%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP068^2 : 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 : n005.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 08:55:17 AM UTC 2026
% Result : Theorem 8.42s 2.58s
% Output : Refutation 8.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP068^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:25:29 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP068^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer HeapImperative problem prob_383__5342344_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : HeapImperative/prob_383__5342344_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.33 v9.1.0, 0.00 v9.0.0, 0.33 v8.1.0, 0.50 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 351 ( 89 unt; 74 typ; 0 def)
% 0.30/0.46 % Number of atoms : 871 ( 295 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.30/0.46 % Number of connectives : 5675 ( 97 ~; 11 |; 70 &;5006 @)
% 0.30/0.46 % ( 0 <=>; 491 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 28 ( 10 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 419 ( 419 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 76 ( 73 usr; 13 con; 0-8 aty)
% 0.30/0.46 % Number of variables : 1469 ( 65 ^;1307 !; 21 ?;1469 :)
% 0.30/0.46 % ( 76 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:15:51.638
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (6)
% 0.30/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.46 product_prod: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Multiset_Omultiset,type,
% 0.30/0.46 multiset: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_List_Olist,type,
% 0.30/0.46 list: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Heap_OTree,type,
% 0.30/0.46 tree: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (68)
% 0.30/0.46 thf(sy_cl_HOL_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.46 ord:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.46 order:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.46 linorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.46 preorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.30/0.46 cancel1352612707id_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.30/0.46 linord219039673up_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.30/0.46 ordere216010020id_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.30/0.46 ordere779506340up_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.30/0.46 linord1659791738miring:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.30/0.46 canoni770627133id_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.30/0.46 ordere236663937imp_le:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 0.30/0.46 unique1598680935umeral:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.30/0.46 ordere516151231imp_le:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain,type,
% 0.30/0.46 bNF_Ca1785829860lChain:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( A > B ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux,type,
% 0.30/0.46 unique455577585es_aux:
% 0.30/0.46 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.30/0.46 plus_plus:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.30/0.46 zero_zero:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_HOL_ONO__MATCH,type,
% 0.30/0.46 nO_MATCH:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oleft,type,
% 0.30/0.46 heapIm1271749598e_left:
% 0.30/0.46 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oright,type,
% 0.30/0.46 heapIm1434396069_right:
% 0.30/0.46 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_OsiftDown,type,
% 0.30/0.46 heapIm748920189ftDown:
% 0.30/0.46 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OHeap,type,
% 0.30/0.46 heap:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( tree @ A ) ) > ( B > ( product_prod @ A @ B ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OHeap__axioms,type,
% 0.30/0.46 heap_axioms:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( tree @ A ) ) > ( B > ( product_prod @ A @ B ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OTree_OE,type,
% 0.30/0.46 e:
% 0.30/0.46 !>[A: $tType] : ( tree @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OTree_OT,type,
% 0.30/0.46 t:
% 0.30/0.46 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OTree_Ocase__Tree,type,
% 0.30/0.46 case_Tree:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( B > ( A > ( tree @ A ) > ( tree @ A ) > B ) > ( tree @ A ) > B ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OTree_Orec__Tree,type,
% 0.30/0.46 rec_Tree:
% 0.30/0.46 !>[C: $tType,A: $tType] : ( C > ( A > ( tree @ A ) > ( tree @ A ) > C > C > C ) > ( tree @ A ) > C ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OTree_Orel__Tree,type,
% 0.30/0.46 rel_Tree:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( tree @ A ) > ( tree @ B ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_Oin__tree,type,
% 0.30/0.46 in_tree:
% 0.30/0.46 !>[A: $tType] : ( A > ( tree @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_Ois__heap,type,
% 0.30/0.46 is_heap:
% 0.30/0.46 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_Omultiset,type,
% 0.30/0.46 multiset2:
% 0.30/0.46 !>[A: $tType] : ( ( tree @ A ) > ( multiset @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_Oval,type,
% 0.30/0.46 val:
% 0.30/0.46 !>[A: $tType] : ( ( tree @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices__Big_Olinorder__class_OMax,type,
% 0.30/0.46 lattic929149872er_Max:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Oadd__mset,type,
% 0.30/0.46 add_mset:
% 0.30/0.46 !>[A: $tType] : ( A > ( multiset @ A ) > ( multiset @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Ocomm__monoid__add_Osum__mset,type,
% 0.30/0.46 comm_monoid_sum_mset:
% 0.30/0.46 !>[A: $tType] : ( ( A > A > A ) > A > ( multiset @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Ofold__mset,type,
% 0.30/0.46 fold_mset:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > B > B ) > B > ( multiset @ A ) > B ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Oimage__mset,type,
% 0.30/0.46 image_mset:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( multiset @ A ) > ( multiset @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Omult,type,
% 0.30/0.46 mult:
% 0.30/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Omult1,type,
% 0.30/0.46 mult1:
% 0.30/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Omultp,type,
% 0.30/0.46 multp:
% 0.30/0.46 !>[A: $tType] : ( ( A > A > $o ) > ( multiset @ A ) > ( multiset @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Oset__mset,type,
% 0.30/0.46 set_mset:
% 0.30/0.46 !>[A: $tType] : ( ( multiset @ A ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Osubseteq__mset,type,
% 0.30/0.46 subseteq_mset:
% 0.30/0.46 !>[A: $tType] : ( ( multiset @ A ) > ( multiset @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.46 ord_less_eq:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder_Oantimono,type,
% 0.30/0.46 antimono:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.30/0.46 order_Greatest:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.46 product_Pair:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.30/0.46 produc2004651681e_prod:
% 0.30/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.30/0.46 product_rec_prod:
% 0.30/0.46 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_Oirrefl,type,
% 0.30/0.46 irrefl:
% 0.30/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_Otrans,type,
% 0.30/0.46 trans:
% 0.30/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_RemoveMax_OCollection,type,
% 0.30/0.46 collection:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_RemoveMax_OCollection_Oset,type,
% 0.30/0.46 set2:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( ( B > ( multiset @ A ) ) > B > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_RemoveMax_ORemoveMax,type,
% 0.30/0.46 removeMax:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( product_prod @ A @ B ) ) > ( B > $o ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_RemoveMax_ORemoveMax__axioms,type,
% 0.30/0.46 removeMax_axioms:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( product_prod @ A @ B ) ) > ( B > $o ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_l,type,
% 0.30/0.46 l: tree @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_l1____,type,
% 0.30/0.46 l1: tree @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_la____,type,
% 0.30/0.46 la: tree @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_r,type,
% 0.30/0.46 r: tree @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_r1____,type,
% 0.30/0.46 r1: tree @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_ra____,type,
% 0.30/0.46 ra: tree @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_t,type,
% 0.30/0.46 t2: tree @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_v,type,
% 0.30/0.46 v: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_v1____,type,
% 0.30/0.46 v1: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_v2____,type,
% 0.30/0.46 v2: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_va____,type,
% 0.30/0.46 va: a ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (256)
% 0.30/0.46 thf(fact_0__C4_Oprems_C_I2_J,axiom,
% 0.30/0.46 is_heap @ a @ ra ).
% 0.30/0.46
% 0.30/0.46 % "4.prems"(2)
% 0.30/0.46 thf(fact_1__C4_Oprems_C_I1_J,axiom,
% 0.30/0.46 is_heap @ a @ la ).
% 0.30/0.46
% 0.30/0.46 % "4.prems"(1)
% 0.30/0.46 thf(fact_2_assms_I2_J,axiom,
% 0.30/0.46 is_heap @ a @ r ).
% 0.30/0.46
% 0.30/0.46 % assms(2)
% 0.30/0.46 thf(fact_3_assms_I1_J,axiom,
% 0.30/0.46 is_heap @ a @ l ).
% 0.30/0.46
% 0.30/0.46 % assms(1)
% 0.30/0.46 thf(fact_4_True,axiom,
% 0.30/0.46 ord_less_eq @ a @ v1 @ v2 ).
% 0.30/0.46
% 0.30/0.46 % True
% 0.30/0.46 thf(fact_5__C4_Oprems_C_I3_J,axiom,
% 0.30/0.46 ( ( t @ a @ v2 @ ( e @ a ) @ ( t @ a @ v1 @ l1 @ r1 ) )
% 0.30/0.46 = ( t @ a @ va @ la @ ra ) ) ).
% 0.30/0.46
% 0.30/0.46 % "4.prems"(3)
% 0.30/0.46 thf(fact_6_siftDown_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [V: A] :
% 0.30/0.46 ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) )
% 0.30/0.46 = ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(2)
% 0.30/0.46 thf(fact_7_siftDown_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( e @ A ) )
% 0.30/0.46 = ( e @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(1)
% 0.30/0.46 thf(fact_8_siftDown_Ocases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: tree @ A] :
% 0.30/0.46 ( ( X
% 0.30/0.46 != ( e @ A ) )
% 0.30/0.46 => ( ! [V2: A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t @ A @ V2 @ ( e @ A ) @ ( e @ A ) ) )
% 0.30/0.46 => ( ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t @ A @ V2 @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 0.30/0.46 => ( ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t @ A @ V2 @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.30/0.46 => ~ ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t @ A @ V2 @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.cases
% 0.30/0.46 thf(fact_9_assms_I3_J,axiom,
% 0.30/0.46 ( t2
% 0.30/0.46 = ( t @ a @ v @ l @ r ) ) ).
% 0.30/0.46
% 0.30/0.46 % assms(3)
% 0.30/0.46 thf(fact_10_is__heap_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [V: A] : ( is_heap @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(2)
% 0.30/0.46 thf(fact_11_siftDown__Node,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T2: tree @ A,V: A,L: tree @ A,R: tree @ A] :
% 0.30/0.46 ( ( T2
% 0.30/0.46 = ( t @ A @ V @ L @ R ) )
% 0.30/0.46 => ? [L2: tree @ A,V3: A,R2: tree @ A] :
% 0.30/0.46 ( ( ( heapIm748920189ftDown @ A @ T2 )
% 0.30/0.46 = ( t @ A @ V3 @ L2 @ R2 ) )
% 0.30/0.46 & ( ord_less_eq @ A @ V @ V3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown_Node
% 0.30/0.46 thf(fact_12__C4_Ohyps_C,axiom,
% 0.30/0.46 ! [L: tree @ a,R: tree @ a,V: a] :
% 0.30/0.46 ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ v2 )
% 0.30/0.46 => ( ( is_heap @ a @ L )
% 0.30/0.46 => ( ( is_heap @ a @ R )
% 0.30/0.46 => ( ( ( t @ a @ v2 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
% 0.30/0.46 = ( t @ a @ V @ L @ R ) )
% 0.30/0.46 => ( is_heap @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v2 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % "4.hyps"
% 0.30/0.46 thf(fact_13_Tree_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: tree @ A,X23: tree @ A,Y21: A,Y22: tree @ A,Y23: tree @ A] :
% 0.30/0.46 ( ( ( t @ A @ X21 @ X22 @ X23 )
% 0.30/0.46 = ( t @ A @ Y21 @ Y22 @ Y23 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X22 = Y22 )
% 0.30/0.46 & ( X23 = Y23 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.inject
% 0.30/0.46 thf(fact_14_is__heap_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( is_heap @ A @ ( e @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(1)
% 0.30/0.46 thf(fact_15_Tree_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: tree @ A,X23: tree @ A] :
% 0.30/0.46 ( ( e @ A )
% 0.30/0.46 != ( t @ A @ X21 @ X22 @ X23 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.distinct(1)
% 0.30/0.46 thf(fact_16_Tree_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( tree @ A ) > $o,Tree: tree @ A] :
% 0.30/0.46 ( ( P @ ( e @ A ) )
% 0.30/0.46 => ( ! [X1: A,X2: tree @ A,X3: tree @ A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( ( P @ X3 )
% 0.30/0.46 => ( P @ ( t @ A @ X1 @ X2 @ X3 ) ) ) )
% 0.30/0.46 => ( P @ Tree ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.induct
% 0.30/0.46 thf(fact_17_Tree_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Y: tree @ A] :
% 0.30/0.46 ( ( Y
% 0.30/0.46 != ( e @ A ) )
% 0.30/0.46 => ~ ! [X212: A,X222: tree @ A,X232: tree @ A] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( t @ A @ X212 @ X222 @ X232 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.exhaust
% 0.30/0.46 thf(fact_18_is__heap_Ocases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: tree @ A] :
% 0.30/0.46 ( ( X
% 0.30/0.46 != ( e @ A ) )
% 0.30/0.46 => ( ! [V2: A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t @ A @ V2 @ ( e @ A ) @ ( e @ A ) ) )
% 0.30/0.46 => ( ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t @ A @ V2 @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 0.30/0.46 => ( ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t @ A @ V2 @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 0.30/0.46 => ~ ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t @ A @ V2 @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.cases
% 0.30/0.46 thf(fact_19_siftDown__in__tree__set,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( ( in_tree @ A )
% 0.30/0.46 = ( ^ [V4: A,T3: tree @ A] : ( in_tree @ A @ V4 @ ( heapIm748920189ftDown @ A @ T3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown_in_tree_set
% 0.30/0.46 thf(fact_20_left_Osimps,axiom,
% 0.30/0.46 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 0.30/0.46 ( ( heapIm1271749598e_left @ A @ ( t @ A @ V @ L @ R ) )
% 0.30/0.46 = L ) ).
% 0.30/0.46
% 0.30/0.46 % left.simps
% 0.30/0.46 thf(fact_21_is__heap__max,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [V: A,T2: tree @ A] :
% 0.30/0.46 ( ( in_tree @ A @ V @ T2 )
% 0.30/0.46 => ( ( is_heap @ A @ T2 )
% 0.30/0.46 => ( ord_less_eq @ A @ V @ ( val @ A @ T2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap_max
% 0.30/0.46 thf(fact_22_val_Osimps,axiom,
% 0.30/0.46 ! [A: $tType,V: A,Uu: tree @ A,Uv: tree @ A] :
% 0.30/0.46 ( ( val @ A @ ( t @ A @ V @ Uu @ Uv ) )
% 0.30/0.46 = V ) ).
% 0.30/0.46
% 0.30/0.46 % val.simps
% 0.30/0.46 thf(fact_23_in__tree_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,V: A,V5: A,L: tree @ A,R: tree @ A] :
% 0.30/0.46 ( ( in_tree @ A @ V @ ( t @ A @ V5 @ L @ R ) )
% 0.30/0.46 = ( ( V = V5 )
% 0.30/0.46 | ( in_tree @ A @ V @ L )
% 0.30/0.46 | ( in_tree @ A @ V @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_tree.simps(2)
% 0.30/0.46 thf(fact_24_siftDown_Osimps_I5_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Vd2: A,Ve2: tree @ A,Vf2: tree @ A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,V: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( t @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( t @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(5)
% 0.30/0.46 thf(fact_25_siftDown_Osimps_I6_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A,V: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(6)
% 0.30/0.46 thf(fact_26_in__tree_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,V: A] :
% 0.30/0.46 ~ ( in_tree @ A @ V @ ( e @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_tree.simps(1)
% 0.30/0.46 thf(fact_27_is__heap_Osimps_I5_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [V: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 0.30/0.46 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 & ( is_heap @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) )
% 0.30/0.46 & ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 & ( is_heap @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(5)
% 0.30/0.46 thf(fact_28_is__heap_Osimps_I6_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [V: A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.30/0.46 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 & ( is_heap @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 0.30/0.46 & ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 & ( is_heap @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(6)
% 0.30/0.46 thf(fact_29_siftDown_Osimps_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Va2: A,Vb2: tree @ A,Vc2: tree @ A,V: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 0.30/0.46 = ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 0.30/0.46 = ( t @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ ( e @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(3)
% 0.30/0.46 thf(fact_30_siftDown_Osimps_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Va2: A,Vb2: tree @ A,Vc2: tree @ A,V: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( e @ A ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(4)
% 0.30/0.46 thf(fact_31_siftDown__in__tree,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T2: tree @ A] :
% 0.30/0.46 ( ( T2
% 0.30/0.46 != ( e @ A ) )
% 0.30/0.46 => ( in_tree @ A @ ( val @ A @ ( heapIm748920189ftDown @ A @ T2 ) ) @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown_in_tree
% 0.30/0.46 thf(fact_32_is__heap_Osimps_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [V: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.30/0.46 ( ( is_heap @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 & ( is_heap @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(3)
% 0.30/0.46 thf(fact_33_is__heap_Osimps_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [V: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 0.30/0.46 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 0.30/0.46 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 & ( is_heap @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(4)
% 0.30/0.46 thf(fact_34_right_Osimps,axiom,
% 0.30/0.46 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 0.30/0.46 ( ( heapIm1434396069_right @ A @ ( t @ A @ V @ L @ R ) )
% 0.30/0.46 = R ) ).
% 0.30/0.46
% 0.30/0.46 % right.simps
% 0.30/0.46 thf(fact_35_order__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_36_le__funD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G: A > B,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funD
% 0.30/0.46 thf(fact_37_le__funE,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G: A > B,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funE
% 0.30/0.46 thf(fact_38_le__funI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funI
% 0.30/0.46 thf(fact_39_le__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.30/0.46 = ( ^ [F2: A > B,G2: A > B] :
% 0.30/0.46 ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_fun_def
% 0.30/0.46 thf(fact_40_order__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.30/0.46 => ( ! [X4: B,Y2: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_41_order__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( order @ C )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 0.30/0.46 => ( ! [X4: A,Y2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_42_verit__la__disequality,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % verit_la_disequality
% 0.30/0.46 thf(fact_43_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.30/0.46 => ( ! [X4: B,Y2: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_44_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ( F @ B2 )
% 0.30/0.46 = C2 )
% 0.30/0.46 => ( ! [X4: A,Y2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ A3 ) )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X4: A] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 = ( Q @ X4 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X4: A] :
% 0.30/0.46 ( ( F @ X4 )
% 0.30/0.46 = ( G @ X4 ) )
% 0.30/0.46 => ( F = G ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_49_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_50_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A4: A,B3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.30/0.46 & ( ord_less_eq @ A @ A4 @ B3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_51_dual__order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_52_linorder__wlog,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.30/0.46 ( ! [A5: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.30/0.46 => ( P @ A5 @ B4 ) )
% 0.30/0.46 => ( ! [A5: A,B4: A] :
% 0.30/0.46 ( ( P @ B4 @ A5 )
% 0.30/0.46 => ( P @ A5 @ B4 ) )
% 0.30/0.46 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_wlog
% 0.30/0.46 thf(fact_53_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_54_order__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_55_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_56_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( B2 = C2 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_57_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_58_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A4: A,B3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.30/0.46 & ( ord_less_eq @ A @ B3 @ A4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_59_antisym__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [Y: A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_60_le__cases3,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases3
% 0.30/0.46 thf(fact_61_order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_62_le__cases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases
% 0.30/0.46 thf(fact_63_eq__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( X = Y )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_64_linear,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linear
% 0.30/0.46 thf(fact_65_antisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_66_eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [X5: A,Y4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.30/0.46 & ( ord_less_eq @ A @ Y4 @ X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_67_Greatest__equality,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [P: A > $o,X: A] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: A] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y2 @ X ) )
% 0.30/0.46 => ( ( order_Greatest @ A @ P )
% 0.30/0.46 = X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Greatest_equality
% 0.30/0.46 thf(fact_68_GreatestI2__order,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [P: A > $o,X: A,Q: A > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: A] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y2 @ X ) )
% 0.30/0.46 => ( ! [X4: A] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 => ( ! [Y5: A] :
% 0.30/0.46 ( ( P @ Y5 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y5 @ X4 ) )
% 0.30/0.46 => ( Q @ X4 ) ) )
% 0.30/0.46 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % GreatestI2_order
% 0.30/0.46 thf(fact_69_le__rel__bool__arg__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ( ( ord_less_eq @ ( $o > A ) )
% 0.30/0.46 = ( ^ [X6: $o > A,Y6: $o > A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 0.30/0.46 & ( ord_less_eq @ A @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_rel_bool_arg_iff
% 0.30/0.46 thf(fact_70_Tree_Osimps_I4_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F1: B,F22: A > ( tree @ A ) > ( tree @ A ) > B] :
% 0.30/0.46 ( ( case_Tree @ B @ A @ F1 @ F22 @ ( e @ A ) )
% 0.30/0.46 = F1 ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.simps(4)
% 0.30/0.46 thf(fact_71_Tree_Osimps_I5_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F1: B,F22: A > ( tree @ A ) > ( tree @ A ) > B,X21: A,X22: tree @ A,X23: tree @ A] :
% 0.30/0.46 ( ( case_Tree @ B @ A @ F1 @ F22 @ ( t @ A @ X21 @ X22 @ X23 ) )
% 0.30/0.46 = ( F22 @ X21 @ X22 @ X23 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.simps(5)
% 0.30/0.46 thf(fact_72_Tree_Osimps_I6_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,F1: C,F22: A > ( tree @ A ) > ( tree @ A ) > C > C > C] :
% 0.30/0.46 ( ( rec_Tree @ C @ A @ F1 @ F22 @ ( e @ A ) )
% 0.30/0.46 = F1 ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.simps(6)
% 0.30/0.46 thf(fact_73_Heap_Ois__heap__of__list,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Empty: 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 ),I: list @ A] :
% 0.30/0.46 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.30/0.46 => ( is_heap @ A @ ( As_tree @ ( Of_list @ I ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap.is_heap_of_list
% 0.30/0.46 thf(fact_74_Tree_Osimps_I7_J,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,F1: C,F22: A > ( tree @ A ) > ( tree @ A ) > C > C > C,X21: A,X22: tree @ A,X23: tree @ A] :
% 0.30/0.46 ( ( rec_Tree @ C @ A @ F1 @ F22 @ ( t @ A @ X21 @ X22 @ X23 ) )
% 0.30/0.46 = ( F22 @ X21 @ X22 @ X23 @ ( rec_Tree @ C @ A @ F1 @ F22 @ X22 ) @ ( rec_Tree @ C @ A @ F1 @ F22 @ X23 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.simps(7)
% 0.30/0.46 thf(fact_75_Heap_Oas__tree__empty,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Empty: 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 ),T2: B] :
% 0.30/0.46 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.30/0.46 => ( ( ( As_tree @ T2 )
% 0.30/0.46 = ( e @ A ) )
% 0.30/0.46 = ( Is_empty @ T2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap.as_tree_empty
% 0.30/0.46 thf(fact_76_Heap_Oaxioms_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Empty: 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 )] :
% 0.30/0.46 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.30/0.46 => ( heap_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap.axioms(2)
% 0.30/0.46 thf(fact_77_Heap_Omultiset,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Empty: 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 ),L: B] :
% 0.30/0.46 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.30/0.46 => ( ( Multiset @ L )
% 0.30/0.46 = ( multiset2 @ A @ ( As_tree @ L ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap.multiset
% 0.30/0.46 thf(fact_78_Heap_Oremove__max__val,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Empty: 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 ),T2: B,M: A,T4: B] :
% 0.30/0.46 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.30/0.46 => ( ~ ( Is_empty @ T2 )
% 0.30/0.46 => ( ( ( product_Pair @ A @ B @ M @ T4 )
% 0.30/0.46 = ( Remove_max @ T2 ) )
% 0.30/0.46 => ( M
% 0.30/0.46 = ( val @ A @ ( As_tree @ T2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap.remove_max_val
% 0.30/0.46 thf(fact_79_Heap_Oremove__max__is__heap,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Empty: 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 ),L: B,M: A,L3: B] :
% 0.30/0.46 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.30/0.46 => ( ~ ( Is_empty @ L )
% 0.30/0.46 => ( ( is_heap @ A @ ( As_tree @ L ) )
% 0.30/0.46 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 0.30/0.46 = ( Remove_max @ L ) )
% 0.30/0.46 => ( is_heap @ A @ ( As_tree @ L3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap.remove_max_is_heap
% 0.30/0.46 thf(fact_80_Heap_Oaxioms_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Empty: 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 )] :
% 0.30/0.46 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.30/0.46 => ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap.axioms(1)
% 0.30/0.46 thf(fact_81_Tree_Orel__induct,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R3: A > B > $o,X: tree @ A,Y: tree @ B,Q: ( tree @ A ) > ( tree @ B ) > $o] :
% 0.30/0.46 ( ( rel_Tree @ A @ B @ R3 @ X @ Y )
% 0.30/0.46 => ( ( Q @ ( e @ A ) @ ( e @ B ) )
% 0.30/0.46 => ( ! [A21: A,A22: tree @ A,A23: tree @ A,B21: B,B22: tree @ B,B23: tree @ B] :
% 0.30/0.46 ( ( R3 @ A21 @ B21 )
% 0.30/0.46 => ( ( Q @ A22 @ B22 )
% 0.30/0.46 => ( ( Q @ A23 @ B23 )
% 0.30/0.46 => ( Q @ ( t @ A @ A21 @ A22 @ A23 ) @ ( t @ B @ B21 @ B22 @ B23 ) ) ) ) )
% 0.30/0.46 => ( Q @ X @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_induct
% 0.30/0.46 thf(fact_82_Tree_Orel__mono,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R3: A > B > $o,Ra: A > B > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B > $o ) @ R3 @ Ra )
% 0.30/0.46 => ( ord_less_eq @ ( ( tree @ A ) > ( tree @ B ) > $o ) @ ( rel_Tree @ A @ B @ R3 ) @ ( rel_Tree @ A @ B @ Ra ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_mono
% 0.30/0.46 thf(fact_83_Tree_Orel__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( rel_Tree @ A @ A
% 0.30/0.46 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [Y3: tree @ A,Z: tree @ A] : ( Y3 = Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_eq
% 0.30/0.46 thf(fact_84_Tree_Orel__refl,axiom,
% 0.30/0.46 ! [B: $tType,Ra: B > B > $o,X: tree @ B] :
% 0.30/0.46 ( ! [X4: B] : ( Ra @ X4 @ X4 )
% 0.30/0.46 => ( rel_Tree @ B @ B @ Ra @ X @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_refl
% 0.30/0.46 thf(fact_85_Tree_Orel__inject_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R3: A > B > $o,X21: A,X22: tree @ A,X23: tree @ A,Y21: B,Y22: tree @ B,Y23: tree @ B] :
% 0.30/0.46 ( ( rel_Tree @ A @ B @ R3 @ ( t @ A @ X21 @ X22 @ X23 ) @ ( t @ B @ Y21 @ Y22 @ Y23 ) )
% 0.30/0.46 = ( ( R3 @ X21 @ Y21 )
% 0.30/0.46 & ( rel_Tree @ A @ B @ R3 @ X22 @ Y22 )
% 0.30/0.46 & ( rel_Tree @ A @ B @ R3 @ X23 @ Y23 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_inject(2)
% 0.30/0.46 thf(fact_86_Tree_Orel__intros_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R3: A > B > $o,X21: A,Y21: B,X22: tree @ A,Y22: tree @ B,X23: tree @ A,Y23: tree @ B] :
% 0.30/0.46 ( ( R3 @ X21 @ Y21 )
% 0.30/0.46 => ( ( rel_Tree @ A @ B @ R3 @ X22 @ Y22 )
% 0.30/0.46 => ( ( rel_Tree @ A @ B @ R3 @ X23 @ Y23 )
% 0.30/0.46 => ( rel_Tree @ A @ B @ R3 @ ( t @ A @ X21 @ X22 @ X23 ) @ ( t @ B @ Y21 @ Y22 @ Y23 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_intros(2)
% 0.30/0.46 thf(fact_87_Tree_Octr__transfer_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R3: A > B > $o] : ( rel_Tree @ A @ B @ R3 @ ( e @ A ) @ ( e @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.ctr_transfer(1)
% 0.30/0.46 thf(fact_88_Heap__def,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( ( heap @ B @ A )
% 0.30/0.46 = ( ^ [Empty2: 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 )] :
% 0.30/0.46 ( ( collection @ B @ A @ Empty2 @ Is_empty2 @ Of_list2 @ Multiset2 )
% 0.30/0.46 & ( heap_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap_def
% 0.30/0.46 thf(fact_89_Heap_Ointro,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Empty: 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 )] :
% 0.30/0.46 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 0.30/0.46 => ( ( heap_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.30/0.46 => ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap.intro
% 0.30/0.46 thf(fact_90_Tree_Orel__distinct_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R3: A > B > $o,Y21: A,Y22: tree @ A,Y23: tree @ A] :
% 0.30/0.46 ~ ( rel_Tree @ A @ B @ R3 @ ( t @ A @ Y21 @ Y22 @ Y23 ) @ ( e @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_distinct(2)
% 0.30/0.46 thf(fact_91_Tree_Orel__distinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R3: A > B > $o,Y21: B,Y22: tree @ B,Y23: tree @ B] :
% 0.30/0.46 ~ ( rel_Tree @ A @ B @ R3 @ ( e @ A ) @ ( t @ B @ Y21 @ Y22 @ Y23 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_distinct(1)
% 0.30/0.46 thf(fact_92_Tree_Orel__cases,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R3: A > B > $o,A2: tree @ A,B2: tree @ B] :
% 0.30/0.46 ( ( rel_Tree @ A @ B @ R3 @ A2 @ B2 )
% 0.30/0.46 => ( ( ( A2
% 0.30/0.46 = ( e @ A ) )
% 0.30/0.46 => ( B2
% 0.30/0.46 != ( e @ B ) ) )
% 0.30/0.46 => ~ ! [X1: A,X2: tree @ A,X3: tree @ A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( t @ A @ X1 @ X2 @ X3 ) )
% 0.30/0.46 => ! [Y1: B,Y24: tree @ B,Y32: tree @ B] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 = ( t @ B @ Y1 @ Y24 @ Y32 ) )
% 0.30/0.46 => ( ( R3 @ X1 @ Y1 )
% 0.30/0.46 => ( ( rel_Tree @ A @ B @ R3 @ X2 @ Y24 )
% 0.30/0.46 => ~ ( rel_Tree @ A @ B @ R3 @ X3 @ Y32 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_cases
% 0.30/0.46 thf(fact_93_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B5: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A6 @ B5 ) )
% 0.30/0.46 = ( ( A2 = A6 )
% 0.30/0.46 & ( B2 = B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_94_prod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X12: A,X24: B,Y12: A,Y25: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ X12 @ X24 )
% 0.30/0.46 = ( product_Pair @ A @ B @ Y12 @ Y25 ) )
% 0.30/0.46 = ( ( X12 = Y12 )
% 0.30/0.46 & ( X24 = Y25 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_95_Heap__axioms__def,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( ( heap_axioms @ B @ A )
% 0.30/0.46 = ( ^ [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 )] :
% 0.30/0.46 ( ! [L4: B] :
% 0.30/0.46 ( ( Multiset2 @ L4 )
% 0.30/0.46 = ( multiset2 @ A @ ( As_tree2 @ L4 ) ) )
% 0.30/0.46 & ! [I2: list @ A] : ( is_heap @ A @ ( As_tree2 @ ( Of_list2 @ I2 ) ) )
% 0.30/0.46 & ! [T3: B] :
% 0.30/0.46 ( ( ( As_tree2 @ T3 )
% 0.30/0.46 = ( e @ A ) )
% 0.30/0.46 = ( Is_empty2 @ T3 ) )
% 0.30/0.46 & ! [L4: B,M2: A,L5: B] :
% 0.30/0.46 ( ~ ( Is_empty2 @ L4 )
% 0.30/0.46 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 0.30/0.46 = ( Remove_max2 @ L4 ) )
% 0.30/0.46 => ( ( add_mset @ A @ M2 @ ( Multiset2 @ L5 ) )
% 0.30/0.46 = ( Multiset2 @ L4 ) ) ) )
% 0.30/0.46 & ! [L4: B,M2: A,L5: B] :
% 0.30/0.46 ( ~ ( Is_empty2 @ L4 )
% 0.30/0.46 => ( ( is_heap @ A @ ( As_tree2 @ L4 ) )
% 0.30/0.46 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 0.30/0.46 = ( Remove_max2 @ L4 ) )
% 0.30/0.46 => ( is_heap @ A @ ( As_tree2 @ L5 ) ) ) ) )
% 0.30/0.46 & ! [T3: B,M2: A,T5: B] :
% 0.30/0.46 ( ~ ( Is_empty2 @ T3 )
% 0.30/0.46 => ( ( ( product_Pair @ A @ B @ M2 @ T5 )
% 0.30/0.46 = ( Remove_max2 @ T3 ) )
% 0.30/0.46 => ( M2
% 0.30/0.46 = ( val @ A @ ( As_tree2 @ T3 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap_axioms_def
% 0.30/0.46 thf(fact_96_Heap__axioms_Ointro,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Multiset: B > ( multiset @ A ),As_tree: B > ( tree @ A ),Of_list: ( list @ A ) > B,Is_empty: B > $o,Remove_max: B > ( product_prod @ A @ B )] :
% 0.30/0.46 ( ! [L6: B] :
% 0.30/0.46 ( ( Multiset @ L6 )
% 0.30/0.46 = ( multiset2 @ A @ ( As_tree @ L6 ) ) )
% 0.30/0.46 => ( ! [I3: list @ A] : ( is_heap @ A @ ( As_tree @ ( Of_list @ I3 ) ) )
% 0.30/0.46 => ( ! [T6: B] :
% 0.30/0.46 ( ( ( As_tree @ T6 )
% 0.30/0.46 = ( e @ A ) )
% 0.30/0.46 = ( Is_empty @ T6 ) )
% 0.30/0.46 => ( ! [L6: B,M3: A,L2: B] :
% 0.30/0.46 ( ~ ( Is_empty @ L6 )
% 0.30/0.46 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 0.30/0.46 = ( Remove_max @ L6 ) )
% 0.30/0.46 => ( ( add_mset @ A @ M3 @ ( Multiset @ L2 ) )
% 0.30/0.46 = ( Multiset @ L6 ) ) ) )
% 0.30/0.46 => ( ! [L6: B,M3: A,L2: B] :
% 0.30/0.46 ( ~ ( Is_empty @ L6 )
% 0.30/0.46 => ( ( is_heap @ A @ ( As_tree @ L6 ) )
% 0.30/0.46 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 0.30/0.46 = ( Remove_max @ L6 ) )
% 0.30/0.46 => ( is_heap @ A @ ( As_tree @ L2 ) ) ) ) )
% 0.30/0.46 => ( ! [T6: B,M3: A,T7: B] :
% 0.30/0.46 ( ~ ( Is_empty @ T6 )
% 0.30/0.46 => ( ( ( product_Pair @ A @ B @ M3 @ T7 )
% 0.30/0.46 = ( Remove_max @ T6 ) )
% 0.30/0.46 => ( M3
% 0.30/0.46 = ( val @ A @ ( As_tree @ T6 ) ) ) ) )
% 0.30/0.46 => ( heap_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Heap_axioms.intro
% 0.30/0.46 thf(fact_97_heap__top__geq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [A2: A,T2: tree @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( set_mset @ A @ ( multiset2 @ A @ T2 ) ) )
% 0.30/0.46 => ( ( is_heap @ A @ T2 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( val @ A @ T2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % heap_top_geq
% 0.30/0.46 thf(fact_98_Collection_Ois__empty__empty,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A )] :
% 0.30/0.46 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 0.30/0.46 => ( Is_empty @ Empty ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collection.is_empty_empty
% 0.30/0.46 thf(fact_99_predicate2I,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 0.30/0.46 ( ! [X4: A,Y2: B] :
% 0.30/0.46 ( ( P @ X4 @ Y2 )
% 0.30/0.46 => ( Q @ X4 @ Y2 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 0.30/0.46
% 0.30/0.46 % predicate2I
% 0.30/0.46 thf(fact_100_rev__predicate2D,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y: B,Q: A > B > $o] :
% 0.30/0.46 ( ( P @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.30/0.47 => ( Q @ X @ Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rev_predicate2D
% 0.30/0.47 thf(fact_101_predicate2D,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y: B] :
% 0.30/0.47 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.30/0.47 => ( ( P @ X @ Y )
% 0.30/0.47 => ( Q @ X @ Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % predicate2D
% 0.30/0.47 thf(fact_102_Heap_Oremove__max__multiset_H,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Empty: 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 ),L: B,M: A,L3: B] :
% 0.30/0.47 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.30/0.47 => ( ~ ( Is_empty @ L )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 0.30/0.47 = ( Remove_max @ L ) )
% 0.30/0.47 => ( ( add_mset @ A @ M @ ( Multiset @ L3 ) )
% 0.30/0.47 = ( Multiset @ L ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Heap.remove_max_multiset'
% 0.30/0.47 thf(fact_103_surj__pair,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.30/0.47 ? [X4: A,Y2: B] :
% 0.30/0.47 ( P2
% 0.30/0.47 = ( product_Pair @ A @ B @ X4 @ Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % surj_pair
% 0.30/0.47 thf(fact_104_prod__cases,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.30/0.47 ( ! [A5: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.30/0.47 => ( P @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases
% 0.30/0.47 thf(fact_105_Pair__inject,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B5: B] :
% 0.30/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.47 = ( product_Pair @ A @ B @ A6 @ B5 ) )
% 0.30/0.47 => ~ ( ( A2 = A6 )
% 0.30/0.47 => ( B2 != B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Pair_inject
% 0.30/0.47 thf(fact_106_prod__cases3,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases3
% 0.30/0.47 thf(fact_107_prod__cases4,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C,D2: D] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases4
% 0.30/0.47 thf(fact_108_prod__cases5,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases5
% 0.30/0.47 thf(fact_109_prod__cases6,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E,F4: F3] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases6
% 0.30/0.47 thf(fact_110_prod__cases7,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 0.30/0.47 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E,F4: F3,G4: G3] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_cases7
% 0.30/0.47 thf(fact_111_prod__induct3,axiom,
% 0.30/0.47 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 0.30/0.47 => ( P @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct3
% 0.30/0.47 thf(fact_112_prod__induct4,axiom,
% 0.30/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 0.30/0.47 => ( P @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct4
% 0.30/0.47 thf(fact_113_prod__induct5,axiom,
% 0.30/0.47 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( 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 ) ) )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.30/0.47 => ( P @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct5
% 0.30/0.47 thf(fact_114_prod__induct6,axiom,
% 0.30/0.47 ! [F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) )
% 0.30/0.47 => ( P @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct6
% 0.30/0.47 thf(fact_115_prod__induct7,axiom,
% 0.30/0.47 ! [G3: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 0.30/0.47 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E,F4: F3,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) )
% 0.30/0.47 => ( P @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_induct7
% 0.30/0.47 thf(fact_116_old_Oprod_Oexhaust,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.30/0.47 ~ ! [A5: A,B4: B] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( product_Pair @ A @ B @ A5 @ B4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % old.prod.exhaust
% 0.30/0.47 thf(fact_117_old_Oprod_Oinducts,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.30/0.47 ( ! [A5: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.30/0.47 => ( P @ Prod ) ) ).
