X3 @ X4) @ (t @ X0 @ X5 @ X6 @ X7)))))),
% 129.09/19.78 inference(rectify,[status(thm)],[f7])).
% 129.09/19.78 thf(f7,axiom,(
% 129.09/19.78 ! [X0 : $tType] : (linorder @ X0 => ! [X11 : X0,X15 : X0,X16 : tree @ X0,X17 : tree @ X0,X12 : X0,X13 : tree @ X0,X14 : tree @ X0] : ((heapIm970386777veLeaf @ X0 @ (t @ X0 @ X11 @ (t @ X0 @ X15 @ X16 @ X17) @ (t @ X0 @ X12 @ X13 @ X14))) = (product_Pair @ X0 @ tree @ X0 @ (product_fst @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X15 @ X16 @ X17))) @ (t @ X0 @ X11 @ (product_snd @ X0 @ tree @ X0 @ (heapIm970386777veLeaf @ X0 @ (t @ X0 @ X15 @ X16 @ X17))) @ (t @ X0 @ X12 @ X13 @ X14)))))),
% 129.09/19.78 file('/export/starexec/sandbox/tmp/tmp.P5IR1jFQuE/DTF2THF_10235.p',fact_6_removeLeaf_Osimps_I4_J)).
% 129.09/19.78 % SZS output end Proof for DTF2THF_10235
% 129.09/19.78 % (11222)------------------------------
% 129.09/19.78 % (11222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 129.09/19.78 % (11222)Termination reason: Refutation
% 129.09/19.78
% 129.09/19.78 % (11222)Memory used [KB]: 12025
% 129.09/19.78 % (11222)Time elapsed: 1.285 s
% 129.09/19.78 % (11222)Instructions burned: 4204 (million)
% 129.09/19.78 % (11222)------------------------------
% 129.09/19.78 % (11222)------------------------------
% 129.09/19.78 % (10482)Success in time 18.142 s
%------------------------------------------------------------------------------