%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM193^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 08:41:54 AM UTC 2026
% Result : Theorem 28.88s 5.41s
% Output : Refutation 28.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : COM193^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n002.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 04:17:33 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 ---- Original DTF file ---
% 0.17/0.43 thf(spec,logic,$$dhol).
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % File : COM193^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.43 % Domain : Computing Theory
% 0.17/0.43 % Problem : Grammars and languages 1154
% 0.17/0.43 % Version : [Bla16] axioms : Especial.
% 0.17/0.43 % English :
% 0.17/0.43
% 0.17/0.43 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.17/0.43 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.17/0.43 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.17/0.43 % Source : [Bla16]
% 0.17/0.43 % Names : gram_lang__1154.p [Bla16]
% 0.17/0.43
% 0.17/0.43 % Status : Theorem
% 0.17/0.43 % Rating : 0.33 v9.1.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.17/0.43 % Syntax : Number of formulae : 340 ( 127 unt; 57 typ; 0 def)
% 0.17/0.43 % Number of atoms : 712 ( 215 equ; 0 cnn)
% 0.17/0.43 % Maximal formula atoms : 13 ( 2 avg)
% 0.17/0.43 % Number of connectives : 3215 ( 70 ~; 6 |; 38 &;2817 @)
% 0.17/0.43 % ( 0 <=>; 284 =>; 0 <=; 0 <~>)
% 0.17/0.43 % Maximal formula depth : 17 ( 7 avg)
% 0.17/0.43 % Number of types : 4 ( 3 usr)
% 0.17/0.43 % Number of type conns : 172 ( 172 >; 0 *; 0 +; 0 <<)
% 0.17/0.43 % Number of symbols : 56 ( 54 usr; 3 con; 0-6 aty)
% 0.17/0.43 % Number of variables : 847 ( 46 ^; 759 !; 11 ?; 847 :)
% 0.17/0.43 % ( 31 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.43 % SPC : TH1_THM_EQU_NAR
% 0.17/0.43
% 0.17/0.43 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.17/0.43 % 2016-07-13 14:47:18.227
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 %----Could-be-implicit typings (6)
% 0.17/0.43 thf(ty_t_Sum__Type_Osum,type,
% 0.17/0.43 sum_sum: $tType > $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_DTree_Odtree,type,
% 0.17/0.43 dtree: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Set_Oset,type,
% 0.17/0.43 set: $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_DTree_OT,type,
% 0.17/0.43 t: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_DTree_ON,type,
% 0.17/0.43 n: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_itself,type,
% 0.17/0.43 itself: $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 %----Explicit typings (51)
% 0.17/0.43 thf(sy_cl_HOL_Otype,type,
% 0.17/0.43 type:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Obot,type,
% 0.17/0.43 bot:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Oord,type,
% 0.17/0.43 ord:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Otop,type,
% 0.17/0.43 top:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Oorder,type,
% 0.17/0.43 order:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Olinorder,type,
% 0.17/0.43 linorder:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Opreorder,type,
% 0.17/0.43 preorder:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.17/0.43 order_bot:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Oorder__top,type,
% 0.17/0.43 order_top:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.17/0.43 boolean_algebra:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.17/0.43 ordered_ab_group_add:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_DTree_ONode,type,
% 0.17/0.43 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_DTree_Ocorec,type,
% 0.17/0.43 corec:
% 0.17/0.43 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ) ) > A > dtree ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_DTree_Odtree_Oroot,type,
% 0.17/0.43 root: dtree > n ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_DTree_Ounfold,type,
% 0.17/0.43 unfold:
% 0.17/0.43 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFr,type,
% 0.17/0.43 gram_L861583724lle_Fr: ( set @ n ) > dtree > ( set @ t ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH,type,
% 0.17/0.43 gram_L1451583624elle_H: dtree > n > dtree ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c,type,
% 0.17/0.43 gram_L1221482011le_H_c: dtree > n > ( set @ ( sum_sum @ t @ n ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r,type,
% 0.17/0.43 gram_L1221482026le_H_r: dtree > n > n ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OL,type,
% 0.17/0.43 gram_L1451583628elle_L: ( set @ n ) > n > ( set @ ( set @ t ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 0.17/0.43 gram_L1231612515_deftr: n > dtree ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 0.17/0.43 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 0.17/0.43 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 0.17/0.43 gram_L1905609017ubst_r: dtree > n ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 0.17/0.43 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 0.17/0.43 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Opick,type,
% 0.17/0.43 gram_L315592705e_pick: dtree > n > dtree ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Orcut,type,
% 0.17/0.43 gram_L1828378864e_rcut: dtree > dtree ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oreg,type,
% 0.17/0.43 gram_L1918716148le_reg: ( n > dtree ) > dtree > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oregular,type,
% 0.17/0.43 gram_L646766332egular: dtree > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 0.17/0.43 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 0.17/0.43 gram_L864798063lle_wf: dtree > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.17/0.43 minus_minus:
% 0.17/0.43 !>[A: $tType] : ( A > A > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.17/0.43 uminus_uminus:
% 0.17/0.43 !>[A: $tType] : ( A > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.17/0.43 bot_bot:
% 0.17/0.43 !>[A: $tType] : A ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.17/0.43 ord_less:
% 0.17/0.43 !>[A: $tType] : ( A > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.17/0.43 ord_less_eq:
% 0.17/0.43 !>[A: $tType] : ( A > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.17/0.43 top_top:
% 0.17/0.43 !>[A: $tType] : A ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Pure_Otype,type,
% 0.17/0.43 type2:
% 0.17/0.43 !>[A: $tType] : ( itself @ A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Relation_Oinv__imagep,type,
% 0.17/0.43 inv_imagep:
% 0.17/0.43 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_OCollect,type,
% 0.17/0.43 collect:
% 0.17/0.43 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_OPow,type,
% 0.17/0.43 pow:
% 0.17/0.43 !>[A: $tType] : ( ( set @ A ) > ( set @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Oinsert,type,
% 0.17/0.43 insert:
% 0.17/0.43 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Ois__empty,type,
% 0.17/0.43 is_empty:
% 0.17/0.43 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Ois__singleton,type,
% 0.17/0.43 is_singleton:
% 0.17/0.43 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Opairwise,type,
% 0.17/0.43 pairwise:
% 0.17/0.43 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Oremove,type,
% 0.17/0.43 remove:
% 0.17/0.43 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Othe__elem,type,
% 0.17/0.43 the_elem:
% 0.17/0.43 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_member,type,
% 0.17/0.43 member:
% 0.17/0.43 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_n,type,
% 0.17/0.43 n2: n ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_ns,type,
% 0.17/0.43 ns: set @ n ).
% 0.17/0.43
% 0.17/0.43 %----Relevant facts (256)
% 0.17/0.43 thf(fact_0_assms,axiom,
% 0.17/0.43 ~ ( member @ n @ n2 @ ns ) ).
% 0.17/0.43
% 0.17/0.43 % assms
% 0.17/0.43 thf(fact_1_not__root__Fr,axiom,
% 0.17/0.43 ! [Tr: dtree,Ns: set @ n] :
% 0.17/0.43 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 0.17/0.43 => ( ( gram_L861583724lle_Fr @ Ns @ Tr )
% 0.17/0.43 = ( bot_bot @ ( set @ t ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % not_root_Fr
% 0.17/0.43 thf(fact_2_empty__iff,axiom,
% 0.17/0.43 ! [A: $tType,C: A] :
% 0.17/0.43 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % empty_iff
% 0.17/0.43 thf(fact_3_all__not__in__conv,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( ! [X: A] :
% 0.17/0.43 ~ ( member @ A @ X @ A2 ) )
% 0.17/0.43 = ( A2
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % all_not_in_conv
% 0.17/0.43 thf(fact_4_Collect__empty__eq,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o] :
% 0.17/0.43 ( ( ( collect @ A @ P )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( ! [X: A] :
% 0.17/0.43 ~ ( P @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_empty_eq
% 0.17/0.43 thf(fact_5_empty__Collect__eq,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o] :
% 0.17/0.43 ( ( ( bot_bot @ ( set @ A ) )
% 0.17/0.43 = ( collect @ A @ P ) )
% 0.17/0.43 = ( ! [X: A] :
% 0.17/0.43 ~ ( P @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % empty_Collect_eq
% 0.17/0.43 thf(fact_6_bot__apply,axiom,
% 0.17/0.43 ! [C2: $tType,D: $tType] :
% 0.17/0.43 ( ( bot @ C2 @ ( type2 @ C2 ) )
% 0.17/0.43 => ( ( bot_bot @ ( D > C2 ) )
% 0.17/0.43 = ( ^ [X: D] : ( bot_bot @ C2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_apply
% 0.17/0.43 thf(fact_7_hsubst__r__def,axiom,
% 0.17/0.43 gram_L1905609017ubst_r = root ).
% 0.17/0.43
% 0.17/0.43 % hsubst_r_def
% 0.17/0.43 thf(fact_8_root__rcut,axiom,
% 0.17/0.43 ! [Tr0: dtree] :
% 0.17/0.43 ( ( root @ ( gram_L1828378864e_rcut @ Tr0 ) )
% 0.17/0.43 = ( root @ Tr0 ) ) ).