% 0.30/0.47
% 0.30/0.47 % old.prod.inducts
% 0.30/0.47 thf(fact_118_Collection_Ois__empty__inj,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),E3: B] :
% 0.30/0.47 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 0.30/0.47 => ( ( Is_empty @ E3 )
% 0.30/0.47 => ( E3 = Empty ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collection.is_empty_inj
% 0.30/0.47 thf(fact_119_old_Oprod_Orec,axiom,
% 0.30/0.47 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.30/0.47 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.47 = ( F1 @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % old.prod.rec
% 0.30/0.47 thf(fact_120_add__mset__add__mset__same__iff,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: multiset @ A,B6: multiset @ A] :
% 0.30/0.47 ( ( ( add_mset @ A @ A2 @ A3 )
% 0.30/0.47 = ( add_mset @ A @ A2 @ B6 ) )
% 0.30/0.47 = ( A3 = B6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mset_add_mset_same_iff
% 0.30/0.47 thf(fact_121_multi__self__add__other__not__self,axiom,
% 0.30/0.47 ! [A: $tType,M4: multiset @ A,X: A] :
% 0.30/0.47 ( M4
% 0.30/0.47 != ( add_mset @ A @ X @ M4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % multi_self_add_other_not_self
% 0.30/0.47 thf(fact_122_mset__add,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: multiset @ A] :
% 0.30/0.47 ( ( member @ A @ A2 @ ( set_mset @ A @ A3 ) )
% 0.30/0.47 => ~ ! [B7: multiset @ A] :
% 0.30/0.47 ( A3
% 0.30/0.47 != ( add_mset @ A @ A2 @ B7 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mset_add
% 0.30/0.47 thf(fact_123_multi__member__split,axiom,
% 0.30/0.47 ! [A: $tType,X: A,M4: multiset @ A] :
% 0.30/0.47 ( ( member @ A @ X @ ( set_mset @ A @ M4 ) )
% 0.30/0.47 => ? [A7: multiset @ A] :
% 0.30/0.47 ( M4
% 0.30/0.47 = ( add_mset @ A @ X @ A7 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multi_member_split
% 0.30/0.47 thf(fact_124_add__mset__commute,axiom,
% 0.30/0.47 ! [A: $tType,X: A,Y: A,M4: multiset @ A] :
% 0.30/0.47 ( ( add_mset @ A @ X @ ( add_mset @ A @ Y @ M4 ) )
% 0.30/0.47 = ( add_mset @ A @ Y @ ( add_mset @ A @ X @ M4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mset_commute
% 0.30/0.47 thf(fact_125_add__eq__conv__ex,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,M4: multiset @ A,B2: A,N: multiset @ A] :
% 0.30/0.47 ( ( ( add_mset @ A @ A2 @ M4 )
% 0.30/0.47 = ( add_mset @ A @ B2 @ N ) )
% 0.30/0.47 = ( ( ( M4 = N )
% 0.30/0.47 & ( A2 = B2 ) )
% 0.30/0.47 | ? [K: multiset @ A] :
% 0.30/0.47 ( ( M4
% 0.30/0.47 = ( add_mset @ A @ B2 @ K ) )
% 0.30/0.47 & ( N
% 0.30/0.47 = ( add_mset @ A @ A2 @ K ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_eq_conv_ex
% 0.30/0.47 thf(fact_126_union__single__eq__member,axiom,
% 0.30/0.47 ! [A: $tType,X: A,M4: multiset @ A,N: multiset @ A] :
% 0.30/0.47 ( ( ( add_mset @ A @ X @ M4 )
% 0.30/0.47 = N )
% 0.30/0.47 => ( member @ A @ X @ ( set_mset @ A @ N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % union_single_eq_member
% 0.30/0.47 thf(fact_127_insert__noteq__member,axiom,
% 0.30/0.47 ! [A: $tType,B2: A,B6: multiset @ A,C2: A,C4: multiset @ A] :
% 0.30/0.47 ( ( ( add_mset @ A @ B2 @ B6 )
% 0.30/0.47 = ( add_mset @ A @ C2 @ C4 ) )
% 0.30/0.47 => ( ( B2 != C2 )
% 0.30/0.47 => ( member @ A @ C2 @ ( set_mset @ A @ B6 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_noteq_member
% 0.30/0.47 thf(fact_128_heap__top__max,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T2: tree @ A] :
% 0.30/0.47 ( ( T2
% 0.30/0.47 != ( e @ A ) )
% 0.30/0.47 => ( ( is_heap @ A @ T2 )
% 0.30/0.47 => ( ( val @ A @ T2 )
% 0.30/0.47 = ( lattic929149872er_Max @ A @ ( set_mset @ A @ ( multiset2 @ A @ T2 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % heap_top_max
% 0.30/0.47 thf(fact_129_internal__case__prod__conv,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 0.30/0.47 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.30/0.47 = ( C2 @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % internal_case_prod_conv
% 0.30/0.47 thf(fact_130_Collection_Oset__def,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),L: B] :
% 0.30/0.47 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 0.30/0.47 => ( ( set2 @ B @ A @ Multiset @ L )
% 0.30/0.47 = ( set_mset @ A @ ( Multiset @ L ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collection.set_def
% 0.30/0.47 thf(fact_131_relChain__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( ord @ B )
% 0.30/0.47 => ( ( bNF_Ca1785829860lChain @ A @ B )
% 0.30/0.47 = ( ^ [R4: set @ ( product_prod @ A @ A ),As: A > B] :
% 0.30/0.47 ! [I2: A,J: A] :
% 0.30/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ I2 @ J ) @ R4 )
% 0.30/0.47 => ( ord_less_eq @ B @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % relChain_def
% 0.30/0.47 thf(fact_132_Collection_Oset_Ocong,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( set2 @ B @ A )
% 0.30/0.47 = ( set2 @ B @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collection.set.cong
% 0.30/0.47 thf(fact_133_RemoveMax__axioms_Ointro,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Inv: B > $o,Of_list: ( list @ A ) > B,Is_empty: B > $o,Remove_max: B > ( product_prod @ A @ B ),Multiset: B > ( multiset @ A )] :
% 0.30/0.47 ( ! [X4: list @ A] : ( Inv @ ( Of_list @ X4 ) )
% 0.30/0.47 => ( ! [L6: B,M3: A,L2: B] :
% 0.30/0.47 ( ~ ( Is_empty @ L6 )
% 0.30/0.47 => ( ( Inv @ L6 )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 0.30/0.47 = ( Remove_max @ L6 ) )
% 0.30/0.47 => ( M3
% 0.30/0.47 = ( lattic929149872er_Max @ A @ ( set2 @ B @ A @ Multiset @ L6 ) ) ) ) ) )
% 0.30/0.47 => ( ! [L6: B,M3: A,L2: B] :
% 0.30/0.47 ( ~ ( Is_empty @ L6 )
% 0.30/0.47 => ( ( Inv @ L6 )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 0.30/0.47 = ( Remove_max @ L6 ) )
% 0.30/0.47 => ( ( add_mset @ A @ M3 @ ( Multiset @ L2 ) )
% 0.30/0.47 = ( Multiset @ L6 ) ) ) ) )
% 0.30/0.47 => ( ! [L6: B,M3: A,L2: B] :
% 0.30/0.47 ( ~ ( Is_empty @ L6 )
% 0.30/0.47 => ( ( Inv @ L6 )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 0.30/0.47 = ( Remove_max @ L6 ) )
% 0.30/0.47 => ( Inv @ L2 ) ) ) )
% 0.30/0.47 => ( removeMax_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax_axioms.intro
% 0.30/0.47 thf(fact_134_RemoveMax__axioms__def,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( ( removeMax_axioms @ B @ A )
% 0.30/0.47 = ( ^ [Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),Remove_max2: B > ( product_prod @ A @ B ),Inv2: B > $o] :
% 0.30/0.47 ( ! [X5: list @ A] : ( Inv2 @ ( Of_list2 @ X5 ) )
% 0.30/0.47 & ! [L4: B,M2: A,L5: B] :
% 0.30/0.47 ( ~ ( Is_empty2 @ L4 )
% 0.30/0.47 => ( ( Inv2 @ L4 )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 0.30/0.47 = ( Remove_max2 @ L4 ) )
% 0.30/0.47 => ( M2
% 0.30/0.47 = ( lattic929149872er_Max @ A @ ( set2 @ B @ A @ Multiset2 @ L4 ) ) ) ) ) )
% 0.30/0.47 & ! [L4: B,M2: A,L5: B] :
% 0.30/0.47 ( ~ ( Is_empty2 @ L4 )
% 0.30/0.47 => ( ( Inv2 @ L4 )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 0.30/0.47 = ( Remove_max2 @ L4 ) )
% 0.30/0.47 => ( ( add_mset @ A @ M2 @ ( Multiset2 @ L5 ) )
% 0.30/0.47 = ( Multiset2 @ L4 ) ) ) ) )
% 0.30/0.47 & ! [L4: B,M2: A,L5: B] :
% 0.30/0.47 ( ~ ( Is_empty2 @ L4 )
% 0.30/0.47 => ( ( Inv2 @ L4 )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 0.30/0.47 = ( Remove_max2 @ L4 ) )
% 0.30/0.47 => ( Inv2 @ L5 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax_axioms_def
% 0.30/0.47 thf(fact_135_RemoveMax_Oremove__max__max,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o,L: B,M: A,L3: B] :
% 0.30/0.47 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 0.30/0.47 => ( ~ ( Is_empty @ L )
% 0.30/0.47 => ( ( Inv @ L )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 0.30/0.47 = ( Remove_max @ L ) )
% 0.30/0.47 => ( M
% 0.30/0.47 = ( lattic929149872er_Max @ A @ ( set2 @ B @ A @ Multiset @ L ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax.remove_max_max
% 0.30/0.47 thf(fact_136_predicate2D__conj,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,R3: $o,X: A,Y: B] :
% 0.30/0.47 ( ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.30/0.47 & R3 )
% 0.30/0.47 => ( R3
% 0.30/0.47 & ( ( P @ X @ Y )
% 0.30/0.47 => ( Q @ X @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % predicate2D_conj
% 0.30/0.47 thf(fact_137_RemoveMax_Oremove__max__inv,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o,L: B,M: A,L3: B] :
% 0.30/0.47 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 0.30/0.47 => ( ~ ( Is_empty @ L )
% 0.30/0.47 => ( ( Inv @ L )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 0.30/0.47 = ( Remove_max @ L ) )
% 0.30/0.47 => ( Inv @ L3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax.remove_max_inv
% 0.30/0.47 thf(fact_138_RemoveMax_Oaxioms_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o] :
% 0.30/0.47 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 0.30/0.47 => ( removeMax_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax.axioms(2)
% 0.30/0.47 thf(fact_139_RemoveMax_Oof__list__inv,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o,X: list @ A] :
% 0.30/0.47 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 0.30/0.47 => ( Inv @ ( Of_list @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax.of_list_inv
% 0.30/0.47 thf(fact_140_RemoveMax_Ointro,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o] :
% 0.30/0.47 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 0.30/0.47 => ( ( removeMax_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 0.30/0.47 => ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax.intro
% 0.30/0.47 thf(fact_141_RemoveMax__def,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( ( removeMax @ B @ A )
% 0.30/0.47 = ( ^ [Empty2: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),Remove_max2: B > ( product_prod @ A @ B ),Inv2: B > $o] :
% 0.30/0.47 ( ( collection @ B @ A @ Empty2 @ Is_empty2 @ Of_list2 @ Multiset2 )
% 0.30/0.47 & ( removeMax_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax_def
% 0.30/0.47 thf(fact_142_RemoveMax_Oaxioms_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o] :
% 0.30/0.47 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 0.30/0.47 => ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax.axioms(1)
% 0.30/0.47 thf(fact_143_RemoveMax_Oremove__max__multiset,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o,L: B,M: A,L3: B] :
% 0.30/0.47 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 0.30/0.47 => ( ~ ( Is_empty @ L )
% 0.30/0.47 => ( ( Inv @ L )
% 0.30/0.47 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 0.30/0.47 = ( Remove_max @ L ) )
% 0.30/0.47 => ( ( add_mset @ A @ M @ ( Multiset @ L3 ) )
% 0.30/0.47 = ( Multiset @ L ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RemoveMax.remove_max_multiset
% 0.30/0.47 thf(fact_144_ge__eq__refl,axiom,
% 0.30/0.47 ! [A: $tType,R3: A > A > $o,X: A] :
% 0.30/0.47 ( ( ord_less_eq @ ( A > A > $o )
% 0.30/0.47 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.30/0.47 @ R3 )
% 0.30/0.47 => ( R3 @ X @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % ge_eq_refl
% 0.30/0.47 thf(fact_145_refl__ge__eq,axiom,
% 0.30/0.47 ! [A: $tType,R3: A > A > $o] :
% 0.30/0.47 ( ! [X4: A] : ( R3 @ X4 @ X4 )
% 0.30/0.47 => ( ord_less_eq @ ( A > A > $o )
% 0.30/0.47 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.30/0.47 @ R3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % refl_ge_eq
% 0.30/0.47 thf(fact_146_multiset__induct__max,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: ( multiset @ A ) > $o,M4: multiset @ A] :
% 0.30/0.47 ( ( P @ ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 => ( ! [X4: A,M5: multiset @ A] :
% 0.30/0.47 ( ( P @ M5 )
% 0.30/0.47 => ( ! [Xa: A] :
% 0.30/0.47 ( ( member @ A @ Xa @ ( set_mset @ A @ M5 ) )
% 0.30/0.47 => ( ord_less_eq @ A @ Xa @ X4 ) )
% 0.30/0.47 => ( P @ ( add_mset @ A @ X4 @ M5 ) ) ) )
% 0.30/0.47 => ( P @ M4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset_induct_max
% 0.30/0.47 thf(fact_147_multiset__induct__min,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: ( multiset @ A ) > $o,M4: multiset @ A] :
% 0.30/0.47 ( ( P @ ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 => ( ! [X4: A,M5: multiset @ A] :
% 0.30/0.47 ( ( P @ M5 )
% 0.30/0.47 => ( ! [Xa: A] :
% 0.30/0.47 ( ( member @ A @ Xa @ ( set_mset @ A @ M5 ) )
% 0.30/0.47 => ( ord_less_eq @ A @ X4 @ Xa ) )
% 0.30/0.47 => ( P @ ( add_mset @ A @ X4 @ M5 ) ) ) )
% 0.30/0.47 => ( P @ M4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset_induct_min
% 0.30/0.47 thf(fact_148_add__mset__eq__singleton__iff,axiom,
% 0.30/0.47 ! [A: $tType,X: A,M4: multiset @ A,Y: A] :
% 0.30/0.47 ( ( ( add_mset @ A @ X @ M4 )
% 0.30/0.47 = ( add_mset @ A @ Y @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.30/0.47 = ( ( M4
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 & ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mset_eq_singleton_iff
% 0.30/0.47 thf(fact_149_single__eq__add__mset,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B2: A,M4: multiset @ A] :
% 0.30/0.47 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 = ( add_mset @ A @ B2 @ M4 ) )
% 0.30/0.47 = ( ( B2 = A2 )
% 0.30/0.47 & ( M4
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % single_eq_add_mset
% 0.30/0.47 thf(fact_150_add__mset__eq__single,axiom,
% 0.30/0.47 ! [A: $tType,B2: A,M4: multiset @ A,A2: A] :
% 0.30/0.47 ( ( ( add_mset @ A @ B2 @ M4 )
% 0.30/0.47 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.30/0.47 = ( ( B2 = A2 )
% 0.30/0.47 & ( M4
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mset_eq_single
% 0.30/0.47 thf(fact_151_single__eq__single,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B2: A] :
% 0.30/0.47 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 = ( add_mset @ A @ B2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.30/0.47 = ( A2 = B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % single_eq_single
% 0.30/0.47 thf(fact_152_multiset__cases,axiom,
% 0.30/0.47 ! [A: $tType,M4: multiset @ A] :
% 0.30/0.47 ( ( M4
% 0.30/0.47 != ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 => ~ ! [X4: A,N2: multiset @ A] :
% 0.30/0.47 ( M4
% 0.30/0.47 != ( add_mset @ A @ X4 @ N2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset_cases
% 0.30/0.47 thf(fact_153_multiset__induct,axiom,
% 0.30/0.47 ! [A: $tType,P: ( multiset @ A ) > $o,M4: multiset @ A] :
% 0.30/0.47 ( ( P @ ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 => ( ! [X4: A,M5: multiset @ A] :
% 0.30/0.47 ( ( P @ M5 )
% 0.30/0.47 => ( P @ ( add_mset @ A @ X4 @ M5 ) ) )
% 0.30/0.47 => ( P @ M4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset_induct
% 0.30/0.47 thf(fact_154_multiset__induct2,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,P: ( multiset @ A ) > ( multiset @ B ) > $o,M4: multiset @ A,N: multiset @ B] :
% 0.30/0.47 ( ( P @ ( zero_zero @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ B ) ) )
% 0.30/0.47 => ( ! [A5: A,M5: multiset @ A,N2: multiset @ B] :
% 0.30/0.47 ( ( P @ M5 @ N2 )
% 0.30/0.47 => ( P @ ( add_mset @ A @ A5 @ M5 ) @ N2 ) )
% 0.30/0.47 => ( ! [A5: B,M5: multiset @ A,N2: multiset @ B] :
% 0.30/0.47 ( ( P @ M5 @ N2 )
% 0.30/0.47 => ( P @ M5 @ ( add_mset @ B @ A5 @ N2 ) ) )
% 0.30/0.47 => ( P @ M4 @ N ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset_induct2
% 0.30/0.47 thf(fact_155_empty__not__add__mset,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: multiset @ A] :
% 0.30/0.47 ( ( zero_zero @ ( multiset @ A ) )
% 0.30/0.47 != ( add_mset @ A @ A2 @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_not_add_mset
% 0.30/0.47 thf(fact_156_multiset__nonemptyE,axiom,
% 0.30/0.47 ! [A: $tType,A3: multiset @ A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 != ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 => ~ ! [X4: A] :
% 0.30/0.47 ~ ( member @ A @ X4 @ ( set_mset @ A @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset_nonemptyE
% 0.30/0.47 thf(fact_157_multi__nonempty__split,axiom,
% 0.30/0.47 ! [A: $tType,M4: multiset @ A] :
% 0.30/0.47 ( ( M4
% 0.30/0.47 != ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 => ? [A7: multiset @ A,A5: A] :
% 0.30/0.47 ( M4
% 0.30/0.47 = ( add_mset @ A @ A5 @ A7 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multi_nonempty_split
% 0.30/0.47 thf(fact_158_Collection_Ois__empty__as__list,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),E3: B] :
% 0.30/0.47 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 0.30/0.47 => ( ( Is_empty @ E3 )
% 0.30/0.47 => ( ( Multiset @ E3 )
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collection.is_empty_as_list
% 0.30/0.47 thf(fact_159_Collection_Omultiset__empty,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A )] :
% 0.30/0.47 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 0.30/0.47 => ( ( Multiset @ Empty )
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collection.multiset_empty
% 0.30/0.47 thf(fact_160_multi__member__last,axiom,
% 0.30/0.47 ! [A: $tType,X: A] : ( member @ A @ X @ ( set_mset @ A @ ( add_mset @ A @ X @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multi_member_last
% 0.30/0.47 thf(fact_161_multiset_Osimps_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( multiset2 @ A @ ( e @ A ) )
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset.simps(1)
% 0.30/0.47 thf(fact_162_le__zero__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( canoni770627133id_add @ A )
% 0.30/0.47 => ! [N3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ N3 @ ( zero_zero @ A ) )
% 0.30/0.47 = ( N3
% 0.30/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_zero_eq
% 0.30/0.47 thf(fact_163_zero__le,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( canoni770627133id_add @ A )
% 0.30/0.47 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_le
% 0.30/0.47 thf(fact_164_le__numeral__extra_I3_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linord1659791738miring @ A )
% 0.30/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_numeral_extra(3)
% 0.30/0.47 thf(fact_165_multiset_Osimps_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 0.30/0.47 ( ( multiset2 @ A @ ( t @ A @ V @ L @ R ) )
% 0.30/0.47 = ( plus_plus @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ ( multiset2 @ A @ L ) @ ( add_mset @ A @ V @ ( zero_zero @ ( multiset @ A ) ) ) ) @ ( multiset2 @ A @ R ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset.simps(2)
% 0.30/0.47 thf(fact_166_divides__aux__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( unique1598680935umeral @ A )
% 0.30/0.47 => ! [Q2: A,R: A] :
% 0.30/0.47 ( ( unique455577585es_aux @ A @ ( product_Pair @ A @ A @ Q2 @ R ) )
% 0.30/0.47 = ( R
% 0.30/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % divides_aux_eq
% 0.30/0.47 thf(fact_167_single__subset__iff,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,M4: multiset @ A] :
% 0.30/0.47 ( ( subseteq_mset @ A @ ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) @ M4 )
% 0.30/0.47 = ( member @ A @ A2 @ ( set_mset @ A @ M4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % single_subset_iff
% 0.30/0.47 thf(fact_168_add__le__cancel__left,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere236663937imp_le @ A )
% 0.30/0.47 => ! [C2: A,A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_le_cancel_left
% 0.30/0.47 thf(fact_169_add__le__cancel__right,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere236663937imp_le @ A )
% 0.30/0.47 => ! [A2: A,C2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_le_cancel_right
% 0.30/0.47 thf(fact_170_union__mset__add__mset__left,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: multiset @ A,B6: multiset @ A] :
% 0.30/0.47 ( ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ A2 @ A3 ) @ B6 )
% 0.30/0.47 = ( add_mset @ A @ A2 @ ( plus_plus @ ( multiset @ A ) @ A3 @ B6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % union_mset_add_mset_left
% 0.30/0.47 thf(fact_171_union__mset__add__mset__right,axiom,
% 0.30/0.47 ! [A: $tType,A3: multiset @ A,A2: A,B6: multiset @ A] :
% 0.30/0.47 ( ( plus_plus @ ( multiset @ A ) @ A3 @ ( add_mset @ A @ A2 @ B6 ) )
% 0.30/0.47 = ( add_mset @ A @ A2 @ ( plus_plus @ ( multiset @ A ) @ A3 @ B6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % union_mset_add_mset_right
% 0.30/0.47 thf(fact_172_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linord219039673up_add @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_le_double_add_iff_zero_le_single_add
% 0.30/0.47 thf(fact_173_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linord219039673up_add @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.30/0.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % double_add_le_zero_iff_single_add_le_zero
% 0.30/0.47 thf(fact_174_le__add__same__cancel2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere516151231imp_le @ A )
% 0.30/0.47 => ! [A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_add_same_cancel2
% 0.30/0.47 thf(fact_175_le__add__same__cancel1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere516151231imp_le @ A )
% 0.30/0.47 => ! [A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_add_same_cancel1
% 0.30/0.47 thf(fact_176_add__le__same__cancel2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere516151231imp_le @ A )
% 0.30/0.47 => ! [A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.30/0.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_le_same_cancel2
% 0.30/0.47 thf(fact_177_add__le__same__cancel1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere516151231imp_le @ A )
% 0.30/0.47 => ! [B2: A,A2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.30/0.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_le_same_cancel1
% 0.30/0.47 thf(fact_178_add__mset__subseteq__single__iff,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,M4: multiset @ A,B2: A] :
% 0.30/0.47 ( ( subseteq_mset @ A @ ( add_mset @ A @ A2 @ M4 ) @ ( add_mset @ A @ B2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.30/0.47 = ( ( M4
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 & ( A2 = B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mset_subseteq_single_iff
% 0.30/0.47 thf(fact_179_verit__sum__simplify,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( cancel1352612707id_add @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.47 = A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % verit_sum_simplify
% 0.30/0.47 thf(fact_180_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere779506340up_add @ A )
% 0.30/0.47 => ! [I: A,J2: A,K2: A,L: A] :
% 0.30/0.47 ( ( ( ord_less_eq @ A @ I @ J2 )
% 0.30/0.47 & ( K2 = L ) )
% 0.30/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J2 @ L ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mono_thms_linordered_semiring(3)
% 0.30/0.47 thf(fact_181_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere779506340up_add @ A )
% 0.30/0.47 => ! [I: A,J2: A,K2: A,L: A] :
% 0.30/0.47 ( ( ( I = J2 )
% 0.30/0.47 & ( ord_less_eq @ A @ K2 @ L ) )
% 0.30/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J2 @ L ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mono_thms_linordered_semiring(2)
% 0.30/0.47 thf(fact_182_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere779506340up_add @ A )
% 0.30/0.47 => ! [I: A,J2: A,K2: A,L: A] :
% 0.30/0.47 ( ( ( ord_less_eq @ A @ I @ J2 )
% 0.30/0.47 & ( ord_less_eq @ A @ K2 @ L ) )
% 0.30/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J2 @ L ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mono_thms_linordered_semiring(1)
% 0.30/0.47 thf(fact_183_add__mono,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere779506340up_add @ A )
% 0.30/0.47 => ! [A2: A,B2: A,C2: A,D3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ C2 @ D3 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mono
% 0.30/0.47 thf(fact_184_add__left__mono,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere779506340up_add @ A )
% 0.30/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_left_mono
% 0.30/0.47 thf(fact_185_less__eqE,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( canoni770627133id_add @ A )
% 0.30/0.47 => ! [A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ~ ! [C3: A] :
% 0.30/0.47 ( B2
% 0.30/0.47 != ( plus_plus @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_eqE
% 0.30/0.47 thf(fact_186_add__right__mono,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere779506340up_add @ A )
% 0.30/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_right_mono
% 0.30/0.47 thf(fact_187_le__iff__add,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( canoni770627133id_add @ A )
% 0.30/0.47 => ( ( ord_less_eq @ A )
% 0.30/0.47 = ( ^ [A4: A,B3: A] :
% 0.30/0.47 ? [C5: A] :
% 0.30/0.47 ( B3
% 0.30/0.47 = ( plus_plus @ A @ A4 @ C5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_iff_add
% 0.30/0.47 thf(fact_188_add__le__imp__le__left,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere236663937imp_le @ A )
% 0.30/0.47 => ! [C2: A,A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 0.30/0.47 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_le_imp_le_left
% 0.30/0.47 thf(fact_189_add__le__imp__le__right,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere236663937imp_le @ A )
% 0.30/0.47 => ! [A2: A,C2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.30/0.47 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_le_imp_le_right
% 0.30/0.47 thf(fact_190_union__iff,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: multiset @ A,B6: multiset @ A] :
% 0.30/0.47 ( ( member @ A @ A2 @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ A3 @ B6 ) ) )
% 0.30/0.47 = ( ( member @ A @ A2 @ ( set_mset @ A @ A3 ) )
% 0.30/0.47 | ( member @ A @ A2 @ ( set_mset @ A @ B6 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % union_iff
% 0.30/0.47 thf(fact_191_mset__subset__eqD,axiom,
% 0.30/0.47 ! [A: $tType,A3: multiset @ A,B6: multiset @ A,X: A] :
% 0.30/0.47 ( ( subseteq_mset @ A @ A3 @ B6 )
% 0.30/0.47 => ( ( member @ A @ X @ ( set_mset @ A @ A3 ) )
% 0.30/0.47 => ( member @ A @ X @ ( set_mset @ A @ B6 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mset_subset_eqD
% 0.30/0.47 thf(fact_192_mset__subset__eq__add__mset__cancel,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: multiset @ A,B6: multiset @ A] :
% 0.30/0.47 ( ( subseteq_mset @ A @ ( add_mset @ A @ A2 @ A3 ) @ ( add_mset @ A @ A2 @ B6 ) )
% 0.30/0.47 = ( subseteq_mset @ A @ A3 @ B6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mset_subset_eq_add_mset_cancel
% 0.30/0.47 thf(fact_193_set__mset__mono,axiom,
% 0.30/0.47 ! [A: $tType,A3: multiset @ A,B6: multiset @ A] :
% 0.30/0.47 ( ( subseteq_mset @ A @ A3 @ B6 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ ( set_mset @ A @ A3 ) @ ( set_mset @ A @ B6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_mset_mono
% 0.30/0.47 thf(fact_194_add__nonpos__eq__0__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere216010020id_add @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 0.30/0.47 => ( ( ord_less_eq @ A @ Y @ ( zero_zero @ A ) )
% 0.30/0.47 => ( ( ( plus_plus @ A @ X @ Y )
% 0.30/0.47 = ( zero_zero @ A ) )
% 0.30/0.47 = ( ( X
% 0.30/0.47 = ( zero_zero @ A ) )
% 0.30/0.47 & ( Y
% 0.30/0.47 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_nonpos_eq_0_iff
% 0.30/0.47 thf(fact_195_add__nonneg__eq__0__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere216010020id_add @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.30/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 0.30/0.47 => ( ( ( plus_plus @ A @ X @ Y )
% 0.30/0.47 = ( zero_zero @ A ) )
% 0.30/0.47 = ( ( X
% 0.30/0.47 = ( zero_zero @ A ) )
% 0.30/0.47 & ( Y
% 0.30/0.47 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_nonneg_eq_0_iff
% 0.30/0.47 thf(fact_196_add__nonpos__nonpos,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere216010020id_add @ A )
% 0.30/0.47 => ! [A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.47 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_nonpos_nonpos
% 0.30/0.47 thf(fact_197_add__nonneg__nonneg,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere216010020id_add @ A )
% 0.30/0.47 => ! [A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_nonneg_nonneg
% 0.30/0.47 thf(fact_198_add__increasing2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere216010020id_add @ A )
% 0.30/0.47 => ! [C2: A,B2: A,A2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.47 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_increasing2
% 0.30/0.47 thf(fact_199_add__decreasing2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere216010020id_add @ A )
% 0.30/0.47 => ! [C2: A,A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ C2 @ ( zero_zero @ A ) )
% 0.30/0.47 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_decreasing2
% 0.30/0.47 thf(fact_200_add__increasing,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere216010020id_add @ A )
% 0.30/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.30/0.47 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_increasing
% 0.30/0.47 thf(fact_201_add__decreasing,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordere216010020id_add @ A )
% 0.30/0.47 => ! [A2: A,C2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.47 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_decreasing
% 0.30/0.47 thf(fact_202_single__is__union,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,M4: multiset @ A,N: multiset @ A] :
% 0.30/0.47 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 = ( plus_plus @ ( multiset @ A ) @ M4 @ N ) )
% 0.30/0.47 = ( ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 = M4 )
% 0.30/0.47 & ( N
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) ) )
% 0.30/0.47 | ( ( M4
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 & ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 = N ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % single_is_union
% 0.30/0.47 thf(fact_203_union__is__single,axiom,
% 0.30/0.47 ! [A: $tType,M4: multiset @ A,N: multiset @ A,A2: A] :
% 0.30/0.47 ( ( ( plus_plus @ ( multiset @ A ) @ M4 @ N )
% 0.30/0.47 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.30/0.47 = ( ( ( M4
% 0.30/0.47 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 0.30/0.47 & ( N
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) ) )
% 0.30/0.47 | ( ( M4
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 & ( N
% 0.30/0.47 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % union_is_single
% 0.30/0.47 thf(fact_204_add__mset__add__single,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( add_mset @ A )
% 0.30/0.47 = ( ^ [A4: A,A8: multiset @ A] : ( plus_plus @ ( multiset @ A ) @ A8 @ ( add_mset @ A @ A4 @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mset_add_single
% 0.30/0.47 thf(fact_205_multi__subset__induct,axiom,
% 0.30/0.47 ! [A: $tType,F5: multiset @ A,A3: multiset @ A,P: ( multiset @ A ) > $o] :
% 0.30/0.47 ( ( subseteq_mset @ A @ F5 @ A3 )
% 0.30/0.47 => ( ( P @ ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 => ( ! [A5: A,F6: multiset @ A] :
% 0.30/0.47 ( ( member @ A @ A5 @ ( set_mset @ A @ A3 ) )
% 0.30/0.47 => ( ( P @ F6 )
% 0.30/0.47 => ( P @ ( add_mset @ A @ A5 @ F6 ) ) ) )
% 0.30/0.47 => ( P @ F5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multi_subset_induct
% 0.30/0.47 thf(fact_206_mset__subset__eq__single,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B6: multiset @ A] :
% 0.30/0.47 ( ( member @ A @ A2 @ ( set_mset @ A @ B6 ) )
% 0.30/0.47 => ( subseteq_mset @ A @ ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) @ B6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mset_subset_eq_single
% 0.30/0.47 thf(fact_207_multi__member__skip,axiom,
% 0.30/0.47 ! [A: $tType,X: A,XS: multiset @ A,Y: A] :
% 0.30/0.47 ( ( member @ A @ X @ ( set_mset @ A @ XS ) )
% 0.30/0.47 => ( member @ A @ X @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ Y @ ( zero_zero @ ( multiset @ A ) ) ) @ XS ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multi_member_skip
% 0.30/0.47 thf(fact_208_multi__member__this,axiom,
% 0.30/0.47 ! [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 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multi_member_this
% 0.30/0.47 thf(fact_209_mult1E,axiom,
% 0.30/0.47 ! [A: $tType,N: multiset @ A,M4: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.47 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M4 ) @ ( mult1 @ A @ R ) )
% 0.30/0.47 => ~ ! [A5: A,M0: multiset @ A] :
% 0.30/0.47 ( ( M4
% 0.30/0.47 = ( add_mset @ A @ A5 @ M0 ) )
% 0.30/0.47 => ! [K3: multiset @ A] :
% 0.30/0.47 ( ( N
% 0.30/0.47 = ( plus_plus @ ( multiset @ A ) @ M0 @ K3 ) )
% 0.30/0.47 => ~ ! [B8: A] :
% 0.30/0.47 ( ( member @ A @ B8 @ ( set_mset @ A @ K3 ) )
% 0.30/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B8 @ A5 ) @ R ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mult1E
% 0.30/0.47 thf(fact_210_mult1I,axiom,
% 0.30/0.47 ! [A: $tType,M4: multiset @ A,A2: A,M02: multiset @ A,N: multiset @ A,K4: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.47 ( ( M4
% 0.30/0.47 = ( add_mset @ A @ A2 @ M02 ) )
% 0.30/0.47 => ( ( N
% 0.30/0.47 = ( plus_plus @ ( multiset @ A ) @ M02 @ K4 ) )
% 0.30/0.47 => ( ! [B4: A] :
% 0.30/0.47 ( ( member @ A @ B4 @ ( set_mset @ A @ K4 ) )
% 0.30/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A2 ) @ R ) )
% 0.30/0.47 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M4 ) @ ( mult1 @ A @ R ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mult1I
% 0.30/0.47 thf(fact_211_less__add,axiom,
% 0.30/0.47 ! [A: $tType,N: multiset @ A,A2: A,M02: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.47 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ ( add_mset @ A @ A2 @ M02 ) ) @ ( mult1 @ A @ R ) )
% 0.30/0.47 => ( ? [M5: multiset @ A] :
% 0.30/0.47 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M5 @ M02 ) @ ( mult1 @ A @ R ) )
% 0.30/0.47 & ( N
% 0.30/0.47 = ( add_mset @ A @ A2 @ M5 ) ) )
% 0.30/0.47 | ? [K3: multiset @ A] :
% 0.30/0.47 ( ! [B8: A] :
% 0.30/0.47 ( ( member @ A @ B8 @ ( set_mset @ A @ K3 ) )
% 0.30/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B8 @ A2 ) @ R ) )
% 0.30/0.47 & ( N
% 0.30/0.47 = ( plus_plus @ ( multiset @ A ) @ M02 @ K3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_add
% 0.30/0.47 thf(fact_212_mono__mult1,axiom,
% 0.30/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),R5: set @ ( product_prod @ A @ A )] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ R5 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) @ ( mult1 @ A @ R ) @ ( mult1 @ A @ R5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mono_mult1
% 0.30/0.47 thf(fact_213_subset__antisym,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 0.30/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ A3 )
% 0.30/0.47 => ( A3 = B6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_antisym
% 0.30/0.47 thf(fact_214_subsetI,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 0.30/0.47 ( ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ A3 )
% 0.30/0.47 => ( member @ A @ X4 @ B6 ) )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % subsetI
% 0.30/0.47 thf(fact_215_in__mono,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B6: set @ A,X: A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 0.30/0.47 => ( ( member @ A @ X @ A3 )
% 0.30/0.47 => ( member @ A @ X @ B6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_mono
% 0.30/0.47 thf(fact_216_subsetD,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B6: set @ A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 0.30/0.47 => ( ( member @ A @ C2 @ A3 )
% 0.30/0.47 => ( member @ A @ C2 @ B6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subsetD
% 0.30/0.47 thf(fact_217_equalityE,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 0.30/0.47 ( ( A3 = B6 )
% 0.30/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 0.30/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % equalityE
% 0.30/0.47 thf(fact_218_subset__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A8: set @ A,B9: set @ A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( member @ A @ X5 @ A8 )
% 0.30/0.47 => ( member @ A @ X5 @ B9 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_eq
% 0.30/0.47 thf(fact_219_equalityD1,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 0.30/0.47 ( ( A3 = B6 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equalityD1
% 0.30/0.47 thf(fact_220_equalityD2,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 0.30/0.47 ( ( A3 = B6 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ B6 @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equalityD2
% 0.30/0.47 thf(fact_221_subset__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A8: set @ A,B9: set @ A] :
% 0.30/0.47 ! [T3: A] :
% 0.30/0.47 ( ( member @ A @ T3 @ A8 )
% 0.30/0.47 => ( member @ A @ T3 @ B9 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_iff
% 0.30/0.47 thf(fact_222_subset__refl,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.30/0.47
% 0.30/0.47 % subset_refl
% 0.30/0.47 thf(fact_223_Collect__mono,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.47 ( ! [X4: A] :
% 0.30/0.47 ( ( P @ X4 )
% 0.30/0.47 => ( Q @ X4 ) )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mono
% 0.30/0.47 thf(fact_224_subset__trans,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B6: set @ A,C4: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 0.30/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ C4 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_trans
% 0.30/0.47 thf(fact_225_set__eq__subset,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ^ [Y3: set @ A,Z: set @ A] : ( Y3 = Z ) )
% 0.30/0.47 = ( ^ [A8: set @ A,B9: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A8 @ B9 )
% 0.30/0.47 & ( ord_less_eq @ ( set @ A ) @ B9 @ A8 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_eq_subset
% 0.30/0.47 thf(fact_226_Collect__mono__iff,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.30/0.47 = ( ! [X5: A] :
% 0.30/0.47 ( ( P @ X5 )
% 0.30/0.47 => ( Q @ X5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mono_iff
% 0.30/0.47 thf(fact_227_one__step__implies__mult,axiom,
% 0.30/0.47 ! [A: $tType,J3: multiset @ A,K4: multiset @ A,R: set @ ( product_prod @ A @ A ),I4: multiset @ A] :
% 0.30/0.47 ( ( J3
% 0.30/0.47 != ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 => ( ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ ( set_mset @ A @ K4 ) )
% 0.30/0.47 => ? [Xa: A] :
% 0.30/0.47 ( ( member @ A @ Xa @ ( set_mset @ A @ J3 ) )
% 0.30/0.47 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Xa ) @ R ) ) )
% 0.30/0.47 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ I4 @ K4 ) @ ( plus_plus @ ( multiset @ A ) @ I4 @ J3 ) ) @ ( mult @ A @ R ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % one_step_implies_mult
% 0.30/0.47 thf(fact_228_subrelI,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.30/0.47 ( ! [X4: A,Y2: B] :
% 0.30/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y2 ) @ R )
% 0.30/0.47 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y2 ) @ S ) )
% 0.30/0.47 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 0.30/0.47
% 0.30/0.47 % subrelI
% 0.30/0.47 thf(fact_229_mono__mult,axiom,
% 0.30/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),R5: set @ ( product_prod @ A @ A )] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ R5 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) @ ( mult @ A @ R ) @ ( mult @ A @ R5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mono_mult
% 0.30/0.47 thf(fact_230_mult__implies__one__step,axiom,
% 0.30/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),M4: multiset @ A,N: multiset @ A] :
% 0.30/0.47 ( ( trans @ A @ R )
% 0.30/0.47 => ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M4 @ N ) @ ( mult @ A @ R ) )
% 0.30/0.47 => ? [I5: multiset @ A,J4: multiset @ A] :
% 0.30/0.47 ( ( N
% 0.30/0.47 = ( plus_plus @ ( multiset @ A ) @ I5 @ J4 ) )
% 0.30/0.47 & ? [K3: multiset @ A] :
% 0.30/0.47 ( ( M4
% 0.30/0.47 = ( plus_plus @ ( multiset @ A ) @ I5 @ K3 ) )
% 0.30/0.47 & ( J4
% 0.30/0.47 != ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 & ! [X7: A] :
% 0.30/0.47 ( ( member @ A @ X7 @ ( set_mset @ A @ K3 ) )
% 0.30/0.47 => ? [Xa2: A] :
% 0.30/0.47 ( ( member @ A @ Xa2 @ ( set_mset @ A @ J4 ) )
% 0.30/0.47 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ Xa2 ) @ R ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mult_implies_one_step
% 0.30/0.47 thf(fact_231_subset__mset_Osum__mset__0__iff,axiom,
% 0.30/0.47 ! [A: $tType,M4: multiset @ ( multiset @ A )] :
% 0.30/0.47 ( ( ( comm_monoid_sum_mset @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ A ) ) @ M4 )
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) )
% 0.30/0.47 = ( ! [X5: multiset @ A] :
% 0.30/0.47 ( ( member @ ( multiset @ A ) @ X5 @ ( set_mset @ ( multiset @ A ) @ M4 ) )
% 0.30/0.47 => ( X5
% 0.30/0.47 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_mset.sum_mset_0_iff
% 0.30/0.47 thf(fact_232_transD,axiom,
% 0.30/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A,Z2: A] :
% 0.30/0.47 ( ( trans @ A @ R )
% 0.30/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 0.30/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ R )
% 0.30/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ R ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transD
% 0.30/0.47 thf(fact_233_transE,axiom,
% 0.30/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A,Z2: A] :
% 0.30/0.47 ( ( trans @ A @ R )
% 0.30/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 0.30/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ R )
% 0.30/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ R ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transE
% 0.30/0.47 thf(fact_234_transI,axiom,
% 0.30/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 0.30/0.47 ( ! [X4: A,Y2: A,Z3: A] :
% 0.30/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y2 ) @ R )
% 0.30/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z3 ) @ R )
% 0.30/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Z3 ) @ R ) ) )
% 0.30/0.47 => ( trans @ A @ R ) ) ).
% 0.30/0.47
% 0.30/0.47 % transI
% 0.30/0.47 thf(fact_235_trans__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( trans @ A )
% 0.30/0.47 = ( ^ [R4: set @ ( product_prod @ A @ A )] :
% 0.30/0.47 ! [X5: A,Y4: A,Z4: A] :
% 0.30/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X5 @ Y4 ) @ R4 )
% 0.30/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ Z4 ) @ R4 )
% 0.30/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X5 @ Z4 ) @ R4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trans_def
% 0.30/0.47 thf(fact_236_mult__cancel__add__mset,axiom,
% 0.30/0.47 ! [A: $tType,S: set @ ( product_prod @ A @ A ),Uu: A,X8: multiset @ A,Y7: multiset @ A] :
% 0.30/0.47 ( ( trans @ A @ S )
% 0.30/0.47 => ( ( irrefl @ A @ S )
% 0.30/0.47 => ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( add_mset @ A @ Uu @ X8 ) @ ( add_mset @ A @ Uu @ Y7 ) ) @ ( mult @ A @ S ) )
% 0.30/0.47 = ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ X8 @ Y7 ) @ ( mult @ A @ S ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mult_cancel_add_mset
% 0.30/0.47 thf(fact_237_in__mset__fold__plus__iff,axiom,
% 0.30/0.47 ! [A: $tType,X: A,M4: multiset @ A,NN: multiset @ ( multiset @ A )] :
% 0.30/0.47 ( ( member @ A @ X @ ( set_mset @ A @ ( fold_mset @ ( multiset @ A ) @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ M4 @ NN ) ) )
% 0.30/0.47 = ( ( member @ A @ X @ ( set_mset @ A @ M4 ) )
% 0.30/0.47 | ? [N4: multiset @ A] :
% 0.30/0.47 ( ( member @ ( multiset @ A ) @ N4 @ ( set_mset @ ( multiset @ A ) @ NN ) )
% 0.30/0.47 & ( member @ A @ X @ ( set_mset @ A @ N4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_mset_fold_plus_iff
% 0.30/0.47 thf(fact_238_irrefl__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( irrefl @ A )
% 0.30/0.47 = ( ^ [R4: set @ ( product_prod @ A @ A )] :
% 0.30/0.47 ! [A4: A] :
% 0.30/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ A4 ) @ R4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % irrefl_def
% 0.30/0.47 thf(fact_239_irreflI,axiom,
% 0.30/0.47 ! [A: $tType,R3: set @ ( product_prod @ A @ A )] :
% 0.30/0.47 ( ! [A5: A] :
% 0.30/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A5 @ A5 ) @ R3 )
% 0.30/0.47 => ( irrefl @ A @ R3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % irreflI
% 0.30/0.47 thf(fact_240_union__fold__mset__add__mset,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( plus_plus @ ( multiset @ A ) )
% 0.30/0.47 = ( fold_mset @ A @ ( multiset @ A ) @ ( add_mset @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % union_fold_mset_add_mset
% 0.30/0.47 thf(fact_241_multp__iff,axiom,
% 0.30/0.47 ! [A: $tType,R3: set @ ( product_prod @ A @ A ),P: A > A > $o,N: multiset @ A,M4: multiset @ A] :
% 0.30/0.47 ( ( irrefl @ A @ R3 )
% 0.30/0.47 => ( ( trans @ A @ R3 )
% 0.30/0.47 => ( ! [X4: A,Y2: A] :
% 0.30/0.47 ( ( P @ X4 @ Y2 )
% 0.30/0.47 = ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y2 ) @ R3 ) )
% 0.30/0.47 => ( ( multp @ A @ P @ N @ M4 )
% 0.30/0.47 = ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M4 ) @ ( mult @ A @ R3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multp_iff
% 0.30/0.47 thf(fact_242_add__mset__replicate__mset__safe,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,M4: multiset @ B,A2: B] :
% 0.30/0.47 ( ( nO_MATCH @ ( multiset @ A ) @ ( multiset @ B ) @ ( zero_zero @ ( multiset @ A ) ) @ M4 )
% 0.30/0.47 => ( ( add_mset @ B @ A2 @ M4 )
% 0.30/0.47 = ( plus_plus @ ( multiset @ B ) @ ( add_mset @ B @ A2 @ ( zero_zero @ ( multiset @ B ) ) ) @ M4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add_mset_replicate_mset_safe
% 0.30/0.47 thf(fact_243_subset__mset_Osum__mset__mono,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,K4: multiset @ B,F: B > ( multiset @ A ),G: B > ( multiset @ A )] :
% 0.30/0.47 ( ! [I3: B] :
% 0.30/0.47 ( ( member @ B @ I3 @ ( set_mset @ B @ K4 ) )
% 0.30/0.47 => ( subseteq_mset @ A @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.30/0.47 => ( subseteq_mset @ A @ ( comm_monoid_sum_mset @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ A ) ) @ ( image_mset @ B @ ( multiset @ A ) @ F @ K4 ) ) @ ( comm_monoid_sum_mset @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ A ) ) @ ( image_mset @ B @ ( multiset @ A ) @ G @ K4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_mset.sum_mset_mono
% 0.30/0.47 thf(fact_244_subset__mset_Oantimono__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( order @ B )
% 0.30/0.47 => ! [F: ( multiset @ A ) > B] :
% 0.30/0.47 ( ( antimono @ ( multiset @ A ) @ B @ ( subseteq_mset @ A ) @ F )
% 0.30/0.47 = ( ! [X5: multiset @ A,Y4: multiset @ A] :
% 0.30/0.47 ( ( subseteq_mset @ A @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X5 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_mset.antimono_def
% 0.30/0.47 thf(fact_245_image__mset__add__mset,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,F: B > A,A2: B,M4: multiset @ B] :
% 0.30/0.47 ( ( image_mset @ B @ A @ F @ ( add_mset @ B @ A2 @ M4 ) )
% 0.30/0.47 = ( add_mset @ A @ ( F @ A2 ) @ ( image_mset @ B @ A @ F @ M4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % image_mset_add_mset
% 0.30/0.47 thf(fact_246_multiset_Omap__cong,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,X: multiset @ A,Ya: multiset @ A,F: A > B,G: A > B] :
% 0.30/0.47 ( ( X = Ya )
% 0.30/0.47 => ( ! [Z3: A] :
% 0.30/0.47 ( ( member @ A @ Z3 @ ( set_mset @ A @ Ya ) )
% 0.30/0.47 => ( ( F @ Z3 )
% 0.30/0.47 = ( G @ Z3 ) ) )
% 0.30/0.47 => ( ( image_mset @ A @ B @ F @ X )
% 0.30/0.47 = ( image_mset @ A @ B @ G @ Ya ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset.map_cong
% 0.30/0.47 thf(fact_247_multiset_Omap__cong0,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,X: multiset @ A,F: A > B,G: A > B] :
% 0.30/0.47 ( ! [Z3: A] :
% 0.30/0.47 ( ( member @ A @ Z3 @ ( set_mset @ A @ X ) )
% 0.30/0.47 => ( ( F @ Z3 )
% 0.30/0.47 = ( G @ Z3 ) ) )
% 0.30/0.47 => ( ( image_mset @ A @ B @ F @ X )
% 0.30/0.47 = ( image_mset @ A @ B @ G @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset.map_cong0
% 0.30/0.47 thf(fact_248_multiset_Oinj__map__strong,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,X: multiset @ A,Xa3: multiset @ A,F: A > B,Fa: A > B] :
% 0.30/0.47 ( ! [Z3: A,Za: A] :
% 0.30/0.47 ( ( member @ A @ Z3 @ ( set_mset @ A @ X ) )
% 0.30/0.47 => ( ( member @ A @ Za @ ( set_mset @ A @ Xa3 ) )
% 0.30/0.47 => ( ( ( F @ Z3 )
% 0.30/0.47 = ( Fa @ Za ) )
% 0.30/0.47 => ( Z3 = Za ) ) ) )
% 0.30/0.47 => ( ( ( image_mset @ A @ B @ F @ X )
% 0.30/0.47 = ( image_mset @ A @ B @ Fa @ Xa3 ) )
% 0.30/0.47 => ( X = Xa3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % multiset.inj_map_strong
% 0.30/0.47 thf(fact_249_order_Oantimono_Ocong,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( order @ B )
% 0.30/0.47 => ( ( antimono @ A @ B )
% 0.30/0.47 = ( antimono @ A @ B ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.antimono.cong
% 0.30/0.47 thf(fact_250_msed__map__invR,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F: B > A,M4: multiset @ B,B2: A,N: multiset @ A] :
% 0.30/0.47 ( ( ( image_mset @ B @ A @ F @ M4 )
% 0.30/0.47 = ( add_mset @ A @ B2 @ N ) )
% 0.30/0.47 => ? [M1: multiset @ B,A5: B] :
% 0.30/0.47 ( ( M4
% 0.30/0.47 = ( add_mset @ B @ A5 @ M1 ) )
% 0.30/0.47 & ( ( F @ A5 )
% 0.30/0.47 = B2 )
% 0.30/0.47 & ( ( image_mset @ B @ A @ F @ M1 )
% 0.30/0.47 = N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % msed_map_invR
% 0.30/0.47 thf(fact_251_msed__map__invL,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F: B > A,A2: B,M4: multiset @ B,N: multiset @ A] :
% 0.30/0.47 ( ( ( image_mset @ B @ A @ F @ ( add_mset @ B @ A2 @ M4 ) )
% 0.30/0.47 = N )
% 0.30/0.47 => ? [N1: multiset @ A] :
% 0.30/0.47 ( ( N
% 0.30/0.47 = ( add_mset @ A @ ( F @ A2 ) @ N1 ) )
% 0.30/0.47 & ( ( image_mset @ B @ A @ F @ M4 )
% 0.30/0.47 = N1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % msed_map_invL
% 0.30/0.47 thf(fact_252_image__mset__single,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F: B > A,X: B] :
% 0.30/0.47 ( ( image_mset @ B @ A @ F @ ( add_mset @ B @ X @ ( zero_zero @ ( multiset @ B ) ) ) )
% 0.30/0.47 = ( add_mset @ A @ ( F @ X ) @ ( zero_zero @ ( multiset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % image_mset_single
% 0.30/0.47 thf(fact_253_subset__mset_OantimonoD,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( order @ B )
% 0.30/0.47 => ! [F: ( multiset @ A ) > B,X: multiset @ A,Y: multiset @ A] :
% 0.30/0.47 ( ( antimono @ ( multiset @ A ) @ B @ ( subseteq_mset @ A ) @ F )
% 0.30/0.47 => ( ( subseteq_mset @ A @ X @ Y )
% 0.30/0.47 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_mset.antimonoD
% 0.30/0.47 thf(fact_254_subset__mset_OantimonoE,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( order @ B )
% 0.30/0.47 => ! [F: ( multiset @ A ) > B,X: multiset @ A,Y: multiset @ A] :
% 0.30/0.47 ( ( antimono @ ( multiset @ A ) @ B @ ( subseteq_mset @ A ) @ F )
% 0.30/0.47 => ( ( subseteq_mset @ A @ X @ Y )
% 0.30/0.47 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_mset.antimonoE
% 0.30/0.47 thf(fact_255_subset__mset_OantimonoI,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( order @ B )
% 0.30/0.47 => ! [F: ( multiset @ A ) > B] :
% 0.30/0.47 ( ! [X4: multiset @ A,Y2: multiset @ A] :
% 0.30/0.47 ( ( subseteq_mset @ A @ X4 @ Y2 )
% 0.30/0.47 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X4 ) ) )
% 0.30/0.47 => ( antimono @ ( multiset @ A ) @ B @ ( subseteq_mset @ A ) @ F ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_mset.antimonoI
% 0.30/0.47
% 0.30/0.47 % Subclasses (4)
% 0.30/0.47 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( type @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( ord @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( order @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( preorder @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % Type constructors (15)
% 0.30/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.47 ! [A9: $tType,A10: $tType] :
% 0.30/0.47 ( ( preorder @ A10 )
% 0.30/0.47 => ( preorder @ ( A9 > A10 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.47 ! [A9: $tType,A10: $tType] :
% 0.30/0.47 ( ( order @ A10 )
% 0.30/0.47 => ( order @ ( A9 > A10 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.47 ! [A9: $tType,A10: $tType] :
% 0.30/0.47 ( ( ord @ A10 )
% 0.30/0.47 => ( ord @ ( A9 > A10 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 0.30/0.47 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 0.30/0.47 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 0.30/0.47 ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.30/0.47 preorder @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.30/0.47 linorder @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 0.30/0.47 order @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 0.30/0.47 ord @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Multiset_Omultiset___Groups_Oordered__ab__semigroup__add,axiom,
% 0.30/0.47 ! [A9: $tType] :
% 0.30/0.47 ( ( preorder @ A9 )
% 0.30/0.47 => ( ordere779506340up_add @ ( multiset @ A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add,axiom,
% 0.30/0.47 ! [A9: $tType] : ( cancel1352612707id_add @ ( multiset @ A9 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Multiset_Omultiset___Orderings_Opreorder_7,axiom,
% 0.30/0.47 ! [A9: $tType] :
% 0.30/0.47 ( ( preorder @ A9 )
% 0.30/0.47 => ( preorder @ ( multiset @ A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Multiset_Omultiset___Orderings_Oorder_8,axiom,
% 0.30/0.47 ! [A9: $tType] :
% 0.30/0.47 ( ( preorder @ A9 )
% 0.30/0.47 => ( order @ ( multiset @ A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Multiset_Omultiset___Orderings_Oord_9,axiom,
% 0.30/0.47 ! [A9: $tType] :
% 0.30/0.47 ( ( preorder @ A9 )
% 0.30/0.47 => ( ord @ ( multiset @ A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Free types (1)
% 0.30/0.47 thf(tfree_0,hypothesis,
% 0.30/0.47 linorder @ a ).
% 0.30/0.47
% 0.30/0.47 % Conjectures (1)
% 0.30/0.47 thf(conj_0,conjecture,
% 0.30/0.47 is_heap @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v2 @ ( e @ a ) @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 2.64/1.57 ---- Embedded in THF ---
% 2.64/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.64/1.57 %%% Generated on Tue Feb 24 08:25:30 EST 2026
% 2.64/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.64/1.57 %%% Logic specification used:
% 2.64/1.57 %%% thf(spec, logic, $$dhol).
% 2.64/1.57
% 2.64/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2DTF5214.p
% 2.64/1.57 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.64/1.57 thf(ty_t_Multiset_Omultiset, type, multiset: ($tType > $tType)).
% 2.64/1.57 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.64/1.57 thf(ty_t_Heap_OTree, type, tree: ($tType > $tType)).
% 2.64/1.57 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.64/1.57 thf(ty_tf_a, type, a: $tType).
% 2.64/1.57 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Groups_Oordered__comm__monoid__add, type, ordere216010020id_add: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral, type, unique1598680935umeral: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le, type, ordere516151231imp_le: (!> [A:$tType]: ($o))).
% 2.64/1.57 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain, type, bNF_Ca1785829860lChain: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > ((A > B) > $o))))).
% 2.64/1.57 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux, type, unique455577585es_aux: (!> [A:$tType]: ((((product_prod @ A) @ A) > $o)))).
% 2.64/1.57 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.64/1.57 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.64/1.57 thf(sy_c_HOL_ONO__MATCH, type, nO_MATCH: (!> [A:$tType,B:$tType]: ((A > (B > $o))))).
% 2.64/1.57 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oleft, type, heapIm1271749598e_left: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.64/1.57 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oright, type, heapIm1434396069_right: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.64/1.57 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_OsiftDown, type, heapIm748920189ftDown: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.64/1.57 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)) > $o))))))))).
% 2.64/1.57 thf(sy_c_Heap_OHeap__axioms, type, heap_axioms: (!> [B:$tType,A:$tType]: (((B > $o) > (((list @ A) > B) > ((B > (multiset @ A)) > ((B > (tree @ A)) > ((B > ((product_prod @ A) @ B)) > $o)))))))).
% 2.64/1.57 thf(sy_c_Heap_OTree_OE, type, e: (!> [A:$tType]: ((tree @ A)))).
% 2.64/1.57 thf(sy_c_Heap_OTree_OT, type, t: (!> [A:$tType]: ((A > ((tree @ A) > ((tree @ A) > (tree @ A))))))).
% 2.64/1.57 thf(sy_c_Heap_OTree_Ocase__Tree, type, case_Tree: (!> [B:$tType,A:$tType]: ((B > ((A > ((tree @ A) > ((tree @ A) > B))) > ((tree @ A) > B)))))).
% 2.64/1.57 thf(sy_c_Heap_OTree_Orec__Tree, type, rec_Tree: (!> [C:$tType,A:$tType]: ((C > ((A > ((tree @ A) > ((tree @ A) > (C > (C > C))))) > ((tree @ A) > C)))))).
% 2.64/1.57 thf(sy_c_Heap_OTree_Orel__Tree, type, rel_Tree: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((tree @ A) > ((tree @ B) > $o)))))).
% 2.64/1.57 thf(sy_c_Heap_Oin__tree, type, in_tree: (!> [A:$tType]: ((A > ((tree @ A) > $o))))).
% 2.64/1.57 thf(sy_c_Heap_Ois__heap, type, is_heap: (!> [A:$tType]: (((tree @ A) > $o)))).
% 2.64/1.57 thf(sy_c_Heap_Omultiset, type, multiset2: (!> [A:$tType]: (((tree @ A) > (multiset @ A))))).
% 2.64/1.57 thf(sy_c_Heap_Oval, type, val: (!> [A:$tType]: (((tree @ A) > A)))).
% 2.64/1.57 thf(sy_c_Lattices__Big_Olinorder__class_OMax, type, lattic929149872er_Max: (!> [A:$tType]: (((set @ A) > A)))).
% 2.64/1.57 thf(sy_c_Multiset_Oadd__mset, type, add_mset: (!> [A:$tType]: ((A > ((multiset @ A) > (multiset @ A)))))).
% 2.64/1.57 thf(sy_c_Multiset_Ocomm__monoid__add_Osum__mset, type, comm_monoid_sum_mset: (!> [A:$tType]: (((A > (A > A)) > (A > ((multiset @ A) > A)))))).
% 2.64/1.57 thf(sy_c_Multiset_Ofold__mset, type, fold_mset: (!> [A:$tType,B:$tType]: (((A > (B > B)) > (B > ((multiset @ A) > B)))))).
% 2.64/1.57 thf(sy_c_Multiset_Oimage__mset, type, image_mset: (!> [A:$tType,B:$tType]: (((A > B) > ((multiset @ A) > (multiset @ B)))))).
% 2.64/1.57 thf(sy_c_Multiset_Omult, type, mult: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (multiset @ A)) @ (multiset @ A))))))).
% 2.64/1.57 thf(sy_c_Multiset_Omult1, type, mult1: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (multiset @ A)) @ (multiset @ A))))))).
% 2.64/1.57 thf(sy_c_Multiset_Omultp, type, multp: (!> [A:$tType]: (((A > (A > $o)) > ((multiset @ A) > ((multiset @ A) > $o)))))).
% 2.64/1.57 thf(sy_c_Multiset_Oset__mset, type, set_mset: (!> [A:$tType]: (((multiset @ A) > (set @ A))))).
% 2.64/1.57 thf(sy_c_Multiset_Osubseteq__mset, type, subseteq_mset: (!> [A:$tType]: (((multiset @ A) > ((multiset @ A) > $o))))).
% 2.64/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.64/1.57 thf(sy_c_Orderings_Oorder_Oantimono, type, antimono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.64/1.57 thf(sy_c_Orderings_Oorder__class_OGreatest, type, order_Greatest: (!> [A:$tType]: (((A > $o) > A)))).
% 2.64/1.57 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.64/1.57 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.64/1.57 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.64/1.57 thf(sy_c_Relation_Oirrefl, type, irrefl: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.64/1.57 thf(sy_c_Relation_Otrans, type, trans: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.64/1.57 thf(sy_c_RemoveMax_OCollection, type, collection: (!> [B:$tType,A:$tType]: ((B > ((B > $o) > (((list @ A) > B) > ((B > (multiset @ A)) > $o))))))).
% 2.64/1.57 thf(sy_c_RemoveMax_OCollection_Oset, type, set2: (!> [B:$tType,A:$tType]: (((B > (multiset @ A)) > (B > (set @ A)))))).
% 2.64/1.57 thf(sy_c_RemoveMax_ORemoveMax, type, removeMax: (!> [B:$tType,A:$tType]: ((B > ((B > $o) > (((list @ A) > B) > ((B > (multiset @ A)) > ((B > ((product_prod @ A) @ B)) > ((B > $o) > $o))))))))).
% 2.64/1.57 thf(sy_c_RemoveMax_ORemoveMax__axioms, type, removeMax_axioms: (!> [B:$tType,A:$tType]: (((B > $o) > (((list @ A) > B) > ((B > (multiset @ A)) > ((B > ((product_prod @ A) @ B)) > ((B > $o) > $o)))))))).
% 2.64/1.57 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.64/1.57 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.64/1.57 thf(sy_v_l, type, l: (tree @ a)).
% 2.64/1.57 thf(sy_v_l1____, type, l1: (tree @ a)).
% 2.64/1.57 thf(sy_v_la____, type, la: (tree @ a)).
% 2.64/1.57 thf(sy_v_r, type, r: (tree @ a)).
% 2.64/1.57 thf(sy_v_r1____, type, r1: (tree @ a)).
% 2.64/1.57 thf(sy_v_ra____, type, ra: (tree @ a)).
% 2.64/1.57 thf(sy_v_t, type, t2: (tree @ a)).
% 2.64/1.57 thf(sy_v_v, type, v: a).
% 2.64/1.57 thf(sy_v_v1____, type, v1: a).
% 2.64/1.57 thf(sy_v_v2____, type, v2: a).
% 2.64/1.57 thf(sy_v_va____, type, va: a).
% 2.64/1.57 thf(fact_0__C4_Oprems_C_I2_J, axiom, ((is_heap @ a) @ ra)).
% 2.64/1.57 thf(fact_1__C4_Oprems_C_I1_J, axiom, ((is_heap @ a) @ la)).
% 2.64/1.57 thf(fact_2_assms_I2_J, axiom, ((is_heap @ a) @ r)).
% 2.64/1.57 thf(fact_3_assms_I1_J, axiom, ((is_heap @ a) @ l)).
% 2.64/1.57 thf(fact_4_True, axiom, (((ord_less_eq @ a) @ v1) @ v2)).
% 2.64/1.57 thf(fact_5__C4_Oprems_C_I3_J, axiom, (((((t @ a) @ v2) @ (e @ a)) @ ((((t @ a) @ v1) @ l1) @ r1)) = ((((t @ a) @ va) @ la) @ ra))).
% 2.64/1.57 thf(fact_6_siftDown_Osimps_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A]: ((((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ (e @ A)) @ (e @ A))) = ((((t @ A) @ V) @ (e @ A)) @ (e @ A))))))))).
% 2.64/1.57 thf(fact_7_siftDown_Osimps_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (((heapIm748920189ftDown @ A) @ (e @ A)) = (e @ A)))))).
% 2.64/1.57 thf(fact_8_siftDown_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:(tree @ A)]: (((X != (e @ A)) => ((! [V2:A]: ((X != ((((t @ A) @ V2) @ (e @ A)) @ (e @ A))))) => ((! [V2:A,Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((X != ((((t @ A) @ V2) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ (e @ A))))) => ((! [V2:A,Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((X != ((((t @ A) @ V2) @ (e @ A)) @ ((((t @ A) @ Va) @ Vb) @ Vc))))) => (~ ((! [V2:A,Va:A,Vb:(tree @ A),Vc:(tree @ A),Vd:A,Ve:(tree @ A),Vf:(tree @ A)]: ((X != ((((t @ A) @ V2) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf))))))))))))))))).
% 2.64/1.57 thf(fact_9_assms_I3_J, axiom, (t2 = ((((t @ a) @ v) @ l) @ r))).
% 2.64/1.57 thf(fact_10_is__heap_Osimps_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A]: (((is_heap @ A) @ ((((t @ A) @ V) @ (e @ A)) @ (e @ A))))))))).
% 2.64/1.57 thf(fact_11_siftDown__Node, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:(tree @ A),V:A,L:(tree @ A),R:(tree @ A)]: (((T2 = ((((t @ A) @ V) @ L) @ R)) => (? [L2:(tree @ A),V3:A,R2:(tree @ A)]: (((((heapIm748920189ftDown @ A) @ T2) = ((((t @ A) @ V3) @ L2) @ R2)) & (((ord_less_eq @ A) @ V) @ V3))))))))))).
% 2.64/1.57 thf(fact_12__C4_Ohyps_C, axiom, (! [L:(tree @ a),R:(tree @ a),V:a]: (((~ ((((ord_less_eq @ a) @ ((val @ a) @ ((((t @ a) @ v1) @ l1) @ r1))) @ v2))) => (((is_heap @ a) @ L) => (((is_heap @ a) @ R) => ((((((t @ a) @ v2) @ ((heapIm1271749598e_left @ a) @ ((((t @ a) @ v1) @ l1) @ r1))) @ ((heapIm1434396069_right @ a) @ ((((t @ a) @ v1) @ l1) @ r1))) = ((((t @ a) @ V) @ L) @ R)) => ((is_heap @ a) @ ((heapIm748920189ftDown @ a) @ ((((t @ a) @ v2) @ ((heapIm1271749598e_left @ a) @ ((((t @ a) @ v1) @ l1) @ r1))) @ ((heapIm1434396069_right @ a) @ ((((t @ a) @ v1) @ l1) @ r1)))))))))))).
% 2.64/1.57 thf(fact_13_Tree_Oinject, axiom, (! [A:$tType,X21:A,X22:(tree @ A),X23:(tree @ A),Y21:A,Y22:(tree @ A),Y23:(tree @ A)]: (((((((t @ A) @ X21) @ X22) @ X23) = ((((t @ A) @ Y21) @ Y22) @ Y23)) = ((X21 = Y21) & ((X22 = Y22) & (X23 = Y23))))))).
% 2.64/1.57 thf(fact_14_is__heap_Osimps_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => ((is_heap @ A) @ (e @ A)))))).
% 2.64/1.57 thf(fact_15_Tree_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(tree @ A),X23:(tree @ A)]: (((e @ A) != ((((t @ A) @ X21) @ X22) @ X23))))).
% 2.64/1.57 thf(fact_16_Tree_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),Tree:(tree @ A)]: (((P @ (e @ A)) => ((! [X1:A,X2:(tree @ A),X3:(tree @ A)]: (((P @ X2) => ((P @ X3) => (P @ ((((t @ A) @ X1) @ X2) @ X3)))))) => (P @ Tree)))))).
% 2.64/1.57 thf(fact_17_Tree_Oexhaust, axiom, (! [A:$tType,Y:(tree @ A)]: (((Y != (e @ A)) => (~ ((! [X212:A,X222:(tree @ A),X232:(tree @ A)]: ((Y != ((((t @ A) @ X212) @ X222) @ X232)))))))))).
% 2.64/1.57 thf(fact_18_is__heap_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:(tree @ A)]: (((X != (e @ A)) => ((! [V2:A]: ((X != ((((t @ A) @ V2) @ (e @ A)) @ (e @ A))))) => ((! [V2:A,Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((X != ((((t @ A) @ V2) @ (e @ A)) @ ((((t @ A) @ Va) @ Vb) @ Vc))))) => ((! [V2:A,Va:A,Vb:(tree @ A),Vc:(tree @ A)]: ((X != ((((t @ A) @ V2) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ (e @ A))))) => (~ ((! [V2:A,Va:A,Vb:(tree @ A),Vc:(tree @ A),Vd:A,Ve:(tree @ A),Vf:(tree @ A)]: ((X != ((((t @ A) @ V2) @ ((((t @ A) @ Va) @ Vb) @ Vc)) @ ((((t @ A) @ Vd) @ Ve) @ Vf))))))))))))))))).
% 2.64/1.57 thf(fact_19_siftDown__in__tree__set, axiom, (! [A:$tType]: (((linorder @ A) => ((in_tree @ A) = (^ [V4:A,T3:(tree @ A)]: ((((in_tree @ A) @ V4) @ ((heapIm748920189ftDown @ A) @ T3))))))))).
% 2.64/1.57 thf(fact_20_left_Osimps, axiom, (! [A:$tType,V:A,L:(tree @ A),R:(tree @ A)]: ((((heapIm1271749598e_left @ A) @ ((((t @ A) @ V) @ L) @ R)) = L)))).
% 2.64/1.57 thf(fact_21_is__heap__max, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,T2:(tree @ A)]: (((((in_tree @ A) @ V) @ T2) => (((is_heap @ A) @ T2) => (((ord_less_eq @ A) @ V) @ ((val @ A) @ T2)))))))))).
% 2.64/1.57 thf(fact_22_val_Osimps, axiom, (! [A:$tType,V:A,Uu:(tree @ A),Uv:(tree @ A)]: ((((val @ A) @ ((((t @ A) @ V) @ Uu) @ Uv)) = V)))).
% 2.64/1.57 thf(fact_23_in__tree_Osimps_I2_J, axiom, (! [A:$tType,V:A,V5:A,L:(tree @ A),R:(tree @ A)]: (((((in_tree @ A) @ V) @ ((((t @ A) @ V5) @ L) @ R)) = ((V = V5) | ((((in_tree @ A) @ V) @ L) | (((in_tree @ A) @ V) @ R))))))).
% 2.64/1.57 thf(fact_24_siftDown_Osimps_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A),Va2:A,Vb2:(tree @ A),Vc2:(tree @ A),V:A]: ((((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) => (((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) = ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))))) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)))))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))))) => (((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) = ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)))))))))))))))).
% 2.64/1.57 thf(fact_25_siftDown_Osimps_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [Va2:A,Vb2:(tree @ A),Vc2:(tree @ A),Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A),V:A]: ((((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) => (((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) = ((((t @ A) @ V) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))))) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)))))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))))) => (((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) = ((((t @ A) @ V) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)))))))))))))))).
% 2.64/1.57 thf(fact_26_in__tree_Osimps_I1_J, axiom, (! [A:$tType,V:A]: ((~ ((((in_tree @ A) @ V) @ (e @ A))))))).
% 2.64/1.57 thf(fact_27_is__heap_Osimps_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A),Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A)]: ((((is_heap @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) = ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ V) & (((is_heap @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) & ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V) & ((is_heap @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)))))))))))).
% 2.64/1.57 thf(fact_28_is__heap_Osimps_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Vd2:A,Ve2:(tree @ A),Vf2:(tree @ A),Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((((is_heap @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) = ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V) & (((is_heap @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) & ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2))) @ V) & ((is_heap @ A) @ ((((t @ A) @ Vd2) @ Ve2) @ Vf2)))))))))))).
% 2.64/1.57 thf(fact_29_siftDown_Osimps_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [Va2:A,Vb2:(tree @ A),Vc2:(tree @ A),V:A]: ((((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ (e @ A))) = ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ (e @ A)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ (e @ A))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))))) @ (e @ A))))))))))).
% 2.64/1.57 thf(fact_30_siftDown_Osimps_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [Va2:A,Vb2:(tree @ A),Vc2:(tree @ A),V:A]: ((((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ (e @ A)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) = ((((t @ A) @ V) @ (e @ A)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)))) & ((~ ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V))) => (((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ (e @ A)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) = ((((t @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ (e @ A)) @ ((heapIm748920189ftDown @ A) @ ((((t @ A) @ V) @ ((heapIm1271749598e_left @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ ((heapIm1434396069_right @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)))))))))))))).
% 2.64/1.57 thf(fact_31_siftDown__in__tree, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:(tree @ A)]: (((T2 != (e @ A)) => (((in_tree @ A) @ ((val @ A) @ ((heapIm748920189ftDown @ A) @ T2))) @ T2)))))))).
% 2.64/1.57 thf(fact_32_is__heap_Osimps_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((((is_heap @ A) @ ((((t @ A) @ V) @ (e @ A)) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) = ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V) & ((is_heap @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)))))))))).
% 2.64/1.57 thf(fact_33_is__heap_Osimps_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [V:A,Va2:A,Vb2:(tree @ A),Vc2:(tree @ A)]: ((((is_heap @ A) @ ((((t @ A) @ V) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)) @ (e @ A))) = ((((ord_less_eq @ A) @ ((val @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2))) @ V) & ((is_heap @ A) @ ((((t @ A) @ Va2) @ Vb2) @ Vc2)))))))))).
% 2.64/1.57 thf(fact_34_right_Osimps, axiom, (! [A:$tType,V:A,L:(tree @ A),R:(tree @ A)]: ((((heapIm1434396069_right @ A) @ ((((t @ A) @ V) @ L) @ R)) = R)))).
% 2.64/1.57 thf(fact_35_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.64/1.57 thf(fact_36_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.64/1.57 thf(fact_37_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.64/1.57 thf(fact_38_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X4:A]: ((((ord_less_eq @ B) @ (F @ X4)) @ (G @ X4)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.64/1.57 thf(fact_39_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X5:A]: ((((ord_less_eq @ B) @ (F2 @ X5)) @ (G2 @ X5))))))))))).
% 2.64/1.57 thf(fact_40_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X4:B,Y2:B]: (((((ord_less_eq @ B) @ X4) @ Y2) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.64/1.57 thf(fact_41_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B2:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C) @ (F @ B2)) @ C2) => ((! [X4:A,Y2:A]: (((((ord_less_eq @ A) @ X4) @ Y2) => (((ord_less_eq @ C) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C2)))))))))).
% 2.64/1.57 thf(fact_42_verit__la__disequality, axiom, (! [A:$tType]: (((linorder @ A) => (! [A2:A,B2:A]: (((A2 = B2) | ((~ ((((ord_less_eq @ A) @ A2) @ B2))) | (~ ((((ord_less_eq @ A) @ B2) @ A2))))))))))).
% 2.64/1.57 thf(fact_43_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B2:B,C2:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X4:B,Y2:B]: (((((ord_less_eq @ B) @ X4) @ Y2) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.64/1.57 thf(fact_44_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C2) => ((! [X4:A,Y2:A]: (((((ord_less_eq @ A) @ X4) @ Y2) => (((ord_less_eq @ B) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C2)))))))))).
% 2.64/1.57 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.64/1.57 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X5:A]: ((((member @ A) @ X5) @ A3)))) = A3)))).
% 2.64/1.57 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.64/1.57 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.64/1.57 thf(fact_49_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.64/1.57 thf(fact_50_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [A4:A,B3:A]: (((((ord_less_eq @ A) @ B3) @ A4) & (((ord_less_eq @ A) @ A4) @ B3))))))))).
% 2.64/1.57 thf(fact_51_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.64/1.57 thf(fact_52_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A5:A,B4:A]: (((((ord_less_eq @ A) @ A5) @ B4) => ((P @ A5) @ B4)))) => ((! [A5:A,B4:A]: ((((P @ B4) @ A5) => ((P @ A5) @ B4)))) => ((P @ A2) @ B2))))))))).
% 2.64/1.57 thf(fact_53_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.64/1.57 thf(fact_54_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 2.64/1.57 thf(fact_55_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.64/1.57 thf(fact_56_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.64/1.57 thf(fact_57_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.64/1.57 thf(fact_58_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) & (((ord_less_eq @ A) @ B3) @ A4))))))))).
% 2.64/1.57 thf(fact_59_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 2.64/1.57 thf(fact_60_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 2.64/1.57 thf(fact_61_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.64/1.57 thf(fact_62_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.64/1.57 thf(fact_63_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.64/1.57 thf(fact_64_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.64/1.57 thf(fact_65_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.64/1.57 thf(fact_66_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [X5:A,Y4:A]: (((((ord_less_eq @ A) @ X5) @ Y4) & (((ord_less_eq @ A) @ Y4) @ X5))))))))).
% 2.64/1.57 thf(fact_67_Greatest__equality, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X:A]: (((P @ X) => ((! [Y2:A]: (((P @ Y2) => (((ord_less_eq @ A) @ Y2) @ X)))) => (((order_Greatest @ A) @ P) = X))))))))).
% 2.64/1.57 thf(fact_68_GreatestI2__order, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X:A,Q:(A > $o)]: (((P @ X) => ((! [Y2:A]: (((P @ Y2) => (((ord_less_eq @ A) @ Y2) @ X)))) => ((! [X4:A]: (((P @ X4) => ((! [Y5:A]: (((P @ Y5) => (((ord_less_eq @ A) @ Y5) @ X4)))) => (Q @ X4))))) => (Q @ ((order_Greatest @ A) @ P))))))))))).
% 2.64/1.57 thf(fact_69_le__rel__bool__arg__iff, axiom, (! [A:$tType]: (((ord @ A) => ((ord_less_eq @ ($o > A)) = (^ [X6:($o > A),Y6:($o > A)]: (((((ord_less_eq @ A) @ (X6 @ $false)) @ (Y6 @ $false)) & (((ord_less_eq @ A) @ (X6 @ $true)) @ (Y6 @ $true)))))))))).
% 2.64/1.57 thf(fact_70_Tree_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:(A > ((tree @ A) > ((tree @ A) > B)))]: (((((((case_Tree @ B) @ A) @ F1) @ F22) @ (e @ A)) = F1)))).
% 2.64/1.57 thf(fact_71_Tree_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:(A > ((tree @ A) > ((tree @ A) > B))),X21:A,X22:(tree @ A),X23:(tree @ A)]: (((((((case_Tree @ B) @ A) @ F1) @ F22) @ ((((t @ A) @ X21) @ X22) @ X23)) = (((F22 @ X21) @ X22) @ X23))))).
% 2.64/1.57 thf(fact_72_Tree_Osimps_I6_J, axiom, (! [A:$tType,C:$tType,F1:C,F22:(A > ((tree @ A) > ((tree @ A) > (C > (C > C)))))]: (((((((rec_Tree @ C) @ A) @ F1) @ F22) @ (e @ A)) = F1)))).
% 2.64/1.57 thf(fact_73_Heap_Ois__heap__of__list, axiom, (! [B:$tType,A:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B)),I:(list @ A)]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max) => ((is_heap @ A) @ (As_tree @ (Of_list @ I)))))))))).
% 2.64/1.57 thf(fact_74_Tree_Osimps_I7_J, axiom, (! [C:$tType,A:$tType,F1:C,F22:(A > ((tree @ A) > ((tree @ A) > (C > (C > C))))),X21:A,X22:(tree @ A),X23:(tree @ A)]: (((((((rec_Tree @ C) @ A) @ F1) @ F22) @ ((((t @ A) @ X21) @ X22) @ X23)) = (((((F22 @ X21) @ X22) @ X23) @ (((((rec_Tree @ C) @ A) @ F1) @ F22) @ X22)) @ (((((rec_Tree @ C) @ A) @ F1) @ F22) @ X23)))))).
% 2.64/1.57 thf(fact_75_Heap_Oas__tree__empty, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B)),T2:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max) => (((As_tree @ T2) = (e @ A)) = (Is_empty @ T2))))))))).
% 2.64/1.57 thf(fact_76_Heap_Oaxioms_I2_J, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B))]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max) => (((((((heap_axioms @ B) @ A) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max)))))))).
% 2.64/1.57 thf(fact_77_Heap_Omultiset, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B)),L:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max) => ((Multiset @ L) = ((multiset2 @ A) @ (As_tree @ L)))))))))).
% 2.64/1.57 thf(fact_78_Heap_Oremove__max__val, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B)),T2:B,M:A,T4:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max) => ((~ ((Is_empty @ T2))) => ((((((product_Pair @ A) @ B) @ M) @ T4) = (Remove_max @ T2)) => (M = ((val @ A) @ (As_tree @ T2)))))))))))).
% 2.64/1.57 thf(fact_79_Heap_Oremove__max__is__heap, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B)),L:B,M:A,L3:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max) => ((~ ((Is_empty @ L))) => (((is_heap @ A) @ (As_tree @ L)) => ((((((product_Pair @ A) @ B) @ M) @ L3) = (Remove_max @ L)) => ((is_heap @ A) @ (As_tree @ L3)))))))))))).
% 2.64/1.57 thf(fact_80_Heap_Oaxioms_I1_J, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B))]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max) => ((((((collection @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset)))))))).
% 2.64/1.57 thf(fact_81_Tree_Orel__induct, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),X:(tree @ A),Y:(tree @ B),Q:((tree @ A) > ((tree @ B) > $o))]: (((((((rel_Tree @ A) @ B) @ R3) @ X) @ Y) => (((Q @ (e @ A)) @ (e @ B)) => ((! [A21:A,A22:(tree @ A),A23:(tree @ A),B21:B,B22:(tree @ B),B23:(tree @ B)]: ((((R3 @ A21) @ B21) => (((Q @ A22) @ B22) => (((Q @ A23) @ B23) => ((Q @ ((((t @ A) @ A21) @ A22) @ A23)) @ ((((t @ B) @ B21) @ B22) @ B23))))))) => ((Q @ X) @ Y))))))).
% 2.64/1.57 thf(fact_82_Tree_Orel__mono, axiom, (! [B:$tType,A:$tType,R3:(A > (B > $o)),Ra:(A > (B > $o))]: (((((ord_less_eq @ (A > (B > $o))) @ R3) @ Ra) => (((ord_less_eq @ ((tree @ A) > ((tree @ B) > $o))) @ (((rel_Tree @ A) @ B) @ R3)) @ (((rel_Tree @ A) @ B) @ Ra)))))).
% 2.64/1.57 thf(fact_83_Tree_Orel__eq, axiom, (! [A:$tType]: (((((rel_Tree @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) = (^ [Y3:(tree @ A),Z:(tree @ A)]: ((Y3 = Z))))))).
% 2.64/1.57 thf(fact_84_Tree_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(tree @ B)]: (((! [X4:B]: (((Ra @ X4) @ X4))) => (((((rel_Tree @ B) @ B) @ Ra) @ X) @ X))))).
% 2.64/1.57 thf(fact_85_Tree_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),X21:A,X22:(tree @ A),X23:(tree @ A),Y21:B,Y22:(tree @ B),Y23:(tree @ B)]: (((((((rel_Tree @ A) @ B) @ R3) @ ((((t @ A) @ X21) @ X22) @ X23)) @ ((((t @ B) @ Y21) @ Y22) @ Y23)) = (((R3 @ X21) @ Y21) & ((((((rel_Tree @ A) @ B) @ R3) @ X22) @ Y22) & (((((rel_Tree @ A) @ B) @ R3) @ X23) @ Y23))))))).
% 2.64/1.57 thf(fact_86_Tree_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),X21:A,Y21:B,X22:(tree @ A),Y22:(tree @ B),X23:(tree @ A),Y23:(tree @ B)]: ((((R3 @ X21) @ Y21) => ((((((rel_Tree @ A) @ B) @ R3) @ X22) @ Y22) => ((((((rel_Tree @ A) @ B) @ R3) @ X23) @ Y23) => (((((rel_Tree @ A) @ B) @ R3) @ ((((t @ A) @ X21) @ X22) @ X23)) @ ((((t @ B) @ Y21) @ Y22) @ Y23)))))))).
% 2.64/1.57 thf(fact_87_Tree_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o))]: ((((((rel_Tree @ A) @ B) @ R3) @ (e @ A)) @ (e @ B))))).
% 2.64/1.57 thf(fact_88_Heap__def, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (((heap @ B) @ A) = (^ [Empty2:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B))]: ((((((((collection @ B) @ A) @ Empty2) @ Is_empty2) @ Of_list2) @ Multiset2) & (((((((heap_axioms @ B) @ A) @ Is_empty2) @ Of_list2) @ Multiset2) @ As_tree2) @ Remove_max2))))))))).
% 2.64/1.57 thf(fact_89_Heap_Ointro, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B))]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) => ((((((((heap_axioms @ B) @ A) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max) => ((((((((heap @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max))))))))).
% 2.64/1.57 thf(fact_90_Tree_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),Y21:A,Y22:(tree @ A),Y23:(tree @ A)]: ((~ ((((((rel_Tree @ A) @ B) @ R3) @ ((((t @ A) @ Y21) @ Y22) @ Y23)) @ (e @ B))))))).
% 2.64/1.57 thf(fact_91_Tree_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),Y21:B,Y22:(tree @ B),Y23:(tree @ B)]: ((~ ((((((rel_Tree @ A) @ B) @ R3) @ (e @ A)) @ ((((t @ B) @ Y21) @ Y22) @ Y23))))))).
% 2.64/1.57 thf(fact_92_Tree_Orel__cases, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),A2:(tree @ A),B2:(tree @ B)]: (((((((rel_Tree @ A) @ B) @ R3) @ A2) @ B2) => (((A2 = (e @ A)) => (B2 != (e @ B))) => (~ ((! [X1:A,X2:(tree @ A),X3:(tree @ A)]: (((A2 = ((((t @ A) @ X1) @ X2) @ X3)) => (! [Y1:B,Y24:(tree @ B),Y32:(tree @ B)]: (((B2 = ((((t @ B) @ Y1) @ Y24) @ Y32)) => (((R3 @ X1) @ Y1) => ((((((rel_Tree @ A) @ B) @ R3) @ X2) @ Y24) => (~ ((((((rel_Tree @ A) @ B) @ R3) @ X3) @ Y32)))))))))))))))))).
% 2.64/1.57 thf(fact_93_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B5:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B5)) = ((A2 = A6) & (B2 = B5)))))).
% 2.64/1.57 thf(fact_94_prod_Oinject, axiom, (! [A:$tType,B:$tType,X12:A,X24:B,Y12:A,Y25:B]: (((((((product_Pair @ A) @ B) @ X12) @ X24) = ((((product_Pair @ A) @ B) @ Y12) @ Y25)) = ((X12 = Y12) & (X24 = Y25)))))).
% 2.64/1.57 thf(fact_95_Heap__axioms__def, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (((heap_axioms @ B) @ A) = (^ [Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),As_tree2:(B > (tree @ A)),Remove_max2:(B > ((product_prod @ A) @ B))]: (((! [L4:B]: (((Multiset2 @ L4) = ((multiset2 @ A) @ (As_tree2 @ L4))))) & ((! [I2:(list @ A)]: (((is_heap @ A) @ (As_tree2 @ (Of_list2 @ I2))))) & ((! [T3:B]: ((((As_tree2 @ T3) = (e @ A)) = (Is_empty2 @ T3)))) & ((! [L4:B,M2:A,L5:B]: (((~ ((Is_empty2 @ L4))) => ((((((product_Pair @ A) @ B) @ M2) @ L5) = (Remove_max2 @ L4)) => ((((add_mset @ A) @ M2) @ (Multiset2 @ L5)) = (Multiset2 @ L4)))))) & ((! [L4:B,M2:A,L5:B]: (((~ ((Is_empty2 @ L4))) => (((is_heap @ A) @ (As_tree2 @ L4)) => ((((((product_Pair @ A) @ B) @ M2) @ L5) = (Remove_max2 @ L4)) => ((is_heap @ A) @ (As_tree2 @ L5))))))) & (! [T3:B,M2:A,T5:B]: (((~ ((Is_empty2 @ T3))) => ((((((product_Pair @ A) @ B) @ M2) @ T5) = (Remove_max2 @ T3)) => (M2 = ((val @ A) @ (As_tree2 @ T3))))))))))))))))))).
% 2.64/1.57 thf(fact_96_Heap__axioms_Ointro, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Of_list:((list @ A) > B),Is_empty:(B > $o),Remove_max:(B > ((product_prod @ A) @ B))]: (((! [L6:B]: (((Multiset @ L6) = ((multiset2 @ A) @ (As_tree @ L6))))) => ((! [I3:(list @ A)]: (((is_heap @ A) @ (As_tree @ (Of_list @ I3))))) => ((! [T6:B]: ((((As_tree @ T6) = (e @ A)) = (Is_empty @ T6)))) => ((! [L6:B,M3:A,L2:B]: (((~ ((Is_empty @ L6))) => ((((((product_Pair @ A) @ B) @ M3) @ L2) = (Remove_max @ L6)) => ((((add_mset @ A) @ M3) @ (Multiset @ L2)) = (Multiset @ L6)))))) => ((! [L6:B,M3:A,L2:B]: (((~ ((Is_empty @ L6))) => (((is_heap @ A) @ (As_tree @ L6)) => ((((((product_Pair @ A) @ B) @ M3) @ L2) = (Remove_max @ L6)) => ((is_heap @ A) @ (As_tree @ L2))))))) => ((! [T6:B,M3:A,T7:B]: (((~ ((Is_empty @ T6))) => ((((((product_Pair @ A) @ B) @ M3) @ T7) = (Remove_max @ T6)) => (M3 = ((val @ A) @ (As_tree @ T6))))))) => (((((((heap_axioms @ B) @ A) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max))))))))))))).
% 2.64/1.57 thf(fact_97_heap__top__geq, axiom, (! [A:$tType]: (((linorder @ A) => (! [A2:A,T2:(tree @ A)]: (((((member @ A) @ A2) @ ((set_mset @ A) @ ((multiset2 @ A) @ T2))) => (((is_heap @ A) @ T2) => (((ord_less_eq @ A) @ A2) @ ((val @ A) @ T2)))))))))).
% 2.64/1.57 thf(fact_98_Collection_Ois__empty__empty, axiom, (! [A:$tType,B:$tType,Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A))]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) => (Is_empty @ Empty))))).
% 2.64/1.57 thf(fact_99_predicate2I, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Q:(A > (B > $o))]: (((! [X4:A,Y2:B]: ((((P @ X4) @ Y2) => ((Q @ X4) @ Y2)))) => (((ord_less_eq @ (A > (B > $o))) @ P) @ Q))))).
% 2.64/1.57 thf(fact_100_rev__predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),X:A,Y:B,Q:(A > (B > $o))]: ((((P @ X) @ Y) => ((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => ((Q @ X) @ Y)))))).
% 2.64/1.57 thf(fact_101_predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),X:A,Y:B]: (((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => (((P @ X) @ Y) => ((Q @ X) @ Y)))))).
% 2.64/1.57 thf(fact_102_Heap_Oremove__max__multiset_H, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),As_tree:(B > (tree @ A)),Remove_max:(B > ((product_prod @ A) @ B)),L:B,M:A,L3:B]: ((((((((((heap @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ As_tree) @ Remove_max) => ((~ ((Is_empty @ L))) => ((((((product_Pair @ A) @ B) @ M) @ L3) = (Remove_max @ L)) => ((((add_mset @ A) @ M) @ (Multiset @ L3)) = (Multiset @ L))))))))))).
% 2.64/1.57 thf(fact_103_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X4:A,Y2:B]: ((P2 = ((((product_Pair @ A) @ B) @ X4) @ Y2))))))).
% 2.64/1.57 thf(fact_104_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A5:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B4)))) => (P @ P2))))).
% 2.64/1.57 thf(fact_105_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B5:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B5)) => (~ (((A2 = A6) => (B2 != B5)))))))).
% 2.64/1.57 thf(fact_106_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A5:A,B4:B,C3:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B4) @ C3)))))))))).
% 2.64/1.57 thf(fact_107_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A5:A,B4:B,C3:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C3) @ D2))))))))))).
% 2.64/1.57 thf(fact_108_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A5:A,B4:B,C3:C,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.64/1.57 thf(fact_109_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: ((~ ((! [A5:A,B4:B,C3:C,D2:D,E2:E,F4:F3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D2) @ ((((product_Pair @ E) @ F3) @ E2) @ F4))))))))))))).
% 2.64/1.57 thf(fact_110_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,G3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))))]: ((~ ((! [A5:A,B4:B,C3:C,D2:D,E2:E,F4:F3,G4:G3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G3)) @ E2) @ ((((product_Pair @ F3) @ G3) @ F4) @ G4)))))))))))))).
% 2.64/1.57 thf(fact_111_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A5:A,B4:B,C3:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B4) @ C3))))) => (P @ X))))).
% 2.64/1.57 thf(fact_112_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A5:A,B4:B,C3:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C3) @ D2)))))) => (P @ X))))).
% 2.64/1.57 thf(fact_113_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A5:A,B4:B,C3:C,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X))))).
% 2.64/1.57 thf(fact_114_prod__induct6, axiom, (! [F3:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: (((! [A5:A,B4:B,C3:C,D2:D,E2:E,F4:F3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D2) @ ((((product_Pair @ E) @ F3) @ E2) @ F4)))))))) => (P @ X))))).
% 2.64/1.57 thf(fact_115_prod__induct7, axiom, (! [G3:$tType,F3:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))))]: (((! [A5:A,B4:B,C3:C,D2:D,E2:E,F4:F3,G4:G3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G3)) @ E2) @ ((((product_Pair @ F3) @ G3) @ F4) @ G4))))))))) => (P @ X))))).
% 2.64/1.57 thf(fact_116_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A5:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A5) @ B4))))))))).
% 2.64/1.57 thf(fact_117_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A5:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B4)))) => (P @ Prod))))).
% 2.64/1.57 thf(fact_118_Collection_Ois__empty__inj, axiom, (! [A:$tType,B:$tType,Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),E3:B]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) => ((Is_empty @ E3) => (E3 = Empty)))))).
% 2.64/1.57 thf(fact_119_old_Oprod_Orec, axiom, (! [A:$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))))).
% 2.64/1.57 thf(fact_120_add__mset__add__mset__same__iff, axiom, (! [A:$tType,A2:A,A3:(multiset @ A),B6:(multiset @ A)]: ((((((add_mset @ A) @ A2) @ A3) = (((add_mset @ A) @ A2) @ B6)) = (A3 = B6))))).
% 2.64/1.57 thf(fact_121_multi__self__add__other__not__self, axiom, (! [A:$tType,M4:(multiset @ A),X:A]: ((M4 != (((add_mset @ A) @ X) @ M4))))).
% 2.64/1.57 thf(fact_122_mset__add, axiom, (! [A:$tType,A2:A,A3:(multiset @ A)]: (((((member @ A) @ A2) @ ((set_mset @ A) @ A3)) => (~ ((! [B7:(multiset @ A)]: ((A3 != (((add_mset @ A) @ A2) @ B7)))))))))).
% 2.64/1.57 thf(fact_123_multi__member__split, axiom, (! [A:$tType,X:A,M4:(multiset @ A)]: (((((member @ A) @ X) @ ((set_mset @ A) @ M4)) => (? [A7:(multiset @ A)]: ((M4 = (((add_mset @ A) @ X) @ A7)))))))).
% 2.64/1.57 thf(fact_124_add__mset__commute, axiom, (! [A:$tType,X:A,Y:A,M4:(multiset @ A)]: (((((add_mset @ A) @ X) @ (((add_mset @ A) @ Y) @ M4)) = (((add_mset @ A) @ Y) @ (((add_mset @ A) @ X) @ M4)))))).
% 2.64/1.57 thf(fact_125_add__eq__conv__ex, axiom, (! [A:$tType,A2:A,M4:(multiset @ A),B2:A,N:(multiset @ A)]: ((((((add_mset @ A) @ A2) @ M4) = (((add_mset @ A) @ B2) @ N)) = (((M4 = N) & (A2 = B2)) | (? [K:(multiset @ A)]: (((M4 = (((add_mset @ A) @ B2) @ K)) & (N = (((add_mset @ A) @ A2) @ K)))))))))).
% 2.64/1.57 thf(fact_126_union__single__eq__member, axiom, (! [A:$tType,X:A,M4:(multiset @ A),N:(multiset @ A)]: ((((((add_mset @ A) @ X) @ M4) = N) => (((member @ A) @ X) @ ((set_mset @ A) @ N)))))).
% 2.64/1.57 thf(fact_127_insert__noteq__member, axiom, (! [A:$tType,B2:A,B6:(multiset @ A),C2:A,C4:(multiset @ A)]: ((((((add_mset @ A) @ B2) @ B6) = (((add_mset @ A) @ C2) @ C4)) => ((B2 != C2) => (((member @ A) @ C2) @ ((set_mset @ A) @ B6))))))).
% 2.64/1.57 thf(fact_128_heap__top__max, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:(tree @ A)]: (((T2 != (e @ A)) => (((is_heap @ A) @ T2) => (((val @ A) @ T2) = ((lattic929149872er_Max @ A) @ ((set_mset @ A) @ ((multiset2 @ A) @ T2)))))))))))).
% 2.64/1.57 thf(fact_129_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C2:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C2) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C2 @ A2) @ B2))))).
% 2.64/1.57 thf(fact_130_Collection_Oset__def, axiom, (! [A:$tType,B:$tType,Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),L:B]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) => (((((set2 @ B) @ A) @ Multiset) @ L) = ((set_mset @ A) @ (Multiset @ L))))))).
% 2.64/1.57 thf(fact_131_relChain__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (((bNF_Ca1785829860lChain @ A) @ B) = (^ [R4:(set @ ((product_prod @ A) @ A)),As:(A > B)]: ((! [I2:A,J:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ I2) @ J)) @ R4) => (((ord_less_eq @ B) @ (As @ I2)) @ (As @ J)))))))))))).
% 2.64/1.57 thf(fact_132_Collection_Oset_Ocong, axiom, (! [A:$tType,B:$tType]: ((((set2 @ B) @ A) = ((set2 @ B) @ A))))).
% 2.64/1.57 thf(fact_133_RemoveMax__axioms_Ointro, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Inv:(B > $o),Of_list:((list @ A) > B),Is_empty:(B > $o),Remove_max:(B > ((product_prod @ A) @ B)),Multiset:(B > (multiset @ A))]: (((! [X4:(list @ A)]: ((Inv @ (Of_list @ X4)))) => ((! [L6:B,M3:A,L2:B]: (((~ ((Is_empty @ L6))) => ((Inv @ L6) => ((((((product_Pair @ A) @ B) @ M3) @ L2) = (Remove_max @ L6)) => (M3 = ((lattic929149872er_Max @ A) @ ((((set2 @ B) @ A) @ Multiset) @ L6)))))))) => ((! [L6:B,M3:A,L2:B]: (((~ ((Is_empty @ L6))) => ((Inv @ L6) => ((((((product_Pair @ A) @ B) @ M3) @ L2) = (Remove_max @ L6)) => ((((add_mset @ A) @ M3) @ (Multiset @ L2)) = (Multiset @ L6))))))) => ((! [L6:B,M3:A,L2:B]: (((~ ((Is_empty @ L6))) => ((Inv @ L6) => ((((((product_Pair @ A) @ B) @ M3) @ L2) = (Remove_max @ L6)) => (Inv @ L2)))))) => (((((((removeMax_axioms @ B) @ A) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv))))))))))).
% 2.64/1.57 thf(fact_134_RemoveMax__axioms__def, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (((removeMax_axioms @ B) @ A) = (^ [Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),Remove_max2:(B > ((product_prod @ A) @ B)),Inv2:(B > $o)]: (((! [X5:(list @ A)]: ((Inv2 @ (Of_list2 @ X5)))) & ((! [L4:B,M2:A,L5:B]: (((~ ((Is_empty2 @ L4))) => ((Inv2 @ L4) => ((((((product_Pair @ A) @ B) @ M2) @ L5) = (Remove_max2 @ L4)) => (M2 = ((lattic929149872er_Max @ A) @ ((((set2 @ B) @ A) @ Multiset2) @ L4)))))))) & ((! [L4:B,M2:A,L5:B]: (((~ ((Is_empty2 @ L4))) => ((Inv2 @ L4) => ((((((product_Pair @ A) @ B) @ M2) @ L5) = (Remove_max2 @ L4)) => ((((add_mset @ A) @ M2) @ (Multiset2 @ L5)) = (Multiset2 @ L4))))))) & (! [L4:B,M2:A,L5:B]: (((~ ((Is_empty2 @ L4))) => ((Inv2 @ L4) => ((((((product_Pair @ A) @ B) @ M2) @ L5) = (Remove_max2 @ L4)) => (Inv2 @ L5)))))))))))))))).
% 2.64/1.57 thf(fact_135_RemoveMax_Oremove__max__max, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),Remove_max:(B > ((product_prod @ A) @ B)),Inv:(B > $o),L:B,M:A,L3:B]: ((((((((((removeMax @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv) => ((~ ((Is_empty @ L))) => ((Inv @ L) => ((((((product_Pair @ A) @ B) @ M) @ L3) = (Remove_max @ L)) => (M = ((lattic929149872er_Max @ A) @ ((((set2 @ B) @ A) @ Multiset) @ L))))))))))))).