% 0.17/0.43
% 0.17/0.43 % root_rcut
% 0.17/0.43 thf(fact_9_regular__def2,axiom,
% 0.17/0.43 ( gram_L646766332egular
% 0.17/0.43 = ( ^ [Tr2: dtree] :
% 0.17/0.43 ? [F: n > dtree] :
% 0.17/0.43 ( ( gram_L1918716148le_reg @ F @ Tr2 )
% 0.17/0.43 & ! [N: n] :
% 0.17/0.43 ( ( root @ ( F @ N ) )
% 0.17/0.43 = N ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % regular_def2
% 0.17/0.43 thf(fact_10_emptyE,axiom,
% 0.17/0.43 ! [A: $tType,A3: A] :
% 0.17/0.43 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % emptyE
% 0.17/0.43 thf(fact_11_equals0D,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,A3: A] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % equals0D
% 0.17/0.43 thf(fact_12_equals0I,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ! [Y: A] :
% 0.17/0.43 ~ ( member @ A @ Y @ A2 )
% 0.17/0.43 => ( A2
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % equals0I
% 0.17/0.43 thf(fact_13_ex__in__conv,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( ? [X: A] : ( member @ A @ X @ A2 ) )
% 0.17/0.43 = ( A2
% 0.17/0.43 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ex_in_conv
% 0.17/0.43 thf(fact_14_bot__set__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bot_bot @ ( set @ A ) )
% 0.17/0.43 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_set_def
% 0.17/0.43 thf(fact_15_reg__root,axiom,
% 0.17/0.43 ! [F2: n > dtree,Tr: dtree] :
% 0.17/0.43 ( ( gram_L1918716148le_reg @ F2 @ Tr )
% 0.17/0.43 => ( ( F2 @ ( root @ Tr ) )
% 0.17/0.43 = Tr ) ) ).
% 0.17/0.43
% 0.17/0.43 % reg_root
% 0.17/0.43 thf(fact_16_regular__def,axiom,
% 0.17/0.43 ( gram_L646766332egular
% 0.17/0.43 = ( ^ [Tr2: dtree] :
% 0.17/0.43 ? [F: n > dtree] : ( gram_L1918716148le_reg @ F @ Tr2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % regular_def
% 0.17/0.43 thf(fact_17_wf__rcut,axiom,
% 0.17/0.43 ! [Tr0: dtree] :
% 0.17/0.43 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.17/0.43 => ( gram_L864798063lle_wf @ ( gram_L1828378864e_rcut @ Tr0 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % wf_rcut
% 0.17/0.43 thf(fact_18_regular__rcut,axiom,
% 0.17/0.43 ! [Tr0: dtree] : ( gram_L646766332egular @ ( gram_L1828378864e_rcut @ Tr0 ) ) ).
% 0.17/0.43
% 0.17/0.43 % regular_rcut
% 0.17/0.43 thf(fact_19_bot__fun__def,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( bot @ B @ ( type2 @ B ) )
% 0.17/0.43 => ( ( bot_bot @ ( A > B ) )
% 0.17/0.43 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_fun_def
% 0.17/0.43 thf(fact_20_Set_Ois__empty__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( is_empty @ A )
% 0.17/0.43 = ( ^ [A4: set @ A] :
% 0.17/0.43 ( A4
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Set.is_empty_def
% 0.17/0.43 thf(fact_21_rcut__eq,axiom,
% 0.17/0.43 ! [Tr0: dtree] :
% 0.17/0.43 ( ( ( gram_L1828378864e_rcut @ Tr0 )
% 0.17/0.43 = Tr0 )
% 0.17/0.43 = ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ Tr0 ) ) ).
% 0.17/0.43
% 0.17/0.43 % rcut_eq
% 0.17/0.43 thf(fact_22_rcut__reg,axiom,
% 0.17/0.43 ! [Tr0: dtree] :
% 0.17/0.43 ( ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ Tr0 )
% 0.17/0.43 => ( ( gram_L1828378864e_rcut @ Tr0 )
% 0.17/0.43 = Tr0 ) ) ).
% 0.17/0.43
% 0.17/0.43 % rcut_reg
% 0.17/0.43 thf(fact_23_reg__rcut,axiom,
% 0.17/0.43 ! [Tr0: dtree] : ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ ( gram_L1828378864e_rcut @ Tr0 ) ) ).
% 0.17/0.43
% 0.17/0.43 % reg_rcut
% 0.17/0.43 thf(fact_24_rcut__def,axiom,
% 0.17/0.43 ( gram_L1828378864e_rcut
% 0.17/0.43 = ( ^ [Tr02: dtree] : ( gram_L1451583624elle_H @ Tr02 @ ( root @ Tr02 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rcut_def
% 0.17/0.43 thf(fact_25_Collect__empty__eq__bot,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o] :
% 0.17/0.43 ( ( ( collect @ A @ P )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( P
% 0.17/0.43 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_empty_eq_bot
% 0.17/0.43 thf(fact_26_bot__empty__eq,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bot_bot @ ( A > $o ) )
% 0.17/0.43 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_empty_eq
% 0.17/0.43 thf(fact_27_root__deftr,axiom,
% 0.17/0.43 ! [N2: n] :
% 0.17/0.43 ( ( root @ ( gram_L1231612515_deftr @ N2 ) )
% 0.17/0.43 = N2 ) ).
% 0.17/0.43
% 0.17/0.43 % root_deftr
% 0.17/0.43 thf(fact_28_is__singletonI_H,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 != ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 => ( ! [X2: A,Y: A] :
% 0.17/0.43 ( ( member @ A @ X2 @ A2 )
% 0.17/0.43 => ( ( member @ A @ Y @ A2 )
% 0.17/0.43 => ( X2 = Y ) ) )
% 0.17/0.43 => ( is_singleton @ A @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singletonI'
% 0.17/0.43 thf(fact_29_reg__deftr,axiom,
% 0.17/0.43 ! [N2: n] : ( gram_L1918716148le_reg @ gram_L1231612515_deftr @ ( gram_L1231612515_deftr @ N2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % reg_deftr
% 0.17/0.43 thf(fact_30_reg__def2,axiom,
% 0.17/0.43 ( gram_L1918716148le_reg
% 0.17/0.43 = ( ^ [F: n > dtree,Tr2: dtree] :
% 0.17/0.43 ! [Ns2: set @ n,Tr3: dtree] :
% 0.17/0.43 ( ( gram_L716654942_subtr @ Ns2 @ Tr3 @ Tr2 )
% 0.17/0.43 => ( Tr3
% 0.17/0.43 = ( F @ ( root @ Tr3 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % reg_def2
% 0.17/0.43 thf(fact_31_subtr__trans,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr32: dtree] :
% 0.17/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.17/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr32 )
% 0.17/0.43 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr32 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr_trans
% 0.17/0.43 thf(fact_32_subtr__deftr,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr4: dtree,N2: n] :
% 0.17/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr4 @ ( gram_L1231612515_deftr @ N2 ) )
% 0.17/0.43 => ( Tr4
% 0.17/0.43 = ( gram_L1231612515_deftr @ ( root @ Tr4 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr_deftr
% 0.17/0.43 thf(fact_33_subtr_ORefl,axiom,
% 0.17/0.43 ! [Tr: dtree,Ns: set @ n] :
% 0.17/0.43 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.17/0.43 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr.Refl
% 0.17/0.43 thf(fact_34_subtr__rootL__in,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.17/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.17/0.43 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr_rootL_in
% 0.17/0.43 thf(fact_35_subtr__rootR__in,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.17/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.17/0.43 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr_rootR_in
% 0.17/0.43 thf(fact_36_wf__subtr,axiom,
% 0.17/0.43 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.17/0.43 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.17/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.17/0.43 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % wf_subtr
% 0.17/0.43 thf(fact_37_reg__subtr,axiom,
% 0.17/0.43 ! [F2: n > dtree,Tr: dtree,Ns: set @ n,Tr4: dtree] :
% 0.17/0.43 ( ( gram_L1918716148le_reg @ F2 @ Tr )
% 0.17/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr4 @ Tr )
% 0.17/0.43 => ( gram_L1918716148le_reg @ F2 @ Tr4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % reg_subtr
% 0.17/0.43 thf(fact_38_regular__subtr,axiom,
% 0.17/0.43 ! [Tr: dtree,Ns: set @ n,Tr4: dtree] :
% 0.17/0.43 ( ( gram_L646766332egular @ Tr )
% 0.17/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr4 @ Tr )
% 0.17/0.43 => ( gram_L646766332egular @ Tr4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % regular_subtr
% 0.17/0.43 thf(fact_39_wf__deftr,axiom,
% 0.17/0.43 ! [N2: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % wf_deftr
% 0.17/0.43 thf(fact_40_root__H__pick,axiom,
% 0.17/0.43 ! [Tr0: dtree,N2: n] :
% 0.17/0.43 ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N2 ) )
% 0.17/0.43 = ( root @ ( gram_L315592705e_pick @ Tr0 @ N2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % root_H_pick
% 0.17/0.43 thf(fact_41_reg__def,axiom,
% 0.17/0.43 ( gram_L1918716148le_reg
% 0.17/0.43 = ( ^ [F: n > dtree,Tr2: dtree] :
% 0.17/0.43 ! [Tr3: dtree] :
% 0.17/0.43 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr3 @ Tr2 )
% 0.17/0.43 => ( Tr3
% 0.17/0.43 = ( F @ ( root @ Tr3 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % reg_def
% 0.17/0.43 thf(fact_42_in__inv__imagep,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( inv_imagep @ A @ B )
% 0.17/0.43 = ( ^ [R: A > A > $o,F: B > A,X: B,Y2: B] : ( R @ ( F @ X ) @ ( F @ Y2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % in_inv_imagep
% 0.17/0.43 thf(fact_43_is__singletonI,axiom,
% 0.17/0.43 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singletonI
% 0.17/0.43 thf(fact_44_inItr__subtr,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr: dtree,N2: n] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ Ns @ Tr @ N2 )
% 0.17/0.43 => ? [Tr5: dtree] :
% 0.17/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 0.17/0.43 & ( ( root @ Tr5 )
% 0.17/0.43 = N2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % inItr_subtr
% 0.17/0.43 thf(fact_45_mem__Collect__eq,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,P: A > $o] :
% 0.17/0.43 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.17/0.43 = ( P @ A3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % mem_Collect_eq
% 0.17/0.43 thf(fact_46_Collect__mem__eq,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( collect @ A
% 0.17/0.43 @ ^ [X: A] : ( member @ A @ X @ A2 ) )
% 0.17/0.43 = A2 ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_mem_eq
% 0.17/0.43 thf(fact_47_Collect__cong,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.17/0.43 ( ! [X2: A] :
% 0.17/0.43 ( ( P @ X2 )
% 0.17/0.43 = ( Q @ X2 ) )
% 0.17/0.43 => ( ( collect @ A @ P )
% 0.17/0.43 = ( collect @ A @ Q ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_cong
% 0.17/0.43 thf(fact_48_ext,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 0.17/0.43 ( ! [X2: A] :
% 0.17/0.43 ( ( F2 @ X2 )
% 0.17/0.43 = ( G @ X2 ) )
% 0.17/0.43 => ( F2 = G ) ) ).