% 2.64/1.57 thf(fact_136_predicate2D__conj, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),R3:$o,X:A,Y:B]: ((((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) & R3) => (R3 & (((P @ X) @ Y) => ((Q @ X) @ Y))))))).
% 2.64/1.57 thf(fact_137_RemoveMax_Oremove__max__inv, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),Remove_max:(B > ((product_prod @ A) @ B)),Inv:(B > $o),L:B,M:A,L3:B]: ((((((((((removeMax @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv) => ((~ ((Is_empty @ L))) => ((Inv @ L) => ((((((product_Pair @ A) @ B) @ M) @ L3) = (Remove_max @ L)) => (Inv @ L3))))))))))).
% 2.64/1.57 thf(fact_138_RemoveMax_Oaxioms_I2_J, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),Remove_max:(B > ((product_prod @ A) @ B)),Inv:(B > $o)]: ((((((((((removeMax @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv) => (((((((removeMax_axioms @ B) @ A) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv)))))))).
% 2.64/1.57 thf(fact_139_RemoveMax_Oof__list__inv, axiom, (! [B:$tType,A:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),Remove_max:(B > ((product_prod @ A) @ B)),Inv:(B > $o),X:(list @ A)]: ((((((((((removeMax @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv) => (Inv @ (Of_list @ X))))))))).
% 2.64/1.57 thf(fact_140_RemoveMax_Ointro, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),Remove_max:(B > ((product_prod @ A) @ B)),Inv:(B > $o)]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) => ((((((((removeMax_axioms @ B) @ A) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv) => ((((((((removeMax @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv))))))))).
% 2.64/1.57 thf(fact_141_RemoveMax__def, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (((removeMax @ B) @ A) = (^ [Empty2:B,Is_empty2:(B > $o),Of_list2:((list @ A) > B),Multiset2:(B > (multiset @ A)),Remove_max2:(B > ((product_prod @ A) @ B)),Inv2:(B > $o)]: ((((((((collection @ B) @ A) @ Empty2) @ Is_empty2) @ Of_list2) @ Multiset2) & (((((((removeMax_axioms @ B) @ A) @ Is_empty2) @ Of_list2) @ Multiset2) @ Remove_max2) @ Inv2))))))))).
% 2.64/1.57 thf(fact_142_RemoveMax_Oaxioms_I1_J, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),Remove_max:(B > ((product_prod @ A) @ B)),Inv:(B > $o)]: ((((((((((removeMax @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv) => ((((((collection @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset)))))))).
% 2.64/1.57 thf(fact_143_RemoveMax_Oremove__max__multiset, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),Remove_max:(B > ((product_prod @ A) @ B)),Inv:(B > $o),L:B,M:A,L3:B]: ((((((((((removeMax @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) @ Remove_max) @ Inv) => ((~ ((Is_empty @ L))) => ((Inv @ L) => ((((((product_Pair @ A) @ B) @ M) @ L3) = (Remove_max @ L)) => ((((add_mset @ A) @ M) @ (Multiset @ L3)) = (Multiset @ L)))))))))))).
% 2.64/1.57 thf(fact_144_ge__eq__refl, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A]: (((((ord_less_eq @ (A > (A > $o))) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ R3) => ((R3 @ X) @ X))))).
% 2.64/1.57 thf(fact_145_refl__ge__eq, axiom, (! [A:$tType,R3:(A > (A > $o))]: (((! [X4:A]: (((R3 @ X4) @ X4))) => (((ord_less_eq @ (A > (A > $o))) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ R3))))).
% 2.64/1.57 thf(fact_146_multiset__induct__max, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((multiset @ A) > $o),M4:(multiset @ A)]: (((P @ (zero_zero @ (multiset @ A))) => ((! [X4:A,M5:(multiset @ A)]: (((P @ M5) => ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set_mset @ A) @ M5)) => (((ord_less_eq @ A) @ Xa) @ X4)))) => (P @ (((add_mset @ A) @ X4) @ M5)))))) => (P @ M4))))))))).
% 2.64/1.57 thf(fact_147_multiset__induct__min, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((multiset @ A) > $o),M4:(multiset @ A)]: (((P @ (zero_zero @ (multiset @ A))) => ((! [X4:A,M5:(multiset @ A)]: (((P @ M5) => ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set_mset @ A) @ M5)) => (((ord_less_eq @ A) @ X4) @ Xa)))) => (P @ (((add_mset @ A) @ X4) @ M5)))))) => (P @ M4))))))))).
% 2.64/1.57 thf(fact_148_add__mset__eq__singleton__iff, axiom, (! [A:$tType,X:A,M4:(multiset @ A),Y:A]: ((((((add_mset @ A) @ X) @ M4) = (((add_mset @ A) @ Y) @ (zero_zero @ (multiset @ A)))) = ((M4 = (zero_zero @ (multiset @ A))) & (X = Y)))))).
% 2.64/1.57 thf(fact_149_single__eq__add__mset, axiom, (! [A:$tType,A2:A,B2:A,M4:(multiset @ A)]: ((((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = (((add_mset @ A) @ B2) @ M4)) = ((B2 = A2) & (M4 = (zero_zero @ (multiset @ A)))))))).
% 2.64/1.57 thf(fact_150_add__mset__eq__single, axiom, (! [A:$tType,B2:A,M4:(multiset @ A),A2:A]: ((((((add_mset @ A) @ B2) @ M4) = (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))) = ((B2 = A2) & (M4 = (zero_zero @ (multiset @ A)))))))).
% 2.64/1.57 thf(fact_151_single__eq__single, axiom, (! [A:$tType,A2:A,B2:A]: ((((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = (((add_mset @ A) @ B2) @ (zero_zero @ (multiset @ A)))) = (A2 = B2))))).
% 2.64/1.57 thf(fact_152_multiset__cases, axiom, (! [A:$tType,M4:(multiset @ A)]: (((M4 != (zero_zero @ (multiset @ A))) => (~ ((! [X4:A,N2:(multiset @ A)]: ((M4 != (((add_mset @ A) @ X4) @ N2)))))))))).
% 2.64/1.57 thf(fact_153_multiset__induct, axiom, (! [A:$tType,P:((multiset @ A) > $o),M4:(multiset @ A)]: (((P @ (zero_zero @ (multiset @ A))) => ((! [X4:A,M5:(multiset @ A)]: (((P @ M5) => (P @ (((add_mset @ A) @ X4) @ M5))))) => (P @ M4)))))).
% 2.64/1.57 thf(fact_154_multiset__induct2, axiom, (! [A:$tType,B:$tType,P:((multiset @ A) > ((multiset @ B) > $o)),M4:(multiset @ A),N:(multiset @ B)]: ((((P @ (zero_zero @ (multiset @ A))) @ (zero_zero @ (multiset @ B))) => ((! [A5:A,M5:(multiset @ A),N2:(multiset @ B)]: ((((P @ M5) @ N2) => ((P @ (((add_mset @ A) @ A5) @ M5)) @ N2)))) => ((! [A5:B,M5:(multiset @ A),N2:(multiset @ B)]: ((((P @ M5) @ N2) => ((P @ M5) @ (((add_mset @ B) @ A5) @ N2))))) => ((P @ M4) @ N))))))).
% 2.64/1.57 thf(fact_155_empty__not__add__mset, axiom, (! [A:$tType,A2:A,A3:(multiset @ A)]: (((zero_zero @ (multiset @ A)) != (((add_mset @ A) @ A2) @ A3))))).
% 2.64/1.57 thf(fact_156_multiset__nonemptyE, axiom, (! [A:$tType,A3:(multiset @ A)]: (((A3 != (zero_zero @ (multiset @ A))) => (~ ((! [X4:A]: ((~ ((((member @ A) @ X4) @ ((set_mset @ A) @ A3)))))))))))).
% 2.64/1.57 thf(fact_157_multi__nonempty__split, axiom, (! [A:$tType,M4:(multiset @ A)]: (((M4 != (zero_zero @ (multiset @ A))) => (? [A7:(multiset @ A),A5:A]: ((M4 = (((add_mset @ A) @ A5) @ A7)))))))).
% 2.64/1.57 thf(fact_158_Collection_Ois__empty__as__list, axiom, (! [B:$tType,A:$tType,Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A)),E3:B]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) => ((Is_empty @ E3) => ((Multiset @ E3) = (zero_zero @ (multiset @ A)))))))).
% 2.64/1.57 thf(fact_159_Collection_Omultiset__empty, axiom, (! [B:$tType,A:$tType,Empty:B,Is_empty:(B > $o),Of_list:((list @ A) > B),Multiset:(B > (multiset @ A))]: ((((((((collection @ B) @ A) @ Empty) @ Is_empty) @ Of_list) @ Multiset) => ((Multiset @ Empty) = (zero_zero @ (multiset @ A))))))).
% 2.64/1.57 thf(fact_160_multi__member__last, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ ((set_mset @ A) @ (((add_mset @ A) @ X) @ (zero_zero @ (multiset @ A)))))))).
% 2.64/1.57 thf(fact_161_multiset_Osimps_I1_J, axiom, (! [A:$tType]: ((((multiset2 @ A) @ (e @ A)) = (zero_zero @ (multiset @ A)))))).
% 2.64/1.57 thf(fact_162_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N3:A]: (((((ord_less_eq @ A) @ N3) @ (zero_zero @ A)) = (N3 = (zero_zero @ A))))))))).
% 2.64/1.57 thf(fact_163_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X))))))).
% 2.64/1.57 thf(fact_164_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.64/1.57 thf(fact_165_multiset_Osimps_I2_J, axiom, (! [A:$tType,V:A,L:(tree @ A),R:(tree @ A)]: ((((multiset2 @ A) @ ((((t @ A) @ V) @ L) @ R)) = (((plus_plus @ (multiset @ A)) @ (((plus_plus @ (multiset @ A)) @ ((multiset2 @ A) @ L)) @ (((add_mset @ A) @ V) @ (zero_zero @ (multiset @ A))))) @ ((multiset2 @ A) @ R)))))).
% 2.64/1.57 thf(fact_166_divides__aux__eq, axiom, (! [A:$tType]: (((unique1598680935umeral @ A) => (! [Q2:A,R:A]: ((((unique455577585es_aux @ A) @ ((((product_Pair @ A) @ A) @ Q2) @ R)) = (R = (zero_zero @ A))))))))).
% 2.64/1.57 thf(fact_167_single__subset__iff, axiom, (! [A:$tType,A2:A,M4:(multiset @ A)]: (((((subseteq_mset @ A) @ (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))) @ M4) = (((member @ A) @ A2) @ ((set_mset @ A) @ M4)))))).
% 2.64/1.57 thf(fact_168_add__le__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.64/1.57 thf(fact_169_add__le__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.64/1.57 thf(fact_170_union__mset__add__mset__left, axiom, (! [A:$tType,A2:A,A3:(multiset @ A),B6:(multiset @ A)]: (((((plus_plus @ (multiset @ A)) @ (((add_mset @ A) @ A2) @ A3)) @ B6) = (((add_mset @ A) @ A2) @ (((plus_plus @ (multiset @ A)) @ A3) @ B6)))))).
% 2.64/1.57 thf(fact_171_union__mset__add__mset__right, axiom, (! [A:$tType,A3:(multiset @ A),A2:A,B6:(multiset @ A)]: (((((plus_plus @ (multiset @ A)) @ A3) @ (((add_mset @ A) @ A2) @ B6)) = (((add_mset @ A) @ A2) @ (((plus_plus @ (multiset @ A)) @ A3) @ B6)))))).
% 2.64/1.57 thf(fact_172_zero__le__double__add__iff__zero__le__single__add, axiom, (! [A:$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)))))))).
% 2.64/1.57 thf(fact_173_double__add__le__zero__iff__single__add__le__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.64/1.57 thf(fact_174_le__add__same__cancel2, axiom, (! [A:$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)))))))).
% 2.64/1.57 thf(fact_175_le__add__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.64/1.57 thf(fact_176_add__le__same__cancel2, axiom, (! [A:$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))))))))).
% 2.64/1.57 thf(fact_177_add__le__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ B2) @ A2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.64/1.57 thf(fact_178_add__mset__subseteq__single__iff, axiom, (! [A:$tType,A2:A,M4:(multiset @ A),B2:A]: (((((subseteq_mset @ A) @ (((add_mset @ A) @ A2) @ M4)) @ (((add_mset @ A) @ B2) @ (zero_zero @ (multiset @ A)))) = ((M4 = (zero_zero @ (multiset @ A))) & (A2 = B2)))))).
% 2.64/1.57 thf(fact_179_verit__sum__simplify, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.64/1.57 thf(fact_180_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J2:A,K2:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J2) & (K2 = L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J2) @ L))))))))).
% 2.64/1.57 thf(fact_181_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J2:A,K2:A,L:A]: ((((I = J2) & (((ord_less_eq @ A) @ K2) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J2) @ L))))))))).
% 2.64/1.57 thf(fact_182_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J2:A,K2:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J2) & (((ord_less_eq @ A) @ K2) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J2) @ L))))))))).
% 2.64/1.57 thf(fact_183_add__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C2:A,D3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C2) @ D3) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ D3)))))))))).
% 2.64/1.57 thf(fact_184_add__left__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2))))))))).
% 2.64/1.57 thf(fact_185_less__eqE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (~ ((! [C3:A]: ((B2 != (((plus_plus @ A) @ A2) @ C3))))))))))))).
% 2.64/1.57 thf(fact_186_add__right__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.64/1.57 thf(fact_187_le__iff__add, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => ((ord_less_eq @ A) = (^ [A4:A,B3:A]: ((? [C5:A]: ((B3 = (((plus_plus @ A) @ A4) @ C5))))))))))).
% 2.64/1.57 thf(fact_188_add__le__imp__le__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.64/1.57 thf(fact_189_add__le__imp__le__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.64/1.57 thf(fact_190_union__iff, axiom, (! [A:$tType,A2:A,A3:(multiset @ A),B6:(multiset @ A)]: (((((member @ A) @ A2) @ ((set_mset @ A) @ (((plus_plus @ (multiset @ A)) @ A3) @ B6))) = ((((member @ A) @ A2) @ ((set_mset @ A) @ A3)) | (((member @ A) @ A2) @ ((set_mset @ A) @ B6))))))).
% 2.64/1.57 thf(fact_191_mset__subset__eqD, axiom, (! [A:$tType,A3:(multiset @ A),B6:(multiset @ A),X:A]: (((((subseteq_mset @ A) @ A3) @ B6) => ((((member @ A) @ X) @ ((set_mset @ A) @ A3)) => (((member @ A) @ X) @ ((set_mset @ A) @ B6))))))).
% 2.64/1.57 thf(fact_192_mset__subset__eq__add__mset__cancel, axiom, (! [A:$tType,A2:A,A3:(multiset @ A),B6:(multiset @ A)]: (((((subseteq_mset @ A) @ (((add_mset @ A) @ A2) @ A3)) @ (((add_mset @ A) @ A2) @ B6)) = (((subseteq_mset @ A) @ A3) @ B6))))).
% 2.64/1.57 thf(fact_193_set__mset__mono, axiom, (! [A:$tType,A3:(multiset @ A),B6:(multiset @ A)]: (((((subseteq_mset @ A) @ A3) @ B6) => (((ord_less_eq @ (set @ A)) @ ((set_mset @ A) @ A3)) @ ((set_mset @ A) @ B6)))))).
% 2.64/1.57 thf(fact_194_add__nonpos__eq__0__iff, axiom, (! [A:$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)))))))))))).
% 2.64/1.57 thf(fact_195_add__nonneg__eq__0__iff, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y) => (((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))))).
% 2.64/1.57 thf(fact_196_add__nonpos__nonpos, axiom, (! [A:$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)))))))))).
% 2.64/1.57 thf(fact_197_add__nonneg__nonneg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.64/1.57 thf(fact_198_add__increasing2, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [C2:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ C2) => ((((ord_less_eq @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)))))))))).
% 2.64/1.57 thf(fact_199_add__decreasing2, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ C2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ B2))))))))).
% 2.64/1.57 thf(fact_200_add__increasing, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)))))))))).
% 2.64/1.57 thf(fact_201_add__decreasing, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ B2))))))))).
% 2.64/1.57 thf(fact_202_single__is__union, axiom, (! [A:$tType,A2:A,M4:(multiset @ A),N:(multiset @ A)]: ((((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = (((plus_plus @ (multiset @ A)) @ M4) @ N)) = ((((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = M4) & (N = (zero_zero @ (multiset @ A)))) | ((M4 = (zero_zero @ (multiset @ A))) & ((((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A))) = N))))))).
% 2.64/1.57 thf(fact_203_union__is__single, axiom, (! [A:$tType,M4:(multiset @ A),N:(multiset @ A),A2:A]: ((((((plus_plus @ (multiset @ A)) @ M4) @ N) = (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))) = (((M4 = (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))) & (N = (zero_zero @ (multiset @ A)))) | ((M4 = (zero_zero @ (multiset @ A))) & (N = (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))))))))).
% 2.64/1.57 thf(fact_204_add__mset__add__single, axiom, (! [A:$tType]: (((add_mset @ A) = (^ [A4:A,A8:(multiset @ A)]: ((((plus_plus @ (multiset @ A)) @ A8) @ (((add_mset @ A) @ A4) @ (zero_zero @ (multiset @ A)))))))))).
% 2.64/1.57 thf(fact_205_multi__subset__induct, axiom, (! [A:$tType,F5:(multiset @ A),A3:(multiset @ A),P:((multiset @ A) > $o)]: (((((subseteq_mset @ A) @ F5) @ A3) => ((P @ (zero_zero @ (multiset @ A))) => ((! [A5:A,F6:(multiset @ A)]: (((((member @ A) @ A5) @ ((set_mset @ A) @ A3)) => ((P @ F6) => (P @ (((add_mset @ A) @ A5) @ F6)))))) => (P @ F5))))))).
% 2.64/1.57 thf(fact_206_mset__subset__eq__single, axiom, (! [A:$tType,A2:A,B6:(multiset @ A)]: (((((member @ A) @ A2) @ ((set_mset @ A) @ B6)) => (((subseteq_mset @ A) @ (((add_mset @ A) @ A2) @ (zero_zero @ (multiset @ A)))) @ B6))))).
% 2.64/1.57 thf(fact_207_multi__member__skip, axiom, (! [A:$tType,X:A,XS:(multiset @ A),Y:A]: (((((member @ A) @ X) @ ((set_mset @ A) @ XS)) => (((member @ A) @ X) @ ((set_mset @ A) @ (((plus_plus @ (multiset @ A)) @ (((add_mset @ A) @ Y) @ (zero_zero @ (multiset @ A)))) @ XS))))))).
% 2.64/1.57 thf(fact_208_multi__member__this, axiom, (! [A:$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)))))).
% 2.64/1.57 thf(fact_209_mult1E, axiom, (! [A:$tType,N:(multiset @ A),M4:(multiset @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ N) @ M4)) @ ((mult1 @ A) @ R)) => (~ ((! [A5:A,M0:(multiset @ A)]: (((M4 = (((add_mset @ A) @ A5) @ M0)) => (! [K3:(multiset @ A)]: (((N = (((plus_plus @ (multiset @ A)) @ M0) @ K3)) => (~ ((! [B8:A]: (((((member @ A) @ B8) @ ((set_mset @ A) @ K3)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B8) @ A5)) @ R)))))))))))))))))).
% 2.64/1.57 thf(fact_210_mult1I, axiom, (! [A:$tType,M4:(multiset @ A),A2:A,M02:(multiset @ A),N:(multiset @ A),K4:(multiset @ A),R:(set @ ((product_prod @ A) @ A))]: (((M4 = (((add_mset @ A) @ A2) @ M02)) => ((N = (((plus_plus @ (multiset @ A)) @ M02) @ K4)) => ((! [B4:A]: (((((member @ A) @ B4) @ ((set_mset @ A) @ K4)) => (((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) @ M4)) @ ((mult1 @ A) @ R)))))))).
% 2.64/1.57 thf(fact_211_less__add, axiom, (! [A:$tType,N:(multiset @ A),A2:A,M02:(multiset @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ N) @ (((add_mset @ A) @ A2) @ M02))) @ ((mult1 @ A) @ R)) => ((? [M5:(multiset @ A)]: (((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ M5) @ M02)) @ ((mult1 @ A) @ R)) & (N = (((add_mset @ A) @ A2) @ M5))))) | (? [K3:(multiset @ A)]: (((! [B8:A]: (((((member @ A) @ B8) @ ((set_mset @ A) @ K3)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B8) @ A2)) @ R)))) & (N = (((plus_plus @ (multiset @ A)) @ M02) @ K3)))))))))).
% 2.64/1.57 thf(fact_212_mono__mult1, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),R5:(set @ ((product_prod @ A) @ A))]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ R) @ R5) => (((ord_less_eq @ (set @ ((product_prod @ (multiset @ A)) @ (multiset @ A)))) @ ((mult1 @ A) @ R)) @ ((mult1 @ A) @ R5)))))).
% 2.64/1.57 thf(fact_213_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B6) => ((((ord_less_eq @ (set @ A)) @ B6) @ A3) => (A3 = B6)))))).
% 2.64/1.57 thf(fact_214_subsetI, axiom, (! [A:$tType,A3:(set @ A),B6:(set @ A)]: (((! [X4:A]: (((((member @ A) @ X4) @ A3) => (((member @ A) @ X4) @ B6)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B6))))).
% 2.64/1.57 thf(fact_215_in__mono, axiom, (! [A:$tType,A3:(set @ A),B6:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B6) => ((((member @ A) @ X) @ A3) => (((member @ A) @ X) @ B6)))))).
% 2.64/1.57 thf(fact_216_subsetD, axiom, (! [A:$tType,A3:(set @ A),B6:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B6) => ((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B6)))))).
% 2.64/1.57 thf(fact_217_equalityE, axiom, (! [A:$tType,A3:(set @ A),B6:(set @ A)]: (((A3 = B6) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B6) => (~ ((((ord_less_eq @ (set @ A)) @ B6) @ A3)))))))))).
% 2.64/1.57 thf(fact_218_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A8:(set @ A),B9:(set @ A)]: ((! [X5:A]: (((((member @ A) @ X5) @ A8) => (((member @ A) @ X5) @ B9)))))))))).
% 2.64/1.57 thf(fact_219_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B6:(set @ A)]: (((A3 = B6) => (((ord_less_eq @ (set @ A)) @ A3) @ B6))))).
% 2.64/1.57 thf(fact_220_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B6:(set @ A)]: (((A3 = B6) => (((ord_less_eq @ (set @ A)) @ B6) @ A3))))).
% 2.64/1.57 thf(fact_221_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A8:(set @ A),B9:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A8) => (((member @ A) @ T3) @ B9)))))))))).
% 2.64/1.57 thf(fact_222_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 2.64/1.57 thf(fact_223_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) => (Q @ X4)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.64/1.57 thf(fact_224_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B6:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B6) => ((((ord_less_eq @ (set @ A)) @ B6) @ C4) => (((ord_less_eq @ (set @ A)) @ A3) @ C4)))))).
% 2.64/1.57 thf(fact_225_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y3:(set @ A),Z:(set @ A)]: ((Y3 = Z))) = (^ [A8:(set @ A),B9:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A8) @ B9) & (((ord_less_eq @ (set @ A)) @ B9) @ A8)))))))).
% 2.64/1.57 thf(fact_226_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X5:A]: (((P @ X5) => (Q @ X5)))))))).
% 2.64/1.57 thf(fact_227_one__step__implies__mult, axiom, (! [A:$tType,J3:(multiset @ A),K4:(multiset @ A),R:(set @ ((product_prod @ A) @ A)),I4:(multiset @ A)]: (((J3 != (zero_zero @ (multiset @ A))) => ((! [X4:A]: (((((member @ A) @ X4) @ ((set_mset @ A) @ K4)) => (? [Xa:A]: (((((member @ A) @ Xa) @ ((set_mset @ A) @ J3)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Xa)) @ R))))))) => (((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ (((plus_plus @ (multiset @ A)) @ I4) @ K4)) @ (((plus_plus @ (multiset @ A)) @ I4) @ J3))) @ ((mult @ A) @ R))))))).
% 2.64/1.57 thf(fact_228_subrelI, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((! [X4:A,Y2:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y2)) @ R) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y2)) @ S)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R) @ S))))).
% 2.64/1.57 thf(fact_229_mono__mult, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),R5:(set @ ((product_prod @ A) @ A))]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ R) @ R5) => (((ord_less_eq @ (set @ ((product_prod @ (multiset @ A)) @ (multiset @ A)))) @ ((mult @ A) @ R)) @ ((mult @ A) @ R5)))))).
% 2.64/1.57 thf(fact_230_mult__implies__one__step, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),M4:(multiset @ A),N:(multiset @ A)]: ((((trans @ A) @ R) => ((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ M4) @ N)) @ ((mult @ A) @ R)) => (? [I5:(multiset @ A),J4:(multiset @ A)]: (((N = (((plus_plus @ (multiset @ A)) @ I5) @ J4)) & (? [K3:(multiset @ A)]: (((M4 = (((plus_plus @ (multiset @ A)) @ I5) @ K3)) & ((J4 != (zero_zero @ (multiset @ A))) & (! [X7:A]: (((((member @ A) @ X7) @ ((set_mset @ A) @ K3)) => (? [Xa2:A]: (((((member @ A) @ Xa2) @ ((set_mset @ A) @ J4)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X7) @ Xa2)) @ R))))))))))))))))))).
% 2.64/1.57 thf(fact_231_subset__mset_Osum__mset__0__iff, axiom, (! [A:$tType,M4:(multiset @ (multiset @ A))]: (((((((comm_monoid_sum_mset @ (multiset @ A)) @ (plus_plus @ (multiset @ A))) @ (zero_zero @ (multiset @ A))) @ M4) = (zero_zero @ (multiset @ A))) = (! [X5:(multiset @ A)]: (((((member @ (multiset @ A)) @ X5) @ ((set_mset @ (multiset @ A)) @ M4)) => (X5 = (zero_zero @ (multiset @ A)))))))))).
% 2.64/1.57 thf(fact_232_transD, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X:A,Y:A,Z2: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) @ Z2)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z2)) @ R))))))).
% 2.64/1.57 thf(fact_233_transE, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X:A,Y:A,Z2:A]: ((((trans @ A) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ Z2)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z2)) @ R))))))).
% 2.64/1.57 thf(fact_234_transI, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A))]: (((! [X4:A,Y2:A,Z3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Y2)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ Z3)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Z3)) @ R))))) => ((trans @ A) @ R))))).
% 2.64/1.57 thf(fact_235_trans__def, axiom, (! [A:$tType]: (((trans @ A) = (^ [R4:(set @ ((product_prod @ A) @ A))]: ((! [X5:A,Y4:A,Z4:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X5) @ Y4)) @ R4) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ Z4)) @ R4) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X5) @ Z4)) @ R4))))))))))).
% 2.64/1.57 thf(fact_236_mult__cancel__add__mset, axiom, (! [A:$tType,S:(set @ ((product_prod @ A) @ A)),Uu:A,X8:(multiset @ A),Y7:(multiset @ A)]: ((((trans @ A) @ S) => (((irrefl @ A) @ S) => ((((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ (((add_mset @ A) @ Uu) @ X8)) @ (((add_mset @ A) @ Uu) @ Y7))) @ ((mult @ A) @ S)) = (((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ X8) @ Y7)) @ ((mult @ A) @ S)))))))).
% 2.64/1.57 thf(fact_237_in__mset__fold__plus__iff, axiom, (! [A:$tType,X:A,M4:(multiset @ A),NN:(multiset @ (multiset @ A))]: (((((member @ A) @ X) @ ((set_mset @ A) @ (((((fold_mset @ (multiset @ A)) @ (multiset @ A)) @ (plus_plus @ (multiset @ A))) @ M4) @ NN))) = ((((member @ A) @ X) @ ((set_mset @ A) @ M4)) | (? [N4:(multiset @ A)]: (((((member @ (multiset @ A)) @ N4) @ ((set_mset @ (multiset @ A)) @ NN)) & (((member @ A) @ X) @ ((set_mset @ A) @ N4)))))))))).
% 2.64/1.57 thf(fact_238_irrefl__def, axiom, (! [A:$tType]: (((irrefl @ A) = (^ [R4:(set @ ((product_prod @ A) @ A))]: ((! [A4:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A4) @ A4)) @ R4))))))))))).
% 2.64/1.57 thf(fact_239_irreflI, axiom, (! [A:$tType,R3:(set @ ((product_prod @ A) @ A))]: (((! [A5:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A5) @ A5)) @ R3))))) => ((irrefl @ A) @ R3))))).
% 2.64/1.57 thf(fact_240_union__fold__mset__add__mset, axiom, (! [A:$tType]: (((plus_plus @ (multiset @ A)) = (((fold_mset @ A) @ (multiset @ A)) @ (add_mset @ A)))))).
% 2.64/1.57 thf(fact_241_multp__iff, axiom, (! [A:$tType,R3:(set @ ((product_prod @ A) @ A)),P:(A > (A > $o)),N:(multiset @ A),M4:(multiset @ A)]: ((((irrefl @ A) @ R3) => (((trans @ A) @ R3) => ((! [X4:A,Y2:A]: ((((P @ X4) @ Y2) = (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Y2)) @ R3)))) => (((((multp @ A) @ P) @ N) @ M4) = (((member @ ((product_prod @ (multiset @ A)) @ (multiset @ A))) @ ((((product_Pair @ (multiset @ A)) @ (multiset @ A)) @ N) @ M4)) @ ((mult @ A) @ R3))))))))).
% 2.64/1.57 thf(fact_242_add__mset__replicate__mset__safe, axiom, (! [A:$tType,B:$tType,M4:(multiset @ B),A2:B]: ((((((nO_MATCH @ (multiset @ A)) @ (multiset @ B)) @ (zero_zero @ (multiset @ A))) @ M4) => ((((add_mset @ B) @ A2) @ M4) = (((plus_plus @ (multiset @ B)) @ (((add_mset @ B) @ A2) @ (zero_zero @ (multiset @ B)))) @ M4)))))).
% 2.64/1.57 thf(fact_243_subset__mset_Osum__mset__mono, axiom, (! [A:$tType,B:$tType,K4:(multiset @ B),F:(B > (multiset @ A)),G:(B > (multiset @ A))]: (((! [I3:B]: (((((member @ B) @ I3) @ ((set_mset @ B) @ K4)) => (((subseteq_mset @ A) @ (F @ I3)) @ (G @ I3))))) => (((subseteq_mset @ A) @ ((((comm_monoid_sum_mset @ (multiset @ A)) @ (plus_plus @ (multiset @ A))) @ (zero_zero @ (multiset @ A))) @ ((((image_mset @ B) @ (multiset @ A)) @ F) @ K4))) @ ((((comm_monoid_sum_mset @ (multiset @ A)) @ (plus_plus @ (multiset @ A))) @ (zero_zero @ (multiset @ A))) @ ((((image_mset @ B) @ (multiset @ A)) @ G) @ K4))))))).
% 2.64/1.57 thf(fact_244_subset__mset_Oantimono__def, axiom, (! [B:$tType,A:$tType]: (((order @ B) => (! [F:((multiset @ A) > B)]: ((((((antimono @ (multiset @ A)) @ B) @ (subseteq_mset @ A)) @ F) = (! [X5:(multiset @ A),Y4:(multiset @ A)]: (((((subseteq_mset @ A) @ X5) @ Y4) => (((ord_less_eq @ B) @ (F @ Y4)) @ (F @ X5)))))))))))).
% 2.64/1.57 thf(fact_245_image__mset__add__mset, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:B,M4:(multiset @ B)]: ((((((image_mset @ B) @ A) @ F) @ (((add_mset @ B) @ A2) @ M4)) = (((add_mset @ A) @ (F @ A2)) @ ((((image_mset @ B) @ A) @ F) @ M4)))))).
% 2.64/1.57 thf(fact_246_multiset_Omap__cong, axiom, (! [B:$tType,A:$tType,X:(multiset @ A),Ya:(multiset @ A),F:(A > B),G:(A > B)]: (((X = Ya) => ((! [Z3:A]: (((((member @ A) @ Z3) @ ((set_mset @ A) @ Ya)) => ((F @ Z3) = (G @ Z3))))) => (((((image_mset @ A) @ B) @ F) @ X) = ((((image_mset @ A) @ B) @ G) @ Ya))))))).
% 2.64/1.57 thf(fact_247_multiset_Omap__cong0, axiom, (! [B:$tType,A:$tType,X:(multiset @ A),F:(A > B),G:(A > B)]: (((! [Z3:A]: (((((member @ A) @ Z3) @ ((set_mset @ A) @ X)) => ((F @ Z3) = (G @ Z3))))) => (((((image_mset @ A) @ B) @ F) @ X) = ((((image_mset @ A) @ B) @ G) @ X)))))).
% 2.64/1.57 thf(fact_248_multiset_Oinj__map__strong, axiom, (! [B:$tType,A:$tType,X:(multiset @ A),Xa3:(multiset @ A),F:(A > B),Fa:(A > B)]: (((! [Z3:A,Za:A]: (((((member @ A) @ Z3) @ ((set_mset @ A) @ X)) => ((((member @ A) @ Za) @ ((set_mset @ A) @ Xa3)) => (((F @ Z3) = (Fa @ Za)) => (Z3 = Za)))))) => ((((((image_mset @ A) @ B) @ F) @ X) = ((((image_mset @ A) @ B) @ Fa) @ Xa3)) => (X = Xa3)))))).
% 2.64/1.57 thf(fact_249_order_Oantimono_Ocong, axiom, (! [B:$tType,A:$tType]: (((order @ B) => (((antimono @ A) @ B) = ((antimono @ A) @ B)))))).
% 2.64/1.57 thf(fact_250_msed__map__invR, axiom, (! [B:$tType,A:$tType,F:(B > A),M4:(multiset @ B),B2:A,N:(multiset @ A)]: (((((((image_mset @ B) @ A) @ F) @ M4) = (((add_mset @ A) @ B2) @ N)) => (? [M1:(multiset @ B),A5:B]: (((M4 = (((add_mset @ B) @ A5) @ M1)) & (((F @ A5) = B2) & (((((image_mset @ B) @ A) @ F) @ M1) = N))))))))).
% 2.64/1.57 thf(fact_251_msed__map__invL, axiom, (! [B:$tType,A:$tType,F:(B > A),A2:B,M4:(multiset @ B),N:(multiset @ A)]: (((((((image_mset @ B) @ A) @ F) @ (((add_mset @ B) @ A2) @ M4)) = N) => (? [N1:(multiset @ A)]: (((N = (((add_mset @ A) @ (F @ A2)) @ N1)) & (((((image_mset @ B) @ A) @ F) @ M4) = N1)))))))).
% 2.64/1.57 thf(fact_252_image__mset__single, axiom, (! [B:$tType,A:$tType,F:(B > A),X:B]: ((((((image_mset @ B) @ A) @ F) @ (((add_mset @ B) @ X) @ (zero_zero @ (multiset @ B)))) = (((add_mset @ A) @ (F @ X)) @ (zero_zero @ (multiset @ A))))))).
% 2.64/1.57 thf(fact_253_subset__mset_OantimonoD, axiom, (! [B:$tType,A:$tType]: (((order @ B) => (! [F:((multiset @ A) > B),X:(multiset @ A),Y:(multiset @ A)]: ((((((antimono @ (multiset @ A)) @ B) @ (subseteq_mset @ A)) @ F) => ((((subseteq_mset @ A) @ X) @ Y) => (((ord_less_eq @ B) @ (F @ Y)) @ (F @ X)))))))))).
% 2.64/1.57 thf(fact_254_subset__mset_OantimonoE, axiom, (! [B:$tType,A:$tType]: (((order @ B) => (! [F:((multiset @ A) > B),X:(multiset @ A),Y:(multiset @ A)]: ((((((antimono @ (multiset @ A)) @ B) @ (subseteq_mset @ A)) @ F) => ((((subseteq_mset @ A) @ X) @ Y) => (((ord_less_eq @ B) @ (F @ Y)) @ (F @ X)))))))))).
% 2.64/1.57 thf(fact_255_subset__mset_OantimonoI, axiom, (! [B:$tType,A:$tType]: (((order @ B) => (! [F:((multiset @ A) > B)]: (((! [X4:(multiset @ A),Y2:(multiset @ A)]: (((((subseteq_mset @ A) @ X4) @ Y2) => (((ord_less_eq @ B) @ (F @ Y2)) @ (F @ X4))))) => ((((antimono @ (multiset @ A)) @ B) @ (subseteq_mset @ A)) @ F)))))))).
% 2.64/1.57 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: (((linorder @ A) => (type @ A))))).
% 2.64/1.57 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: (((linorder @ A) => (ord @ A))))).
% 2.64/1.57 thf(subcl_Orderings_Olinorder___Orderings_Oorder, axiom, (! [A:$tType]: (((linorder @ A) => (order @ A))))).
% 2.64/1.57 thf(subcl_Orderings_Olinorder___Orderings_Opreorder, axiom, (! [A:$tType]: (((linorder @ A) => (preorder @ A))))).
% 2.64/1.57 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A9:$tType,A10:$tType]: (((preorder @ A10) => (preorder @ (A9 > A10)))))).
% 2.64/1.57 thf(tcon_fun___Orderings_Oorder, axiom, (! [A9:$tType,A10:$tType]: (((order @ A10) => (order @ (A9 > A10)))))).
% 2.64/1.57 thf(tcon_fun___Orderings_Oord, axiom, (! [A9:$tType,A10:$tType]: (((ord @ A10) => (ord @ (A9 > A10)))))).
% 2.64/1.57 thf(tcon_Set_Oset___Orderings_Opreorder_1, axiom, (! [A9:$tType]: ((preorder @ (set @ A9))))).
% 2.64/1.57 thf(tcon_Set_Oset___Orderings_Oorder_2, axiom, (! [A9:$tType]: ((order @ (set @ A9))))).
% 2.64/1.57 thf(tcon_Set_Oset___Orderings_Oord_3, axiom, (! [A9:$tType]: ((ord @ (set @ A9))))).
% 2.64/1.57 thf(tcon_HOL_Obool___Orderings_Opreorder_4, axiom, (preorder @ $o)).
% 2.64/1.57 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.64/1.57 thf(tcon_HOL_Obool___Orderings_Oorder_5, axiom, (order @ $o)).
% 2.64/1.57 thf(tcon_HOL_Obool___Orderings_Oord_6, axiom, (ord @ $o)).
% 2.64/1.57 thf(tcon_Multiset_Omultiset___Groups_Oordered__ab__semigroup__add, axiom, (! [A9:$tType]: (((preorder @ A9) => (ordere779506340up_add @ (multiset @ A9)))))).
% 2.64/1.57 thf(tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add, axiom, (! [A9:$tType]: ((cancel1352612707id_add @ (multiset @ A9))))).
% 2.64/1.57 thf(tcon_Multiset_Omultiset___Orderings_Opreorder_7, axiom, (! [A9:$tType]: (((preorder @ A9) => (preorder @ (multiset @ A9)))))).
% 2.64/1.57 thf(tcon_Multiset_Omultiset___Orderings_Oorder_8, axiom, (! [A9:$tType]: (((preorder @ A9) => (order @ (multiset @ A9)))))).
% 2.64/1.57 thf(tcon_Multiset_Omultiset___Orderings_Oord_9, axiom, (! [A9:$tType]: (((preorder @ A9) => (ord @ (multiset @ A9)))))).
% 2.64/1.57 thf(tfree_0, hypothesis, (linorder @ a)).
% 2.64/1.57 thf(conj_0, conjecture, ((is_heap @ a) @ ((heapIm748920189ftDown @ a) @ ((((t @ a) @ v2) @ (e @ a)) @ ((((t @ a) @ v1) @ l1) @ r1))))).
% 2.64/1.57 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2DTF5214.p
% 2.64/1.57 ------------------------
% 2.83/1.60 ---- Cleaned THF ---
% 2.83/1.60 thf(ty_t_Product__Type_Oprod,type,
% 2.83/1.60 product_prod: $tType > $tType > $tType ).
% 2.83/1.60
% 2.83/1.60 thf(ty_t_Multiset_Omultiset,type,
% 2.83/1.60 multiset: $tType > $tType ).
% 2.83/1.60
% 2.83/1.60 thf(ty_t_List_Olist,type,
% 2.83/1.60 list: $tType > $tType ).
% 2.83/1.60
% 2.83/1.60 thf(ty_t_Heap_OTree,type,
% 2.83/1.60 tree: $tType > $tType ).
% 2.83/1.60
% 2.83/1.60 thf(ty_t_Set_Oset,type,
% 2.83/1.60 set: $tType > $tType ).
% 2.83/1.60
% 2.83/1.60 thf(ty_tf_a,type,
% 2.83/1.60 a: $tType ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_HOL_Otype,type,
% 2.83/1.60 type:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Orderings_Oord,type,
% 2.83/1.60 ord:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Orderings_Oorder,type,
% 2.83/1.60 order:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Orderings_Olinorder,type,
% 2.83/1.60 linorder:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Orderings_Opreorder,type,
% 2.83/1.60 preorder:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.83/1.60 cancel1352612707id_add:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.83/1.60 linord219039673up_add:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 2.83/1.60 ordere216010020id_add:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.83/1.60 ordere779506340up_add:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.83/1.60 linord1659791738miring:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.83/1.60 canoni770627133id_add:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.83/1.60 ordere236663937imp_le:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 2.83/1.60 unique1598680935umeral:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 2.83/1.60 ordere516151231imp_le:
% 2.83/1.60 !>[A: $tType] : $o ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain,type,
% 2.83/1.60 bNF_Ca1785829860lChain:
% 2.83/1.60 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( A > B ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux,type,
% 2.83/1.60 unique455577585es_aux:
% 2.83/1.60 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.83/1.60 plus_plus:
% 2.83/1.60 !>[A: $tType] : ( A > A > A ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.83/1.60 zero_zero:
% 2.83/1.60 !>[A: $tType] : A ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_HOL_ONO__MATCH,type,
% 2.83/1.60 nO_MATCH:
% 2.83/1.60 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oleft,type,
% 2.83/1.60 heapIm1271749598e_left:
% 2.83/1.60 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_Oright,type,
% 2.83/1.60 heapIm1434396069_right:
% 2.83/1.60 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_HeapImperative__Mirabelle__oitemzccmr_OsiftDown,type,
% 2.83/1.60 heapIm748920189ftDown:
% 2.83/1.60 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_OHeap,type,
% 2.83/1.60 heap:
% 2.83/1.60 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( tree @ A ) ) > ( B > ( product_prod @ A @ B ) ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_OHeap__axioms,type,
% 2.83/1.60 heap_axioms:
% 2.83/1.60 !>[B: $tType,A: $tType] : ( ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( tree @ A ) ) > ( B > ( product_prod @ A @ B ) ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_OTree_OE,type,
% 2.83/1.60 e:
% 2.83/1.60 !>[A: $tType] : ( tree @ A ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_OTree_OT,type,
% 2.83/1.60 t:
% 2.83/1.60 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) > ( tree @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_OTree_Ocase__Tree,type,
% 2.83/1.60 case_Tree:
% 2.83/1.60 !>[B: $tType,A: $tType] : ( B > ( A > ( tree @ A ) > ( tree @ A ) > B ) > ( tree @ A ) > B ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_OTree_Orec__Tree,type,
% 2.83/1.60 rec_Tree:
% 2.83/1.60 !>[C: $tType,A: $tType] : ( C > ( A > ( tree @ A ) > ( tree @ A ) > C > C > C ) > ( tree @ A ) > C ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_OTree_Orel__Tree,type,
% 2.83/1.60 rel_Tree:
% 2.83/1.60 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( tree @ A ) > ( tree @ B ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_Oin__tree,type,
% 2.83/1.60 in_tree:
% 2.83/1.60 !>[A: $tType] : ( A > ( tree @ A ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_Ois__heap,type,
% 2.83/1.60 is_heap:
% 2.83/1.60 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_Omultiset,type,
% 2.83/1.60 multiset2:
% 2.83/1.60 !>[A: $tType] : ( ( tree @ A ) > ( multiset @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Heap_Oval,type,
% 2.83/1.60 val:
% 2.83/1.60 !>[A: $tType] : ( ( tree @ A ) > A ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Lattices__Big_Olinorder__class_OMax,type,
% 2.83/1.60 lattic929149872er_Max:
% 2.83/1.60 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Multiset_Oadd__mset,type,
% 2.83/1.60 add_mset:
% 2.83/1.60 !>[A: $tType] : ( A > ( multiset @ A ) > ( multiset @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Multiset_Ocomm__monoid__add_Osum__mset,type,
% 2.83/1.60 comm_monoid_sum_mset:
% 2.83/1.60 !>[A: $tType] : ( ( A > A > A ) > A > ( multiset @ A ) > A ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Multiset_Ofold__mset,type,
% 2.83/1.60 fold_mset:
% 2.83/1.60 !>[A: $tType,B: $tType] : ( ( A > B > B ) > B > ( multiset @ A ) > B ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Multiset_Oimage__mset,type,
% 2.83/1.60 image_mset:
% 2.83/1.60 !>[A: $tType,B: $tType] : ( ( A > B ) > ( multiset @ A ) > ( multiset @ B ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Multiset_Omult,type,
% 2.83/1.60 mult:
% 2.83/1.60 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Multiset_Omult1,type,
% 2.83/1.60 mult1:
% 2.83/1.60 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Multiset_Omultp,type,
% 2.83/1.60 multp:
% 2.83/1.60 !>[A: $tType] : ( ( A > A > $o ) > ( multiset @ A ) > ( multiset @ A ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Multiset_Oset__mset,type,
% 2.83/1.60 set_mset:
% 2.83/1.60 !>[A: $tType] : ( ( multiset @ A ) > ( set @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Multiset_Osubseteq__mset,type,
% 2.83/1.60 subseteq_mset:
% 2.83/1.60 !>[A: $tType] : ( ( multiset @ A ) > ( multiset @ A ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.83/1.60 ord_less_eq:
% 2.83/1.60 !>[A: $tType] : ( A > A > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Orderings_Oorder_Oantimono,type,
% 2.83/1.60 antimono:
% 2.83/1.60 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 2.83/1.60 order_Greatest:
% 2.83/1.60 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Product__Type_OPair,type,
% 2.83/1.60 product_Pair:
% 2.83/1.60 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.83/1.60 produc2004651681e_prod:
% 2.83/1.60 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.83/1.60 product_rec_prod:
% 2.83/1.60 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Relation_Oirrefl,type,
% 2.83/1.60 irrefl:
% 2.83/1.60 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Relation_Otrans,type,
% 2.83/1.60 trans:
% 2.83/1.60 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_RemoveMax_OCollection,type,
% 2.83/1.60 collection:
% 2.83/1.60 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_RemoveMax_OCollection_Oset,type,
% 2.83/1.60 set2:
% 2.83/1.60 !>[B: $tType,A: $tType] : ( ( B > ( multiset @ A ) ) > B > ( set @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_RemoveMax_ORemoveMax,type,
% 2.83/1.60 removeMax:
% 2.83/1.60 !>[B: $tType,A: $tType] : ( B > ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( product_prod @ A @ B ) ) > ( B > $o ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_RemoveMax_ORemoveMax__axioms,type,
% 2.83/1.60 removeMax_axioms:
% 2.83/1.60 !>[B: $tType,A: $tType] : ( ( B > $o ) > ( ( list @ A ) > B ) > ( B > ( multiset @ A ) ) > ( B > ( product_prod @ A @ B ) ) > ( B > $o ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_Set_OCollect,type,
% 2.83/1.60 collect:
% 2.83/1.60 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_c_member,type,
% 2.83/1.60 member:
% 2.83/1.60 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_l,type,
% 2.83/1.60 l: tree @ a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_l1____,type,
% 2.83/1.60 l1: tree @ a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_la____,type,
% 2.83/1.60 la: tree @ a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_r,type,
% 2.83/1.60 r: tree @ a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_r1____,type,
% 2.83/1.60 r1: tree @ a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_ra____,type,
% 2.83/1.60 ra: tree @ a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_t,type,
% 2.83/1.60 t2: tree @ a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_v,type,
% 2.83/1.60 v: a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_v1____,type,
% 2.83/1.60 v1: a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_v2____,type,
% 2.83/1.60 v2: a ).
% 2.83/1.60
% 2.83/1.60 thf(sy_v_va____,type,
% 2.83/1.60 va: a ).
% 2.83/1.60
% 2.83/1.60 thf(fact_0__C4_Oprems_C_I2_J,axiom,
% 2.83/1.60 is_heap @ a @ ra ).
% 2.83/1.60
% 2.83/1.60 thf(fact_1__C4_Oprems_C_I1_J,axiom,
% 2.83/1.60 is_heap @ a @ la ).
% 2.83/1.60
% 2.83/1.60 thf(fact_2_assms_I2_J,axiom,
% 2.83/1.60 is_heap @ a @ r ).
% 2.83/1.60
% 2.83/1.60 thf(fact_3_assms_I1_J,axiom,
% 2.83/1.60 is_heap @ a @ l ).
% 2.83/1.60
% 2.83/1.60 thf(fact_4_True,axiom,
% 2.83/1.60 ord_less_eq @ a @ v1 @ v2 ).
% 2.83/1.60
% 2.83/1.60 thf(fact_5__C4_Oprems_C_I3_J,axiom,
% 2.83/1.60 ( ( t @ a @ v2 @ ( e @ a ) @ ( t @ a @ v1 @ l1 @ r1 ) )
% 2.83/1.60 = ( t @ a @ va @ la @ ra ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_6_siftDown_Osimps_I2_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [V: A] :
% 2.83/1.60 ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) )
% 2.83/1.60 = ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_7_siftDown_Osimps_I1_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( e @ A ) )
% 2.83/1.60 = ( e @ A ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_8_siftDown_Ocases,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [X: tree @ A] :
% 2.83/1.60 ( ( X
% 2.83/1.60 != ( e @ A ) )
% 2.83/1.60 => ( ! [V2: A] :
% 2.83/1.60 ( X
% 2.83/1.60 != ( t @ A @ V2 @ ( e @ A ) @ ( e @ A ) ) )
% 2.83/1.60 => ( ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.83/1.60 ( X
% 2.83/1.60 != ( t @ A @ V2 @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 2.83/1.60 => ( ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.83/1.60 ( X
% 2.83/1.60 != ( t @ A @ V2 @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.83/1.60 => ~ ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A] :
% 2.83/1.60 ( X
% 2.83/1.60 != ( t @ A @ V2 @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_9_assms_I3_J,axiom,
% 2.83/1.60 ( t2
% 2.83/1.60 = ( t @ a @ v @ l @ r ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_10_is__heap_Osimps_I2_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [V: A] : ( is_heap @ A @ ( t @ A @ V @ ( e @ A ) @ ( e @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_11_siftDown__Node,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [T2: tree @ A,V: A,L: tree @ A,R: tree @ A] :
% 2.83/1.60 ( ( T2
% 2.83/1.60 = ( t @ A @ V @ L @ R ) )
% 2.83/1.60 => ? [L2: tree @ A,V3: A,R2: tree @ A] :
% 2.83/1.60 ( ( ( heapIm748920189ftDown @ A @ T2 )
% 2.83/1.60 = ( t @ A @ V3 @ L2 @ R2 ) )
% 2.83/1.60 & ( ord_less_eq @ A @ V @ V3 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_12__C4_Ohyps_C,axiom,
% 2.83/1.60 ! [L: tree @ a,R: tree @ a,V: a] :
% 2.83/1.60 ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ v2 )
% 2.83/1.60 => ( ( is_heap @ a @ L )
% 2.83/1.60 => ( ( is_heap @ a @ R )
% 2.83/1.60 => ( ( ( t @ a @ v2 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
% 2.83/1.60 = ( t @ a @ V @ L @ R ) )
% 2.83/1.60 => ( is_heap @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v2 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_13_Tree_Oinject,axiom,
% 2.83/1.60 ! [A: $tType,X21: A,X22: tree @ A,X23: tree @ A,Y21: A,Y22: tree @ A,Y23: tree @ A] :
% 2.83/1.60 ( ( ( t @ A @ X21 @ X22 @ X23 )
% 2.83/1.60 = ( t @ A @ Y21 @ Y22 @ Y23 ) )
% 2.83/1.60 = ( ( X21 = Y21 )
% 2.83/1.60 & ( X22 = Y22 )
% 2.83/1.60 & ( X23 = Y23 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_14_is__heap_Osimps_I1_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( is_heap @ A @ ( e @ A ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_15_Tree_Odistinct_I1_J,axiom,
% 2.83/1.60 ! [A: $tType,X21: A,X22: tree @ A,X23: tree @ A] :
% 2.83/1.60 ( ( e @ A )
% 2.83/1.60 != ( t @ A @ X21 @ X22 @ X23 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_16_Tree_Oinduct,axiom,
% 2.83/1.60 ! [A: $tType,P: ( tree @ A ) > $o,Tree: tree @ A] :
% 2.83/1.60 ( ( P @ ( e @ A ) )
% 2.83/1.60 => ( ! [X1: A,X2: tree @ A,X3: tree @ A] :
% 2.83/1.60 ( ( P @ X2 )
% 2.83/1.60 => ( ( P @ X3 )
% 2.83/1.60 => ( P @ ( t @ A @ X1 @ X2 @ X3 ) ) ) )
% 2.83/1.60 => ( P @ Tree ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_17_Tree_Oexhaust,axiom,
% 2.83/1.60 ! [A: $tType,Y: tree @ A] :
% 2.83/1.60 ( ( Y
% 2.83/1.60 != ( e @ A ) )
% 2.83/1.60 => ~ ! [X212: A,X222: tree @ A,X232: tree @ A] :
% 2.83/1.60 ( Y
% 2.83/1.60 != ( t @ A @ X212 @ X222 @ X232 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_18_is__heap_Ocases,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [X: tree @ A] :
% 2.83/1.60 ( ( X
% 2.83/1.60 != ( e @ A ) )
% 2.83/1.60 => ( ! [V2: A] :
% 2.83/1.60 ( X
% 2.83/1.60 != ( t @ A @ V2 @ ( e @ A ) @ ( e @ A ) ) )
% 2.83/1.60 => ( ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.83/1.60 ( X
% 2.83/1.60 != ( t @ A @ V2 @ ( e @ A ) @ ( t @ A @ Va @ Vb @ Vc ) ) )
% 2.83/1.60 => ( ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A] :
% 2.83/1.60 ( X
% 2.83/1.60 != ( t @ A @ V2 @ ( t @ A @ Va @ Vb @ Vc ) @ ( e @ A ) ) )
% 2.83/1.60 => ~ ! [V2: A,Va: A,Vb: tree @ A,Vc: tree @ A,Vd: A,Ve: tree @ A,Vf: tree @ A] :
% 2.83/1.60 ( X
% 2.83/1.60 != ( t @ A @ V2 @ ( t @ A @ Va @ Vb @ Vc ) @ ( t @ A @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_19_siftDown__in__tree__set,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( ( in_tree @ A )
% 2.83/1.60 = ( ^ [V4: A,T3: tree @ A] : ( in_tree @ A @ V4 @ ( heapIm748920189ftDown @ A @ T3 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_20_left_Osimps,axiom,
% 2.83/1.60 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 2.83/1.60 ( ( heapIm1271749598e_left @ A @ ( t @ A @ V @ L @ R ) )
% 2.83/1.60 = L ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_21_is__heap__max,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [V: A,T2: tree @ A] :
% 2.83/1.60 ( ( in_tree @ A @ V @ T2 )
% 2.83/1.60 => ( ( is_heap @ A @ T2 )
% 2.83/1.60 => ( ord_less_eq @ A @ V @ ( val @ A @ T2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_22_val_Osimps,axiom,
% 2.83/1.60 ! [A: $tType,V: A,Uu: tree @ A,Uv: tree @ A] :
% 2.83/1.60 ( ( val @ A @ ( t @ A @ V @ Uu @ Uv ) )
% 2.83/1.60 = V ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_23_in__tree_Osimps_I2_J,axiom,
% 2.83/1.60 ! [A: $tType,V: A,V5: A,L: tree @ A,R: tree @ A] :
% 2.83/1.60 ( ( in_tree @ A @ V @ ( t @ A @ V5 @ L @ R ) )
% 2.83/1.60 = ( ( V = V5 )
% 2.83/1.60 | ( in_tree @ A @ V @ L )
% 2.83/1.60 | ( in_tree @ A @ V @ R ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_24_siftDown_Osimps_I5_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Vd2: A,Ve2: tree @ A,Vf2: tree @ A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,V: A] :
% 2.83/1.60 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.83/1.60 = ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 2.83/1.60 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.83/1.60 = ( t @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) )
% 2.83/1.60 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.83/1.60 = ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 2.83/1.60 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.83/1.60 = ( t @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_25_siftDown_Osimps_I6_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A,V: A] :
% 2.83/1.60 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.83/1.60 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 = ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.83/1.60 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 = ( t @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) )
% 2.83/1.60 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.83/1.60 => ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 = ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.83/1.60 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 = ( t @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_26_in__tree_Osimps_I1_J,axiom,
% 2.83/1.60 ! [A: $tType,V: A] :
% 2.83/1.60 ~ ( in_tree @ A @ V @ ( e @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_27_is__heap_Osimps_I5_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [V: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A] :
% 2.83/1.60 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.83/1.60 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.83/1.60 & ( is_heap @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) )
% 2.83/1.60 & ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 & ( is_heap @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_28_is__heap_Osimps_I6_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [V: A,Vd2: A,Ve2: tree @ A,Vf2: tree @ A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.83/1.60 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 & ( is_heap @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) )
% 2.83/1.60 & ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.83/1.60 & ( is_heap @ A @ ( t @ A @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_29_siftDown_Osimps_I3_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Va2: A,Vb2: tree @ A,Vc2: tree @ A,V: A] :
% 2.83/1.60 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 2.83/1.60 = ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) ) )
% 2.83/1.60 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 2.83/1.60 = ( t @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ ( e @ A ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_30_siftDown_Osimps_I4_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Va2: A,Vb2: tree @ A,Vc2: tree @ A,V: A] :
% 2.83/1.60 ( ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 = ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.83/1.60 & ( ~ ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 => ( ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 = ( t @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( e @ A ) @ ( heapIm748920189ftDown @ A @ ( t @ A @ V @ ( heapIm1271749598e_left @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1434396069_right @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_31_siftDown__in__tree,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [T2: tree @ A] :
% 2.83/1.60 ( ( T2
% 2.83/1.60 != ( e @ A ) )
% 2.83/1.60 => ( in_tree @ A @ ( val @ A @ ( heapIm748920189ftDown @ A @ T2 ) ) @ T2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_32_is__heap_Osimps_I3_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [V: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.83/1.60 ( ( is_heap @ A @ ( t @ A @ V @ ( e @ A ) @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.83/1.60 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 & ( is_heap @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_33_is__heap_Osimps_I4_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [V: A,Va2: A,Vb2: tree @ A,Vc2: tree @ A] :
% 2.83/1.60 ( ( is_heap @ A @ ( t @ A @ V @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) @ ( e @ A ) ) )
% 2.83/1.60 = ( ( ord_less_eq @ A @ ( val @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.83/1.60 & ( is_heap @ A @ ( t @ A @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_34_right_Osimps,axiom,
% 2.83/1.60 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 2.83/1.60 ( ( heapIm1434396069_right @ A @ ( t @ A @ V @ L @ R ) )
% 2.83/1.60 = R ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_35_order__refl,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( preorder @ A )
% 2.83/1.60 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_36_le__funD,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( ord @ B )
% 2.83/1.60 => ! [F: A > B,G: A > B,X: A] :
% 2.83/1.60 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.83/1.60 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_37_le__funE,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( ord @ B )
% 2.83/1.60 => ! [F: A > B,G: A > B,X: A] :
% 2.83/1.60 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.83/1.60 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_38_le__funI,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( ord @ B )
% 2.83/1.60 => ! [F: A > B,G: A > B] :
% 2.83/1.60 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 2.83/1.60 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_39_le__fun__def,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( ord @ B )
% 2.83/1.60 => ( ( ord_less_eq @ ( A > B ) )
% 2.83/1.60 = ( ^ [F2: A > B,G2: A > B] :
% 2.83/1.60 ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_40_order__subst1,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( ( order @ B )
% 2.83/1.60 & ( order @ A ) )
% 2.83/1.60 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 2.83/1.60 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.83/1.60 => ( ! [X4: B,Y2: B] :
% 2.83/1.60 ( ( ord_less_eq @ B @ X4 @ Y2 )
% 2.83/1.60 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.83/1.60 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_41_order__subst2,axiom,
% 2.83/1.60 ! [A: $tType,C: $tType] :
% 2.83/1.60 ( ( ( order @ C )
% 2.83/1.60 & ( order @ A ) )
% 2.83/1.60 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 2.83/1.60 => ( ! [X4: A,Y2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ X4 @ Y2 )
% 2.83/1.60 => ( ord_less_eq @ C @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.83/1.60 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_42_verit__la__disequality,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [A2: A,B2: A] :
% 2.83/1.60 ( ( A2 = B2 )
% 2.83/1.60 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_43_ord__eq__le__subst,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( ( ord @ B )
% 2.83/1.60 & ( ord @ A ) )
% 2.83/1.60 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 2.83/1.60 ( ( A2
% 2.83/1.60 = ( F @ B2 ) )
% 2.83/1.60 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.83/1.60 => ( ! [X4: B,Y2: B] :
% 2.83/1.60 ( ( ord_less_eq @ B @ X4 @ Y2 )
% 2.83/1.60 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.83/1.60 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_44_ord__le__eq__subst,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( ( ord @ B )
% 2.83/1.60 & ( ord @ A ) )
% 2.83/1.60 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( ( ( F @ B2 )
% 2.83/1.60 = C2 )
% 2.83/1.60 => ( ! [X4: A,Y2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ X4 @ Y2 )
% 2.83/1.60 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.83/1.60 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_45_mem__Collect__eq,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,P: A > $o] :
% 2.83/1.60 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.83/1.60 = ( P @ A2 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_46_Collect__mem__eq,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A] :
% 2.83/1.60 ( ( collect @ A
% 2.83/1.60 @ ^ [X5: A] : ( member @ A @ X5 @ A3 ) )
% 2.83/1.60 = A3 ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_47_Collect__cong,axiom,
% 2.83/1.60 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.60 ( ! [X4: A] :
% 2.83/1.60 ( ( P @ X4 )
% 2.83/1.60 = ( Q @ X4 ) )
% 2.83/1.60 => ( ( collect @ A @ P )
% 2.83/1.60 = ( collect @ A @ Q ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_48_ext,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.83/1.60 ( ! [X4: A] :
% 2.83/1.60 ( ( F @ X4 )
% 2.83/1.60 = ( G @ X4 ) )
% 2.83/1.60 => ( F = G ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_49_dual__order_Oantisym,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ! [B2: A,A2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.60 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( A2 = B2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_50_dual__order_Oeq__iff,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.83/1.60 = ( ^ [A4: A,B3: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ B3 @ A4 )
% 2.83/1.60 & ( ord_less_eq @ A @ A4 @ B3 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_51_dual__order_Otrans,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ! [B2: A,A2: A,C2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.60 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 2.83/1.60 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_52_linorder__wlog,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [P: A > A > $o,A2: A,B2: A] :
% 2.83/1.60 ( ! [A5: A,B4: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A5 @ B4 )
% 2.83/1.60 => ( P @ A5 @ B4 ) )
% 2.83/1.60 => ( ! [A5: A,B4: A] :
% 2.83/1.60 ( ( P @ B4 @ A5 )
% 2.83/1.60 => ( P @ A5 @ B4 ) )
% 2.83/1.60 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_53_dual__order_Orefl,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_54_order__trans,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( preorder @ A )
% 2.83/1.60 => ! [X: A,Y: A,Z2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ X @ Y )
% 2.83/1.60 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.83/1.60 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_55_order__class_Oorder_Oantisym,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ! [A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.60 => ( A2 = B2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_56_ord__le__eq__trans,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ord @ A )
% 2.83/1.60 => ! [A2: A,B2: A,C2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( ( B2 = C2 )
% 2.83/1.60 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_57_ord__eq__le__trans,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ord @ A )
% 2.83/1.60 => ! [A2: A,B2: A,C2: A] :
% 2.83/1.60 ( ( A2 = B2 )
% 2.83/1.60 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.83/1.60 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_58_order__class_Oorder_Oeq__iff,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.83/1.60 = ( ^ [A4: A,B3: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.83/1.60 & ( ord_less_eq @ A @ B3 @ A4 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_59_antisym__conv,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ! [Y: A,X: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ Y @ X )
% 2.83/1.60 => ( ( ord_less_eq @ A @ X @ Y )
% 2.83/1.60 = ( X = Y ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_60_le__cases3,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [X: A,Y: A,Z2: A] :
% 2.83/1.60 ( ( ( ord_less_eq @ A @ X @ Y )
% 2.83/1.60 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 2.83/1.60 => ( ( ( ord_less_eq @ A @ Y @ X )
% 2.83/1.60 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 2.83/1.60 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 2.83/1.60 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 2.83/1.60 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 2.83/1.60 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 2.83/1.60 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.83/1.60 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 2.83/1.60 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 2.83/1.60 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_61_order_Otrans,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ! [A2: A,B2: A,C2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.83/1.60 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_62_le__cases,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [X: A,Y: A] :
% 2.83/1.60 ( ~ ( ord_less_eq @ A @ X @ Y )
% 2.83/1.60 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_63_eq__refl,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( preorder @ A )
% 2.83/1.60 => ! [X: A,Y: A] :
% 2.83/1.60 ( ( X = Y )
% 2.83/1.60 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_64_linear,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [X: A,Y: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ X @ Y )
% 2.83/1.60 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_65_antisym,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ! [X: A,Y: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ X @ Y )
% 2.83/1.60 => ( ( ord_less_eq @ A @ Y @ X )
% 2.83/1.60 => ( X = Y ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_66_eq__iff,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.83/1.60 = ( ^ [X5: A,Y4: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 2.83/1.60 & ( ord_less_eq @ A @ Y4 @ X5 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_67_Greatest__equality,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ! [P: A > $o,X: A] :
% 2.83/1.60 ( ( P @ X )
% 2.83/1.60 => ( ! [Y2: A] :
% 2.83/1.60 ( ( P @ Y2 )
% 2.83/1.60 => ( ord_less_eq @ A @ Y2 @ X ) )
% 2.83/1.60 => ( ( order_Greatest @ A @ P )
% 2.83/1.60 = X ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_68_GreatestI2__order,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( order @ A )
% 2.83/1.60 => ! [P: A > $o,X: A,Q: A > $o] :
% 2.83/1.60 ( ( P @ X )
% 2.83/1.60 => ( ! [Y2: A] :
% 2.83/1.60 ( ( P @ Y2 )
% 2.83/1.60 => ( ord_less_eq @ A @ Y2 @ X ) )
% 2.83/1.60 => ( ! [X4: A] :
% 2.83/1.60 ( ( P @ X4 )
% 2.83/1.60 => ( ! [Y5: A] :
% 2.83/1.60 ( ( P @ Y5 )
% 2.83/1.60 => ( ord_less_eq @ A @ Y5 @ X4 ) )
% 2.83/1.60 => ( Q @ X4 ) ) )
% 2.83/1.60 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_69_le__rel__bool__arg__iff,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ord @ A )
% 2.83/1.60 => ( ( ord_less_eq @ ( $o > A ) )
% 2.83/1.60 = ( ^ [X6: $o > A,Y6: $o > A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 2.83/1.60 & ( ord_less_eq @ A @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_70_Tree_Osimps_I4_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,F1: B,F22: A > ( tree @ A ) > ( tree @ A ) > B] :
% 2.83/1.60 ( ( case_Tree @ B @ A @ F1 @ F22 @ ( e @ A ) )
% 2.83/1.60 = F1 ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_71_Tree_Osimps_I5_J,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,F1: B,F22: A > ( tree @ A ) > ( tree @ A ) > B,X21: A,X22: tree @ A,X23: tree @ A] :
% 2.83/1.60 ( ( case_Tree @ B @ A @ F1 @ F22 @ ( t @ A @ X21 @ X22 @ X23 ) )
% 2.83/1.60 = ( F22 @ X21 @ X22 @ X23 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_72_Tree_Osimps_I6_J,axiom,
% 2.83/1.60 ! [A: $tType,C: $tType,F1: C,F22: A > ( tree @ A ) > ( tree @ A ) > C > C > C] :
% 2.83/1.60 ( ( rec_Tree @ C @ A @ F1 @ F22 @ ( e @ A ) )
% 2.83/1.60 = F1 ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_73_Heap_Ois__heap__of__list,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: 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 ),I: list @ A] :
% 2.83/1.60 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.83/1.60 => ( is_heap @ A @ ( As_tree @ ( Of_list @ I ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_74_Tree_Osimps_I7_J,axiom,
% 2.83/1.60 ! [C: $tType,A: $tType,F1: C,F22: A > ( tree @ A ) > ( tree @ A ) > C > C > C,X21: A,X22: tree @ A,X23: tree @ A] :
% 2.83/1.60 ( ( rec_Tree @ C @ A @ F1 @ F22 @ ( t @ A @ X21 @ X22 @ X23 ) )
% 2.83/1.60 = ( F22 @ X21 @ X22 @ X23 @ ( rec_Tree @ C @ A @ F1 @ F22 @ X22 ) @ ( rec_Tree @ C @ A @ F1 @ F22 @ X23 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_75_Heap_Oas__tree__empty,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: 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 ),T2: B] :
% 2.83/1.60 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.83/1.60 => ( ( ( As_tree @ T2 )
% 2.83/1.60 = ( e @ A ) )
% 2.83/1.60 = ( Is_empty @ T2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_76_Heap_Oaxioms_I2_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: 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 )] :
% 2.83/1.60 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.83/1.60 => ( heap_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_77_Heap_Omultiset,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: 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 ),L: B] :
% 2.83/1.60 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.83/1.60 => ( ( Multiset @ L )
% 2.83/1.60 = ( multiset2 @ A @ ( As_tree @ L ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_78_Heap_Oremove__max__val,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: 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 ),T2: B,M: A,T4: B] :
% 2.83/1.60 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.83/1.60 => ( ~ ( Is_empty @ T2 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M @ T4 )
% 2.83/1.60 = ( Remove_max @ T2 ) )
% 2.83/1.60 => ( M
% 2.83/1.60 = ( val @ A @ ( As_tree @ T2 ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_79_Heap_Oremove__max__is__heap,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: 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 ),L: B,M: A,L3: B] :
% 2.83/1.60 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.83/1.60 => ( ~ ( Is_empty @ L )
% 2.83/1.60 => ( ( is_heap @ A @ ( As_tree @ L ) )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 2.83/1.60 = ( Remove_max @ L ) )
% 2.83/1.60 => ( is_heap @ A @ ( As_tree @ L3 ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_80_Heap_Oaxioms_I1_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: 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 )] :
% 2.83/1.60 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.83/1.60 => ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_81_Tree_Orel__induct,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,R3: A > B > $o,X: tree @ A,Y: tree @ B,Q: ( tree @ A ) > ( tree @ B ) > $o] :
% 2.83/1.60 ( ( rel_Tree @ A @ B @ R3 @ X @ Y )
% 2.83/1.60 => ( ( Q @ ( e @ A ) @ ( e @ B ) )
% 2.83/1.60 => ( ! [A21: A,A22: tree @ A,A23: tree @ A,B21: B,B22: tree @ B,B23: tree @ B] :
% 2.83/1.60 ( ( R3 @ A21 @ B21 )
% 2.83/1.60 => ( ( Q @ A22 @ B22 )
% 2.83/1.60 => ( ( Q @ A23 @ B23 )
% 2.83/1.60 => ( Q @ ( t @ A @ A21 @ A22 @ A23 ) @ ( t @ B @ B21 @ B22 @ B23 ) ) ) ) )
% 2.83/1.60 => ( Q @ X @ Y ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_82_Tree_Orel__mono,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,R3: A > B > $o,Ra: A > B > $o] :
% 2.83/1.60 ( ( ord_less_eq @ ( A > B > $o ) @ R3 @ Ra )
% 2.83/1.60 => ( ord_less_eq @ ( ( tree @ A ) > ( tree @ B ) > $o ) @ ( rel_Tree @ A @ B @ R3 ) @ ( rel_Tree @ A @ B @ Ra ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_83_Tree_Orel__eq,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( rel_Tree @ A @ A
% 2.83/1.60 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.83/1.60 = ( ^ [Y3: tree @ A,Z: tree @ A] : ( Y3 = Z ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_84_Tree_Orel__refl,axiom,
% 2.83/1.60 ! [B: $tType,Ra: B > B > $o,X: tree @ B] :
% 2.83/1.60 ( ! [X4: B] : ( Ra @ X4 @ X4 )
% 2.83/1.60 => ( rel_Tree @ B @ B @ Ra @ X @ X ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_85_Tree_Orel__inject_I2_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,R3: A > B > $o,X21: A,X22: tree @ A,X23: tree @ A,Y21: B,Y22: tree @ B,Y23: tree @ B] :
% 2.83/1.60 ( ( rel_Tree @ A @ B @ R3 @ ( t @ A @ X21 @ X22 @ X23 ) @ ( t @ B @ Y21 @ Y22 @ Y23 ) )
% 2.83/1.60 = ( ( R3 @ X21 @ Y21 )
% 2.83/1.60 & ( rel_Tree @ A @ B @ R3 @ X22 @ Y22 )
% 2.83/1.60 & ( rel_Tree @ A @ B @ R3 @ X23 @ Y23 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_86_Tree_Orel__intros_I2_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,R3: A > B > $o,X21: A,Y21: B,X22: tree @ A,Y22: tree @ B,X23: tree @ A,Y23: tree @ B] :
% 2.83/1.60 ( ( R3 @ X21 @ Y21 )
% 2.83/1.60 => ( ( rel_Tree @ A @ B @ R3 @ X22 @ Y22 )
% 2.83/1.60 => ( ( rel_Tree @ A @ B @ R3 @ X23 @ Y23 )
% 2.83/1.60 => ( rel_Tree @ A @ B @ R3 @ ( t @ A @ X21 @ X22 @ X23 ) @ ( t @ B @ Y21 @ Y22 @ Y23 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_87_Tree_Octr__transfer_I1_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,R3: A > B > $o] : ( rel_Tree @ A @ B @ R3 @ ( e @ A ) @ ( e @ B ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_88_Heap__def,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( ( heap @ B @ A )
% 2.83/1.60 = ( ^ [Empty2: 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 )] :
% 2.83/1.60 ( ( collection @ B @ A @ Empty2 @ Is_empty2 @ Of_list2 @ Multiset2 )
% 2.83/1.60 & ( heap_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_89_Heap_Ointro,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: 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 )] :
% 2.83/1.60 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 2.83/1.60 => ( ( heap_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.83/1.60 => ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_90_Tree_Orel__distinct_I2_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,R3: A > B > $o,Y21: A,Y22: tree @ A,Y23: tree @ A] :
% 2.83/1.60 ~ ( rel_Tree @ A @ B @ R3 @ ( t @ A @ Y21 @ Y22 @ Y23 ) @ ( e @ B ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_91_Tree_Orel__distinct_I1_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,R3: A > B > $o,Y21: B,Y22: tree @ B,Y23: tree @ B] :
% 2.83/1.60 ~ ( rel_Tree @ A @ B @ R3 @ ( e @ A ) @ ( t @ B @ Y21 @ Y22 @ Y23 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_92_Tree_Orel__cases,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,R3: A > B > $o,A2: tree @ A,B2: tree @ B] :
% 2.83/1.60 ( ( rel_Tree @ A @ B @ R3 @ A2 @ B2 )
% 2.83/1.60 => ( ( ( A2
% 2.83/1.60 = ( e @ A ) )
% 2.83/1.60 => ( B2
% 2.83/1.60 != ( e @ B ) ) )
% 2.83/1.60 => ~ ! [X1: A,X2: tree @ A,X3: tree @ A] :
% 2.83/1.60 ( ( A2
% 2.83/1.60 = ( t @ A @ X1 @ X2 @ X3 ) )
% 2.83/1.60 => ! [Y1: B,Y24: tree @ B,Y32: tree @ B] :
% 2.83/1.60 ( ( B2
% 2.83/1.60 = ( t @ B @ Y1 @ Y24 @ Y32 ) )
% 2.83/1.60 => ( ( R3 @ X1 @ Y1 )
% 2.83/1.60 => ( ( rel_Tree @ A @ B @ R3 @ X2 @ Y24 )
% 2.83/1.60 => ~ ( rel_Tree @ A @ B @ R3 @ X3 @ Y32 ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_93_old_Oprod_Oinject,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B5: B] :
% 2.83/1.60 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.83/1.60 = ( product_Pair @ A @ B @ A6 @ B5 ) )
% 2.83/1.60 = ( ( A2 = A6 )
% 2.83/1.60 & ( B2 = B5 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_94_prod_Oinject,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,X12: A,X24: B,Y12: A,Y25: B] :
% 2.83/1.60 ( ( ( product_Pair @ A @ B @ X12 @ X24 )
% 2.83/1.60 = ( product_Pair @ A @ B @ Y12 @ Y25 ) )
% 2.83/1.60 = ( ( X12 = Y12 )
% 2.83/1.60 & ( X24 = Y25 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_95_Heap__axioms__def,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( ( heap_axioms @ B @ A )
% 2.83/1.60 = ( ^ [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 )] :
% 2.83/1.60 ( ! [L4: B] :
% 2.83/1.60 ( ( Multiset2 @ L4 )
% 2.83/1.60 = ( multiset2 @ A @ ( As_tree2 @ L4 ) ) )
% 2.83/1.60 & ! [I2: list @ A] : ( is_heap @ A @ ( As_tree2 @ ( Of_list2 @ I2 ) ) )
% 2.83/1.60 & ! [T3: B] :
% 2.83/1.60 ( ( ( As_tree2 @ T3 )
% 2.83/1.60 = ( e @ A ) )
% 2.83/1.60 = ( Is_empty2 @ T3 ) )
% 2.83/1.60 & ! [L4: B,M2: A,L5: B] :
% 2.83/1.60 ( ~ ( Is_empty2 @ L4 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 2.83/1.60 = ( Remove_max2 @ L4 ) )
% 2.83/1.60 => ( ( add_mset @ A @ M2 @ ( Multiset2 @ L5 ) )
% 2.83/1.60 = ( Multiset2 @ L4 ) ) ) )
% 2.83/1.60 & ! [L4: B,M2: A,L5: B] :
% 2.83/1.60 ( ~ ( Is_empty2 @ L4 )
% 2.83/1.60 => ( ( is_heap @ A @ ( As_tree2 @ L4 ) )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 2.83/1.60 = ( Remove_max2 @ L4 ) )
% 2.83/1.60 => ( is_heap @ A @ ( As_tree2 @ L5 ) ) ) ) )
% 2.83/1.60 & ! [T3: B,M2: A,T5: B] :
% 2.83/1.60 ( ~ ( Is_empty2 @ T3 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M2 @ T5 )
% 2.83/1.60 = ( Remove_max2 @ T3 ) )
% 2.83/1.60 => ( M2
% 2.83/1.60 = ( val @ A @ ( As_tree2 @ T3 ) ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_96_Heap__axioms_Ointro,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Multiset: B > ( multiset @ A ),As_tree: B > ( tree @ A ),Of_list: ( list @ A ) > B,Is_empty: B > $o,Remove_max: B > ( product_prod @ A @ B )] :
% 2.83/1.60 ( ! [L6: B] :
% 2.83/1.60 ( ( Multiset @ L6 )
% 2.83/1.60 = ( multiset2 @ A @ ( As_tree @ L6 ) ) )
% 2.83/1.60 => ( ! [I3: list @ A] : ( is_heap @ A @ ( As_tree @ ( Of_list @ I3 ) ) )
% 2.83/1.60 => ( ! [T6: B] :
% 2.83/1.60 ( ( ( As_tree @ T6 )
% 2.83/1.60 = ( e @ A ) )
% 2.83/1.60 = ( Is_empty @ T6 ) )
% 2.83/1.60 => ( ! [L6: B,M3: A,L2: B] :
% 2.83/1.60 ( ~ ( Is_empty @ L6 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 2.83/1.60 = ( Remove_max @ L6 ) )
% 2.83/1.60 => ( ( add_mset @ A @ M3 @ ( Multiset @ L2 ) )
% 2.83/1.60 = ( Multiset @ L6 ) ) ) )
% 2.83/1.60 => ( ! [L6: B,M3: A,L2: B] :
% 2.83/1.60 ( ~ ( Is_empty @ L6 )
% 2.83/1.60 => ( ( is_heap @ A @ ( As_tree @ L6 ) )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 2.83/1.60 = ( Remove_max @ L6 ) )
% 2.83/1.60 => ( is_heap @ A @ ( As_tree @ L2 ) ) ) ) )
% 2.83/1.60 => ( ! [T6: B,M3: A,T7: B] :
% 2.83/1.60 ( ~ ( Is_empty @ T6 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M3 @ T7 )
% 2.83/1.60 = ( Remove_max @ T6 ) )
% 2.83/1.60 => ( M3
% 2.83/1.60 = ( val @ A @ ( As_tree @ T6 ) ) ) ) )
% 2.83/1.60 => ( heap_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_97_heap__top__geq,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [A2: A,T2: tree @ A] :
% 2.83/1.60 ( ( member @ A @ A2 @ ( set_mset @ A @ ( multiset2 @ A @ T2 ) ) )
% 2.83/1.60 => ( ( is_heap @ A @ T2 )
% 2.83/1.60 => ( ord_less_eq @ A @ A2 @ ( val @ A @ T2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_98_Collection_Ois__empty__empty,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A )] :
% 2.83/1.60 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 2.83/1.60 => ( Is_empty @ Empty ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_99_predicate2I,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 2.83/1.60 ( ! [X4: A,Y2: B] :
% 2.83/1.60 ( ( P @ X4 @ Y2 )
% 2.83/1.60 => ( Q @ X4 @ Y2 ) )
% 2.83/1.60 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_100_rev__predicate2D,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y: B,Q: A > B > $o] :
% 2.83/1.60 ( ( P @ X @ Y )
% 2.83/1.60 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.83/1.60 => ( Q @ X @ Y ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_101_predicate2D,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y: B] :
% 2.83/1.60 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.83/1.60 => ( ( P @ X @ Y )
% 2.83/1.60 => ( Q @ X @ Y ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_102_Heap_Oremove__max__multiset_H,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: 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 ),L: B,M: A,L3: B] :
% 2.83/1.60 ( ( heap @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.83/1.60 => ( ~ ( Is_empty @ L )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 2.83/1.60 = ( Remove_max @ L ) )
% 2.83/1.60 => ( ( add_mset @ A @ M @ ( Multiset @ L3 ) )
% 2.83/1.60 = ( Multiset @ L ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_103_surj__pair,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 2.83/1.60 ? [X4: A,Y2: B] :
% 2.83/1.60 ( P2
% 2.83/1.60 = ( product_Pair @ A @ B @ X4 @ Y2 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_104_prod__cases,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 2.83/1.60 ( ! [A5: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B4 ) )
% 2.83/1.60 => ( P @ P2 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_105_Pair__inject,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B5: B] :
% 2.83/1.60 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.83/1.60 = ( product_Pair @ A @ B @ A6 @ B5 ) )
% 2.83/1.60 => ~ ( ( A2 = A6 )
% 2.83/1.60 => ( B2 != B5 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_106_prod__cases3,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.83/1.60 ~ ! [A5: A,B4: B,C3: C] :
% 2.83/1.60 ( Y
% 2.83/1.60 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_107_prod__cases4,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.83/1.60 ~ ! [A5: A,B4: B,C3: C,D2: D] :
% 2.83/1.60 ( Y
% 2.83/1.60 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_108_prod__cases5,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.83/1.60 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E] :
% 2.83/1.60 ( Y
% 2.83/1.60 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_109_prod__cases6,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 2.83/1.60 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E,F4: F3] :
% 2.83/1.60 ( Y
% 2.83/1.60 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_110_prod__cases7,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 2.83/1.60 ~ ! [A5: A,B4: B,C3: C,D2: D,E2: E,F4: F3,G4: G3] :
% 2.83/1.60 ( Y
% 2.83/1.60 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_111_prod__induct3,axiom,
% 2.83/1.60 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.83/1.60 ( ! [A5: A,B4: B,C3: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 2.83/1.60 => ( P @ X ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_112_prod__induct4,axiom,
% 2.83/1.60 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.83/1.60 ( ! [A5: A,B4: B,C3: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 2.83/1.60 => ( P @ X ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_113_prod__induct5,axiom,
% 2.83/1.60 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( 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 ) ) )] :
% 2.83/1.60 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 2.83/1.60 => ( P @ X ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_114_prod__induct6,axiom,
% 2.83/1.60 ! [F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 2.83/1.60 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) )
% 2.83/1.60 => ( P @ X ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_115_prod__induct7,axiom,
% 2.83/1.60 ! [G3: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 2.83/1.60 ( ! [A5: A,B4: B,C3: C,D2: D,E2: E,F4: F3,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) )
% 2.83/1.60 => ( P @ X ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_116_old_Oprod_Oexhaust,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.83/1.60 ~ ! [A5: A,B4: B] :
% 2.83/1.60 ( Y
% 2.83/1.60 != ( product_Pair @ A @ B @ A5 @ B4 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_117_old_Oprod_Oinducts,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.83/1.60 ( ! [A5: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B4 ) )
% 2.83/1.60 => ( P @ Prod ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_118_Collection_Ois__empty__inj,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),E3: B] :
% 2.83/1.60 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 2.83/1.60 => ( ( Is_empty @ E3 )
% 2.83/1.60 => ( E3 = Empty ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_119_old_Oprod_Orec,axiom,
% 2.83/1.60 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.83/1.60 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.83/1.60 = ( F1 @ A2 @ B2 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_120_add__mset__add__mset__same__iff,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,A3: multiset @ A,B6: multiset @ A] :
% 2.83/1.60 ( ( ( add_mset @ A @ A2 @ A3 )
% 2.83/1.60 = ( add_mset @ A @ A2 @ B6 ) )
% 2.83/1.60 = ( A3 = B6 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_121_multi__self__add__other__not__self,axiom,
% 2.83/1.60 ! [A: $tType,M4: multiset @ A,X: A] :
% 2.83/1.60 ( M4
% 2.83/1.60 != ( add_mset @ A @ X @ M4 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_122_mset__add,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,A3: multiset @ A] :
% 2.83/1.60 ( ( member @ A @ A2 @ ( set_mset @ A @ A3 ) )
% 2.83/1.60 => ~ ! [B7: multiset @ A] :
% 2.83/1.60 ( A3
% 2.83/1.60 != ( add_mset @ A @ A2 @ B7 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_123_multi__member__split,axiom,
% 2.83/1.60 ! [A: $tType,X: A,M4: multiset @ A] :
% 2.83/1.60 ( ( member @ A @ X @ ( set_mset @ A @ M4 ) )
% 2.83/1.60 => ? [A7: multiset @ A] :
% 2.83/1.60 ( M4
% 2.83/1.60 = ( add_mset @ A @ X @ A7 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_124_add__mset__commute,axiom,
% 2.83/1.60 ! [A: $tType,X: A,Y: A,M4: multiset @ A] :
% 2.83/1.60 ( ( add_mset @ A @ X @ ( add_mset @ A @ Y @ M4 ) )
% 2.83/1.60 = ( add_mset @ A @ Y @ ( add_mset @ A @ X @ M4 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_125_add__eq__conv__ex,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,M4: multiset @ A,B2: A,N: multiset @ A] :
% 2.83/1.60 ( ( ( add_mset @ A @ A2 @ M4 )
% 2.83/1.60 = ( add_mset @ A @ B2 @ N ) )
% 2.83/1.60 = ( ( ( M4 = N )
% 2.83/1.60 & ( A2 = B2 ) )
% 2.83/1.60 | ? [K: multiset @ A] :
% 2.83/1.60 ( ( M4
% 2.83/1.60 = ( add_mset @ A @ B2 @ K ) )
% 2.83/1.60 & ( N
% 2.83/1.60 = ( add_mset @ A @ A2 @ K ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_126_union__single__eq__member,axiom,
% 2.83/1.60 ! [A: $tType,X: A,M4: multiset @ A,N: multiset @ A] :
% 2.83/1.60 ( ( ( add_mset @ A @ X @ M4 )
% 2.83/1.60 = N )
% 2.83/1.60 => ( member @ A @ X @ ( set_mset @ A @ N ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_127_insert__noteq__member,axiom,
% 2.83/1.60 ! [A: $tType,B2: A,B6: multiset @ A,C2: A,C4: multiset @ A] :
% 2.83/1.60 ( ( ( add_mset @ A @ B2 @ B6 )
% 2.83/1.60 = ( add_mset @ A @ C2 @ C4 ) )
% 2.83/1.60 => ( ( B2 != C2 )
% 2.83/1.60 => ( member @ A @ C2 @ ( set_mset @ A @ B6 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_128_heap__top__max,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [T2: tree @ A] :
% 2.83/1.60 ( ( T2
% 2.83/1.60 != ( e @ A ) )
% 2.83/1.60 => ( ( is_heap @ A @ T2 )
% 2.83/1.60 => ( ( val @ A @ T2 )
% 2.83/1.60 = ( lattic929149872er_Max @ A @ ( set_mset @ A @ ( multiset2 @ A @ T2 ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_129_internal__case__prod__conv,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 2.83/1.60 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.83/1.60 = ( C2 @ A2 @ B2 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_130_Collection_Oset__def,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),L: B] :
% 2.83/1.60 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 2.83/1.60 => ( ( set2 @ B @ A @ Multiset @ L )
% 2.83/1.60 = ( set_mset @ A @ ( Multiset @ L ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_131_relChain__def,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( ord @ B )
% 2.83/1.60 => ( ( bNF_Ca1785829860lChain @ A @ B )
% 2.83/1.60 = ( ^ [R4: set @ ( product_prod @ A @ A ),As: A > B] :
% 2.83/1.60 ! [I2: A,J: A] :
% 2.83/1.60 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ I2 @ J ) @ R4 )
% 2.83/1.60 => ( ord_less_eq @ B @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_132_Collection_Oset_Ocong,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( set2 @ B @ A )
% 2.83/1.60 = ( set2 @ B @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_133_RemoveMax__axioms_Ointro,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Inv: B > $o,Of_list: ( list @ A ) > B,Is_empty: B > $o,Remove_max: B > ( product_prod @ A @ B ),Multiset: B > ( multiset @ A )] :
% 2.83/1.60 ( ! [X4: list @ A] : ( Inv @ ( Of_list @ X4 ) )
% 2.83/1.60 => ( ! [L6: B,M3: A,L2: B] :
% 2.83/1.60 ( ~ ( Is_empty @ L6 )
% 2.83/1.60 => ( ( Inv @ L6 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 2.83/1.60 = ( Remove_max @ L6 ) )
% 2.83/1.60 => ( M3
% 2.83/1.60 = ( lattic929149872er_Max @ A @ ( set2 @ B @ A @ Multiset @ L6 ) ) ) ) ) )
% 2.83/1.60 => ( ! [L6: B,M3: A,L2: B] :
% 2.83/1.60 ( ~ ( Is_empty @ L6 )
% 2.83/1.60 => ( ( Inv @ L6 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 2.83/1.60 = ( Remove_max @ L6 ) )
% 2.83/1.60 => ( ( add_mset @ A @ M3 @ ( Multiset @ L2 ) )
% 2.83/1.60 = ( Multiset @ L6 ) ) ) ) )
% 2.83/1.60 => ( ! [L6: B,M3: A,L2: B] :
% 2.83/1.60 ( ~ ( Is_empty @ L6 )
% 2.83/1.60 => ( ( Inv @ L6 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M3 @ L2 )
% 2.83/1.60 = ( Remove_max @ L6 ) )
% 2.83/1.60 => ( Inv @ L2 ) ) ) )
% 2.83/1.60 => ( removeMax_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_134_RemoveMax__axioms__def,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( ( removeMax_axioms @ B @ A )
% 2.83/1.60 = ( ^ [Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),Remove_max2: B > ( product_prod @ A @ B ),Inv2: B > $o] :
% 2.83/1.60 ( ! [X5: list @ A] : ( Inv2 @ ( Of_list2 @ X5 ) )
% 2.83/1.60 & ! [L4: B,M2: A,L5: B] :
% 2.83/1.60 ( ~ ( Is_empty2 @ L4 )
% 2.83/1.60 => ( ( Inv2 @ L4 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 2.83/1.60 = ( Remove_max2 @ L4 ) )
% 2.83/1.60 => ( M2
% 2.83/1.60 = ( lattic929149872er_Max @ A @ ( set2 @ B @ A @ Multiset2 @ L4 ) ) ) ) ) )
% 2.83/1.60 & ! [L4: B,M2: A,L5: B] :
% 2.83/1.60 ( ~ ( Is_empty2 @ L4 )
% 2.83/1.60 => ( ( Inv2 @ L4 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 2.83/1.60 = ( Remove_max2 @ L4 ) )
% 2.83/1.60 => ( ( add_mset @ A @ M2 @ ( Multiset2 @ L5 ) )
% 2.83/1.60 = ( Multiset2 @ L4 ) ) ) ) )
% 2.83/1.60 & ! [L4: B,M2: A,L5: B] :
% 2.83/1.60 ( ~ ( Is_empty2 @ L4 )
% 2.83/1.60 => ( ( Inv2 @ L4 )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M2 @ L5 )
% 2.83/1.60 = ( Remove_max2 @ L4 ) )
% 2.83/1.60 => ( Inv2 @ L5 ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_135_RemoveMax_Oremove__max__max,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o,L: B,M: A,L3: B] :
% 2.83/1.60 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 2.83/1.60 => ( ~ ( Is_empty @ L )
% 2.83/1.60 => ( ( Inv @ L )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 2.83/1.60 = ( Remove_max @ L ) )
% 2.83/1.60 => ( M
% 2.83/1.60 = ( lattic929149872er_Max @ A @ ( set2 @ B @ A @ Multiset @ L ) ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_136_predicate2D__conj,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,R3: $o,X: A,Y: B] :
% 2.83/1.60 ( ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.83/1.60 & R3 )
% 2.83/1.60 => ( R3
% 2.83/1.60 & ( ( P @ X @ Y )
% 2.83/1.60 => ( Q @ X @ Y ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_137_RemoveMax_Oremove__max__inv,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o,L: B,M: A,L3: B] :
% 2.83/1.60 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 2.83/1.60 => ( ~ ( Is_empty @ L )