% 0.17/0.43
% 0.17/0.43 % ext
% 0.17/0.43 thf(fact_49_is__singleton__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( is_singleton @ A )
% 0.17/0.43 = ( ^ [A4: set @ A] :
% 0.17/0.43 ? [X: A] :
% 0.17/0.43 ( A4
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singleton_def
% 0.17/0.43 thf(fact_50_is__singletonE,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( is_singleton @ A @ A2 )
% 0.17/0.43 => ~ ! [X2: A] :
% 0.17/0.43 ( A2
% 0.17/0.43 != ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singletonE
% 0.17/0.43 thf(fact_51_root__hsubst,axiom,
% 0.17/0.43 ! [Tr0: dtree,Tr: dtree] :
% 0.17/0.43 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.17/0.43 = ( root @ Tr ) ) ).
% 0.17/0.43
% 0.17/0.43 % root_hsubst
% 0.17/0.43 thf(fact_52_pairwise__empty,axiom,
% 0.17/0.43 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pairwise_empty
% 0.17/0.43 thf(fact_53_top__apply,axiom,
% 0.17/0.43 ! [C2: $tType,D: $tType] :
% 0.17/0.43 ( ( top @ C2 @ ( type2 @ C2 ) )
% 0.17/0.43 => ( ( top_top @ ( D > C2 ) )
% 0.17/0.43 = ( ^ [X: D] : ( top_top @ C2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % top_apply
% 0.17/0.43 thf(fact_54_UNIV__I,axiom,
% 0.17/0.43 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % UNIV_I
% 0.17/0.43 thf(fact_55_insert__absorb2,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A] :
% 0.17/0.43 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A2 ) )
% 0.17/0.43 = ( insert @ A @ X3 @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_absorb2
% 0.17/0.43 thf(fact_56_insert__iff,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 0.17/0.43 = ( ( A3 = B2 )
% 0.17/0.43 | ( member @ A @ A3 @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_iff
% 0.17/0.43 thf(fact_57_insertCI,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,B3: set @ A,B2: A] :
% 0.17/0.43 ( ( ~ ( member @ A @ A3 @ B3 )
% 0.17/0.43 => ( A3 = B2 ) )
% 0.17/0.43 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insertCI
% 0.17/0.43 thf(fact_58_singletonI,axiom,
% 0.17/0.43 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % singletonI
% 0.17/0.43 thf(fact_59_root__H,axiom,
% 0.17/0.43 ! [Tr0: dtree,N2: n] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 0.17/0.43 => ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N2 ) )
% 0.17/0.43 = N2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % root_H
% 0.17/0.43 thf(fact_60_subtr__pick,axiom,
% 0.17/0.43 ! [Tr0: dtree,N2: n] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 0.17/0.43 => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N2 ) @ Tr0 ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr_pick
% 0.17/0.43 thf(fact_61_pairwise__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( pairwise @ A )
% 0.17/0.43 = ( ^ [R2: A > A > $o,S: set @ A] :
% 0.17/0.43 ! [X: A] :
% 0.17/0.43 ( ( member @ A @ X @ S )
% 0.17/0.43 => ! [Y2: A] :
% 0.17/0.43 ( ( member @ A @ Y2 @ S )
% 0.17/0.43 => ( ( X != Y2 )
% 0.17/0.43 => ( R2 @ X @ Y2 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pairwise_def
% 0.17/0.43 thf(fact_62_wf__pick,axiom,
% 0.17/0.43 ! [Tr0: dtree,N2: n] :
% 0.17/0.43 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.17/0.43 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 0.17/0.43 => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ Tr0 @ N2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % wf_pick
% 0.17/0.43 thf(fact_63_root__pick,axiom,
% 0.17/0.43 ! [Tr0: dtree,N2: n] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 0.17/0.43 => ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N2 ) )
% 0.17/0.43 = N2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % root_pick
% 0.17/0.43 thf(fact_64_mk__disjoint__insert,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ A3 @ A2 )
% 0.17/0.43 => ? [B4: set @ A] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 = ( insert @ A @ A3 @ B4 ) )
% 0.17/0.43 & ~ ( member @ A @ A3 @ B4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mk_disjoint_insert
% 0.17/0.43 thf(fact_65_pairwise__insert,axiom,
% 0.17/0.43 ! [A: $tType,R3: A > A > $o,X3: A,S2: set @ A] :
% 0.17/0.43 ( ( pairwise @ A @ R3 @ ( insert @ A @ X3 @ S2 ) )
% 0.17/0.43 = ( ! [Y2: A] :
% 0.17/0.43 ( ( ( member @ A @ Y2 @ S2 )
% 0.17/0.43 & ( Y2 != X3 ) )
% 0.17/0.43 => ( ( R3 @ X3 @ Y2 )
% 0.17/0.43 & ( R3 @ Y2 @ X3 ) ) )
% 0.17/0.43 & ( pairwise @ A @ R3 @ S2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pairwise_insert
% 0.17/0.43 thf(fact_66_insert__commute,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,Y3: A,A2: set @ A] :
% 0.17/0.43 ( ( insert @ A @ X3 @ ( insert @ A @ Y3 @ A2 ) )
% 0.17/0.43 = ( insert @ A @ Y3 @ ( insert @ A @ X3 @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_commute
% 0.17/0.43 thf(fact_67_insert__eq__iff,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,A2: set @ A,B2: A,B3: set @ A] :
% 0.17/0.43 ( ~ ( member @ A @ A3 @ A2 )
% 0.17/0.43 => ( ~ ( member @ A @ B2 @ B3 )
% 0.17/0.43 => ( ( ( insert @ A @ A3 @ A2 )
% 0.17/0.43 = ( insert @ A @ B2 @ B3 ) )
% 0.17/0.43 = ( ( ( A3 = B2 )
% 0.17/0.43 => ( A2 = B3 ) )
% 0.17/0.43 & ( ( A3 != B2 )
% 0.17/0.43 => ? [C3: set @ A] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 = ( insert @ A @ B2 @ C3 ) )
% 0.17/0.43 & ~ ( member @ A @ B2 @ C3 )
% 0.17/0.43 & ( B3
% 0.17/0.43 = ( insert @ A @ A3 @ C3 ) )
% 0.17/0.43 & ~ ( member @ A @ A3 @ C3 ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_eq_iff
% 0.17/0.43 thf(fact_68_insert__absorb,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ A3 @ A2 )
% 0.17/0.43 => ( ( insert @ A @ A3 @ A2 )
% 0.17/0.43 = A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_absorb
% 0.17/0.43 thf(fact_69_insert__ident,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ~ ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ~ ( member @ A @ X3 @ B3 )
% 0.17/0.43 => ( ( ( insert @ A @ X3 @ A2 )
% 0.17/0.43 = ( insert @ A @ X3 @ B3 ) )
% 0.17/0.43 = ( A2 = B3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_ident
% 0.17/0.43 thf(fact_70_UNIV__witness,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ? [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % UNIV_witness
% 0.17/0.43 thf(fact_71_insert__UNIV,axiom,
% 0.17/0.43 ! [A: $tType,X3: A] :
% 0.17/0.43 ( ( insert @ A @ X3 @ ( top_top @ ( set @ A ) ) )
% 0.17/0.43 = ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_UNIV