% 2.83/1.60 => ( ( Inv @ L )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 2.83/1.60 = ( Remove_max @ L ) )
% 2.83/1.60 => ( Inv @ L3 ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_138_RemoveMax_Oaxioms_I2_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o] :
% 2.83/1.60 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 2.83/1.60 => ( removeMax_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_139_RemoveMax_Oof__list__inv,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o,X: list @ A] :
% 2.83/1.60 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 2.83/1.60 => ( Inv @ ( Of_list @ X ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_140_RemoveMax_Ointro,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o] :
% 2.83/1.60 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 2.83/1.60 => ( ( removeMax_axioms @ B @ A @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 2.83/1.60 => ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_141_RemoveMax__def,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( ( removeMax @ B @ A )
% 2.83/1.60 = ( ^ [Empty2: B,Is_empty2: B > $o,Of_list2: ( list @ A ) > B,Multiset2: B > ( multiset @ A ),Remove_max2: B > ( product_prod @ A @ B ),Inv2: B > $o] :
% 2.83/1.60 ( ( collection @ B @ A @ Empty2 @ Is_empty2 @ Of_list2 @ Multiset2 )
% 2.83/1.60 & ( removeMax_axioms @ B @ A @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_142_RemoveMax_Oaxioms_I1_J,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o] :
% 2.83/1.60 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 2.83/1.60 => ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_143_RemoveMax_Oremove__max__multiset,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),Remove_max: B > ( product_prod @ A @ B ),Inv: B > $o,L: B,M: A,L3: B] :
% 2.83/1.60 ( ( removeMax @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset @ Remove_max @ Inv )
% 2.83/1.60 => ( ~ ( Is_empty @ L )
% 2.83/1.60 => ( ( Inv @ L )
% 2.83/1.60 => ( ( ( product_Pair @ A @ B @ M @ L3 )
% 2.83/1.60 = ( Remove_max @ L ) )
% 2.83/1.60 => ( ( add_mset @ A @ M @ ( Multiset @ L3 ) )
% 2.83/1.60 = ( Multiset @ L ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_144_ge__eq__refl,axiom,
% 2.83/1.60 ! [A: $tType,R3: A > A > $o,X: A] :
% 2.83/1.60 ( ( ord_less_eq @ ( A > A > $o )
% 2.83/1.60 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 2.83/1.60 @ R3 )
% 2.83/1.60 => ( R3 @ X @ X ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_145_refl__ge__eq,axiom,
% 2.83/1.60 ! [A: $tType,R3: A > A > $o] :
% 2.83/1.60 ( ! [X4: A] : ( R3 @ X4 @ X4 )
% 2.83/1.60 => ( ord_less_eq @ ( A > A > $o )
% 2.83/1.60 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 2.83/1.60 @ R3 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_146_multiset__induct__max,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [P: ( multiset @ A ) > $o,M4: multiset @ A] :
% 2.83/1.60 ( ( P @ ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 => ( ! [X4: A,M5: multiset @ A] :
% 2.83/1.60 ( ( P @ M5 )
% 2.83/1.60 => ( ! [Xa: A] :
% 2.83/1.60 ( ( member @ A @ Xa @ ( set_mset @ A @ M5 ) )
% 2.83/1.60 => ( ord_less_eq @ A @ Xa @ X4 ) )
% 2.83/1.60 => ( P @ ( add_mset @ A @ X4 @ M5 ) ) ) )
% 2.83/1.60 => ( P @ M4 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_147_multiset__induct__min,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ! [P: ( multiset @ A ) > $o,M4: multiset @ A] :
% 2.83/1.60 ( ( P @ ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 => ( ! [X4: A,M5: multiset @ A] :
% 2.83/1.60 ( ( P @ M5 )
% 2.83/1.60 => ( ! [Xa: A] :
% 2.83/1.60 ( ( member @ A @ Xa @ ( set_mset @ A @ M5 ) )
% 2.83/1.60 => ( ord_less_eq @ A @ X4 @ Xa ) )
% 2.83/1.60 => ( P @ ( add_mset @ A @ X4 @ M5 ) ) ) )
% 2.83/1.60 => ( P @ M4 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_148_add__mset__eq__singleton__iff,axiom,
% 2.83/1.60 ! [A: $tType,X: A,M4: multiset @ A,Y: A] :
% 2.83/1.60 ( ( ( add_mset @ A @ X @ M4 )
% 2.83/1.60 = ( add_mset @ A @ Y @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.83/1.60 = ( ( M4
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 & ( X = Y ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_149_single__eq__add__mset,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,B2: A,M4: multiset @ A] :
% 2.83/1.60 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 = ( add_mset @ A @ B2 @ M4 ) )
% 2.83/1.60 = ( ( B2 = A2 )
% 2.83/1.60 & ( M4
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_150_add__mset__eq__single,axiom,
% 2.83/1.60 ! [A: $tType,B2: A,M4: multiset @ A,A2: A] :
% 2.83/1.60 ( ( ( add_mset @ A @ B2 @ M4 )
% 2.83/1.60 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.83/1.60 = ( ( B2 = A2 )
% 2.83/1.60 & ( M4
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_151_single__eq__single,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,B2: A] :
% 2.83/1.60 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 = ( add_mset @ A @ B2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.83/1.60 = ( A2 = B2 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_152_multiset__cases,axiom,
% 2.83/1.60 ! [A: $tType,M4: multiset @ A] :
% 2.83/1.60 ( ( M4
% 2.83/1.60 != ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 => ~ ! [X4: A,N2: multiset @ A] :
% 2.83/1.60 ( M4
% 2.83/1.60 != ( add_mset @ A @ X4 @ N2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_153_multiset__induct,axiom,
% 2.83/1.60 ! [A: $tType,P: ( multiset @ A ) > $o,M4: multiset @ A] :
% 2.83/1.60 ( ( P @ ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 => ( ! [X4: A,M5: multiset @ A] :
% 2.83/1.60 ( ( P @ M5 )
% 2.83/1.60 => ( P @ ( add_mset @ A @ X4 @ M5 ) ) )
% 2.83/1.60 => ( P @ M4 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_154_multiset__induct2,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,P: ( multiset @ A ) > ( multiset @ B ) > $o,M4: multiset @ A,N: multiset @ B] :
% 2.83/1.60 ( ( P @ ( zero_zero @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ B ) ) )
% 2.83/1.60 => ( ! [A5: A,M5: multiset @ A,N2: multiset @ B] :
% 2.83/1.60 ( ( P @ M5 @ N2 )
% 2.83/1.60 => ( P @ ( add_mset @ A @ A5 @ M5 ) @ N2 ) )
% 2.83/1.60 => ( ! [A5: B,M5: multiset @ A,N2: multiset @ B] :
% 2.83/1.60 ( ( P @ M5 @ N2 )
% 2.83/1.60 => ( P @ M5 @ ( add_mset @ B @ A5 @ N2 ) ) )
% 2.83/1.60 => ( P @ M4 @ N ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_155_empty__not__add__mset,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,A3: multiset @ A] :
% 2.83/1.60 ( ( zero_zero @ ( multiset @ A ) )
% 2.83/1.60 != ( add_mset @ A @ A2 @ A3 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_156_multiset__nonemptyE,axiom,
% 2.83/1.60 ! [A: $tType,A3: multiset @ A] :
% 2.83/1.60 ( ( A3
% 2.83/1.60 != ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 => ~ ! [X4: A] :
% 2.83/1.60 ~ ( member @ A @ X4 @ ( set_mset @ A @ A3 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_157_multi__nonempty__split,axiom,
% 2.83/1.60 ! [A: $tType,M4: multiset @ A] :
% 2.83/1.60 ( ( M4
% 2.83/1.60 != ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 => ? [A7: multiset @ A,A5: A] :
% 2.83/1.60 ( M4
% 2.83/1.60 = ( add_mset @ A @ A5 @ A7 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_158_Collection_Ois__empty__as__list,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A ),E3: B] :
% 2.83/1.60 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 2.83/1.60 => ( ( Is_empty @ E3 )
% 2.83/1.60 => ( ( Multiset @ E3 )
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_159_Collection_Omultiset__empty,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,Empty: B,Is_empty: B > $o,Of_list: ( list @ A ) > B,Multiset: B > ( multiset @ A )] :
% 2.83/1.60 ( ( collection @ B @ A @ Empty @ Is_empty @ Of_list @ Multiset )
% 2.83/1.60 => ( ( Multiset @ Empty )
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_160_multi__member__last,axiom,
% 2.83/1.60 ! [A: $tType,X: A] : ( member @ A @ X @ ( set_mset @ A @ ( add_mset @ A @ X @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_161_multiset_Osimps_I1_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( multiset2 @ A @ ( e @ A ) )
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_162_le__zero__eq,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( canoni770627133id_add @ A )
% 2.83/1.60 => ! [N3: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ N3 @ ( zero_zero @ A ) )
% 2.83/1.60 = ( N3
% 2.83/1.60 = ( zero_zero @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_163_zero__le,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( canoni770627133id_add @ A )
% 2.83/1.60 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_164_le__numeral__extra_I3_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linord1659791738miring @ A )
% 2.83/1.60 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_165_multiset_Osimps_I2_J,axiom,
% 2.83/1.60 ! [A: $tType,V: A,L: tree @ A,R: tree @ A] :
% 2.83/1.60 ( ( multiset2 @ A @ ( t @ A @ V @ L @ R ) )
% 2.83/1.60 = ( plus_plus @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ ( multiset2 @ A @ L ) @ ( add_mset @ A @ V @ ( zero_zero @ ( multiset @ A ) ) ) ) @ ( multiset2 @ A @ R ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_166_divides__aux__eq,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( unique1598680935umeral @ A )
% 2.83/1.60 => ! [Q2: A,R: A] :
% 2.83/1.60 ( ( unique455577585es_aux @ A @ ( product_Pair @ A @ A @ Q2 @ R ) )
% 2.83/1.60 = ( R
% 2.83/1.60 = ( zero_zero @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_167_single__subset__iff,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,M4: multiset @ A] :
% 2.83/1.60 ( ( subseteq_mset @ A @ ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) @ M4 )
% 2.83/1.60 = ( member @ A @ A2 @ ( set_mset @ A @ M4 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_168_add__le__cancel__left,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere236663937imp_le @ A )
% 2.83/1.60 => ! [C2: A,A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 2.83/1.60 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_169_add__le__cancel__right,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere236663937imp_le @ A )
% 2.83/1.60 => ! [A2: A,C2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.83/1.60 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_170_union__mset__add__mset__left,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,A3: multiset @ A,B6: multiset @ A] :
% 2.83/1.60 ( ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ A2 @ A3 ) @ B6 )
% 2.83/1.60 = ( add_mset @ A @ A2 @ ( plus_plus @ ( multiset @ A ) @ A3 @ B6 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_171_union__mset__add__mset__right,axiom,
% 2.83/1.60 ! [A: $tType,A3: multiset @ A,A2: A,B6: multiset @ A] :
% 2.83/1.60 ( ( plus_plus @ ( multiset @ A ) @ A3 @ ( add_mset @ A @ A2 @ B6 ) )
% 2.83/1.60 = ( add_mset @ A @ A2 @ ( plus_plus @ ( multiset @ A ) @ A3 @ B6 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_172_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linord219039673up_add @ A )
% 2.83/1.60 => ! [A2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.83/1.60 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_173_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linord219039673up_add @ A )
% 2.83/1.60 => ! [A2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.83/1.60 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_174_le__add__same__cancel2,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere516151231imp_le @ A )
% 2.83/1.60 => ! [A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 2.83/1.60 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_175_le__add__same__cancel1,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere516151231imp_le @ A )
% 2.83/1.60 => ! [A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 2.83/1.60 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_176_add__le__same__cancel2,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere516151231imp_le @ A )
% 2.83/1.60 => ! [A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.83/1.60 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_177_add__le__same__cancel1,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere516151231imp_le @ A )
% 2.83/1.60 => ! [B2: A,A2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 2.83/1.60 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_178_add__mset__subseteq__single__iff,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,M4: multiset @ A,B2: A] :
% 2.83/1.60 ( ( subseteq_mset @ A @ ( add_mset @ A @ A2 @ M4 ) @ ( add_mset @ A @ B2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.83/1.60 = ( ( M4
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 & ( A2 = B2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_179_verit__sum__simplify,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( cancel1352612707id_add @ A )
% 2.83/1.60 => ! [A2: A] :
% 2.83/1.60 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.83/1.60 = A2 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_180_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere779506340up_add @ A )
% 2.83/1.60 => ! [I: A,J2: A,K2: A,L: A] :
% 2.83/1.60 ( ( ( ord_less_eq @ A @ I @ J2 )
% 2.83/1.60 & ( K2 = L ) )
% 2.83/1.60 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J2 @ L ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_181_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere779506340up_add @ A )
% 2.83/1.60 => ! [I: A,J2: A,K2: A,L: A] :
% 2.83/1.60 ( ( ( I = J2 )
% 2.83/1.60 & ( ord_less_eq @ A @ K2 @ L ) )
% 2.83/1.60 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J2 @ L ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_182_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere779506340up_add @ A )
% 2.83/1.60 => ! [I: A,J2: A,K2: A,L: A] :
% 2.83/1.60 ( ( ( ord_less_eq @ A @ I @ J2 )
% 2.83/1.60 & ( ord_less_eq @ A @ K2 @ L ) )
% 2.83/1.60 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J2 @ L ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_183_add__mono,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere779506340up_add @ A )
% 2.83/1.60 => ! [A2: A,B2: A,C2: A,D3: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( ( ord_less_eq @ A @ C2 @ D3 )
% 2.83/1.60 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_184_add__left__mono,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere779506340up_add @ A )
% 2.83/1.60 => ! [A2: A,B2: A,C2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_185_less__eqE,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( canoni770627133id_add @ A )
% 2.83/1.60 => ! [A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ~ ! [C3: A] :
% 2.83/1.60 ( B2
% 2.83/1.60 != ( plus_plus @ A @ A2 @ C3 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_186_add__right__mono,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere779506340up_add @ A )
% 2.83/1.60 => ! [A2: A,B2: A,C2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_187_le__iff__add,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( canoni770627133id_add @ A )
% 2.83/1.60 => ( ( ord_less_eq @ A )
% 2.83/1.60 = ( ^ [A4: A,B3: A] :
% 2.83/1.60 ? [C5: A] :
% 2.83/1.60 ( B3
% 2.83/1.60 = ( plus_plus @ A @ A4 @ C5 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_188_add__le__imp__le__left,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere236663937imp_le @ A )
% 2.83/1.60 => ! [C2: A,A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 2.83/1.60 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_189_add__le__imp__le__right,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere236663937imp_le @ A )
% 2.83/1.60 => ! [A2: A,C2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.83/1.60 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_190_union__iff,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,A3: multiset @ A,B6: multiset @ A] :
% 2.83/1.60 ( ( member @ A @ A2 @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ A3 @ B6 ) ) )
% 2.83/1.60 = ( ( member @ A @ A2 @ ( set_mset @ A @ A3 ) )
% 2.83/1.60 | ( member @ A @ A2 @ ( set_mset @ A @ B6 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_191_mset__subset__eqD,axiom,
% 2.83/1.60 ! [A: $tType,A3: multiset @ A,B6: multiset @ A,X: A] :
% 2.83/1.60 ( ( subseteq_mset @ A @ A3 @ B6 )
% 2.83/1.60 => ( ( member @ A @ X @ ( set_mset @ A @ A3 ) )
% 2.83/1.60 => ( member @ A @ X @ ( set_mset @ A @ B6 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_192_mset__subset__eq__add__mset__cancel,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,A3: multiset @ A,B6: multiset @ A] :
% 2.83/1.60 ( ( subseteq_mset @ A @ ( add_mset @ A @ A2 @ A3 ) @ ( add_mset @ A @ A2 @ B6 ) )
% 2.83/1.60 = ( subseteq_mset @ A @ A3 @ B6 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_193_set__mset__mono,axiom,
% 2.83/1.60 ! [A: $tType,A3: multiset @ A,B6: multiset @ A] :
% 2.83/1.60 ( ( subseteq_mset @ A @ A3 @ B6 )
% 2.83/1.60 => ( ord_less_eq @ ( set @ A ) @ ( set_mset @ A @ A3 ) @ ( set_mset @ A @ B6 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_194_add__nonpos__eq__0__iff,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere216010020id_add @ A )
% 2.83/1.60 => ! [X: A,Y: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 2.83/1.60 => ( ( ord_less_eq @ A @ Y @ ( zero_zero @ A ) )
% 2.83/1.60 => ( ( ( plus_plus @ A @ X @ Y )
% 2.83/1.60 = ( zero_zero @ A ) )
% 2.83/1.60 = ( ( X
% 2.83/1.60 = ( zero_zero @ A ) )
% 2.83/1.60 & ( Y
% 2.83/1.60 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_195_add__nonneg__eq__0__iff,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere216010020id_add @ A )
% 2.83/1.60 => ! [X: A,Y: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 2.83/1.60 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 2.83/1.60 => ( ( ( plus_plus @ A @ X @ Y )
% 2.83/1.60 = ( zero_zero @ A ) )
% 2.83/1.60 = ( ( X
% 2.83/1.60 = ( zero_zero @ A ) )
% 2.83/1.60 & ( Y
% 2.83/1.60 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_196_add__nonpos__nonpos,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere216010020id_add @ A )
% 2.83/1.60 => ! [A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.83/1.60 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.83/1.60 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_197_add__nonneg__nonneg,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere216010020id_add @ A )
% 2.83/1.60 => ! [A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.83/1.60 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.83/1.60 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_198_add__increasing2,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere216010020id_add @ A )
% 2.83/1.60 => ! [C2: A,B2: A,A2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 2.83/1.60 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.60 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_199_add__decreasing2,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere216010020id_add @ A )
% 2.83/1.60 => ! [C2: A,A2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ C2 @ ( zero_zero @ A ) )
% 2.83/1.60 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.60 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_200_add__increasing,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere216010020id_add @ A )
% 2.83/1.60 => ! [A2: A,B2: A,C2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.83/1.60 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.83/1.60 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_201_add__decreasing,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ordere216010020id_add @ A )
% 2.83/1.60 => ! [A2: A,C2: A,B2: A] :
% 2.83/1.60 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.83/1.60 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 2.83/1.60 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_202_single__is__union,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,M4: multiset @ A,N: multiset @ A] :
% 2.83/1.60 ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 = ( plus_plus @ ( multiset @ A ) @ M4 @ N ) )
% 2.83/1.60 = ( ( ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 = M4 )
% 2.83/1.60 & ( N
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) ) )
% 2.83/1.60 | ( ( M4
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 & ( ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 = N ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_203_union__is__single,axiom,
% 2.83/1.60 ! [A: $tType,M4: multiset @ A,N: multiset @ A,A2: A] :
% 2.83/1.60 ( ( ( plus_plus @ ( multiset @ A ) @ M4 @ N )
% 2.83/1.60 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.83/1.60 = ( ( ( M4
% 2.83/1.60 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) )
% 2.83/1.60 & ( N
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) ) )
% 2.83/1.60 | ( ( M4
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 & ( N
% 2.83/1.60 = ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_204_add__mset__add__single,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( add_mset @ A )
% 2.83/1.60 = ( ^ [A4: A,A8: multiset @ A] : ( plus_plus @ ( multiset @ A ) @ A8 @ ( add_mset @ A @ A4 @ ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_205_multi__subset__induct,axiom,
% 2.83/1.60 ! [A: $tType,F5: multiset @ A,A3: multiset @ A,P: ( multiset @ A ) > $o] :
% 2.83/1.60 ( ( subseteq_mset @ A @ F5 @ A3 )
% 2.83/1.60 => ( ( P @ ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 => ( ! [A5: A,F6: multiset @ A] :
% 2.83/1.60 ( ( member @ A @ A5 @ ( set_mset @ A @ A3 ) )
% 2.83/1.60 => ( ( P @ F6 )
% 2.83/1.60 => ( P @ ( add_mset @ A @ A5 @ F6 ) ) ) )
% 2.83/1.60 => ( P @ F5 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_206_mset__subset__eq__single,axiom,
% 2.83/1.60 ! [A: $tType,A2: A,B6: multiset @ A] :
% 2.83/1.60 ( ( member @ A @ A2 @ ( set_mset @ A @ B6 ) )
% 2.83/1.60 => ( subseteq_mset @ A @ ( add_mset @ A @ A2 @ ( zero_zero @ ( multiset @ A ) ) ) @ B6 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_207_multi__member__skip,axiom,
% 2.83/1.60 ! [A: $tType,X: A,XS: multiset @ A,Y: A] :
% 2.83/1.60 ( ( member @ A @ X @ ( set_mset @ A @ XS ) )
% 2.83/1.60 => ( member @ A @ X @ ( set_mset @ A @ ( plus_plus @ ( multiset @ A ) @ ( add_mset @ A @ Y @ ( zero_zero @ ( multiset @ A ) ) ) @ XS ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_208_multi__member__this,axiom,
% 2.83/1.60 ! [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 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_209_mult1E,axiom,
% 2.83/1.60 ! [A: $tType,N: multiset @ A,M4: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 2.83/1.60 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M4 ) @ ( mult1 @ A @ R ) )
% 2.83/1.60 => ~ ! [A5: A,M0: multiset @ A] :
% 2.83/1.60 ( ( M4
% 2.83/1.60 = ( add_mset @ A @ A5 @ M0 ) )
% 2.83/1.60 => ! [K3: multiset @ A] :
% 2.83/1.60 ( ( N
% 2.83/1.60 = ( plus_plus @ ( multiset @ A ) @ M0 @ K3 ) )
% 2.83/1.60 => ~ ! [B8: A] :
% 2.83/1.60 ( ( member @ A @ B8 @ ( set_mset @ A @ K3 ) )
% 2.83/1.60 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B8 @ A5 ) @ R ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_210_mult1I,axiom,
% 2.83/1.60 ! [A: $tType,M4: multiset @ A,A2: A,M02: multiset @ A,N: multiset @ A,K4: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 2.83/1.60 ( ( M4
% 2.83/1.60 = ( add_mset @ A @ A2 @ M02 ) )
% 2.83/1.60 => ( ( N
% 2.83/1.60 = ( plus_plus @ ( multiset @ A ) @ M02 @ K4 ) )
% 2.83/1.60 => ( ! [B4: A] :
% 2.83/1.60 ( ( member @ A @ B4 @ ( set_mset @ A @ K4 ) )
% 2.83/1.60 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A2 ) @ R ) )
% 2.83/1.60 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M4 ) @ ( mult1 @ A @ R ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_211_less__add,axiom,
% 2.83/1.60 ! [A: $tType,N: multiset @ A,A2: A,M02: multiset @ A,R: set @ ( product_prod @ A @ A )] :
% 2.83/1.60 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ ( add_mset @ A @ A2 @ M02 ) ) @ ( mult1 @ A @ R ) )
% 2.83/1.60 => ( ? [M5: multiset @ A] :
% 2.83/1.60 ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M5 @ M02 ) @ ( mult1 @ A @ R ) )
% 2.83/1.60 & ( N
% 2.83/1.60 = ( add_mset @ A @ A2 @ M5 ) ) )
% 2.83/1.60 | ? [K3: multiset @ A] :
% 2.83/1.60 ( ! [B8: A] :
% 2.83/1.60 ( ( member @ A @ B8 @ ( set_mset @ A @ K3 ) )
% 2.83/1.60 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B8 @ A2 ) @ R ) )
% 2.83/1.60 & ( N
% 2.83/1.60 = ( plus_plus @ ( multiset @ A ) @ M02 @ K3 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_212_mono__mult1,axiom,
% 2.83/1.60 ! [A: $tType,R: set @ ( product_prod @ A @ A ),R5: set @ ( product_prod @ A @ A )] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ R5 )
% 2.83/1.60 => ( ord_less_eq @ ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) @ ( mult1 @ A @ R ) @ ( mult1 @ A @ R5 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_213_subset__antisym,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 2.83/1.60 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ A3 )
% 2.83/1.60 => ( A3 = B6 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_214_subsetI,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 2.83/1.60 ( ! [X4: A] :
% 2.83/1.60 ( ( member @ A @ X4 @ A3 )
% 2.83/1.60 => ( member @ A @ X4 @ B6 ) )
% 2.83/1.60 => ( ord_less_eq @ ( set @ A ) @ A3 @ B6 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_215_in__mono,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A,B6: set @ A,X: A] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 2.83/1.60 => ( ( member @ A @ X @ A3 )
% 2.83/1.60 => ( member @ A @ X @ B6 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_216_subsetD,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A,B6: set @ A,C2: A] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 2.83/1.60 => ( ( member @ A @ C2 @ A3 )
% 2.83/1.60 => ( member @ A @ C2 @ B6 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_217_equalityE,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 2.83/1.60 ( ( A3 = B6 )
% 2.83/1.60 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 2.83/1.60 => ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A3 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_218_subset__eq,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ A ) )
% 2.83/1.60 = ( ^ [A8: set @ A,B9: set @ A] :
% 2.83/1.60 ! [X5: A] :
% 2.83/1.60 ( ( member @ A @ X5 @ A8 )
% 2.83/1.60 => ( member @ A @ X5 @ B9 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_219_equalityD1,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 2.83/1.60 ( ( A3 = B6 )
% 2.83/1.60 => ( ord_less_eq @ ( set @ A ) @ A3 @ B6 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_220_equalityD2,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A,B6: set @ A] :
% 2.83/1.60 ( ( A3 = B6 )
% 2.83/1.60 => ( ord_less_eq @ ( set @ A ) @ B6 @ A3 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_221_subset__iff,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ A ) )
% 2.83/1.60 = ( ^ [A8: set @ A,B9: set @ A] :
% 2.83/1.60 ! [T3: A] :
% 2.83/1.60 ( ( member @ A @ T3 @ A8 )
% 2.83/1.60 => ( member @ A @ T3 @ B9 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_222_subset__refl,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_223_Collect__mono,axiom,
% 2.83/1.60 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.60 ( ! [X4: A] :
% 2.83/1.60 ( ( P @ X4 )
% 2.83/1.60 => ( Q @ X4 ) )
% 2.83/1.60 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_224_subset__trans,axiom,
% 2.83/1.60 ! [A: $tType,A3: set @ A,B6: set @ A,C4: set @ A] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 2.83/1.60 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ C4 )
% 2.83/1.60 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_225_set__eq__subset,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( ^ [Y3: set @ A,Z: set @ A] : ( Y3 = Z ) )
% 2.83/1.60 = ( ^ [A8: set @ A,B9: set @ A] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ A ) @ A8 @ B9 )
% 2.83/1.60 & ( ord_less_eq @ ( set @ A ) @ B9 @ A8 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_226_Collect__mono__iff,axiom,
% 2.83/1.60 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.83/1.60 = ( ! [X5: A] :
% 2.83/1.60 ( ( P @ X5 )
% 2.83/1.60 => ( Q @ X5 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_227_one__step__implies__mult,axiom,
% 2.83/1.60 ! [A: $tType,J3: multiset @ A,K4: multiset @ A,R: set @ ( product_prod @ A @ A ),I4: multiset @ A] :
% 2.83/1.60 ( ( J3
% 2.83/1.60 != ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 => ( ! [X4: A] :
% 2.83/1.60 ( ( member @ A @ X4 @ ( set_mset @ A @ K4 ) )
% 2.83/1.60 => ? [Xa: A] :
% 2.83/1.60 ( ( member @ A @ Xa @ ( set_mset @ A @ J3 ) )
% 2.83/1.60 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Xa ) @ R ) ) )
% 2.83/1.60 => ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) @ I4 @ K4 ) @ ( plus_plus @ ( multiset @ A ) @ I4 @ J3 ) ) @ ( mult @ A @ R ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_228_subrelI,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.83/1.60 ( ! [X4: A,Y2: B] :
% 2.83/1.60 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y2 ) @ R )
% 2.83/1.60 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y2 ) @ S ) )
% 2.83/1.60 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_229_mono__mult,axiom,
% 2.83/1.60 ! [A: $tType,R: set @ ( product_prod @ A @ A ),R5: set @ ( product_prod @ A @ A )] :
% 2.83/1.60 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ R5 )
% 2.83/1.60 => ( ord_less_eq @ ( set @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) ) @ ( mult @ A @ R ) @ ( mult @ A @ R5 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_230_mult__implies__one__step,axiom,
% 2.83/1.60 ! [A: $tType,R: set @ ( product_prod @ A @ A ),M4: multiset @ A,N: multiset @ A] :
% 2.83/1.60 ( ( trans @ A @ R )
% 2.83/1.60 => ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ M4 @ N ) @ ( mult @ A @ R ) )
% 2.83/1.60 => ? [I5: multiset @ A,J4: multiset @ A] :
% 2.83/1.60 ( ( N
% 2.83/1.60 = ( plus_plus @ ( multiset @ A ) @ I5 @ J4 ) )
% 2.83/1.60 & ? [K3: multiset @ A] :
% 2.83/1.60 ( ( M4
% 2.83/1.60 = ( plus_plus @ ( multiset @ A ) @ I5 @ K3 ) )
% 2.83/1.60 & ( J4
% 2.83/1.60 != ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 & ! [X7: A] :
% 2.83/1.60 ( ( member @ A @ X7 @ ( set_mset @ A @ K3 ) )
% 2.83/1.60 => ? [Xa2: A] :
% 2.83/1.60 ( ( member @ A @ Xa2 @ ( set_mset @ A @ J4 ) )
% 2.83/1.60 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ Xa2 ) @ R ) ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_231_subset__mset_Osum__mset__0__iff,axiom,
% 2.83/1.60 ! [A: $tType,M4: multiset @ ( multiset @ A )] :
% 2.83/1.60 ( ( ( comm_monoid_sum_mset @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ A ) ) @ M4 )
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) )
% 2.83/1.60 = ( ! [X5: multiset @ A] :
% 2.83/1.60 ( ( member @ ( multiset @ A ) @ X5 @ ( set_mset @ ( multiset @ A ) @ M4 ) )
% 2.83/1.60 => ( X5
% 2.83/1.60 = ( zero_zero @ ( multiset @ A ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_232_transD,axiom,
% 2.83/1.60 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A,Z2: A] :
% 2.83/1.60 ( ( trans @ A @ R )
% 2.83/1.60 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 2.83/1.60 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ R )
% 2.83/1.60 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ R ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_233_transE,axiom,
% 2.83/1.60 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X: A,Y: A,Z2: A] :
% 2.83/1.60 ( ( trans @ A @ R )
% 2.83/1.60 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 2.83/1.60 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ R )
% 2.83/1.60 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z2 ) @ R ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_234_transI,axiom,
% 2.83/1.60 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 2.83/1.60 ( ! [X4: A,Y2: A,Z3: A] :
% 2.83/1.60 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y2 ) @ R )
% 2.83/1.60 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z3 ) @ R )
% 2.83/1.60 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Z3 ) @ R ) ) )
% 2.83/1.60 => ( trans @ A @ R ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_235_trans__def,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( trans @ A )
% 2.83/1.60 = ( ^ [R4: set @ ( product_prod @ A @ A )] :
% 2.83/1.60 ! [X5: A,Y4: A,Z4: A] :
% 2.83/1.60 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X5 @ Y4 ) @ R4 )
% 2.83/1.60 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ Z4 ) @ R4 )
% 2.83/1.60 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X5 @ Z4 ) @ R4 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_236_mult__cancel__add__mset,axiom,
% 2.83/1.60 ! [A: $tType,S: set @ ( product_prod @ A @ A ),Uu: A,X8: multiset @ A,Y7: multiset @ A] :
% 2.83/1.60 ( ( trans @ A @ S )
% 2.83/1.60 => ( ( irrefl @ A @ S )
% 2.83/1.60 => ( ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ ( add_mset @ A @ Uu @ X8 ) @ ( add_mset @ A @ Uu @ Y7 ) ) @ ( mult @ A @ S ) )
% 2.83/1.60 = ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ X8 @ Y7 ) @ ( mult @ A @ S ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_237_in__mset__fold__plus__iff,axiom,
% 2.83/1.60 ! [A: $tType,X: A,M4: multiset @ A,NN: multiset @ ( multiset @ A )] :
% 2.83/1.60 ( ( member @ A @ X @ ( set_mset @ A @ ( fold_mset @ ( multiset @ A ) @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ M4 @ NN ) ) )
% 2.83/1.60 = ( ( member @ A @ X @ ( set_mset @ A @ M4 ) )
% 2.83/1.60 | ? [N4: multiset @ A] :
% 2.83/1.60 ( ( member @ ( multiset @ A ) @ N4 @ ( set_mset @ ( multiset @ A ) @ NN ) )
% 2.83/1.60 & ( member @ A @ X @ ( set_mset @ A @ N4 ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_238_irrefl__def,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( irrefl @ A )
% 2.83/1.60 = ( ^ [R4: set @ ( product_prod @ A @ A )] :
% 2.83/1.60 ! [A4: A] :
% 2.83/1.60 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ A4 ) @ R4 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_239_irreflI,axiom,
% 2.83/1.60 ! [A: $tType,R3: set @ ( product_prod @ A @ A )] :
% 2.83/1.60 ( ! [A5: A] :
% 2.83/1.60 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A5 @ A5 ) @ R3 )
% 2.83/1.60 => ( irrefl @ A @ R3 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_240_union__fold__mset__add__mset,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( plus_plus @ ( multiset @ A ) )
% 2.83/1.60 = ( fold_mset @ A @ ( multiset @ A ) @ ( add_mset @ A ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_241_multp__iff,axiom,
% 2.83/1.60 ! [A: $tType,R3: set @ ( product_prod @ A @ A ),P: A > A > $o,N: multiset @ A,M4: multiset @ A] :
% 2.83/1.60 ( ( irrefl @ A @ R3 )
% 2.83/1.60 => ( ( trans @ A @ R3 )
% 2.83/1.60 => ( ! [X4: A,Y2: A] :
% 2.83/1.60 ( ( P @ X4 @ Y2 )
% 2.83/1.60 = ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y2 ) @ R3 ) )
% 2.83/1.60 => ( ( multp @ A @ P @ N @ M4 )
% 2.83/1.60 = ( member @ ( product_prod @ ( multiset @ A ) @ ( multiset @ A ) ) @ ( product_Pair @ ( multiset @ A ) @ ( multiset @ A ) @ N @ M4 ) @ ( mult @ A @ R3 ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_242_add__mset__replicate__mset__safe,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,M4: multiset @ B,A2: B] :
% 2.83/1.60 ( ( nO_MATCH @ ( multiset @ A ) @ ( multiset @ B ) @ ( zero_zero @ ( multiset @ A ) ) @ M4 )
% 2.83/1.60 => ( ( add_mset @ B @ A2 @ M4 )
% 2.83/1.60 = ( plus_plus @ ( multiset @ B ) @ ( add_mset @ B @ A2 @ ( zero_zero @ ( multiset @ B ) ) ) @ M4 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_243_subset__mset_Osum__mset__mono,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,K4: multiset @ B,F: B > ( multiset @ A ),G: B > ( multiset @ A )] :
% 2.83/1.60 ( ! [I3: B] :
% 2.83/1.60 ( ( member @ B @ I3 @ ( set_mset @ B @ K4 ) )
% 2.83/1.60 => ( subseteq_mset @ A @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 2.83/1.60 => ( subseteq_mset @ A @ ( comm_monoid_sum_mset @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ A ) ) @ ( image_mset @ B @ ( multiset @ A ) @ F @ K4 ) ) @ ( comm_monoid_sum_mset @ ( multiset @ A ) @ ( plus_plus @ ( multiset @ A ) ) @ ( zero_zero @ ( multiset @ A ) ) @ ( image_mset @ B @ ( multiset @ A ) @ G @ K4 ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_244_subset__mset_Oantimono__def,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( order @ B )
% 2.83/1.60 => ! [F: ( multiset @ A ) > B] :
% 2.83/1.60 ( ( antimono @ ( multiset @ A ) @ B @ ( subseteq_mset @ A ) @ F )
% 2.83/1.60 = ( ! [X5: multiset @ A,Y4: multiset @ A] :
% 2.83/1.60 ( ( subseteq_mset @ A @ X5 @ Y4 )
% 2.83/1.60 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X5 ) ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_245_image__mset__add__mset,axiom,
% 2.83/1.60 ! [A: $tType,B: $tType,F: B > A,A2: B,M4: multiset @ B] :
% 2.83/1.60 ( ( image_mset @ B @ A @ F @ ( add_mset @ B @ A2 @ M4 ) )
% 2.83/1.60 = ( add_mset @ A @ ( F @ A2 ) @ ( image_mset @ B @ A @ F @ M4 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_246_multiset_Omap__cong,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,X: multiset @ A,Ya: multiset @ A,F: A > B,G: A > B] :
% 2.83/1.60 ( ( X = Ya )
% 2.83/1.60 => ( ! [Z3: A] :
% 2.83/1.60 ( ( member @ A @ Z3 @ ( set_mset @ A @ Ya ) )
% 2.83/1.60 => ( ( F @ Z3 )
% 2.83/1.60 = ( G @ Z3 ) ) )
% 2.83/1.60 => ( ( image_mset @ A @ B @ F @ X )
% 2.83/1.60 = ( image_mset @ A @ B @ G @ Ya ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_247_multiset_Omap__cong0,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,X: multiset @ A,F: A > B,G: A > B] :
% 2.83/1.60 ( ! [Z3: A] :
% 2.83/1.60 ( ( member @ A @ Z3 @ ( set_mset @ A @ X ) )
% 2.83/1.60 => ( ( F @ Z3 )
% 2.83/1.60 = ( G @ Z3 ) ) )
% 2.83/1.60 => ( ( image_mset @ A @ B @ F @ X )
% 2.83/1.60 = ( image_mset @ A @ B @ G @ X ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_248_multiset_Oinj__map__strong,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,X: multiset @ A,Xa3: multiset @ A,F: A > B,Fa: A > B] :
% 2.83/1.60 ( ! [Z3: A,Za: A] :
% 2.83/1.60 ( ( member @ A @ Z3 @ ( set_mset @ A @ X ) )
% 2.83/1.60 => ( ( member @ A @ Za @ ( set_mset @ A @ Xa3 ) )
% 2.83/1.60 => ( ( ( F @ Z3 )
% 2.83/1.60 = ( Fa @ Za ) )
% 2.83/1.60 => ( Z3 = Za ) ) ) )
% 2.83/1.60 => ( ( ( image_mset @ A @ B @ F @ X )
% 2.83/1.60 = ( image_mset @ A @ B @ Fa @ Xa3 ) )
% 2.83/1.60 => ( X = Xa3 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_249_order_Oantimono_Ocong,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( order @ B )
% 2.83/1.60 => ( ( antimono @ A @ B )
% 2.83/1.60 = ( antimono @ A @ B ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_250_msed__map__invR,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,F: B > A,M4: multiset @ B,B2: A,N: multiset @ A] :
% 2.83/1.60 ( ( ( image_mset @ B @ A @ F @ M4 )
% 2.83/1.60 = ( add_mset @ A @ B2 @ N ) )
% 2.83/1.60 => ? [M1: multiset @ B,A5: B] :
% 2.83/1.60 ( ( M4
% 2.83/1.60 = ( add_mset @ B @ A5 @ M1 ) )
% 2.83/1.60 & ( ( F @ A5 )
% 2.83/1.60 = B2 )
% 2.83/1.60 & ( ( image_mset @ B @ A @ F @ M1 )
% 2.83/1.60 = N ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_251_msed__map__invL,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,F: B > A,A2: B,M4: multiset @ B,N: multiset @ A] :
% 2.83/1.60 ( ( ( image_mset @ B @ A @ F @ ( add_mset @ B @ A2 @ M4 ) )
% 2.83/1.60 = N )
% 2.83/1.60 => ? [N1: multiset @ A] :
% 2.83/1.60 ( ( N
% 2.83/1.60 = ( add_mset @ A @ ( F @ A2 ) @ N1 ) )
% 2.83/1.60 & ( ( image_mset @ B @ A @ F @ M4 )
% 2.83/1.60 = N1 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_252_image__mset__single,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType,F: B > A,X: B] :
% 2.83/1.60 ( ( image_mset @ B @ A @ F @ ( add_mset @ B @ X @ ( zero_zero @ ( multiset @ B ) ) ) )
% 2.83/1.60 = ( add_mset @ A @ ( F @ X ) @ ( zero_zero @ ( multiset @ A ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_253_subset__mset_OantimonoD,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( order @ B )
% 2.83/1.60 => ! [F: ( multiset @ A ) > B,X: multiset @ A,Y: multiset @ A] :
% 2.83/1.60 ( ( antimono @ ( multiset @ A ) @ B @ ( subseteq_mset @ A ) @ F )
% 2.83/1.60 => ( ( subseteq_mset @ A @ X @ Y )
% 2.83/1.60 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_254_subset__mset_OantimonoE,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( order @ B )
% 2.83/1.60 => ! [F: ( multiset @ A ) > B,X: multiset @ A,Y: multiset @ A] :
% 2.83/1.60 ( ( antimono @ ( multiset @ A ) @ B @ ( subseteq_mset @ A ) @ F )
% 2.83/1.60 => ( ( subseteq_mset @ A @ X @ Y )
% 2.83/1.60 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(fact_255_subset__mset_OantimonoI,axiom,
% 2.83/1.60 ! [B: $tType,A: $tType] :
% 2.83/1.60 ( ( order @ B )
% 2.83/1.60 => ! [F: ( multiset @ A ) > B] :
% 2.83/1.60 ( ! [X4: multiset @ A,Y2: multiset @ A] :
% 2.83/1.60 ( ( subseteq_mset @ A @ X4 @ Y2 )
% 2.83/1.60 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X4 ) ) )
% 2.83/1.60 => ( antimono @ ( multiset @ A ) @ B @ ( subseteq_mset @ A ) @ F ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( type @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( ord @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( order @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 2.83/1.60 ! [A: $tType] :
% 2.83/1.60 ( ( linorder @ A )
% 2.83/1.60 => ( preorder @ A ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.83/1.60 ! [A9: $tType,A10: $tType] :
% 2.83/1.60 ( ( preorder @ A10 )
% 2.83/1.60 => ( preorder @ ( A9 > A10 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.83/1.60 ! [A9: $tType,A10: $tType] :
% 2.83/1.60 ( ( order @ A10 )
% 2.83/1.60 => ( order @ ( A9 > A10 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_fun___Orderings_Oord,axiom,
% 2.83/1.60 ! [A9: $tType,A10: $tType] :
% 2.83/1.60 ( ( ord @ A10 )
% 2.83/1.60 => ( ord @ ( A9 > A10 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 2.83/1.60 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 2.83/1.60 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 2.83/1.60 ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 2.83/1.60 preorder @ $o ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.83/1.60 linorder @ $o ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 2.83/1.60 order @ $o ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 2.83/1.60 ord @ $o ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_Multiset_Omultiset___Groups_Oordered__ab__semigroup__add,axiom,
% 2.83/1.60 ! [A9: $tType] :
% 2.83/1.60 ( ( preorder @ A9 )
% 2.83/1.60 => ( ordere779506340up_add @ ( multiset @ A9 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add,axiom,
% 2.83/1.60 ! [A9: $tType] : ( cancel1352612707id_add @ ( multiset @ A9 ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_Multiset_Omultiset___Orderings_Opreorder_7,axiom,
% 2.83/1.60 ! [A9: $tType] :
% 2.83/1.60 ( ( preorder @ A9 )
% 2.83/1.60 => ( preorder @ ( multiset @ A9 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_Multiset_Omultiset___Orderings_Oorder_8,axiom,
% 2.83/1.60 ! [A9: $tType] :
% 2.83/1.60 ( ( preorder @ A9 )
% 2.83/1.60 => ( order @ ( multiset @ A9 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tcon_Multiset_Omultiset___Orderings_Oord_9,axiom,
% 2.83/1.60 ! [A9: $tType] :
% 2.83/1.60 ( ( preorder @ A9 )
% 2.83/1.60 => ( ord @ ( multiset @ A9 ) ) ) ).
% 2.83/1.60
% 2.83/1.60 thf(tfree_0,hypothesis,
% 2.83/1.60 linorder @ a ).
% 2.83/1.60
% 2.83/1.60 thf(conj_0,conjecture,
% 2.83/1.60 is_heap @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v2 @ ( e @ a ) @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ).
% 2.83/1.60 ------------------------
% 2.83/1.62 % (5343)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/183Mi)
% 2.83/1.62 % (5346)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/2Mi)
% 2.83/1.62 % (5346)Instruction limit reached!
% 2.83/1.62 % (5346)------------------------------
% 2.83/1.62 % (5346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.62 % (5346)Termination reason: Unknown
% 2.83/1.62 % (5346)Termination phase: shuffling
% 2.83/1.62
% 2.83/1.62 % (5346)Memory used [KB]: 1407
% 2.83/1.62 % (5346)Time elapsed: 0.002 s
% 2.83/1.62 % (5346)Instructions burned: 2 (million)
% 2.83/1.62 % (5346)------------------------------
% 2.83/1.62 % (5346)------------------------------
% 2.83/1.63 % (5349)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/18Mi)
% 2.83/1.63 % (5345)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_5214 for (2999ds/27Mi)
% 2.83/1.63 % (5349)Instruction limit reached!
% 2.83/1.63 % (5349)------------------------------
% 2.83/1.63 % (5349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.63 % (5349)Termination reason: Unknown
% 2.83/1.63 % (5349)Termination phase: shuffling
% 2.83/1.63
% 2.83/1.63 % (5349)Memory used [KB]: 1791
% 2.83/1.63 % (5349)Time elapsed: 0.007 s
% 2.83/1.63 % (5349)Instructions burned: 18 (million)
% 2.83/1.63 % (5349)------------------------------
% 2.83/1.63 % (5349)------------------------------
% 2.83/1.63 % (5344)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_5214 for (2999ds/4Mi)
% 2.83/1.63 % (5347)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_5214 for (2999ds/2Mi)
% 2.83/1.63 % (5348)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_5214 for (2999ds/275Mi)
% 2.83/1.63 % (5347)Instruction limit reached!
% 2.83/1.63 % (5347)------------------------------
% 2.83/1.63 % (5347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.63 % (5347)Termination reason: Unknown
% 2.83/1.63 % (5347)Termination phase: shuffling
% 2.83/1.63
% 2.83/1.63 % (5347)Memory used [KB]: 1407
% 2.83/1.63 % (5347)Time elapsed: 0.004 s
% 2.83/1.63 % (5347)Instructions burned: 3 (million)
% 2.83/1.63 % (5347)------------------------------
% 2.83/1.63 % (5347)------------------------------
% 2.83/1.63 % (5350)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/3Mi)
% 2.83/1.63 % (5344)Instruction limit reached!
% 2.83/1.63 % (5344)------------------------------
% 2.83/1.63 % (5344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.63 % (5344)Termination reason: Unknown
% 2.83/1.63 % (5344)Termination phase: shuffling
% 2.83/1.63
% 2.83/1.63 % (5344)Memory used [KB]: 1535
% 2.83/1.63 % (5344)Time elapsed: 0.005 s
% 2.83/1.63 % (5344)Instructions burned: 5 (million)
% 2.83/1.63 % (5344)------------------------------
% 2.83/1.63 % (5344)------------------------------
% 2.83/1.64 % (5350)Instruction limit reached!
% 2.83/1.64 % (5350)------------------------------
% 2.83/1.64 % (5350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.64 % (5350)Termination reason: Unknown
% 2.83/1.64 % (5350)Termination phase: shuffling
% 2.83/1.64
% 2.83/1.64 % (5350)Memory used [KB]: 1407
% 2.83/1.64 % (5350)Time elapsed: 0.002 s
% 2.83/1.64 % (5350)Instructions burned: 3 (million)
% 2.83/1.64 % (5350)------------------------------
% 2.83/1.64 % (5350)------------------------------
% 2.83/1.64 % (5345)Instruction limit reached!
% 2.83/1.64 % (5345)------------------------------
% 2.83/1.64 % (5345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.64 % (5345)Termination reason: Unknown
% 2.83/1.64 % (5345)Termination phase: shuffling
% 2.83/1.64
% 2.83/1.64 % (5345)Memory used [KB]: 2046
% 2.83/1.64 % (5345)Time elapsed: 0.012 s
% 2.83/1.64 % (5345)Instructions burned: 28 (million)
% 2.83/1.64 % (5345)------------------------------
% 2.83/1.64 % (5345)------------------------------
% 2.83/1.64 % (5351)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_5214 for (2999ds/37Mi)
% 2.83/1.64 % (5354)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_5214 for (2999ds/1041Mi)
% 2.83/1.65 % (5355)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/7Mi)
% 2.83/1.65 % (5355)Instruction limit reached!
% 2.83/1.65 % (5355)------------------------------
% 2.83/1.65 % (5355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.65 % (5355)Termination reason: Unknown
% 2.83/1.65 % (5355)Termination phase: shuffling
% 2.83/1.65
% 2.83/1.65 % (5355)Memory used [KB]: 1663
% 2.83/1.65 % (5355)Time elapsed: 0.005 s
% 2.83/1.65 % (5355)Instructions burned: 9 (million)
% 2.83/1.65 % (5355)------------------------------
% 2.83/1.65 % (5355)------------------------------
% 2.83/1.65 % (5351)Instruction limit reached!
% 2.83/1.65 % (5351)------------------------------
% 2.83/1.65 % (5351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.65 % (5351)Termination reason: Unknown
% 2.83/1.65 % (5351)Termination phase: shuffling
% 2.83/1.65
% 2.83/1.65 % (5351)Memory used [KB]: 2174
% 2.83/1.65 % (5351)Time elapsed: 0.011 s
% 2.83/1.65 % (5351)Instructions burned: 37 (million)
% 2.83/1.65 % (5351)------------------------------
% 2.83/1.65 % (5351)------------------------------
% 2.83/1.65 % (5352)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_5214 for (2999ds/15Mi)
% 2.83/1.65 % (5353)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_5214 for (2999ds/3Mi)
% 2.83/1.65 % (5353)Instruction limit reached!
% 2.83/1.65 % (5353)------------------------------
% 2.83/1.65 % (5353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.65 % (5353)Termination reason: Unknown
% 2.83/1.65 % (5353)Termination phase: shuffling
% 2.83/1.65
% 2.83/1.65 % (5353)Memory used [KB]: 1407
% 2.83/1.65 % (5353)Time elapsed: 0.004 s
% 2.83/1.65 % (5353)Instructions burned: 3 (million)
% 2.83/1.65 % (5353)------------------------------
% 2.83/1.65 % (5353)------------------------------
% 2.83/1.66 % (5352)Instruction limit reached!
% 2.83/1.66 % (5352)------------------------------
% 2.83/1.66 % (5352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.66 % (5352)Termination reason: Unknown
% 2.83/1.66 % (5352)Termination phase: shuffling
% 2.83/1.66
% 2.83/1.66 % (5352)Memory used [KB]: 1791
% 2.83/1.66 % (5352)Time elapsed: 0.010 s
% 2.83/1.66 % (5352)Instructions burned: 15 (million)
% 2.83/1.66 % (5352)------------------------------
% 2.83/1.66 % (5352)------------------------------
% 2.83/1.66 % (5356)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/16Mi)
% 2.83/1.66 % (5357)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_5214 for (2999ds/3Mi)
% 2.83/1.66 % (5357)Instruction limit reached!
% 2.83/1.66 % (5357)------------------------------
% 2.83/1.66 % (5357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.66 % (5357)Termination reason: Unknown
% 2.83/1.66 % (5357)Termination phase: shuffling
% 2.83/1.66
% 2.83/1.66 % (5357)Memory used [KB]: 1407
% 2.83/1.66 % (5357)Time elapsed: 0.002 s
% 2.83/1.66 % (5357)Instructions burned: 3 (million)
% 2.83/1.66 % (5357)------------------------------
% 2.83/1.66 % (5357)------------------------------
% 2.83/1.67 % (5356)Instruction limit reached!
% 2.83/1.67 % (5356)------------------------------
% 2.83/1.67 % (5356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.67 % (5356)Termination reason: Unknown
% 2.83/1.67 % (5356)Termination phase: shuffling
% 2.83/1.67
% 2.83/1.67 % (5356)Memory used [KB]: 1791
% 2.83/1.67 % (5356)Time elapsed: 0.008 s
% 2.83/1.67 % (5356)Instructions burned: 18 (million)
% 2.83/1.67 % (5356)------------------------------
% 2.83/1.67 % (5356)------------------------------
% 2.83/1.67 % (5348)Refutation not found, incomplete strategy
% 2.83/1.67 % (5348)------------------------------
% 2.83/1.67 % (5348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.67 % (5348)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.67
% 2.83/1.67
% 2.83/1.67 % (5348)Memory used [KB]: 6908
% 2.83/1.67 % (5348)Time elapsed: 0.040 s
% 2.83/1.67 % (5348)Instructions burned: 96 (million)
% 2.83/1.67 % (5348)------------------------------
% 2.83/1.67 % (5348)------------------------------
% 2.83/1.67 % (5359)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/7Mi)
% 2.83/1.67 % (5360)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/3Mi)
% 2.83/1.67 % (5360)Instruction limit reached!
% 2.83/1.67 % (5360)------------------------------
% 2.83/1.67 % (5360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.67 % (5360)Termination reason: Unknown
% 2.83/1.67 % (5360)Termination phase: shuffling
% 2.83/1.67
% 2.83/1.67 % (5360)Memory used [KB]: 1407
% 2.83/1.67 % (5358)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_5214 for (2999ds/3Mi)
% 2.83/1.67 % (5360)Time elapsed: 0.002 s
% 2.83/1.67 % (5360)Instructions burned: 4 (million)
% 2.83/1.67 % (5360)------------------------------
% 2.83/1.67 % (5360)------------------------------
% 2.83/1.67 % (5359)Instruction limit reached!
% 2.83/1.67 % (5359)------------------------------
% 2.83/1.67 % (5359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.67 % (5359)Termination reason: Unknown
% 2.83/1.67 % (5359)Termination phase: shuffling
% 2.83/1.67
% 2.83/1.67 % (5359)Memory used [KB]: 1535
% 2.83/1.67 % (5359)Time elapsed: 0.004 s
% 2.83/1.67 % (5359)Instructions burned: 7 (million)
% 2.83/1.67 % (5359)------------------------------
% 2.83/1.67 % (5359)------------------------------
% 2.83/1.67 % (5358)Instruction limit reached!
% 2.83/1.67 % (5358)------------------------------
% 2.83/1.67 % (5358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.67 % (5358)Termination reason: Unknown
% 2.83/1.67 % (5358)Termination phase: shuffling
% 2.83/1.67
% 2.83/1.67 % (5358)Memory used [KB]: 1407
% 2.83/1.67 % (5358)Time elapsed: 0.004 s
% 2.83/1.67 % (5358)Instructions burned: 3 (million)
% 2.83/1.67 % (5358)------------------------------
% 2.83/1.67 % (5358)------------------------------
% 2.83/1.68 % (5343)Instruction limit reached!
% 2.83/1.68 % (5343)------------------------------
% 2.83/1.68 % (5343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.68 % (5343)Termination reason: Unknown
% 2.83/1.68 % (5343)Termination phase: Saturation
% 2.83/1.68
% 2.83/1.68 % (5343)Memory used [KB]: 7547
% 2.83/1.68 % (5343)Time elapsed: 0.054 s
% 2.83/1.68 % (5343)Instructions burned: 184 (million)
% 2.83/1.68 % (5343)------------------------------
% 2.83/1.68 % (5343)------------------------------
% 2.83/1.68 % (5361)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/4Mi)
% 2.83/1.68 % (5361)Instruction limit reached!
% 2.83/1.68 % (5361)------------------------------
% 2.83/1.68 % (5361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.68 % (5361)Termination reason: Unknown
% 2.83/1.68 % (5361)Termination phase: shuffling
% 2.83/1.68
% 2.83/1.68 % (5361)Memory used [KB]: 1407
% 2.83/1.68 % (5361)Time elapsed: 0.003 s
% 2.83/1.68 % (5361)Instructions burned: 4 (million)
% 2.83/1.68 % (5361)------------------------------
% 2.83/1.68 % (5361)------------------------------
% 2.83/1.68 % (5362)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/18Mi)
% 2.83/1.68 % (5363)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/710Mi)
% 2.83/1.68 % (5364)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/6Mi)
% 2.83/1.69 % (5364)Instruction limit reached!
% 2.83/1.69 % (5364)------------------------------
% 2.83/1.69 % (5364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.69 % (5364)Termination reason: Unknown
% 2.83/1.69 % (5364)Termination phase: shuffling
% 2.83/1.69
% 2.83/1.69 % (5364)Memory used [KB]: 1535
% 2.83/1.69 % (5364)Time elapsed: 0.004 s
% 2.83/1.69 % (5364)Instructions burned: 6 (million)
% 2.83/1.69 % (5364)------------------------------
% 2.83/1.69 % (5364)------------------------------
% 2.83/1.69 % (5366)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_5214 for (2999ds/21Mi)
% 2.83/1.69 % (5362)Instruction limit reached!
% 2.83/1.69 % (5362)------------------------------
% 2.83/1.69 % (5362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.69 % (5362)Termination reason: Unknown
% 2.83/1.69 % (5362)Termination phase: shuffling
% 2.83/1.69
% 2.83/1.69 % (5362)Memory used [KB]: 1791
% 2.83/1.69 % (5362)Time elapsed: 0.007 s
% 2.83/1.69 % (5362)Instructions burned: 19 (million)
% 2.83/1.69 % (5362)------------------------------
% 2.83/1.69 % (5362)------------------------------
% 2.83/1.69 % (5367)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/5Mi)
% 2.83/1.69 % (5367)Instruction limit reached!
% 2.83/1.69 % (5367)------------------------------
% 2.83/1.69 % (5367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.69 % (5367)Termination reason: Unknown
% 2.83/1.69 % (5367)Termination phase: shuffling
% 2.83/1.69
% 2.83/1.69 % (5367)Memory used [KB]: 1663
% 2.83/1.69 % (5367)Time elapsed: 0.004 s
% 2.83/1.69 % (5367)Instructions burned: 8 (million)
% 2.83/1.69 % (5367)------------------------------
% 2.83/1.69 % (5367)------------------------------
% 2.83/1.69 % (5365)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_5214 for (2999ds/902Mi)
% 2.83/1.69 % (5366)Instruction limit reached!
% 2.83/1.69 % (5366)------------------------------
% 2.83/1.69 % (5366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.69 % (5366)Termination reason: Unknown
% 2.83/1.69 % (5366)Termination phase: shuffling
% 2.83/1.69
% 2.83/1.69 % (5366)Memory used [KB]: 1918
% 2.83/1.69 % (5366)Time elapsed: 0.008 s
% 2.83/1.69 % (5366)Instructions burned: 22 (million)
% 2.83/1.69 % (5366)------------------------------
% 2.83/1.69 % (5366)------------------------------
% 2.83/1.70 % (5368)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_5214 for (2999ds/6Mi)
% 2.83/1.70 % (5369)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/377Mi)
% 2.85/1.70 % (5368)Instruction limit reached!
% 2.85/1.70 % (5368)------------------------------
% 2.85/1.70 % (5368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.70 % (5368)Termination reason: Unknown
% 2.85/1.70 % (5368)Termination phase: shuffling
% 2.85/1.70
% 2.85/1.70 % (5368)Memory used [KB]: 1535
% 2.85/1.70 % (5368)Time elapsed: 0.004 s
% 2.85/1.70 % (5368)Instructions burned: 7 (million)
% 2.85/1.70 % (5368)------------------------------
% 2.85/1.70 % (5368)------------------------------
% 2.85/1.70 % (5370)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_5214 for (2999ds/779Mi)
% 2.85/1.70 % (5371)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_5214 for (2999ds/19Mi)
% 2.85/1.71 % (5372)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/879Mi)
% 2.85/1.71 % (5371)Instruction limit reached!
% 2.85/1.71 % (5371)------------------------------
% 2.85/1.71 % (5371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.71 % (5371)Termination reason: Unknown
% 2.85/1.71 % (5371)Termination phase: shuffling
% 2.85/1.71
% 2.85/1.71 % (5371)Memory used [KB]: 1918
% 2.85/1.71 % (5371)Time elapsed: 0.007 s
% 2.85/1.71 % (5371)Instructions burned: 22 (million)
% 2.85/1.71 % (5371)------------------------------
% 2.85/1.71 % (5371)------------------------------
% 2.85/1.72 % (5373)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5214 for (2999ds/17Mi)
% 2.85/1.72 % (5373)Instruction limit reached!
% 2.85/1.72 % (5373)------------------------------
% 2.85/1.72 % (5373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.72 % (5373)Termination reason: Unknown
% 2.85/1.72 % (5373)Termination phase: shuffling
% 2.85/1.72
% 2.85/1.72 % (5373)Memory used [KB]: 1918
% 2.85/1.72 % (5373)Time elapsed: 0.007 s
% 2.85/1.72 % (5373)Instructions burned: 19 (million)
% 2.85/1.72 % (5373)------------------------------
% 2.85/1.72 % (5373)------------------------------
% 2.85/1.73 % (5374)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5214 for (2998ds/3Mi)
% 2.85/1.73 % (5374)Instruction limit reached!
% 2.85/1.73 % (5374)------------------------------
% 2.85/1.73 % (5374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.73 % (5374)Termination reason: Unknown
% 2.85/1.73 % (5374)Termination phase: shuffling
% 2.85/1.73
% 2.85/1.73 % (5374)Memory used [KB]: 1407
% 2.85/1.73 % (5374)Time elapsed: 0.002 s
% 2.85/1.73 % (5374)Instructions burned: 3 (million)
% 2.85/1.73 % (5374)------------------------------
% 2.85/1.73 % (5374)------------------------------
% 2.85/1.74 % (5375)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5214 for (2998ds/30Mi)
% 2.85/1.75 % (5375)Instruction limit reached!
% 2.85/1.75 % (5375)------------------------------
% 2.85/1.75 % (5375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.75 % (5375)Termination reason: Unknown
% 2.85/1.75 % (5375)Termination phase: shuffling
% 2.85/1.75
% 2.85/1.75 % (5375)Memory used [KB]: 2046
% 2.85/1.75 % (5375)Time elapsed: 0.011 s
% 2.85/1.75 % (5375)Instructions burned: 31 (million)
% 2.85/1.75 % (5375)------------------------------
% 2.85/1.75 % (5375)------------------------------
% 2.85/1.76 % (5376)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5214 for (2998ds/127Mi)
% 2.85/1.76 % (5365)Refutation not found, incomplete strategy
% 2.85/1.76 % (5365)------------------------------
% 2.85/1.76 % (5365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.76 % (5365)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.76
% 2.85/1.76
% 2.85/1.76 % (5365)Memory used [KB]: 7931
% 2.85/1.76 % (5365)Time elapsed: 0.073 s
% 2.85/1.76 % (5365)Instructions burned: 201 (million)
% 2.85/1.76 % (5365)------------------------------
% 2.85/1.76 % (5365)------------------------------
% 2.85/1.77 % (5377)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_5214 for (2998ds/100Mi)
% 2.85/1.80 % (5376)Instruction limit reached!
% 2.85/1.80 % (5376)------------------------------
% 2.85/1.80 % (5376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.80 % (5376)Termination reason: Unknown
% 2.85/1.80 % (5376)Termination phase: Property scanning
% 2.85/1.80
% 2.85/1.80 % (5376)Memory used [KB]: 2814
% 2.85/1.80 % (5376)Time elapsed: 0.038 s
% 2.85/1.80 % (5376)Instructions burned: 127 (million)
% 2.85/1.80 % (5376)------------------------------
% 2.85/1.80 % (5376)------------------------------
% 2.85/1.80 % (5377)Instruction limit reached!
% 2.85/1.80 % (5377)------------------------------
% 2.85/1.80 % (5377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.80 % (5377)Termination reason: Unknown
% 2.85/1.80 % (5377)Termination phase: Preprocessing 1
% 2.85/1.80
% 2.85/1.80 % (5377)Memory used [KB]: 2686
% 2.85/1.80 % (5377)Time elapsed: 0.032 s
% 2.85/1.80 % (5377)Instructions burned: 102 (million)
% 2.85/1.80 % (5377)------------------------------
% 2.85/1.80 % (5377)------------------------------
% 2.85/1.81 % (5369)Instruction limit reached!
% 2.85/1.81 % (5369)------------------------------
% 2.85/1.81 % (5369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.81 % (5369)Termination reason: Unknown
% 2.85/1.81 % (5369)Termination phase: Saturation
% 2.85/1.81
% 2.85/1.81 % (5369)Memory used [KB]: 8827
% 2.85/1.81 % (5369)Time elapsed: 0.113 s
% 2.85/1.81 % (5369)Instructions burned: 378 (million)
% 2.85/1.81 % (5369)------------------------------
% 2.85/1.81 % (5369)------------------------------
% 2.85/1.81 % (5378)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_5214 for (2998ds/3Mi)
% 2.85/1.81 % (5378)Instruction limit reached!
% 2.85/1.81 % (5378)------------------------------
% 2.85/1.81 % (5378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.81 % (5378)Termination reason: Unknown
% 2.85/1.81 % (5378)Termination phase: shuffling
% 2.85/1.81
% 2.85/1.81 % (5378)Memory used [KB]: 1407
% 2.85/1.81 % (5378)Time elapsed: 0.002 s
% 2.85/1.81 % (5378)Instructions burned: 3 (million)
% 2.85/1.81 % (5378)------------------------------
% 2.85/1.81 % (5378)------------------------------
% 2.85/1.81 % (5379)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_5214 for (2997ds/20Mi)
% 2.85/1.82 % (5380)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_5214 for (2997ds/86Mi)
% 2.85/1.82 % (5381)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_5214 for (2997ds/107Mi)
% 2.85/1.82 % (5379)Instruction limit reached!
% 2.85/1.82 % (5379)------------------------------
% 2.85/1.82 % (5379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.82 % (5379)Termination reason: Unknown
% 2.85/1.82 % (5379)Termination phase: shuffling
% 2.85/1.82
% 2.85/1.82 % (5379)Memory used [KB]: 1918
% 2.85/1.82 % (5379)Time elapsed: 0.009 s
% 2.85/1.82 % (5379)Instructions burned: 20 (million)
% 2.85/1.82 % (5379)------------------------------
% 2.85/1.82 % (5379)------------------------------
% 2.85/1.83 % (5382)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_5214 for (2997ds/39Mi)
% 2.85/1.84 % (5380)Instruction limit reached!
% 2.85/1.84 % (5380)------------------------------
% 2.85/1.84 % (5380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.84 % (5380)Termination reason: Unknown
% 2.85/1.84 % (5380)Termination phase: Property scanning
% 2.85/1.84
% 2.85/1.84 % (5380)Memory used [KB]: 2814
% 2.85/1.84 % (5380)Time elapsed: 0.027 s
% 2.85/1.84 % (5380)Instructions burned: 86 (million)
% 2.85/1.84 % (5380)------------------------------
% 2.85/1.84 % (5380)------------------------------
% 2.85/1.84 % (5382)Instruction limit reached!
% 2.85/1.84 % (5382)------------------------------
% 2.85/1.84 % (5382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.84 % (5382)Termination reason: Unknown
% 2.85/1.84 % (5382)Termination phase: shuffling
% 2.85/1.84
% 2.85/1.84 % (5382)Memory used [KB]: 2174
% 2.85/1.84 % (5382)Time elapsed: 0.014 s
% 2.85/1.84 % (5382)Instructions burned: 41 (million)
% 2.85/1.84 % (5382)------------------------------
% 2.85/1.84 % (5382)------------------------------
% 2.85/1.85 % (5381)Instruction limit reached!
% 2.85/1.85 % (5381)------------------------------
% 2.85/1.85 % (5381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.85 % (5381)Termination reason: Unknown
% 2.85/1.85 % (5381)Termination phase: Property scanning
% 2.85/1.85
% 2.85/1.85 % (5381)Memory used [KB]: 2814
% 2.85/1.85 % (5381)Time elapsed: 0.032 s
% 2.85/1.85 % (5381)Instructions burned: 107 (million)
% 2.85/1.85 % (5381)------------------------------
% 2.85/1.85 % (5381)------------------------------
% 2.85/1.85 % (5383)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_5214 for (2997ds/448Mi)
% 2.85/1.86 % (5384)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_5214 for (2997ds/46Mi)
% 2.85/1.86 % (5385)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_5214 for (2997ds/98Mi)
% 2.85/1.87 % (5384)Instruction limit reached!
% 2.85/1.87 % (5384)------------------------------
% 2.85/1.87 % (5384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.87 % (5384)Termination reason: Unknown
% 2.85/1.87 % (5384)Termination phase: Property scanning
% 2.85/1.87
% 2.85/1.87 % (5384)Memory used [KB]: 2174
% 2.85/1.87 % (5384)Time elapsed: 0.018 s
% 2.85/1.87 % (5384)Instructions burned: 48 (million)
% 2.85/1.87 % (5384)------------------------------
% 2.85/1.87 % (5384)------------------------------
% 2.85/1.88 % (5386)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_5214 for (2997ds/507Mi)
% 2.85/1.89 % (5385)Instruction limit reached!
% 2.85/1.89 % (5385)------------------------------
% 2.85/1.89 % (5385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.89 % (5385)Termination reason: Unknown
% 2.85/1.89 % (5385)Termination phase: Preprocessing 1
% 2.85/1.89
% 2.85/1.89 % (5385)Memory used [KB]: 2686
% 2.85/1.89 % (5385)Time elapsed: 0.027 s
% 2.85/1.89 % (5385)Instructions burned: 98 (million)
% 2.85/1.89 % (5385)------------------------------
% 2.85/1.89 % (5385)------------------------------
% 2.85/1.90 % (5387)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_5214 for (2997ds/149Mi)
% 2.85/1.90 % (5363)Instruction limit reached!
% 2.85/1.90 % (5363)------------------------------
% 2.85/1.90 % (5363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.90 % (5363)Termination reason: Unknown
% 2.85/1.90 % (5363)Termination phase: Saturation
% 2.85/1.90
% 2.85/1.90 % (5363)Memory used [KB]: 8187
% 2.85/1.90 % (5363)Time elapsed: 0.218 s
% 2.85/1.90 % (5363)Instructions burned: 711 (million)
% 2.85/1.90 % (5363)------------------------------
% 2.85/1.90 % (5363)------------------------------
% 2.85/1.91 % (5388)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_5214 for (2997ds/39Mi)
% 2.85/1.92 % (5388)Instruction limit reached!
% 2.85/1.92 % (5388)------------------------------
% 2.85/1.92 % (5388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.92 % (5388)Termination reason: Unknown
% 2.85/1.92 % (5388)Termination phase: Property scanning
% 2.85/1.92
% 2.85/1.92 % (5388)Memory used [KB]: 2174
% 2.85/1.92 % (5388)Time elapsed: 0.014 s
% 2.85/1.92 % (5388)Instructions burned: 41 (million)
% 2.85/1.92 % (5388)------------------------------
% 2.85/1.92 % (5388)------------------------------
% 2.85/1.93 % (5389)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_5214 for (2996ds/6Mi)
% 2.85/1.93 % (5389)Instruction limit reached!
% 2.85/1.93 % (5389)------------------------------
% 2.85/1.93 % (5389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.93 % (5389)Termination reason: Unknown
% 2.85/1.93 % (5389)Termination phase: shuffling
% 2.85/1.93
% 2.85/1.93 % (5389)Memory used [KB]: 1535
% 2.85/1.93 % (5389)Time elapsed: 0.003 s
% 2.85/1.93 % (5389)Instructions burned: 7 (million)
% 2.85/1.93 % (5389)------------------------------
% 2.85/1.93 % (5389)------------------------------
% 2.85/1.94 % (5387)Instruction limit reached!
% 2.85/1.94 % (5387)------------------------------
% 2.85/1.94 % (5387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.94 % (5387)Termination reason: Unknown
% 2.85/1.94 % (5387)Termination phase: Property scanning
% 2.85/1.94
% 2.85/1.94 % (5387)Memory used [KB]: 2814
% 2.85/1.94 % (5387)Time elapsed: 0.043 s
% 2.85/1.94 % (5387)Instructions burned: 152 (million)
% 2.85/1.94 % (5387)------------------------------
% 2.85/1.94 % (5387)------------------------------
% 2.85/1.94 % (5390)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_5214 for (2996ds/1087Mi)
% 2.85/1.94 % (5354)Instruction limit reached!
% 2.85/1.94 % (5354)------------------------------
% 2.85/1.94 % (5354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.94 % (5354)Termination reason: Unknown
% 2.85/1.94 % (5354)Termination phase: Saturation
% 2.85/1.94
% 2.85/1.94 % (5354)Memory used [KB]: 10106
% 2.85/1.94 % (5354)Time elapsed: 0.301 s
% 2.85/1.94 % (5354)Instructions burned: 1041 (million)
% 2.85/1.94 % (5354)------------------------------
% 2.85/1.94 % (5354)------------------------------
% 2.85/1.95 % (5391)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_5214 for (2996ds/47Mi)
% 2.85/1.95 % (5370)Instruction limit reached!
% 2.85/1.95 % (5370)------------------------------
% 2.85/1.95 % (5370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.95 % (5370)Termination reason: Unknown
% 2.85/1.95 % (5370)Termination phase: Saturation
% 2.85/1.95
% 2.85/1.95 % (5370)Memory used [KB]: 9338
% 2.85/1.95 % (5370)Time elapsed: 0.249 s
% 2.85/1.95 % (5370)Instructions burned: 780 (million)
% 2.85/1.95 % (5370)------------------------------
% 2.85/1.95 % (5370)------------------------------
% 2.85/1.95 % (5392)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_5214 for (2996ds/44Mi)
% 2.85/1.96 % (5393)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_5214 for (2996ds/432Mi)
% 2.85/1.96 % (5391)Instruction limit reached!
% 2.85/1.96 % (5391)------------------------------
% 2.85/1.96 % (5391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.96 % (5391)Termination reason: Unknown
% 2.85/1.96 % (5391)Termination phase: Property scanning
% 2.85/1.96
% 2.85/1.96 % (5391)Memory used [KB]: 2174
% 2.85/1.96 % (5391)Time elapsed: 0.016 s
% 2.85/1.96 % (5391)Instructions burned: 49 (million)
% 2.85/1.96 % (5391)------------------------------
% 2.85/1.96 % (5391)------------------------------
% 2.85/1.97 % (5392)Instruction limit reached!
% 2.85/1.97 % (5392)------------------------------
% 2.85/1.97 % (5392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.97 % (5392)Termination reason: Unknown
% 2.85/1.97 % (5392)Termination phase: shuffling
% 2.85/1.97
% 2.85/1.97 % (5392)Memory used [KB]: 2302
% 2.85/1.97 % (5392)Time elapsed: 0.013 s
% 2.85/1.97 % (5392)Instructions burned: 44 (million)
% 2.85/1.97 % (5392)------------------------------
% 2.85/1.97 % (5392)------------------------------
% 2.85/1.97 % (5394)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_5214 for (2996ds/62Mi)
% 2.85/1.98 % (5395)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_5214 for (2996ds/31Mi)
% 2.85/1.98 % (5383)Instruction limit reached!
% 2.85/1.98 % (5383)------------------------------
% 2.85/1.98 % (5383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.98 % (5383)Termination reason: Unknown
% 2.85/1.98 % (5383)Termination phase: Saturation
% 2.85/1.98
% 2.85/1.98 % (5383)Memory used [KB]: 8955
% 2.85/1.98 % (5383)Time elapsed: 0.128 s
% 2.85/1.98 % (5383)Instructions burned: 448 (million)
% 2.85/1.98 % (5383)------------------------------
% 2.85/1.98 % (5383)------------------------------
% 2.85/1.99 % (5395)Instruction limit reached!
% 2.85/1.99 % (5395)------------------------------
% 2.85/1.99 % (5395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.99 % (5395)Termination reason: Unknown
% 2.85/1.99 % (5395)Termination phase: shuffling
% 2.85/1.99
% 2.85/1.99 % (5395)Memory used [KB]: 2046
% 2.85/1.99 % (5395)Time elapsed: 0.011 s
% 2.85/1.99 % (5395)Instructions burned: 31 (million)
% 2.85/1.99 % (5395)------------------------------
% 2.85/1.99 % (5395)------------------------------
% 2.85/1.99 % (5394)Instruction limit reached!
% 2.85/1.99 % (5394)------------------------------
% 2.85/1.99 % (5394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.99 % (5394)Termination reason: Unknown
% 2.85/1.99 % (5394)Termination phase: Property scanning
% 2.85/1.99
% 2.85/1.99 % (5394)Memory used [KB]: 2686
% 2.85/1.99 % (5394)Time elapsed: 0.018 s
% 2.85/1.99 % (5394)Instructions burned: 62 (million)
% 2.85/1.99 % (5394)------------------------------
% 2.85/1.99 % (5394)------------------------------
% 2.85/1.99 % (5396)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_5214 for (2996ds/96Mi)
% 2.85/1.99 % (5372)Refutation not found, non-redundant clauses discarded% (5372)------------------------------
% 2.85/1.99 % (5372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.99 % (5372)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.85/1.99
% 2.85/1.99 % (5372)Memory used [KB]: 8315
% 2.85/1.99 % (5372)Time elapsed: 0.305 s
% 2.85/1.99 % (5372)Instructions burned: 853 (million)
% 2.85/1.99 % (5372)------------------------------
% 2.85/1.99 % (5372)------------------------------
% 2.85/2.00 % (5397)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_5214 for (2996ds/453Mi)
% 2.85/2.00 % (5398)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_5214 for (2996ds/71Mi)
% 2.85/2.00 % (5399)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_5214 for (2996ds/83Mi)
% 5.57/2.02 % (5396)Instruction limit reached!
% 5.57/2.02 % (5396)------------------------------
% 5.57/2.02 % (5396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.02 % (5396)Termination reason: Unknown
% 5.57/2.02 % (5396)Termination phase: Property scanning
% 5.57/2.02
% 5.57/2.02 % (5396)Memory used [KB]: 2814
% 5.57/2.02 % (5396)Time elapsed: 0.030 s
% 5.57/2.02 % (5396)Instructions burned: 97 (million)
% 5.57/2.02 % (5396)------------------------------
% 5.57/2.02 % (5396)------------------------------
% 5.57/2.02 % (5398)Instruction limit reached!
% 5.57/2.02 % (5398)------------------------------
% 5.57/2.02 % (5398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.02 % (5398)Termination reason: Unknown
% 5.57/2.02 % (5398)Termination phase: Preprocessing 3
% 5.57/2.02
% 5.57/2.02 % (5398)Memory used [KB]: 2430
% 5.57/2.02 % (5398)Time elapsed: 0.023 s
% 5.57/2.02 % (5398)Instructions burned: 71 (million)
% 5.57/2.02 % (5398)------------------------------
% 5.57/2.02 % (5398)------------------------------
% 5.57/2.03 % (5399)Instruction limit reached!
% 5.57/2.03 % (5399)------------------------------
% 5.57/2.03 % (5399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.03 % (5399)Termination reason: Unknown
% 5.57/2.03 % (5399)Termination phase: Property scanning
% 5.57/2.03
% 5.57/2.03 % (5399)Memory used [KB]: 2430
% 5.57/2.03 % (5399)Time elapsed: 0.028 s
% 5.57/2.03 % (5399)Instructions burned: 84 (million)
% 5.57/2.03 % (5399)------------------------------
% 5.57/2.03 % (5399)------------------------------
% 5.57/2.03 % (5400)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_5214 for (2996ds/11Mi)
% 5.57/2.03 % (5401)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_5214 for (2995ds/41Mi)
% 5.57/2.03 % (5400)Instruction limit reached!
% 5.57/2.03 % (5400)------------------------------
% 5.57/2.03 % (5400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.03 % (5400)Termination reason: Unknown
% 5.57/2.03 % (5400)Termination phase: shuffling
% 5.57/2.03
% 5.57/2.03 % (5400)Memory used [KB]: 1663
% 5.57/2.03 % (5400)Time elapsed: 0.005 s
% 5.57/2.03 % (5400)Instructions burned: 14 (million)
% 5.57/2.03 % (5400)------------------------------
% 5.57/2.03 % (5400)------------------------------
% 5.57/2.04 % (5402)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5214 for (2995ds/6Mi)
% 5.57/2.04 % (5402)Instruction limit reached!
% 5.57/2.04 % (5402)------------------------------
% 5.57/2.04 % (5402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.04 % (5402)Termination reason: Unknown
% 5.57/2.04 % (5402)Termination phase: shuffling
% 5.57/2.04
% 5.57/2.04 % (5402)Memory used [KB]: 1535
% 5.57/2.04 % (5402)Time elapsed: 0.003 s
% 5.57/2.04 % (5402)Instructions burned: 6 (million)
% 5.57/2.04 % (5402)------------------------------
% 5.57/2.04 % (5402)------------------------------
% 5.57/2.04 % (5403)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_5214 for (2995ds/150Mi)
% 5.57/2.04 % (5401)Instruction limit reached!
% 5.57/2.04 % (5401)------------------------------
% 5.57/2.04 % (5401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.04 % (5401)Termination reason: Unknown
% 5.57/2.04 % (5401)Termination phase: shuffling
% 5.57/2.04
% 5.57/2.04 % (5401)Memory used [KB]: 2302
% 5.57/2.04 % (5401)Time elapsed: 0.013 s
% 5.57/2.04 % (5401)Instructions burned: 44 (million)
% 5.57/2.04 % (5401)------------------------------
% 5.57/2.04 % (5401)------------------------------
% 5.57/2.05 % (5386)Instruction limit reached!
% 5.57/2.05 % (5386)------------------------------
% 5.57/2.05 % (5386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.05 % (5386)Termination reason: Unknown
% 5.57/2.05 % (5386)Termination phase: Saturation
% 5.57/2.05
% 5.57/2.05 % (5386)Memory used [KB]: 8955
% 5.57/2.05 % (5386)Time elapsed: 0.166 s
% 5.57/2.05 % (5386)Instructions burned: 508 (million)
% 5.57/2.05 % (5386)------------------------------
% 5.57/2.05 % (5386)------------------------------
% 5.57/2.05 % (5404)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_5214 for (2995ds/343Mi)
% 5.57/2.05 % (5405)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_5214 for (2995ds/109Mi)
% 5.57/2.06 % (5406)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_5214 for (2995ds/253Mi)
% 5.57/2.08 % (5393)Instruction limit reached!
% 5.57/2.08 % (5393)------------------------------
% 5.57/2.08 % (5393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.08 % (5393)Termination reason: Unknown
% 5.57/2.08 % (5393)Termination phase: Saturation
% 5.57/2.08
% 5.57/2.08 % (5393)Memory used [KB]: 4605
% 5.57/2.08 % (5393)Time elapsed: 0.125 s
% 5.57/2.08 % (5393)Instructions burned: 434 (million)
% 5.57/2.08 % (5393)------------------------------
% 5.57/2.08 % (5393)------------------------------
% 5.57/2.08 % (5405)Instruction limit reached!
% 5.57/2.08 % (5405)------------------------------
% 5.57/2.08 % (5405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.08 % (5405)Termination reason: Unknown
% 5.57/2.08 % (5405)Termination phase: Property scanning
% 5.57/2.08
% 5.57/2.08 % (5405)Memory used [KB]: 2686
% 5.57/2.08 % (5405)Time elapsed: 0.033 s
% 5.57/2.08 % (5405)Instructions burned: 110 (million)
% 5.57/2.08 % (5405)------------------------------
% 5.57/2.08 % (5405)------------------------------
% 5.57/2.09 % (5403)Instruction limit reached!
% 5.57/2.09 % (5403)------------------------------
% 5.57/2.09 % (5403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.09 % (5403)Termination reason: Unknown
% 5.57/2.09 % (5403)Termination phase: Property scanning
% 5.57/2.09
% 5.57/2.09 % (5403)Memory used [KB]: 2942
% 5.57/2.09 % (5403)Time elapsed: 0.044 s
% 5.57/2.09 % (5403)Instructions burned: 152 (million)
% 5.57/2.09 % (5403)------------------------------
% 5.57/2.09 % (5403)------------------------------
% 5.57/2.09 % (5407)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_5214 for (2995ds/140Mi)
% 5.57/2.09 % (5408)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_5214 for (2995ds/614Mi)
% 5.57/2.09 % (5409)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_5214 for (2995ds/202Mi)
% 6.08/2.12 % (5397)Instruction limit reached!
% 6.08/2.12 % (5397)------------------------------
% 6.08/2.12 % (5397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.12 % (5397)Termination reason: Unknown
% 6.08/2.12 % (5397)Termination phase: Saturation
% 6.08/2.12
% 6.08/2.12 % (5397)Memory used [KB]: 8571
% 6.08/2.12 % (5397)Time elapsed: 0.125 s
% 6.08/2.12 % (5397)Instructions burned: 455 (million)
% 6.08/2.12 % (5397)------------------------------
% 6.08/2.12 % (5397)------------------------------
% 6.08/2.13 % (5410)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_5214 for (2994ds/339Mi)
% 6.08/2.13 % (5406)Instruction limit reached!
% 6.08/2.13 % (5406)------------------------------
% 6.08/2.13 % (5406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.13 % (5406)Termination reason: Unknown
% 6.08/2.13 % (5406)Termination phase: Saturation
% 6.08/2.13
% 6.08/2.13 % (5406)Memory used [KB]: 7291
% 6.08/2.13 % (5406)Time elapsed: 0.075 s
% 6.08/2.13 % (5406)Instructions burned: 253 (million)
% 6.08/2.13 % (5406)------------------------------
% 6.08/2.13 % (5406)------------------------------
% 6.08/2.13 % (5407)Instruction limit reached!
% 6.08/2.13 % (5407)------------------------------
% 6.08/2.13 % (5407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.13 % (5407)Termination reason: Unknown
% 6.08/2.13 % (5407)Termination phase: Saturation
% 6.08/2.13
% 6.08/2.13 % (5407)Memory used [KB]: 7291
% 6.08/2.13 % (5407)Time elapsed: 0.044 s
% 6.08/2.13 % (5407)Instructions burned: 141 (million)
% 6.08/2.13 % (5407)------------------------------
% 6.08/2.13 % (5407)------------------------------
% 6.08/2.14 % (5411)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_5214 for (2994ds/283Mi)
% 6.08/2.14 % (5412)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_5214 for (2994ds/134Mi)
% 6.08/2.15 % (5404)Instruction limit reached!
% 6.08/2.15 % (5404)------------------------------
% 6.08/2.15 % (5404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.15 % (5404)Termination reason: Unknown
% 6.08/2.15 % (5404)Termination phase: Saturation
% 6.08/2.15
% 6.08/2.15 % (5404)Memory used [KB]: 7931
% 6.08/2.15 % (5404)Time elapsed: 0.104 s
% 6.08/2.15 % (5404)Instructions burned: 345 (million)
% 6.08/2.15 % (5404)------------------------------
% 6.08/2.15 % (5404)------------------------------
% 6.08/2.15 % (5409)Instruction limit reached!
% 6.08/2.15 % (5409)------------------------------
% 6.08/2.15 % (5409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.15 % (5409)Termination reason: Unknown
% 6.08/2.15 % (5409)Termination phase: Saturation
% 6.08/2.15
% 6.08/2.15 % (5409)Memory used [KB]: 7547
% 6.08/2.15 % (5409)Time elapsed: 0.060 s
% 6.08/2.15 % (5409)Instructions burned: 202 (million)
% 6.08/2.15 % (5409)------------------------------
% 6.08/2.15 % (5409)------------------------------
% 6.08/2.16 % (5413)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_5214 for (2994ds/298Mi)
% 6.08/2.16 % (5414)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_5214 for (2994ds/192Mi)
% 6.08/2.18 % (5412)Instruction limit reached!
% 6.08/2.18 % (5412)------------------------------
% 6.08/2.18 % (5412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.18 % (5412)Termination reason: Unknown
% 6.08/2.18 % (5412)Termination phase: Property scanning
% 6.08/2.18
% 6.08/2.18 % (5412)Memory used [KB]: 2814
% 6.08/2.18 % (5412)Time elapsed: 0.040 s
% 6.08/2.18 % (5412)Instructions burned: 136 (million)
% 6.08/2.18 % (5412)------------------------------
% 6.08/2.18 % (5412)------------------------------
% 6.08/2.19 % (5415)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_5214 for (2994ds/258Mi)
% 6.54/2.22 % (5411)Instruction limit reached!
% 6.54/2.22 % (5411)------------------------------
% 6.54/2.22 % (5411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.22 % (5411)Termination reason: Unknown
% 6.54/2.22 % (5411)Termination phase: Saturation
% 6.54/2.22
% 6.54/2.22 % (5411)Memory used [KB]: 7803
% 6.54/2.22 % (5411)Time elapsed: 0.081 s
% 6.54/2.22 % (5411)Instructions burned: 285 (million)
% 6.54/2.22 % (5411)------------------------------
% 6.54/2.22 % (5411)------------------------------
% 6.54/2.22 % (5414)Instruction limit reached!
% 6.54/2.22 % (5414)------------------------------
% 6.54/2.22 % (5414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.22 % (5414)Termination reason: Unknown
% 6.54/2.22 % (5414)Termination phase: Saturation
% 6.54/2.22
% 6.54/2.22 % (5414)Memory used [KB]: 3709
% 6.54/2.22 % (5414)Time elapsed: 0.057 s
% 6.54/2.22 % (5414)Instructions burned: 192 (million)
% 6.54/2.22 % (5414)------------------------------
% 6.54/2.22 % (5414)------------------------------
% 6.54/2.23 % (5410)Instruction limit reached!
% 6.54/2.23 % (5410)------------------------------
% 6.54/2.23 % (5410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.23 % (5410)Termination reason: Unknown
% 6.54/2.23 % (5410)Termination phase: Saturation
% 6.54/2.23
% 6.54/2.23 % (5410)Memory used [KB]: 7931
% 6.54/2.23 % (5410)Time elapsed: 0.098 s
% 6.54/2.23 % (5410)Instructions burned: 341 (million)
% 6.54/2.23 % (5410)------------------------------
% 6.54/2.23 % (5410)------------------------------
% 6.54/2.23 % (5416)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_5214 for (2993ds/90Mi)
% 6.54/2.23 % (5417)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_5214 for (2993ds/231Mi)
% 6.54/2.24 % (5418)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_5214 for (2993ds/458Mi)
% 6.54/2.24 % (5413)Instruction limit reached!
% 6.54/2.24 % (5413)------------------------------
% 6.54/2.24 % (5413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.24 % (5413)Termination reason: Unknown
% 6.54/2.24 % (5413)Termination phase: Saturation
% 6.54/2.24
% 6.54/2.24 % (5413)Memory used [KB]: 7803
% 6.54/2.24 % (5413)Time elapsed: 0.081 s
% 6.54/2.24 % (5413)Instructions burned: 300 (million)
% 6.54/2.24 % (5413)------------------------------
% 6.54/2.24 % (5413)------------------------------
% 6.54/2.25 % (5419)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_5214 for (2993ds/31Mi)
% 6.54/2.26 % (5416)Instruction limit reached!
% 6.54/2.26 % (5416)------------------------------
% 6.54/2.26 % (5416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.26 % (5416)Termination reason: Unknown
% 6.54/2.26 % (5416)Termination phase: Property scanning
% 6.54/2.26
% 6.54/2.26 % (5416)Memory used [KB]: 2814
% 6.54/2.26 % (5416)Time elapsed: 0.029 s
% 6.54/2.26 % (5416)Instructions burned: 93 (million)
% 6.54/2.26 % (5416)------------------------------
% 6.54/2.26 % (5416)------------------------------
% 6.54/2.26 % (5419)Instruction limit reached!
% 6.54/2.26 % (5419)------------------------------
% 6.54/2.26 % (5419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.26 % (5419)Termination reason: Unknown
% 6.54/2.26 % (5419)Termination phase: shuffling
% 6.54/2.26
% 6.54/2.26 % (5419)Memory used [KB]: 2046
% 6.54/2.26 % (5419)Time elapsed: 0.012 s
% 6.54/2.26 % (5419)Instructions burned: 33 (million)
% 6.54/2.26 % (5419)------------------------------
% 6.54/2.26 % (5419)------------------------------
% 6.54/2.27 % (5415)Instruction limit reached!
% 6.54/2.27 % (5415)------------------------------
% 6.54/2.27 % (5415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.27 % (5415)Termination reason: Unknown
% 6.54/2.27 % (5415)Termination phase: Saturation
% 6.54/2.27
% 6.54/2.27 % (5415)Memory used [KB]: 3454
% 6.54/2.27 % (5415)Time elapsed: 0.074 s
% 6.54/2.27 % (5415)Instructions burned: 259 (million)
% 6.54/2.27 % (5415)------------------------------
% 6.54/2.27 % (5415)------------------------------
% 6.54/2.27 % (5420)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_5214 for (2993ds/297Mi)
% 6.54/2.27 % (5421)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_5214 for (2993ds/987Mi)
% 6.54/2.28 % (5422)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_5214 for (2993ds/182Mi)
% 6.54/2.28 % (5408)Instruction limit reached!