% 0.17/0.43 thf(fact_72_Set_Oset__insert,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ~ ! [B4: set @ A] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 = ( insert @ A @ X3 @ B4 ) )
% 0.17/0.43 => ( member @ A @ X3 @ B4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Set.set_insert
% 0.17/0.43 thf(fact_73_UNIV__eq__I,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ! [X2: A] : ( member @ A @ X2 @ A2 )
% 0.17/0.43 => ( ( top_top @ ( set @ A ) )
% 0.17/0.43 = A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % UNIV_eq_I
% 0.17/0.43 thf(fact_74_insertI2,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,B3: set @ A,B2: A] :
% 0.17/0.43 ( ( member @ A @ A3 @ B3 )
% 0.17/0.43 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insertI2
% 0.17/0.43 thf(fact_75_insertI1,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,B3: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % insertI1
% 0.17/0.43 thf(fact_76_insertE,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 0.17/0.43 => ( ( A3 != B2 )
% 0.17/0.43 => ( member @ A @ A3 @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insertE
% 0.17/0.43 thf(fact_77_pairwise__singleton,axiom,
% 0.17/0.43 ! [A: $tType,P: A > A > $o,A2: A] : ( pairwise @ A @ P @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pairwise_singleton
% 0.17/0.43 thf(fact_78_pick,axiom,
% 0.17/0.43 ! [Tr0: dtree,N2: n] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 0.17/0.43 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N2 ) @ Tr0 )
% 0.17/0.43 & ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N2 ) )
% 0.17/0.43 = N2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pick
% 0.17/0.43 thf(fact_79_singleton__inject,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,B2: A] :
% 0.17/0.43 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( A3 = B2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % singleton_inject
% 0.17/0.43 thf(fact_80_insert__not__empty,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.43 ( ( insert @ A @ A3 @ A2 )
% 0.17/0.43 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_not_empty
% 0.17/0.43 thf(fact_81_doubleton__eq__iff,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,B2: A,C: A,D2: A] :
% 0.17/0.43 ( ( ( insert @ A @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = ( insert @ A @ C @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.43 = ( ( ( A3 = C )
% 0.17/0.43 & ( B2 = D2 ) )
% 0.17/0.43 | ( ( A3 = D2 )
% 0.17/0.43 & ( B2 = C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % doubleton_eq_iff
% 0.17/0.43 thf(fact_82_singleton__iff,axiom,
% 0.17/0.43 ! [A: $tType,B2: A,A3: A] :
% 0.17/0.43 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = ( B2 = A3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % singleton_iff
% 0.17/0.43 thf(fact_83_singletonD,axiom,
% 0.17/0.43 ! [A: $tType,B2: A,A3: A] :
% 0.17/0.43 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( B2 = A3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % singletonD
% 0.17/0.43 thf(fact_84_empty__not__UNIV,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bot_bot @ ( set @ A ) )
% 0.17/0.43 != ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % empty_not_UNIV
% 0.17/0.43 thf(fact_85_subtr__H,axiom,
% 0.17/0.43 ! [Tr0: dtree,N2: n,Tr1: dtree] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 0.17/0.43 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ ( gram_L1451583624elle_H @ Tr0 @ N2 ) )
% 0.17/0.43 => ? [N1: n] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N1 )
% 0.17/0.43 & ( Tr1
% 0.17/0.43 = ( gram_L1451583624elle_H @ Tr0 @ N1 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr_H
% 0.17/0.43 thf(fact_86_wf__H,axiom,
% 0.17/0.43 ! [Tr0: dtree,N2: n] :
% 0.17/0.43 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.17/0.43 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 0.17/0.43 => ( gram_L864798063lle_wf @ ( gram_L1451583624elle_H @ Tr0 @ N2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % wf_H
% 0.17/0.43 thf(fact_87_inItr__root__in,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr: dtree,N2: n] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ Ns @ Tr @ N2 )
% 0.17/0.43 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.17/0.43
% 0.17/0.43 % inItr_root_in
% 0.17/0.43 thf(fact_88_inItr_OBase,axiom,
% 0.17/0.43 ! [Tr: dtree,Ns: set @ n] :
% 0.17/0.43 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.17/0.43 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % inItr.Base
% 0.17/0.43 thf(fact_89_hsubst__eq,axiom,
% 0.17/0.43 ! [Tr: dtree,Tr0: dtree] :
% 0.17/0.43 ( ( ( root @ Tr )
% 0.17/0.43 = ( root @ Tr0 ) )
% 0.17/0.43 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 0.17/0.43 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % hsubst_eq
% 0.17/0.43 thf(fact_90_subtr__inItr,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr: dtree,N2: n,Tr1: dtree] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ Ns @ Tr @ N2 )
% 0.17/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.17/0.43 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr_inItr
% 0.17/0.43 thf(fact_91_wf__hsubst,axiom,
% 0.17/0.43 ! [Tr0: dtree,Tr: dtree] :
% 0.17/0.43 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.17/0.43 => ( ( gram_L864798063lle_wf @ Tr )
% 0.17/0.43 => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % wf_hsubst
% 0.17/0.43 thf(fact_92_H__r__def,axiom,
% 0.17/0.43 ( gram_L1221482026le_H_r
% 0.17/0.43 = ( ^ [Tr02: dtree,N: n] : ( root @ ( gram_L315592705e_pick @ Tr02 @ N ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % H_r_def
% 0.17/0.43 thf(fact_93_L__rec__notin,axiom,
% 0.17/0.43 ! [N2: n,Ns: set @ n] :
% 0.17/0.43 ( ~ ( member @ n @ N2 @ Ns )
% 0.17/0.43 => ( ( gram_L1451583628elle_L @ Ns @ N2 )
% 0.17/0.43 = ( insert @ ( set @ t ) @ ( bot_bot @ ( set @ t ) ) @ ( bot_bot @ ( set @ ( set @ t ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % L_rec_notin
% 0.17/0.43 thf(fact_94_iso__tuple__UNIV__I,axiom,
% 0.17/0.43 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % iso_tuple_UNIV_I
% 0.17/0.43 thf(fact_95_is__singleton__the__elem,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( is_singleton @ A )
% 0.17/0.43 = ( ^ [A4: set @ A] :
% 0.17/0.43 ( A4
% 0.17/0.43 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singleton_the_elem
% 0.17/0.43 thf(fact_96_the__elem__eq,axiom,
% 0.17/0.43 ! [A: $tType,X3: A] :
% 0.17/0.43 ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = X3 ) ).
% 0.17/0.43
% 0.17/0.43 % the_elem_eq
% 0.17/0.43 thf(fact_97_hsubst__def,axiom,
% 0.17/0.43 ( gram_L1004374585hsubst
% 0.17/0.43 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % hsubst_def
% 0.17/0.43 thf(fact_98_Fr__rcut,axiom,
% 0.17/0.43 ! [Tr0: dtree] : ( ord_less_eq @ ( set @ t ) @ ( gram_L861583724lle_Fr @ ( top_top @ ( set @ n ) ) @ ( gram_L1828378864e_rcut @ Tr0 ) ) @ ( gram_L861583724lle_Fr @ ( top_top @ ( set @ n ) ) @ Tr0 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Fr_rcut
% 0.17/0.43 thf(fact_99_inFr__hsubst__notin,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr: dtree,T: t,Tr0: dtree] :
% 0.17/0.43 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T )
% 0.17/0.43 => ( ~ ( member @ n @ ( root @ Tr0 ) @ Ns )
% 0.17/0.43 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % inFr_hsubst_notin
% 0.17/0.43 thf(fact_100_order__refl,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % order_refl
% 0.17/0.43 thf(fact_101_subsetI,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ! [X2: A] :
% 0.17/0.43 ( ( member @ A @ X2 @ A2 )
% 0.17/0.43 => ( member @ A @ X2 @ B3 ) )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % subsetI
% 0.17/0.43 thf(fact_102_subset__antisym,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A2 )
% 0.17/0.43 => ( A2 = B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_antisym
% 0.17/0.43 thf(fact_103_subset__empty,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( A2
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_empty
% 0.17/0.43 thf(fact_104_empty__subsetI,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 0.17/0.43
% 0.17/0.43 % empty_subsetI
% 0.17/0.43 thf(fact_105_insert__subset,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 0.17/0.43 = ( ( member @ A @ X3 @ B3 )
% 0.17/0.43 & ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_subset
% 0.17/0.43 thf(fact_106_singleton__insert__inj__eq,axiom,
% 0.17/0.43 ! [A: $tType,B2: A,A3: A,A2: set @ A] :
% 0.17/0.43 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( insert @ A @ A3 @ A2 ) )
% 0.17/0.43 = ( ( A3 = B2 )
% 0.17/0.43 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % singleton_insert_inj_eq
% 0.17/0.43 thf(fact_107_singleton__insert__inj__eq_H,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,A2: set @ A,B2: A] :
% 0.17/0.43 ( ( ( insert @ A @ A3 @ A2 )
% 0.17/0.43 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = ( ( A3 = B2 )
% 0.17/0.43 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % singleton_insert_inj_eq'
% 0.17/0.43 thf(fact_108_set__mp,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( member @ A @ X3 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % set_mp
% 0.17/0.43 thf(fact_109_in__mono,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( member @ A @ X3 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % in_mono
% 0.17/0.43 thf(fact_110_subsetD,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A,C: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ( member @ A @ C @ A2 )
% 0.17/0.43 => ( member @ A @ C @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subsetD
% 0.17/0.43 thf(fact_111_subsetCE,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A,C: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ( member @ A @ C @ A2 )
% 0.17/0.43 => ( member @ A @ C @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subsetCE
% 0.17/0.43 thf(fact_112_equalityE,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( A2 = B3 )
% 0.17/0.43 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % equalityE
% 0.17/0.43 thf(fact_113_subset__eq,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) )
% 0.17/0.43 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.17/0.43 ! [X: A] :
% 0.17/0.43 ( ( member @ A @ X @ A4 )
% 0.17/0.43 => ( member @ A @ X @ B5 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_eq
% 0.17/0.43 thf(fact_114_equalityD1,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( A2 = B3 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % equalityD1
% 0.17/0.43 thf(fact_115_equalityD2,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( A2 = B3 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % equalityD2
% 0.17/0.43 thf(fact_116_set__rev__mp,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( member @ A @ X3 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % set_rev_mp
% 0.17/0.43 thf(fact_117_subset__iff,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) )
% 0.17/0.43 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.17/0.43 ! [T2: A] :
% 0.17/0.43 ( ( member @ A @ T2 @ A4 )
% 0.17/0.43 => ( member @ A @ T2 @ B5 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_iff
% 0.17/0.43 thf(fact_118_rev__subsetD,axiom,
% 0.17/0.43 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C @ A2 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( member @ A @ C @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rev_subsetD
% 0.17/0.43 thf(fact_119_subset__refl,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.17/0.43
% 0.17/0.43 % subset_refl
% 0.17/0.43 thf(fact_120_Collect__mono,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.17/0.43 ( ! [X2: A] :
% 0.17/0.43 ( ( P @ X2 )
% 0.17/0.43 => ( Q @ X2 ) )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_mono
% 0.17/0.43 thf(fact_121_subset__trans,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A,C4: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C4 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_trans
% 0.17/0.43 thf(fact_122_le__funD,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( ord @ B @ ( type2 @ B ) )
% 0.17/0.43 => ! [F2: A > B,G: A > B,X3: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 0.17/0.43 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % le_funD
% 0.17/0.43 thf(fact_123_le__funE,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( ord @ B @ ( type2 @ B ) )
% 0.17/0.43 => ! [F2: A > B,G: A > B,X3: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 0.17/0.43 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % le_funE
% 0.17/0.43 thf(fact_124_le__funI,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( ord @ B @ ( type2 @ B ) )
% 0.17/0.43 => ! [F2: A > B,G: A > B] :
% 0.17/0.43 ( ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G @ X2 ) )
% 0.17/0.43 => ( ord_less_eq @ ( A > B ) @ F2 @ G ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % le_funI
% 0.17/0.43 thf(fact_125_set__eq__subset,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 0.17/0.43 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.17/0.43 & ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % set_eq_subset
% 0.17/0.43 thf(fact_126_contra__subsetD,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A,C: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ~ ( member @ A @ C @ B3 )
% 0.17/0.43 => ~ ( member @ A @ C @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % contra_subsetD
% 0.17/0.43 thf(fact_127_le__fun__def,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( ord @ B @ ( type2 @ B ) )
% 0.17/0.43 => ( ( ord_less_eq @ ( A > B ) )
% 0.17/0.43 = ( ^ [F: A > B,G2: A > B] :
% 0.17/0.43 ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % le_fun_def
% 0.17/0.43 thf(fact_128_Collect__mono__iff,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.17/0.43 = ( ! [X: A] :
% 0.17/0.43 ( ( P @ X )
% 0.17/0.43 => ( Q @ X ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_mono_iff
% 0.17/0.43 thf(fact_129_order__subst1,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType] :
% 0.17/0.43 ( ( ( order @ B @ ( type2 @ B ) )
% 0.17/0.43 & ( order @ A @ ( type2 @ A ) ) )
% 0.17/0.43 => ! [A3: A,F2: B > A,B2: B,C: B] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B2 ) )
% 0.17/0.43 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.17/0.43 => ( ! [X2: B,Y: B] :
% 0.17/0.43 ( ( ord_less_eq @ B @ X2 @ Y )
% 0.17/0.43 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 0.17/0.43 => ( ord_less_eq @ A @ A3 @ ( F2 @ C ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % order_subst1
% 0.17/0.43 thf(fact_130_order__subst2,axiom,
% 0.17/0.43 ! [A: $tType,C2: $tType] :
% 0.17/0.43 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.17/0.43 & ( order @ A @ ( type2 @ A ) ) )
% 0.17/0.43 => ! [A3: A,B2: A,F2: A > C2,C: C2] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 => ( ( ord_less_eq @ C2 @ ( F2 @ B2 ) @ C )
% 0.17/0.43 => ( ! [X2: A,Y: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.17/0.43 => ( ord_less_eq @ C2 @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 0.17/0.43 => ( ord_less_eq @ C2 @ ( F2 @ A3 ) @ C ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % order_subst2
% 0.17/0.43 thf(fact_131_ord__eq__le__subst,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType] :
% 0.17/0.43 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.17/0.43 & ( ord @ A @ ( type2 @ A ) ) )
% 0.17/0.43 => ! [A3: A,F2: B > A,B2: B,C: B] :
% 0.17/0.43 ( ( A3
% 0.17/0.43 = ( F2 @ B2 ) )
% 0.17/0.43 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.17/0.43 => ( ! [X2: B,Y: B] :
% 0.17/0.43 ( ( ord_less_eq @ B @ X2 @ Y )
% 0.17/0.43 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 0.17/0.43 => ( ord_less_eq @ A @ A3 @ ( F2 @ C ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ord_eq_le_subst
% 0.17/0.43 thf(fact_132_ord__le__eq__subst,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType] :
% 0.17/0.43 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.17/0.43 & ( ord @ A @ ( type2 @ A ) ) )
% 0.17/0.43 => ! [A3: A,B2: A,F2: A > B,C: B] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 => ( ( ( F2 @ B2 )
% 0.17/0.43 = C )
% 0.17/0.43 => ( ! [X2: A,Y: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.17/0.43 => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 0.17/0.43 => ( ord_less_eq @ B @ ( F2 @ A3 ) @ C ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ord_le_eq_subst
% 0.17/0.43 thf(fact_133_eq__iff,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.17/0.43 = ( ^ [X: A,Y2: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.17/0.43 & ( ord_less_eq @ A @ Y2 @ X ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % eq_iff
% 0.17/0.43 thf(fact_134_antisym,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A,Y3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.17/0.43 => ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.17/0.43 => ( X3 = Y3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % antisym
% 0.17/0.43 thf(fact_135_linear,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A,Y3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.17/0.43 | ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % linear
% 0.17/0.43 thf(fact_136_eq__refl,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A,Y3: A] :
% 0.17/0.43 ( ( X3 = Y3 )
% 0.17/0.43 => ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % eq_refl
% 0.17/0.43 thf(fact_137_le__cases,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A,Y3: A] :
% 0.17/0.43 ( ~ ( ord_less_eq @ A @ X3 @ Y3 )
% 0.17/0.43 => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % le_cases
% 0.17/0.43 thf(fact_138_order_Otrans,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A,C: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.17/0.43 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % order.trans
% 0.17/0.43 thf(fact_139_le__cases3,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A,Y3: A,Z2: A] :
% 0.17/0.43 ( ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.17/0.43 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 0.17/0.43 => ( ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.17/0.43 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.17/0.43 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.17/0.43 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 0.17/0.43 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 0.17/0.43 => ~ ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.17/0.43 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.17/0.43 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.17/0.43 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.17/0.43 => ~ ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % le_cases3