% 6.54/2.28 % (5408)------------------------------
% 6.54/2.28 % (5408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.28 % (5408)Termination reason: Unknown
% 6.54/2.28 % (5408)Termination phase: Saturation
% 6.54/2.28
% 6.54/2.28 % (5408)Memory used [KB]: 8827
% 6.54/2.28 % (5408)Time elapsed: 0.183 s
% 6.54/2.28 % (5408)Instructions burned: 615 (million)
% 6.54/2.28 % (5408)------------------------------
% 6.54/2.28 % (5408)------------------------------
% 6.54/2.29 % (5423)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_5214 for (2993ds/182Mi)
% 6.54/2.29 % (5417)Instruction limit reached!
% 6.54/2.29 % (5417)------------------------------
% 6.54/2.29 % (5417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.29 % (5417)Termination reason: Unknown
% 6.54/2.29 % (5417)Termination phase: Saturation
% 6.54/2.29
% 6.54/2.29 % (5417)Memory used [KB]: 7419
% 6.54/2.29 % (5417)Time elapsed: 0.062 s
% 6.54/2.29 % (5417)Instructions burned: 234 (million)
% 6.54/2.29 % (5417)------------------------------
% 6.54/2.29 % (5417)------------------------------
% 6.54/2.29 % (5390)Instruction limit reached!
% 6.54/2.29 % (5390)------------------------------
% 6.54/2.29 % (5390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.29 % (5390)Termination reason: Unknown
% 6.54/2.29 % (5390)Termination phase: Saturation
% 6.54/2.29
% 6.54/2.29 % (5390)Memory used [KB]: 8699
% 6.54/2.29 % (5390)Time elapsed: 0.350 s
% 6.54/2.29 % (5390)Instructions burned: 1088 (million)
% 6.54/2.29 % (5390)------------------------------
% 6.54/2.29 % (5390)------------------------------
% 7.41/2.30 % (5424)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_5214 for (2993ds/154Mi)
% 7.41/2.30 % (5425)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_5214 for (2993ds/79Mi)
% 7.41/2.33 % (5422)Instruction limit reached!
% 7.41/2.33 % (5422)------------------------------
% 7.41/2.33 % (5422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.33 % (5422)Termination reason: Unknown
% 7.41/2.33 % (5422)Termination phase: Property scanning
% 7.41/2.33
% 7.41/2.33 % (5422)Memory used [KB]: 2814
% 7.41/2.33 % (5422)Time elapsed: 0.051 s
% 7.41/2.33 % (5422)Instructions burned: 185 (million)
% 7.41/2.33 % (5422)------------------------------
% 7.41/2.33 % (5422)------------------------------
% 7.41/2.33 % (5425)Instruction limit reached!
% 7.41/2.33 % (5425)------------------------------
% 7.41/2.33 % (5425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.33 % (5425)Termination reason: Unknown
% 7.41/2.33 % (5425)Termination phase: Preprocessing 3
% 7.41/2.33
% 7.41/2.33 % (5425)Memory used [KB]: 2686
% 7.41/2.33 % (5425)Time elapsed: 0.026 s
% 7.41/2.33 % (5425)Instructions burned: 79 (million)
% 7.41/2.33 % (5425)------------------------------
% 7.41/2.33 % (5425)------------------------------
% 7.41/2.33 % (5426)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_5214 for (2992ds/216Mi)
% 7.41/2.34 % (5427)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_5214 for (2992ds/114Mi)
% 7.41/2.34 % (5423)Instruction limit reached!
% 7.41/2.34 % (5423)------------------------------
% 7.41/2.34 % (5423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.34 % (5423)Termination reason: Unknown
% 7.41/2.34 % (5423)Termination phase: Saturation
% 7.41/2.34
% 7.41/2.34 % (5423)Memory used [KB]: 7547
% 7.41/2.34 % (5423)Time elapsed: 0.054 s
% 7.41/2.34 % (5423)Instructions burned: 183 (million)
% 7.41/2.34 % (5423)------------------------------
% 7.41/2.34 % (5423)------------------------------
% 7.41/2.34 % (5424)Instruction limit reached!
% 7.41/2.34 % (5424)------------------------------
% 7.41/2.34 % (5424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.34 % (5424)Termination reason: Unknown
% 7.41/2.34 % (5424)Termination phase: Function definition elimination
% 7.41/2.34
% 7.41/2.34 % (5424)Memory used [KB]: 2814
% 7.41/2.34 % (5424)Time elapsed: 0.043 s
% 7.41/2.34 % (5424)Instructions burned: 157 (million)
% 7.41/2.34 % (5424)------------------------------
% 7.41/2.34 % (5424)------------------------------
% 7.41/2.35 % (5428)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_5214 for (2992ds/922Mi)
% 7.41/2.35 % (5420)Instruction limit reached!
% 7.41/2.35 % (5420)------------------------------
% 7.41/2.35 % (5420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.35 % (5420)Termination reason: Unknown
% 7.41/2.35 % (5420)Termination phase: Saturation
% 7.41/2.35
% 7.41/2.35 % (5420)Memory used [KB]: 7803
% 7.41/2.35 % (5420)Time elapsed: 0.084 s
% 7.41/2.35 % (5420)Instructions burned: 297 (million)
% 7.41/2.35 % (5420)------------------------------
% 7.41/2.35 % (5420)------------------------------
% 7.41/2.35 % (5429)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_5214 for (2992ds/182Mi)
% 7.41/2.36 % (5430)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_5214 for (2992ds/164Mi)
% 7.41/2.37 % (5427)Instruction limit reached!
% 7.41/2.37 % (5427)------------------------------
% 7.41/2.37 % (5427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.37 % (5427)Termination reason: Unknown
% 7.41/2.37 % (5427)Termination phase: Property scanning
% 7.41/2.37
% 7.41/2.37 % (5427)Memory used [KB]: 2814
% 7.41/2.37 % (5427)Time elapsed: 0.035 s
% 7.41/2.37 % (5427)Instructions burned: 116 (million)
% 7.41/2.37 % (5427)------------------------------
% 7.41/2.37 % (5427)------------------------------
% 7.41/2.37 % (5418)Instruction limit reached!
% 7.41/2.37 % (5418)------------------------------
% 7.41/2.37 % (5418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.37 % (5418)Termination reason: Unknown
% 7.41/2.37 % (5418)Termination phase: Saturation
% 7.41/2.37
% 7.41/2.37 % (5418)Memory used [KB]: 8699
% 7.41/2.37 % (5418)Time elapsed: 0.138 s
% 7.41/2.37 % (5418)Instructions burned: 459 (million)
% 7.41/2.37 % (5418)------------------------------
% 7.41/2.37 % (5418)------------------------------
% 7.41/2.38 % (5431)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_5214 for (2992ds/50Mi)
% 7.41/2.38 % (5432)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_5214 for (2992ds/368Mi)
% 7.41/2.39 % (5431)Instruction limit reached!
% 7.41/2.39 % (5431)------------------------------
% 7.41/2.39 % (5431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.39 % (5431)Termination reason: Unknown
% 7.41/2.39 % (5431)Termination phase: shuffling
% 7.41/2.39
% 7.41/2.39 % (5431)Memory used [KB]: 2302
% 7.41/2.39 % (5426)Instruction limit reached!
% 7.41/2.39 % (5426)------------------------------
% 7.41/2.39 % (5426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.39 % (5431)Time elapsed: 0.015 s
% 7.41/2.39 % (5431)Instructions burned: 50 (million)
% 7.41/2.39 % (5431)------------------------------
% 7.41/2.39 % (5431)------------------------------
% 7.41/2.39 % (5426)Termination reason: Unknown
% 7.41/2.39 % (5426)Termination phase: Saturation
% 7.41/2.39
% 7.41/2.39 % (5426)Memory used [KB]: 7675
% 7.41/2.39 % (5426)Time elapsed: 0.060 s
% 7.41/2.39 % (5426)Instructions burned: 217 (million)
% 7.41/2.39 % (5426)------------------------------
% 7.41/2.39 % (5426)------------------------------
% 7.99/2.40 % (5429)Instruction limit reached!
% 7.99/2.40 % (5429)------------------------------
% 7.99/2.40 % (5429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.99/2.40 % (5429)Termination reason: Unknown
% 7.99/2.40 % (5429)Termination phase: Property scanning
% 7.99/2.40
% 7.99/2.40 % (5429)Memory used [KB]: 2814
% 7.99/2.40 % (5429)Time elapsed: 0.049 s
% 7.99/2.40 % (5429)Instructions burned: 182 (million)
% 7.99/2.40 % (5429)------------------------------
% 7.99/2.40 % (5429)------------------------------
% 7.99/2.40 % (5433)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_5214 for (2992ds/1021Mi)
% 7.99/2.40 % (5434)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_5214 for (2992ds/267Mi)
% 7.99/2.40 % (5430)Instruction limit reached!
% 7.99/2.40 % (5430)------------------------------
% 7.99/2.40 % (5430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.99/2.40 % (5430)Termination reason: Unknown
% 7.99/2.40 % (5430)Termination phase: Saturation
% 7.99/2.40
% 7.99/2.40 % (5430)Memory used [KB]: 2814
% 7.99/2.40 % (5430)Time elapsed: 0.046 s
% 7.99/2.40 % (5430)Instructions burned: 166 (million)
% 7.99/2.40 % (5430)------------------------------
% 7.99/2.40 % (5430)------------------------------
% 7.99/2.41 % (5435)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_5214 for (2992ds/204Mi)
% 7.99/2.41 % (5436)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_5214 for (2992ds/26Mi)
% 7.99/2.42 % (5436)Instruction limit reached!
% 7.99/2.42 % (5436)------------------------------
% 7.99/2.42 % (5436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.99/2.42 % (5436)Termination reason: Unknown
% 7.99/2.42 % (5436)Termination phase: shuffling
% 7.99/2.42
% 7.99/2.42 % (5436)Memory used [KB]: 2046
% 7.99/2.42 % (5436)Time elapsed: 0.009 s
% 7.99/2.42 % (5436)Instructions burned: 28 (million)
% 7.99/2.42 % (5436)------------------------------
% 7.99/2.42 % (5436)------------------------------
% 7.99/2.43 % (5437)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_5214 for (2992ds/53Mi)
% 7.99/2.45 % (5437)Instruction limit reached!
% 7.99/2.45 % (5437)------------------------------
% 7.99/2.45 % (5437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.99/2.45 % (5437)Termination reason: Unknown
% 7.99/2.45 % (5437)Termination phase: shuffling
% 7.99/2.45
% 7.99/2.45 % (5437)Memory used [KB]: 2430
% 7.99/2.45 % (5437)Time elapsed: 0.016 s
% 7.99/2.45 % (5437)Instructions burned: 53 (million)
% 7.99/2.45 % (5437)------------------------------
% 7.99/2.45 % (5437)------------------------------
% 7.99/2.46 % (5438)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_5214 for (2991ds/4436Mi)
% 7.99/2.47 % (5435)Instruction limit reached!
% 7.99/2.47 % (5435)------------------------------
% 7.99/2.47 % (5435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.99/2.47 % (5435)Termination reason: Unknown
% 7.99/2.47 % (5435)Termination phase: Saturation
% 7.99/2.47
% 7.99/2.47 % (5435)Memory used [KB]: 7547
% 7.99/2.47 % (5435)Time elapsed: 0.060 s
% 7.99/2.47 % (5435)Instructions burned: 205 (million)
% 7.99/2.47 % (5435)------------------------------
% 7.99/2.47 % (5435)------------------------------
% 7.99/2.48 % (5439)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_5214 for (2991ds/1539Mi)
% 7.99/2.48 % (5434)Instruction limit reached!
% 7.99/2.48 % (5434)------------------------------
% 7.99/2.48 % (5434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.99/2.48 % (5434)Termination reason: Unknown
% 7.99/2.48 % (5434)Termination phase: Saturation
% 7.99/2.48
% 7.99/2.48 % (5434)Memory used [KB]: 7675
% 7.99/2.48 % (5434)Time elapsed: 0.075 s
% 7.99/2.48 % (5434)Instructions burned: 267 (million)
% 7.99/2.48 % (5434)------------------------------
% 7.99/2.48 % (5434)------------------------------
% 7.99/2.49 % (5440)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_5214 for (2991ds/408Mi)
% 7.99/2.49 % (5432)Instruction limit reached!
% 7.99/2.49 % (5432)------------------------------
% 7.99/2.49 % (5432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.99/2.49 % (5432)Termination reason: Unknown
% 7.99/2.49 % (5432)Termination phase: Saturation
% 7.99/2.49
% 7.99/2.49 % (5432)Memory used [KB]: 8315
% 7.99/2.49 % (5432)Time elapsed: 0.113 s
% 7.99/2.49 % (5432)Instructions burned: 369 (million)
% 7.99/2.49 % (5432)------------------------------
% 7.99/2.49 % (5432)------------------------------
% 8.42/2.50 % (5441)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_5214 for (2991ds/5205Mi)
% 8.42/2.56 % (5421)Instruction limit reached!
% 8.42/2.56 % (5421)------------------------------
% 8.42/2.56 % (5421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.56 % (5421)Termination reason: Unknown
% 8.42/2.56 % (5421)Termination phase: Saturation
% 8.42/2.56
% 8.42/2.56 % (5421)Memory used [KB]: 9978
% 8.42/2.56 % (5421)Time elapsed: 0.294 s
% 8.42/2.56 % (5421)Instructions burned: 989 (million)
% 8.42/2.56 % (5421)------------------------------
% 8.42/2.56 % (5421)------------------------------
% 8.42/2.57 % (5428)First to succeed.
% 8.42/2.57 % (5442)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_5214 for (2990ds/1913Mi)
% 8.42/2.58 % (5428)Refutation found. Thanks to Tanya!
% 8.42/2.58 % SZS status Theorem for DTF2THF_5214
% 8.42/2.58 % SZS output start Proof for DTF2THF_5214
% 8.42/2.58 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 8.42/2.58 thf(type_def_6, type, set: ($tType) > $tType).
% 8.42/2.58 thf(type_def_8, type, tree: ($tType) > $tType).
% 8.42/2.58 thf(type_def_9, type, list: ($tType) > $tType).
% 8.42/2.58 thf(type_def_10, type, multiset: ($tType) > $tType).
% 8.42/2.58 thf(type_def_11, type, a: $tType).
% 8.42/2.58 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 8.42/2.58 thf(func_def_1, type, multiset: ($tType) > $tType).
% 8.42/2.58 thf(func_def_2, type, list: ($tType) > $tType).
% 8.42/2.58 thf(func_def_3, type, tree: ($tType) > $tType).
% 8.42/2.58 thf(func_def_4, type, set: ($tType) > $tType).
% 8.42/2.58 thf(func_def_5, type, a: $tType).
% 8.42/2.58 thf(func_def_6, type, type: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_7, type, ord: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_8, type, order: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_11, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_12, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_13, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_14, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_15, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_16, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_17, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_18, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_19, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 8.42/2.58 thf(func_def_20, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > (X0 > X1) > $o)).
% 8.42/2.58 thf(func_def_21, type, unique455577585es_aux: !>[X0: $tType]:(product_prod @ X0 @ X0 > $o)).
% 8.42/2.58 thf(func_def_22, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 8.42/2.58 thf(func_def_23, type, zero_zero: !>[X0: $tType]:(X0)).
% 8.42/2.58 thf(func_def_24, type, nO_MATCH: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 8.42/2.58 thf(func_def_25, type, heapIm1271749598e_left: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_26, type, heapIm1434396069_right: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_27, type, heapIm748920189ftDown: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_28, type, heap: !>[X0: $tType, X1: $tType]:(X0 > (X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > tree @ X1) > (X0 > product_prod @ X1 @ X0) > $o)).
% 8.42/2.58 thf(func_def_29, type, heap_axioms: !>[X0: $tType, X1: $tType]:((X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > tree @ X1) > (X0 > product_prod @ X1 @ X0) > $o)).
% 8.42/2.58 thf(func_def_30, type, e: !>[X0: $tType]:(tree @ X0)).
% 8.42/2.58 thf(func_def_31, type, t: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_32, type, case_Tree: !>[X0: $tType, X1: $tType]:(X0 > (X1 > tree @ X1 > tree @ X1 > X0) > tree @ X1 > X0)).
% 8.42/2.58 thf(func_def_33, type, rec_Tree: !>[X0: $tType, X1: $tType]:(X0 > (X1 > tree @ X1 > tree @ X1 > X0 > X0 > X0) > tree @ X1 > X0)).
% 8.42/2.58 thf(func_def_34, type, rel_Tree: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > tree @ X0 > tree @ X1 > $o)).
% 8.42/2.58 thf(func_def_35, type, in_tree: !>[X0: $tType]:(X0 > tree @ X0 > $o)).
% 8.42/2.58 thf(func_def_36, type, is_heap: !>[X0: $tType]:(tree @ X0 > $o)).
% 8.42/2.58 thf(func_def_37, type, multiset2: !>[X0: $tType]:(tree @ X0 > multiset @ X0)).
% 8.42/2.58 thf(func_def_38, type, val: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_39, type, lattic929149872er_Max: !>[X0: $tType]:(set @ X0 > X0)).
% 8.42/2.58 thf(func_def_40, type, add_mset: !>[X0: $tType]:(X0 > multiset @ X0 > multiset @ X0)).
% 8.42/2.58 thf(func_def_41, type, comm_monoid_sum_mset: !>[X0: $tType]:((X0 > X0 > X0) > X0 > multiset @ X0 > X0)).
% 8.42/2.58 thf(func_def_42, type, fold_mset: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > X1 > multiset @ X0 > X1)).
% 8.42/2.58 thf(func_def_43, type, image_mset: !>[X0: $tType, X1: $tType]:((X0 > X1) > multiset @ X0 > multiset @ X1)).
% 8.42/2.58 thf(func_def_44, type, mult: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0)).
% 8.42/2.58 thf(func_def_45, type, mult1: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0)).
% 8.42/2.58 thf(func_def_46, type, multp: !>[X0: $tType]:((X0 > X0 > $o) > multiset @ X0 > multiset @ X0 > $o)).
% 8.42/2.58 thf(func_def_47, type, set_mset: !>[X0: $tType]:(multiset @ X0 > set @ X0)).
% 8.42/2.58 thf(func_def_48, type, subseteq_mset: !>[X0: $tType]:(multiset @ X0 > multiset @ X0 > $o)).
% 8.42/2.58 thf(func_def_49, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 8.42/2.58 thf(func_def_50, type, antimono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 8.42/2.58 thf(func_def_51, type, order_Greatest: !>[X0: $tType]:((X0 > $o) > X0)).
% 8.42/2.58 thf(func_def_52, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 8.42/2.58 thf(func_def_53, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 8.42/2.58 thf(func_def_54, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 8.42/2.58 thf(func_def_55, type, irrefl: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 8.42/2.58 thf(func_def_56, type, trans: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 8.42/2.58 thf(func_def_57, type, collection: !>[X0: $tType, X1: $tType]:(X0 > (X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > $o)).
% 8.42/2.58 thf(func_def_58, type, set2: !>[X0: $tType, X1: $tType]:((X0 > multiset @ X1) > X0 > set @ X1)).
% 8.42/2.58 thf(func_def_59, type, removeMax: !>[X0: $tType, X1: $tType]:(X0 > (X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > product_prod @ X1 @ X0) > (X0 > $o) > $o)).
% 8.42/2.58 thf(func_def_60, type, removeMax_axioms: !>[X0: $tType, X1: $tType]:((X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > product_prod @ X1 @ X0) > (X0 > $o) > $o)).
% 8.42/2.58 thf(func_def_61, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 8.42/2.58 thf(func_def_62, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 8.42/2.58 thf(func_def_63, type, l: tree @ a).
% 8.42/2.58 thf(func_def_64, type, l1: tree @ a).
% 8.42/2.58 thf(func_def_65, type, la: tree @ a).
% 8.42/2.58 thf(func_def_66, type, r: tree @ a).
% 8.42/2.58 thf(func_def_67, type, r1: tree @ a).
% 8.42/2.58 thf(func_def_68, type, ra: tree @ a).
% 8.42/2.58 thf(func_def_69, type, t2: tree @ a).
% 8.42/2.58 thf(func_def_70, type, v: a).
% 8.42/2.58 thf(func_def_71, type, v1: a).
% 8.42/2.58 thf(func_def_72, type, v2: a).
% 8.42/2.58 thf(func_def_73, type, va: a).
% 8.42/2.58 thf(func_def_91, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 8.42/2.58 thf(func_def_92, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 8.42/2.58 thf(func_def_93, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 8.42/2.58 thf(func_def_94, type, sK3: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X1)).
% 8.42/2.58 thf(func_def_95, type, sK4: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X0)).
% 8.42/2.58 thf(func_def_96, type, sK5: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 8.42/2.58 thf(func_def_97, type, sK6: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 8.42/2.58 thf(func_def_98, type, sK7: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 8.42/2.58 thf(func_def_99, type, sK8: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_100, type, sK9: !>[X0: $tType]:(X0 > tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_101, type, sK10: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_102, type, sK11: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 8.42/2.58 thf(func_def_103, type, sK12: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 8.42/2.58 thf(func_def_104, type, sK13: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 8.42/2.58 thf(func_def_105, type, sK14: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 8.42/2.58 thf(func_def_106, type, sK15: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 8.42/2.58 thf(func_def_107, type, sK16: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_108, type, sK17: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_109, type, sK18: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_110, type, sK19: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_111, type, sK20: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_112, type, sK21: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_113, type, sK22: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_114, type, sK23: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_115, type, sK24: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_116, type, sK25: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_117, type, sK26: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_118, type, sK27: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_119, type, sK28: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_120, type, sK29: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_121, type, sK30: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_122, type, sK31: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_123, type, sK32: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_124, type, sK33: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_125, type, sK34: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_126, type, sK35: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_127, type, sK36: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_128, type, sK37: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_129, type, sK38: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_130, type, sK39: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_131, type, sK40: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_132, type, sK41: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_133, type, sK42: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_134, type, sK43: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_135, type, sK44: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_136, type, sK45: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_137, type, sK46: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_138, type, sK47: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_139, type, sK48: !>[X0: $tType]:(tree @ X0 > X0)).
% 8.42/2.58 thf(func_def_140, type, sK49: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_141, type, sK50: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 8.42/2.58 thf(func_def_143, type, ph52: !>[X0: $tType]:(X0)).
% 8.42/2.58 thf(f3043,plain,(
% 8.42/2.58 $false),
% 8.42/2.58 inference(avatar_sat_refutation,[status(thm)],[f946,f951,f961,f966,f971,f1818,f2968,f3039])).
% 8.42/2.58 thf(f3039,plain,(
% 8.42/2.58 ~spl51_73 | ~spl51_2 | ~spl51_4 | ~spl51_5 | spl51_6),
% 8.42/2.58 inference(avatar_split_clause,[status(thm)],[f3038,f968,f963,f958,f948,f2148])).
% 8.42/2.58 thf(f2148,definition,(
% 8.42/2.58 spl51_73 <=> ($true = (is_heap @ a @ (t @ a @ va @ la @ ra)))),
% 8.42/2.58 introduced(definition,[new_symbols(naming,[spl51_73])],[avatar_definition])).
% 8.42/2.58 thf(f948,definition,(
% 8.42/2.58 spl51_2 <=> (linorder @ a = $true)),
% 8.42/2.58 introduced(definition,[new_symbols(naming,[spl51_2])],[avatar_definition])).
% 8.42/2.58 thf(f958,definition,(
% 8.42/2.58 spl51_4 <=> ((t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1)) = (t @ a @ va @ la @ ra))),
% 8.42/2.58 introduced(definition,[new_symbols(naming,[spl51_4])],[avatar_definition])).
% 8.42/2.58 thf(f963,definition,(
% 8.42/2.58 spl51_5 <=> ((ord_less_eq @ a @ v1 @ v2) = $true)),
% 8.42/2.58 introduced(definition,[new_symbols(naming,[spl51_5])],[avatar_definition])).
% 8.42/2.58 thf(f968,definition,(
% 8.42/2.58 spl51_6 <=> ((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1)))) = $true)),
% 8.42/2.58 introduced(definition,[new_symbols(naming,[spl51_6])],[avatar_definition])).
% 8.42/2.58 thf(f3038,plain,(
% 8.42/2.58 ($true != (is_heap @ a @ (t @ a @ va @ la @ ra))) | (~spl51_2 | ~spl51_4 | ~spl51_5 | spl51_6)),
% 8.42/2.58 inference(forward_demodulation,[status(thm)],[f3037,f960])).
% 8.42/2.58 thf(f960,plain,(
% 8.42/2.58 ((t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1)) = (t @ a @ va @ la @ ra)) | ~spl51_4),
% 8.42/2.58 inference(avatar_component_clause,[status(thm)],[f958])).
% 8.42/2.58 thf(f3037,plain,(
% 8.42/2.58 ((is_heap @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1))) != $true) | (~spl51_2 | ~spl51_5 | spl51_6)),
% 8.42/2.58 inference(subsumption_resolution,[status(thm)],[f3036,f965])).
% 8.42/2.58 thf(f965,plain,(
% 8.42/2.58 ((ord_less_eq @ a @ v1 @ v2) = $true) | ~spl51_5),
% 8.42/2.58 inference(avatar_component_clause,[status(thm)],[f963])).
% 8.42/2.58 thf(f3036,plain,(
% 8.42/2.58 ((is_heap @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1))) != $true) | ((ord_less_eq @ a @ v1 @ v2) != $true) | (~spl51_2 | spl51_6)),
% 8.42/2.58 inference(subsumption_resolution,[status(thm)],[f3026,f950])).
% 8.42/2.58 thf(f950,plain,(
% 8.42/2.58 (linorder @ a = $true) | ~spl51_2),
% 8.42/2.58 inference(avatar_component_clause,[status(thm)],[f948])).
% 8.42/2.58 thf(f3026,plain,(
% 8.42/2.58 (linorder @ a != $true) | ((ord_less_eq @ a @ v1 @ v2) != $true) | ((is_heap @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1))) != $true) | spl51_6),
% 8.42/2.58 inference(superposition,[status(thm)],[f970,f3020])).
% 8.42/2.58 thf(f3020,plain,(
% 8.42/2.58 ( ! [X0 : $tType,X2 : tree @ X0,X3 : tree @ X0,X1 : X0,X4 : X0] : (((t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)))) | (linorder @ X0 != $true) | ((ord_less_eq @ X0 @ X1 @ X4) != $true)) )),
% 8.42/2.58 inference(forward_demodulation,[status(thm)],[f858,f860])).
% 8.42/2.58 thf(f860,plain,(
% 8.42/2.58 ( ! [X0 : $tType,X2 : tree @ X0,X3 : tree @ X0,X1 : X0] : (((val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = X1)) )),
% 8.42/2.58 inference(cnf_transformation,[status(thm)],[f766])).
% 8.42/2.58 thf(f766,plain,(
% 8.42/2.58 ! [X0 : $tType,X1 : X0,X2 : tree @ X0,X3 : tree @ X0] : ((val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = X1)),
% 8.42/2.58 inference(rectify,[status(thm)],[f23])).
% 8.42/2.58 thf(f23,axiom,(
% 8.42/2.58 ! [X0 : $tType,X4 : X0,X36 : tree @ X0,X37 : tree @ X0] : ((val @ X0 @ (t @ X0 @ X4 @ X36 @ X37)) = X4)),
% 8.42/2.58 file('/export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2THF_5214.p',fact_22_val_Osimps)).
% 8.42/2.58 thf(f858,plain,(
% 8.42/2.58 ( ! [X0 : $tType,X2 : tree @ X0,X3 : tree @ X0,X1 : X0,X4 : X0] : (((t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)))) | (linorder @ X0 != $true) | ((ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ X4) != $true)) )),
% 8.42/2.58 inference(cnf_transformation,[status(thm)],[f778])).
% 8.42/2.58 thf(f778,plain,(
% 8.42/2.58 ! [X0 : $tType] : (! [X1 : X0,X2 : tree @ X0,X3 : tree @ X0,X4 : X0] : ((((t @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ e @ X0 @ (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ (heapIm1271749598e_left @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ (heapIm1434396069_right @ X0 @ (t @ X0 @ X1 @ X2 @ X3))))) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)))) | ((ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ X4) = $true)) & (((ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ X4) != $true) | ((t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)))))) | (linorder @ X0 != $true))),
% 8.42/2.58 inference(ennf_transformation,[status(thm)],[f761])).
% 8.42/2.58 thf(f761,plain,(
% 8.42/2.58 ! [X0 : $tType] : ((linorder @ X0 = $true) => ! [X1 : X0,X2 : tree @ X0,X3 : tree @ X0,X4 : X0] : ((((ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ X4) = $true) => ((t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3))))) & (((ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ X4) != $true) => ((t @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ e @ X0 @ (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ (heapIm1271749598e_left @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ (heapIm1434396069_right @ X0 @ (t @ X0 @ X1 @ X2 @ X3))))) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)))))))),
% 8.42/2.58 inference(flattening,[status(thm)],[f691])).
% 8.42/2.58 thf(f691,plain,(
% 8.42/2.58 ! [X0 : $tType] : ((linorder @ X0 = $true) => ! [X1 : X0,X2 : tree @ X0,X3 : tree @ X0,X4 : X0] : ((((ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ X4) = $true) => ((t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3))))) & (~((ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ X4) = $true) => ((t @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ e @ X0 @ (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ (heapIm1271749598e_left @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ (heapIm1434396069_right @ X0 @ (t @ X0 @ X1 @ X2 @ X3))))) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)))))))),
% 8.42/2.58 inference(fool_elimination,[status(thm)],[f690])).
% 8.42/2.58 thf(f690,plain,(
% 8.42/2.58 ! [X0 : $tType] : (linorder @ X0 => ! [X1 : X0,X2 : tree @ X0,X3 : tree @ X0,X4 : X0] : (((ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ X4) => ((t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3))))) & (~(ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ X4) => ((t @ X0 @ (val @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ e @ X0 @ (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ (heapIm1271749598e_left @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) @ (heapIm1434396069_right @ X0 @ (t @ X0 @ X1 @ X2 @ X3))))) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X1 @ X2 @ X3)))))))),
% 8.42/2.58 inference(rectify,[status(thm)],[f31])).
% 8.42/2.58 thf(f31,axiom,(
% 8.42/2.58 ! [X0 : $tType] : (linorder @ X0 => ! [X42 : X0,X43 : tree @ X0,X44 : tree @ X0,X4 : X0] : (((ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X42 @ X43 @ X44)) @ X4) => ((t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X42 @ X43 @ X44)) = (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X42 @ X43 @ X44))))) & (~(ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X42 @ X43 @ X44)) @ X4) => ((heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X42 @ X43 @ X44))) = (t @ X0 @ (val @ X0 @ (t @ X0 @ X42 @ X43 @ X44)) @ e @ X0 @ (heapIm748920189ftDown @ X0 @ (t @ X0 @ X4 @ (heapIm1271749598e_left @ X0 @ (t @ X0 @ X42 @ X43 @ X44)) @ (heapIm1434396069_right @ X0 @ (t @ X0 @ X42 @ X43 @ X44)))))))))),
% 8.42/2.58 file('/export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2THF_5214.p',fact_30_siftDown_Osimps_I4_J)).
% 8.42/2.58 thf(f970,plain,(
% 8.42/2.58 ((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1)))) != $true) | spl51_6),
% 8.42/2.58 inference(avatar_component_clause,[status(thm)],[f968])).
% 8.42/2.58 thf(f2968,plain,(
% 8.42/2.58 spl51_73 | ~spl51_1 | ~spl51_2 | ~spl51_4 | ~spl51_5 | ~spl51_50),
% 8.42/2.58 inference(avatar_split_clause,[status(thm)],[f2967,f1815,f963,f958,f948,f943,f2148])).
% 8.42/2.58 thf(f943,definition,(
% 8.42/2.58 spl51_1 <=> ((is_heap @ a @ ra) = $true)),
% 8.42/2.58 introduced(definition,[new_symbols(naming,[spl51_1])],[avatar_definition])).
% 8.42/2.58 thf(f1815,definition,(
% 8.42/2.58 spl51_50 <=> (ra = (t @ a @ v1 @ l1 @ r1))),
% 8.42/2.58 introduced(definition,[new_symbols(naming,[spl51_50])],[avatar_definition])).
% 8.42/2.58 thf(f2967,plain,(
% 8.42/2.58 ($true = (is_heap @ a @ (t @ a @ va @ la @ ra))) | (~spl51_1 | ~spl51_2 | ~spl51_4 | ~spl51_5 | ~spl51_50)),
% 8.42/2.58 inference(subsumption_resolution,[status(thm)],[f2966,f945])).
% 8.42/2.58 thf(f945,plain,(
% 8.42/2.58 ((is_heap @ a @ ra) = $true) | ~spl51_1),
% 8.42/2.58 inference(avatar_component_clause,[status(thm)],[f943])).
% 8.42/2.58 thf(f2966,plain,(
% 8.42/2.58 ($true = (is_heap @ a @ (t @ a @ va @ la @ ra))) | ((is_heap @ a @ ra) != $true) | (~spl51_2 | ~spl51_4 | ~spl51_5 | ~spl51_50)),
% 8.42/2.58 inference(forward_demodulation,[status(thm)],[f2965,f1817])).
% 8.42/2.58 thf(f1817,plain,(
% 8.42/2.58 (ra = (t @ a @ v1 @ l1 @ r1)) | ~spl51_50),
% 8.42/2.58 inference(avatar_component_clause,[status(thm)],[f1815])).
% 8.42/2.58 thf(f2965,plain,(
% 8.42/2.58 ($true = (is_heap @ a @ (t @ a @ va @ la @ ra))) | ($true != (is_heap @ a @ (t @ a @ v1 @ l1 @ r1))) | (~spl51_2 | ~spl51_4 | ~spl51_5)),
% 8.42/2.58 inference(subsumption_resolution,[status(thm)],[f2964,f950])).
% 8.42/2.58 thf(f2964,plain,(
% 8.42/2.58 (linorder @ a != $true) | ($true = (is_heap @ a @ (t @ a @ va @ la @ ra))) | ($true != (is_heap @ a @ (t @ a @ v1 @ l1 @ r1))) | (~spl51_4 | ~spl51_5)),
% 8.42/2.58 inference(subsumption_resolution,[status(thm)],[f2956,f965])).
% 8.42/2.58 thf(f2956,plain,(
% 8.42/2.58 ($true != (is_heap @ a @ (t @ a @ v1 @ l1 @ r1))) | ((ord_less_eq @ a @ v1 @ v2) != $true) | ($true = (is_heap @ a @ (t @ a @ va @ la @ ra))) | (linorder @ a != $true) | ~spl51_4),
% 8.42/2.58 inference(superposition,[status(thm)],[f2951,f960])).
% 8.42/2.58 thf(f2951,plain,(
% 8.42/2.58 ( ! [X0 : $tType,X2 : X0,X3 : tree @ X0,X1 : X0,X4 : tree @ X0] : (((is_heap @ X0 @ (t @ X0 @ X1 @ e @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) = $true) | ($true != (is_heap @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) | (linorder @ X0 != $true) | ((ord_less_eq @ X0 @ X2 @ X1) != $true)) )),
% 8.42/2.58 inference(forward_demodulation,[status(thm)],[f905,f860])).
% 8.42/2.58 thf(f905,plain,(
% 8.42/2.58 ( ! [X0 : $tType,X2 : X0,X3 : tree @ X0,X1 : X0,X4 : tree @ X0] : ((linorder @ X0 != $true) | ($true != (is_heap @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) | ((is_heap @ X0 @ (t @ X0 @ X1 @ e @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) = $true) | ($true != (ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X2 @ X3 @ X4)) @ X1))) )),
% 8.42/2.58 inference(cnf_transformation,[status(thm)],[f826])).
% 8.42/2.58 thf(f826,plain,(
% 8.42/2.58 ! [X0 : $tType] : ((linorder @ X0 != $true) | ! [X1 : X0,X2 : X0,X3 : tree @ X0,X4 : tree @ X0] : ((((is_heap @ X0 @ (t @ X0 @ X1 @ e @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) = $true) | ($true != (ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X2 @ X3 @ X4)) @ X1)) | ($true != (is_heap @ X0 @ (t @ X0 @ X2 @ X3 @ X4)))) & ((($true = (ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X2 @ X3 @ X4)) @ X1)) & ($true = (is_heap @ X0 @ (t @ X0 @ X2 @ X3 @ X4)))) | ((is_heap @ X0 @ (t @ X0 @ X1 @ e @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) != $true))))),
% 8.42/2.58 inference(flattening,[status(thm)],[f825])).
% 8.42/2.58 thf(f825,plain,(
% 8.42/2.58 ! [X0 : $tType] : ((linorder @ X0 != $true) | ! [X1 : X0,X2 : X0,X3 : tree @ X0,X4 : tree @ X0] : ((((is_heap @ X0 @ (t @ X0 @ X1 @ e @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) = $true) | (($true != (ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X2 @ X3 @ X4)) @ X1)) | ($true != (is_heap @ X0 @ (t @ X0 @ X2 @ X3 @ X4))))) & ((($true = (ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X2 @ X3 @ X4)) @ X1)) & ($true = (is_heap @ X0 @ (t @ X0 @ X2 @ X3 @ X4)))) | ((is_heap @ X0 @ (t @ X0 @ X1 @ e @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) != $true))))),
% 8.42/2.58 inference(nnf_transformation,[status(thm)],[f794])).
% 8.42/2.58 thf(f794,plain,(
% 8.42/2.58 ! [X0 : $tType] : ((linorder @ X0 != $true) | ! [X1 : X0,X2 : X0,X3 : tree @ X0,X4 : tree @ X0] : (((is_heap @ X0 @ (t @ X0 @ X1 @ e @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) = $true) <=> (($true = (ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X2 @ X3 @ X4)) @ X1)) & ($true = (is_heap @ X0 @ (t @ X0 @ X2 @ X3 @ X4))))))),
% 8.42/2.58 inference(ennf_transformation,[status(thm)],[f655])).
% 8.42/2.58 thf(f655,plain,(
% 8.42/2.58 ! [X0 : $tType] : ((linorder @ X0 = $true) => ! [X1 : X0,X2 : X0,X3 : tree @ X0,X4 : tree @ X0] : (((is_heap @ X0 @ (t @ X0 @ X1 @ e @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) = $true) <=> (($true = (ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X2 @ X3 @ X4)) @ X1)) & ($true = (is_heap @ X0 @ (t @ X0 @ X2 @ X3 @ X4))))))),
% 8.42/2.58 inference(fool_elimination,[status(thm)],[f654])).
% 8.42/2.58 thf(f654,plain,(
% 8.42/2.58 ! [X0 : $tType] : (linorder @ X0 => ! [X1 : X0,X2 : X0,X3 : tree @ X0,X4 : tree @ X0] : ((is_heap @ X0 @ (t @ X0 @ X1 @ e @ X0 @ (t @ X0 @ X2 @ X3 @ X4))) = (is_heap @ X0 @ (t @ X0 @ X2 @ X3 @ X4)) & (ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X2 @ X3 @ X4)) @ X1)))),
% 8.42/2.58 inference(rectify,[status(thm)],[f33])).
% 8.42/2.58 thf(f33,axiom,(
% 8.42/2.58 ! [X0 : $tType] : (linorder @ X0 => ! [X4 : X0,X42 : X0,X43 : tree @ X0,X44 : tree @ X0] : ((is_heap @ X0 @ (t @ X0 @ X4 @ e @ X0 @ (t @ X0 @ X42 @ X43 @ X44))) = (is_heap @ X0 @ (t @ X0 @ X42 @ X43 @ X44)) & (ord_less_eq @ X0 @ (val @ X0 @ (t @ X0 @ X42 @ X43 @ X44)) @ X4)))),
% 8.42/2.58 file('/export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2THF_5214.p',fact_32_is__heap_Osimps_I3_J)).
% 8.42/2.58 thf(f1818,plain,(
% 8.42/2.58 spl51_50 | ~spl51_4),
% 8.42/2.58 inference(avatar_split_clause,[status(thm)],[f1813,f958,f1815])).
% 8.42/2.58 thf(f1813,plain,(
% 8.42/2.58 (ra = (t @ a @ v1 @ l1 @ r1)) | ~spl51_4),
% 8.42/2.58 inference(forward_demodulation,[status(thm)],[f1802,f886])).
% 8.42/2.58 thf(f886,plain,(
% 8.42/2.58 ( ! [X0 : $tType,X2 : tree @ X0,X3 : tree @ X0,X1 : X0] : (((heapIm1434396069_right @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = X3)) )),
% 8.42/2.58 inference(cnf_transformation,[status(thm)],[f765])).
% 8.42/2.58 thf(f765,plain,(
% 8.42/2.58 ! [X0 : $tType,X1 : X0,X2 : tree @ X0,X3 : tree @ X0] : ((heapIm1434396069_right @ X0 @ (t @ X0 @ X1 @ X2 @ X3)) = X3)),
% 8.42/2.58 inference(rectify,[status(thm)],[f35])).
% 8.42/2.58 thf(f35,axiom,(
% 8.42/2.58 ! [X0 : $tType,X4 : X0,X14 : tree @ X0,X15 : tree @ X0] : ((heapIm1434396069_right @ X0 @ (t @ X0 @ X4 @ X14 @ X15)) = X15)),
% 8.42/2.58 file('/export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2THF_5214.p',fact_34_right_Osimps)).
% 8.42/2.58 thf(f1802,plain,(
% 8.42/2.58 ((t @ a @ v1 @ l1 @ r1) = (heapIm1434396069_right @ a @ (t @ a @ va @ la @ ra))) | ~spl51_4),
% 8.42/2.58 inference(superposition,[status(thm)],[f886,f960])).
% 8.42/2.58 thf(f971,plain,(
% 8.42/2.58 ~spl51_6),
% 8.42/2.58 inference(avatar_split_clause,[status(thm)],[f891,f968])).
% 8.42/2.58 thf(f891,plain,(
% 8.42/2.58 ((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1)))) != $true)),
% 8.42/2.58 inference(cnf_transformation,[status(thm)],[f752])).
% 8.42/2.58 thf(f752,plain,(
% 8.42/2.58 ((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1)))) != $true)),
% 8.42/2.58 inference(flattening,[status(thm)],[f343])).
% 8.42/2.58 thf(f343,plain,(
% 8.42/2.58 ~((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1)))) = $true)),
% 8.42/2.58 inference(fool_elimination,[status(thm)],[f342])).
% 8.42/2.58 thf(f342,plain,(
% 8.42/2.58 ~(is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1))))),
% 8.42/2.58 inference(rectify,[status(thm)],[f278])).
% 8.42/2.58 thf(f278,negated_conjecture,(
% 8.42/2.58 ~(is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1))))),
% 8.42/2.58 inference(negated_conjecture,[status(cth)],[f277])).
% 8.42/2.58 thf(f277,conjecture,(
% 8.42/2.58 (is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1))))),
% 8.42/2.58 file('/export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2THF_5214.p',conj_0)).
% 8.42/2.58 thf(f966,plain,(
% 8.42/2.58 spl51_5),
% 8.42/2.58 inference(avatar_split_clause,[status(thm)],[f902,f963])).
% 8.42/2.58 thf(f902,plain,(
% 8.42/2.58 ((ord_less_eq @ a @ v1 @ v2) = $true)),
% 8.42/2.58 inference(cnf_transformation,[status(thm)],[f737])).
% 8.42/2.58 thf(f737,plain,(
% 8.42/2.58 ((ord_less_eq @ a @ v1 @ v2) = $true)),
% 8.42/2.58 inference(fool_elimination,[status(thm)],[f736])).
% 8.42/2.58 thf(f736,plain,(
% 8.42/2.58 (ord_less_eq @ a @ v1 @ v2)),
% 8.42/2.58 inference(rectify,[status(thm)],[f5])).
% 8.42/2.58 thf(f5,axiom,(
% 8.42/2.58 (ord_less_eq @ a @ v1 @ v2)),
% 8.42/2.58 file('/export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2THF_5214.p',fact_4_True)).
% 8.42/2.58 thf(f961,plain,(
% 8.42/2.58 spl51_4),
% 8.42/2.58 inference(avatar_split_clause,[status(thm)],[f876,f958])).
% 8.42/2.58 thf(f876,plain,(
% 8.42/2.58 ((t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1)) = (t @ a @ va @ la @ ra))),
% 8.42/2.58 inference(cnf_transformation,[status(thm)],[f6])).
% 8.42/2.58 thf(f6,axiom,(
% 8.42/2.58 ((t @ a @ v2 @ e @ a @ (t @ a @ v1 @ l1 @ r1)) = (t @ a @ va @ la @ ra))),
% 8.42/2.58 file('/export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2THF_5214.p',fact_5__C4_Oprems_C_I3_J)).
% 8.42/2.58 thf(f951,plain,(
% 8.42/2.58 spl51_2),
% 8.42/2.58 inference(avatar_split_clause,[status(thm)],[f911,f948])).
% 8.42/2.58 thf(f911,plain,(
% 8.42/2.58 (linorder @ a = $true)),
% 8.42/2.58 inference(cnf_transformation,[status(thm)],[f441])).
% 8.42/2.58 thf(f441,plain,(
% 8.42/2.58 (linorder @ a = $true)),
% 8.42/2.58 inference(fool_elimination,[status(thm)],[f440])).
% 8.42/2.58 thf(f440,plain,(
% 8.42/2.58 linorder @ a),
% 8.42/2.58 inference(rectify,[status(thm)],[f276])).
% 8.42/2.58 thf(f276,axiom,(
% 8.42/2.58 linorder @ a),
% 8.42/2.58 file('/export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2THF_5214.p',tfree_0)).
% 8.42/2.58 thf(f946,plain,(
% 8.42/2.58 spl51_1),
% 8.42/2.58 inference(avatar_split_clause,[status(thm)],[f880,f943])).
% 8.42/2.58 thf(f880,plain,(
% 8.42/2.58 ((is_heap @ a @ ra) = $true)),
% 8.42/2.58 inference(cnf_transformation,[status(thm)],[f529])).
% 8.42/2.58 thf(f529,plain,(
% 8.42/2.58 ((is_heap @ a @ ra) = $true)),
% 8.42/2.58 inference(fool_elimination,[status(thm)],[f528])).
% 8.42/2.58 thf(f528,plain,(
% 8.42/2.58 (is_heap @ a @ ra)),
% 8.42/2.58 inference(rectify,[status(thm)],[f1])).
% 8.42/2.58 thf(f1,axiom,(
% 8.42/2.58 (is_heap @ a @ ra)),
% 8.42/2.58 file('/export/starexec/sandbox/tmp/tmp.3EMIM7h44t/DTF2THF_5214.p',fact_0__C4_Oprems_C_I2_J)).
% 8.42/2.58 % SZS output end Proof for DTF2THF_5214
% 8.42/2.58 % (5428)------------------------------
% 8.42/2.58 % (5428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.58 % (5428)Termination reason: Refutation
% 8.42/2.58
% 8.42/2.58 % (5428)Memory used [KB]: 8059
% 8.42/2.58 % (5428)Time elapsed: 0.228 s
% 8.42/2.58 % (5428)Instructions burned: 731 (million)
% 8.42/2.58 % (5428)------------------------------
% 8.42/2.58 % (5428)------------------------------
% 8.42/2.58 % (5342)Success in time 0.952 s
%------------------------------------------------------------------------------