% 0.17/0.43 thf(fact_140_antisym__conv,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [Y3: A,X3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.17/0.43 => ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.17/0.43 = ( X3 = Y3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % antisym_conv
% 0.17/0.43 thf(fact_141_ord__eq__le__trans,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ord @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A,C: A] :
% 0.17/0.43 ( ( A3 = B2 )
% 0.17/0.43 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.17/0.43 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ord_eq_le_trans
% 0.17/0.43 thf(fact_142_ord__le__eq__trans,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ord @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A,C: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 => ( ( B2 = C )
% 0.17/0.43 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ord_le_eq_trans
% 0.17/0.43 thf(fact_143_order__class_Oorder_Oantisym,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 => ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.17/0.43 => ( A3 = B2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % order_class.order.antisym
% 0.17/0.43 thf(fact_144_order__trans,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A,Y3: A,Z2: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.17/0.43 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.17/0.43 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % order_trans
% 0.17/0.43 thf(fact_145_dual__order_Orefl,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % dual_order.refl
% 0.17/0.43 thf(fact_146_linorder__wlog,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [P: A > A > $o,A3: A,B2: A] :
% 0.17/0.43 ( ! [A5: A,B6: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A5 @ B6 )
% 0.17/0.43 => ( P @ A5 @ B6 ) )
% 0.17/0.43 => ( ! [A5: A,B6: A] :
% 0.17/0.43 ( ( P @ B6 @ A5 )
% 0.17/0.43 => ( P @ A5 @ B6 ) )
% 0.17/0.43 => ( P @ A3 @ B2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % linorder_wlog
% 0.17/0.43 thf(fact_147_dual__order_Otrans,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [B2: A,A3: A,C: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.17/0.43 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.17/0.43 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % dual_order.trans
% 0.17/0.43 thf(fact_148_dual__order_Oantisym,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [B2: A,A3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.17/0.43 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 => ( A3 = B2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % dual_order.antisym
% 0.17/0.43 thf(fact_149_top__set__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( top_top @ ( set @ A ) )
% 0.17/0.43 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % top_set_def
% 0.17/0.43 thf(fact_150_top__empty__eq,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( top_top @ ( A > $o ) )
% 0.17/0.43 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % top_empty_eq
% 0.17/0.43 thf(fact_151_bot_Oextremum,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot.extremum
% 0.17/0.43 thf(fact_152_bot_Oextremum__unique,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 0.17/0.43 = ( A3
% 0.17/0.43 = ( bot_bot @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot.extremum_unique
% 0.17/0.43 thf(fact_153_bot_Oextremum__uniqueI,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 0.17/0.43 => ( A3
% 0.17/0.43 = ( bot_bot @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot.extremum_uniqueI
% 0.17/0.43 thf(fact_154_top__greatest,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order_top @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ ( top_top @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % top_greatest
% 0.17/0.43 thf(fact_155_top_Oextremum__unique,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order_top @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 0.17/0.43 = ( A3
% 0.17/0.43 = ( top_top @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % top.extremum_unique
% 0.17/0.43 thf(fact_156_top_Oextremum__uniqueI,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order_top @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 0.17/0.43 => ( A3
% 0.17/0.43 = ( top_top @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % top.extremum_uniqueI
% 0.17/0.43 thf(fact_157_subset__UNIV,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_UNIV
% 0.17/0.43 thf(fact_158_insert__mono,axiom,
% 0.17/0.43 ! [A: $tType,C4: set @ A,D3: set @ A,A3: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A3 @ C4 ) @ ( insert @ A @ A3 @ D3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_mono
% 0.17/0.43 thf(fact_159_subset__insert,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ~ ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 0.17/0.43 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_insert
% 0.17/0.43 thf(fact_160_subset__insertI,axiom,
% 0.17/0.43 ! [A: $tType,B3: set @ A,A3: A] : ( ord_less_eq @ ( set @ A ) @ B3 @ ( insert @ A @ A3 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_insertI
% 0.17/0.43 thf(fact_161_subset__insertI2,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A,B2: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_insertI2
% 0.17/0.43 thf(fact_162_inFr__root__in,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr: dtree,T: t] :
% 0.17/0.43 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T )
% 0.17/0.43 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.17/0.43
% 0.17/0.43 % inFr_root_in
% 0.17/0.43 thf(fact_163_not__root__inFr,axiom,
% 0.17/0.43 ! [Tr: dtree,Ns: set @ n,T: t] :
% 0.17/0.43 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 0.17/0.43 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T ) ) ).
% 0.17/0.43
% 0.17/0.43 % not_root_inFr
% 0.17/0.43 thf(fact_164_subtr__inFr,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr: dtree,T: t,Tr1: dtree] :
% 0.17/0.43 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T )
% 0.17/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.17/0.43 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr_inFr
% 0.17/0.43 thf(fact_165_pairwise__subset,axiom,
% 0.17/0.43 ! [A: $tType,P: A > A > $o,S3: set @ A,T3: set @ A] :
% 0.17/0.43 ( ( pairwise @ A @ P @ S3 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ T3 @ S3 )
% 0.17/0.43 => ( pairwise @ A @ P @ T3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pairwise_subset
% 0.17/0.43 thf(fact_166_subset__singletonD,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,X3: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( ( A2
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 | ( A2
% 0.17/0.43 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_singletonD
% 0.17/0.43 thf(fact_167_subset__singleton__iff,axiom,
% 0.17/0.43 ! [A: $tType,X4: set @ A,A3: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ X4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = ( ( X4
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 | ( X4
% 0.17/0.43 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_singleton_iff
% 0.17/0.43 thf(fact_168_unfold_I1_J,axiom,
% 0.17/0.43 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 0.17/0.43 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.17/0.43 = ( Rt @ B2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % unfold(1)
% 0.17/0.43 thf(fact_169_insert__subsetI,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A,X4: set @ A] :
% 0.17/0.43 ( ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ X4 @ A2 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X4 ) @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_subsetI
% 0.17/0.43 thf(fact_170_subset__emptyI,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ! [X2: A] :
% 0.17/0.43 ~ ( member @ A @ X2 @ A2 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_emptyI
% 0.17/0.43 thf(fact_171_Pow__empty,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( pow @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( insert @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Pow_empty
% 0.17/0.43 thf(fact_172_Pow__singleton__iff,axiom,
% 0.17/0.43 ! [A: $tType,X4: set @ A,Y5: set @ A] :
% 0.17/0.43 ( ( ( pow @ A @ X4 )
% 0.17/0.43 = ( insert @ ( set @ A ) @ Y5 @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) )
% 0.17/0.43 = ( ( X4
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 & ( Y5
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Pow_singleton_iff
% 0.17/0.43 thf(fact_173_top1I,axiom,
% 0.17/0.43 ! [A: $tType,X3: A] : ( top_top @ ( A > $o ) @ X3 ) ).
% 0.17/0.43
% 0.17/0.43 % top1I
% 0.17/0.43 thf(fact_174_Pow__iff,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ ( set @ A ) @ A2 @ ( pow @ A @ B3 ) )
% 0.17/0.43 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Pow_iff
% 0.17/0.43 thf(fact_175_PowI,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( member @ ( set @ A ) @ A2 @ ( pow @ A @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % PowI
% 0.17/0.43 thf(fact_176_Pow__UNIV,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( pow @ A @ ( top_top @ ( set @ A ) ) )
% 0.17/0.43 = ( top_top @ ( set @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Pow_UNIV
% 0.17/0.43 thf(fact_177_Pow__top,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] : ( member @ ( set @ A ) @ A2 @ ( pow @ A @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Pow_top
% 0.17/0.43 thf(fact_178_Pow__bottom,axiom,
% 0.17/0.43 ! [A: $tType,B3: set @ A] : ( member @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ ( pow @ A @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Pow_bottom
% 0.17/0.43 thf(fact_179_Pow__mono,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( pow @ A @ A2 ) @ ( pow @ A @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Pow_mono
% 0.17/0.43 thf(fact_180_PowD,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ ( set @ A ) @ A2 @ ( pow @ A @ B3 ) )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % PowD
% 0.17/0.43 thf(fact_181_subtr__mono,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Ns3: set @ n] :
% 0.17/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 0.17/0.43 => ( gram_L716654942_subtr @ Ns3 @ Tr1 @ Tr22 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subtr_mono
% 0.17/0.43 thf(fact_182_inFr__mono,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr: dtree,T: t,Ns3: set @ n] :
% 0.17/0.43 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 0.17/0.43 => ( gram_L1333338417e_inFr @ Ns3 @ Tr @ T ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % inFr_mono
% 0.17/0.43 thf(fact_183_inItr__mono,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr: dtree,N2: n,Ns3: set @ n] :
% 0.17/0.43 ( ( gram_L830233218_inItr @ Ns @ Tr @ N2 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 0.17/0.43 => ( gram_L830233218_inItr @ Ns3 @ Tr @ N2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % inItr_mono
% 0.17/0.43 thf(fact_184_Pow__not__empty,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( pow @ A @ A2 )
% 0.17/0.43 != ( bot_bot @ ( set @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Pow_not_empty
% 0.17/0.43 thf(fact_185_H__def,axiom,
% 0.17/0.43 ( gram_L1451583624elle_H
% 0.17/0.43 = ( ^ [Tr02: dtree] : ( unfold @ n @ ( gram_L1221482026le_H_r @ Tr02 ) @ ( gram_L1221482011le_H_c @ Tr02 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % H_def
% 0.17/0.43 thf(fact_186_top__conj_I2_J,axiom,
% 0.17/0.43 ! [A: $tType,P: $o,X3: A] :
% 0.17/0.43 ( ( P
% 0.17/0.43 & ( top_top @ ( A > $o ) @ X3 ) )
% 0.17/0.43 = P ) ).
% 0.17/0.43
% 0.17/0.43 % top_conj(2)
% 0.17/0.43 thf(fact_187_top__conj_I1_J,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,P: $o] :
% 0.17/0.43 ( ( ( top_top @ ( A > $o ) @ X3 )
% 0.17/0.43 & P )
% 0.17/0.43 = P ) ).
% 0.17/0.43
% 0.17/0.43 % top_conj(1)
% 0.17/0.43 thf(fact_188_root__Node,axiom,
% 0.17/0.43 ! [N2: n,As: set @ ( sum_sum @ t @ dtree )] :
% 0.17/0.43 ( ( root @ ( node @ N2 @ As ) )
% 0.17/0.43 = N2 ) ).
% 0.17/0.43
% 0.17/0.43 % root_Node
% 0.17/0.43 thf(fact_189_subset__Compl__singleton,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B2: A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.43 = ( ~ ( member @ A @ B2 @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_Compl_singleton
% 0.17/0.43 thf(fact_190_Compl__eq__Compl__iff,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ( uminus_uminus @ ( set @ A ) @ A2 )
% 0.17/0.43 = ( uminus_uminus @ ( set @ A ) @ B3 ) )
% 0.17/0.43 = ( A2 = B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Compl_eq_Compl_iff
% 0.17/0.43 thf(fact_191_Compl__iff,axiom,
% 0.17/0.43 ! [A: $tType,C: A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.17/0.43 = ( ~ ( member @ A @ C @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Compl_iff
% 0.17/0.43 thf(fact_192_ComplI,axiom,
% 0.17/0.43 ! [A: $tType,C: A,A2: set @ A] :
% 0.17/0.43 ( ~ ( member @ A @ C @ A2 )
% 0.17/0.43 => ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ComplI
% 0.17/0.43 thf(fact_193_Compl__subset__Compl__iff,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( uminus_uminus @ ( set @ A ) @ B3 ) )
% 0.17/0.43 = ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Compl_subset_Compl_iff
% 0.17/0.43 thf(fact_194_Compl__anti__mono,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B3 ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Compl_anti_mono
% 0.17/0.43 thf(fact_195_subset__Compl__self__eq,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.17/0.43 = ( A2
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_Compl_self_eq
% 0.17/0.43 thf(fact_196_Compl__UNIV__eq,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( uminus_uminus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Compl_UNIV_eq
% 0.17/0.43 thf(fact_197_Compl__empty__eq,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( uminus_uminus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Compl_empty_eq
% 0.17/0.43 thf(fact_198_double__complement,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.17/0.43 = A2 ) ).
% 0.17/0.43
% 0.17/0.43 % double_complement
% 0.17/0.43 thf(fact_199_ComplD,axiom,
% 0.17/0.43 ! [A: $tType,C: A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.17/0.43 => ~ ( member @ A @ C @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % ComplD
% 0.17/0.43 thf(fact_200_compl__bot__eq,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.17/0.43 => ( ( uminus_uminus @ A @ ( bot_bot @ A ) )
% 0.17/0.43 = ( top_top @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % compl_bot_eq
% 0.17/0.43 thf(fact_201_compl__top__eq,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.17/0.43 => ( ( uminus_uminus @ A @ ( top_top @ A ) )
% 0.17/0.43 = ( bot_bot @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % compl_top_eq
% 0.17/0.43 thf(fact_202_compl__le__compl__iff,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A,Y3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ ( uminus_uminus @ A @ Y3 ) )
% 0.17/0.43 = ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % compl_le_compl_iff
% 0.17/0.43 thf(fact_203_compl__mono,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A,Y3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.17/0.43 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y3 ) @ ( uminus_uminus @ A @ X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % compl_mono
% 0.17/0.43 thf(fact_204_compl__le__swap1,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [Y3: A,X3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ Y3 @ ( uminus_uminus @ A @ X3 ) )
% 0.17/0.43 => ( ord_less_eq @ A @ X3 @ ( uminus_uminus @ A @ Y3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % compl_le_swap1
% 0.17/0.43 thf(fact_205_compl__le__swap2,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [Y3: A,X3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y3 ) @ X3 )
% 0.17/0.43 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ Y3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % compl_le_swap2
% 0.17/0.43 thf(fact_206_neg__le__iff__le,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [B2: A,A3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A3 ) )
% 0.17/0.43 = ( ord_less_eq @ A @ A3 @ B2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % neg_le_iff_le
% 0.17/0.43 thf(fact_207_le__minus__iff,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ ( uminus_uminus @ A @ B2 ) )
% 0.17/0.43 = ( ord_less_eq @ A @ B2 @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % le_minus_iff
% 0.17/0.43 thf(fact_208_le__imp__neg__le,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % le_imp_neg_le
% 0.17/0.43 thf(fact_209_minus__le__iff,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A3 ) @ B2 )
% 0.17/0.43 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ A3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % minus_le_iff
% 0.17/0.43 thf(fact_210_inFr__hsubst__minus,axiom,
% 0.17/0.43 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T: t] :
% 0.17/0.43 ( ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T )
% 0.17/0.43 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T ) ) ).
% 0.17/0.43
% 0.17/0.43 % inFr_hsubst_minus
% 0.17/0.43 thf(fact_211_corec_I1_J,axiom,
% 0.17/0.43 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ),B2: A] :
% 0.17/0.43 ( ( root @ ( corec @ A @ Rt @ Ct @ B2 ) )
% 0.17/0.43 = ( Rt @ B2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % corec(1)
% 0.17/0.43 thf(fact_212_DiffI,axiom,
% 0.17/0.43 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C @ A2 )
% 0.17/0.43 => ( ~ ( member @ A @ C @ B3 )
% 0.17/0.43 => ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % DiffI
% 0.17/0.43 thf(fact_213_Diff__iff,axiom,
% 0.17/0.43 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 0.17/0.43 = ( ( member @ A @ C @ A2 )
% 0.17/0.43 & ~ ( member @ A @ C @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_iff
% 0.17/0.43 thf(fact_214_Diff__idemp,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ B3 )
% 0.17/0.43 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_idemp
% 0.17/0.43 thf(fact_215_Diff__cancel,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( minus_minus @ ( set @ A ) @ A2 @ A2 )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_cancel
% 0.17/0.43 thf(fact_216_empty__Diff,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % empty_Diff
% 0.17/0.43 thf(fact_217_Diff__empty,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( minus_minus @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = A2 ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_empty
% 0.17/0.43 thf(fact_218_insert__Diff1,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,B3: set @ A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ X3 @ B3 )
% 0.17/0.43 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 0.17/0.43 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_Diff1
% 0.17/0.43 thf(fact_219_Diff__insert0,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ~ ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 0.17/0.43 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_insert0
% 0.17/0.43 thf(fact_220_Diff__eq__empty__iff,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ( minus_minus @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_eq_empty_iff
% 0.17/0.43 thf(fact_221_Diff__UNIV,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ( ( minus_minus @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_UNIV
% 0.17/0.43 thf(fact_222_insert__Diff__single,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.43 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.43 = ( insert @ A @ A3 @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_Diff_single
% 0.17/0.43 thf(fact_223_diff__eq__diff__less__eq,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A,C: A,D2: A] :
% 0.17/0.43 ( ( ( minus_minus @ A @ A3 @ B2 )
% 0.17/0.43 = ( minus_minus @ A @ C @ D2 ) )
% 0.17/0.43 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 = ( ord_less_eq @ A @ C @ D2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % diff_eq_diff_less_eq
% 0.17/0.43 thf(fact_224_diff__right__mono,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A,C: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % diff_right_mono
% 0.17/0.43 thf(fact_225_diff__left__mono,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [B2: A,A3: A,C: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.17/0.43 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A3 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % diff_left_mono
% 0.17/0.43 thf(fact_226_diff__mono,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A,B2: A,D2: A,C: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.17/0.43 => ( ( ord_less_eq @ A @ D2 @ C )
% 0.17/0.43 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B2 @ D2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % diff_mono
% 0.17/0.43 thf(fact_227_insert__Diff__if,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,B3: set @ A,A2: set @ A] :
% 0.17/0.43 ( ( ( member @ A @ X3 @ B3 )
% 0.17/0.43 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 0.17/0.43 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) )
% 0.17/0.43 & ( ~ ( member @ A @ X3 @ B3 )
% 0.17/0.43 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 0.17/0.43 = ( insert @ A @ X3 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_Diff_if
% 0.17/0.43 thf(fact_228_DiffE,axiom,
% 0.17/0.43 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 0.17/0.43 => ~ ( ( member @ A @ C @ A2 )
% 0.17/0.43 => ( member @ A @ C @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % DiffE
% 0.17/0.43 thf(fact_229_DiffD1,axiom,
% 0.17/0.43 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 0.17/0.43 => ( member @ A @ C @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % DiffD1
% 0.17/0.43 thf(fact_230_DiffD2,axiom,
% 0.17/0.43 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 0.17/0.43 => ~ ( member @ A @ C @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % DiffD2
% 0.17/0.43 thf(fact_231_subset__Diff__insert,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A,C4: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B3 @ ( insert @ A @ X3 @ C4 ) ) )
% 0.17/0.43 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B3 @ C4 ) )
% 0.17/0.43 & ~ ( member @ A @ X3 @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_Diff_insert
% 0.17/0.43 thf(fact_232_Diff__insert__absorb,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A] :
% 0.17/0.43 ( ~ ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_insert_absorb
% 0.17/0.43 thf(fact_233_Diff__insert2,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,A3: A,B3: set @ A] :
% 0.17/0.43 ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B3 ) )
% 0.17/0.43 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_insert2
% 0.17/0.43 thf(fact_234_insert__Diff,axiom,
% 0.17/0.43 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ A3 @ A2 )
% 0.17/0.43 => ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.43 = A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_Diff
% 0.17/0.43 thf(fact_235_Diff__insert,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,A3: A,B3: set @ A] :
% 0.17/0.43 ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B3 ) )
% 0.17/0.43 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_insert
% 0.17/0.43 thf(fact_236_Diff__mono,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,C4: set @ A,D3: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ D3 @ B3 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ ( minus_minus @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_mono
% 0.17/0.43 thf(fact_237_Diff__subset,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ A2 ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_subset
% 0.17/0.43 thf(fact_238_double__diff,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A,C4: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C4 )
% 0.17/0.43 => ( ( minus_minus @ ( set @ A ) @ B3 @ ( minus_minus @ ( set @ A ) @ C4 @ A2 ) )
% 0.17/0.43 = A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % double_diff
% 0.17/0.43 thf(fact_239_Compl__eq__Diff__UNIV,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( uminus_uminus @ ( set @ A ) )
% 0.17/0.43 = ( minus_minus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Compl_eq_Diff_UNIV
% 0.17/0.43 thf(fact_240_Diff__single__insert,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,X3: A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B3 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Diff_single_insert
% 0.17/0.43 thf(fact_241_subset__insert__iff,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,X3: A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 0.17/0.43 = ( ( ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B3 ) )
% 0.17/0.43 & ( ~ ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_insert_iff
% 0.17/0.43 thf(fact_242_Compl__insert,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,A2: set @ A] :
% 0.17/0.43 ( ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) )
% 0.17/0.43 = ( minus_minus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Compl_insert
% 0.17/0.43 thf(fact_243_remove__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( remove @ A )
% 0.17/0.43 = ( ^ [X: A,A4: set @ A] : ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % remove_def
% 0.17/0.43 thf(fact_244_psubset__insert__iff,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,X3: A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 0.17/0.43 = ( ( ( member @ A @ X3 @ B3 )
% 0.17/0.43 => ( ord_less @ ( set @ A ) @ A2 @ B3 ) )
% 0.17/0.43 & ( ~ ( member @ A @ X3 @ B3 )
% 0.17/0.43 => ( ( ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ord_less @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B3 ) )
% 0.17/0.43 & ( ~ ( member @ A @ X3 @ A2 )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % psubset_insert_iff
% 0.17/0.43 thf(fact_245_member__remove,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,Y3: A,A2: set @ A] :
% 0.17/0.43 ( ( member @ A @ X3 @ ( remove @ A @ Y3 @ A2 ) )
% 0.17/0.43 = ( ( member @ A @ X3 @ A2 )
% 0.17/0.43 & ( X3 != Y3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % member_remove
% 0.17/0.43 thf(fact_246_psubsetI,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ( ( A2 != B3 )
% 0.17/0.43 => ( ord_less @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % psubsetI
% 0.17/0.43 thf(fact_247_bot_Onot__eq__extremum,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A] :
% 0.17/0.43 ( ( A3
% 0.17/0.43 != ( bot_bot @ A ) )
% 0.17/0.43 = ( ord_less @ A @ ( bot_bot @ A ) @ A3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot.not_eq_extremum
% 0.17/0.43 thf(fact_248_bot_Oextremum__strict,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A3: A] :
% 0.17/0.43 ~ ( ord_less @ A @ A3 @ ( bot_bot @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot.extremum_strict
% 0.17/0.43 thf(fact_249_not__psubset__empty,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A] :
% 0.17/0.43 ~ ( ord_less @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % not_psubset_empty
% 0.17/0.43 thf(fact_250_psubset__imp__ex__mem,axiom,
% 0.17/0.43 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less @ ( set @ A ) @ A2 @ B3 )
% 0.17/0.43 => ? [B6: A] : ( member @ A @ B6 @ ( minus_minus @ ( set @ A ) @ B3 @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % psubset_imp_ex_mem
% 0.17/0.43 thf(fact_251_leD,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [Y3: A,X3: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.17/0.43 => ~ ( ord_less @ A @ X3 @ Y3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % leD
% 0.17/0.43 thf(fact_252_leI,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( linorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X3: A,Y3: A] :
% 0.17/0.43 ( ~ ( ord_less @ A @ X3 @ Y3 )
% 0.17/0.43 => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % leI
% 0.17/0.43 thf(fact_253_le__less,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ( ( ord_less_eq @ A )
% 0.17/0.43 = ( ^ [X: A,Y2: A] :
% 0.17/0.43 ( ( ord_less @ A @ X @ Y2 )
% 0.17/0.43 | ( X = Y2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % le_less
% 0.17/0.43 thf(fact_254_less__le,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( order @ A @ ( type2 @ A ) )
% 0.17/0.43 => ( ( ord_less @ A )
% 0.17/0.43 = ( ^ [X: A,Y2: A] :
% 0.17/0.43 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.17/0.43 & ( X != Y2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % less_le
% 0.17/0.43 thf(fact_255_order__le__less__subst1,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType] :
% 0.17/0.43 ( ( ( order @ B @ ( type2 @ B ) )
% 0.17/0.43 & ( order @ A @ ( type2 @ A ) ) )
% 0.17/0.43 => ! [A3: A,F2: B > A,B2: B,C: B] :
% 0.17/0.43 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B2 ) )
% 0.17/0.43 => ( ( ord_less @ B @ B2 @ C )
% 0.17/0.43 => ( ! [X2: B,Y: B] :
% 0.17/0.43 ( ( ord_less @ B @ X2 @ Y )
% 0.17/0.43 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 0.17/0.43 => ( ord_less @ A @ A3 @ ( F2 @ C ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % order_le_less_subst1
% 0.17/0.43
% 0.17/0.43 %----Type constructors (25)
% 0.17/0.43 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.17/0.43 ! [A6: $tType,A7: $tType] :
% 0.17/0.43 ( ( boolean_algebra @ A7 @ ( type2 @ A7 ) )
% 0.17/0.43 => ( boolean_algebra @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.17/0.43 ! [A6: $tType,A7: $tType] :
% 0.17/0.43 ( ( order_top @ A7 @ ( type2 @ A7 ) )
% 0.17/0.43 => ( order_top @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.17/0.43 ! [A6: $tType,A7: $tType] :
% 0.17/0.43 ( ( order_bot @ A7 @ ( type2 @ A7 ) )
% 0.17/0.43 => ( order_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.17/0.43 ! [A6: $tType,A7: $tType] :
% 0.17/0.43 ( ( preorder @ A7 @ ( type2 @ A7 ) )
% 0.17/0.43 => ( preorder @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.17/0.43 ! [A6: $tType,A7: $tType] :
% 0.17/0.43 ( ( order @ A7 @ ( type2 @ A7 ) )
% 0.17/0.43 => ( order @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_fun___Orderings_Otop,axiom,
% 0.17/0.43 ! [A6: $tType,A7: $tType] :
% 0.17/0.43 ( ( top @ A7 @ ( type2 @ A7 ) )
% 0.17/0.43 => ( top @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_fun___Orderings_Oord,axiom,
% 0.17/0.43 ! [A6: $tType,A7: $tType] :
% 0.17/0.43 ( ( ord @ A7 @ ( type2 @ A7 ) )
% 0.17/0.43 => ( ord @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_fun___Orderings_Obot,axiom,
% 0.17/0.43 ! [A6: $tType,A7: $tType] :
% 0.17/0.43 ( ( bot @ A7 @ ( type2 @ A7 ) )
% 0.17/0.43 => ( bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_1,axiom,
% 0.17/0.43 ! [A6: $tType] : ( boolean_algebra @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_Set_Oset___Orderings_Oorder__top_2,axiom,
% 0.17/0.43 ! [A6: $tType] : ( order_top @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_Set_Oset___Orderings_Oorder__bot_3,axiom,
% 0.17/0.43 ! [A6: $tType] : ( order_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 0.17/0.43 ! [A6: $tType] : ( preorder @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.17/0.43 ! [A6: $tType] : ( order @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_Set_Oset___Orderings_Otop_6,axiom,
% 0.17/0.43 ! [A6: $tType] : ( top @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_Set_Oset___Orderings_Oord_7,axiom,
% 0.17/0.43 ! [A6: $tType] : ( ord @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_Set_Oset___Orderings_Obot_8,axiom,
% 0.17/0.43 ! [A6: $tType] : ( bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_9,axiom,
% 0.17/0.43 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_HOL_Obool___Orderings_Oorder__top_10,axiom,
% 0.17/0.43 order_top @ $o @ ( type2 @ $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_HOL_Obool___Orderings_Oorder__bot_11,axiom,
% 0.17/0.43 order_bot @ $o @ ( type2 @ $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 0.17/0.43 preorder @ $o @ ( type2 @ $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.17/0.43 linorder @ $o @ ( type2 @ $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_HOL_Obool___Orderings_Oorder_13,axiom,
% 0.17/0.43 order @ $o @ ( type2 @ $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_HOL_Obool___Orderings_Otop_14,axiom,
% 0.17/0.43 top @ $o @ ( type2 @ $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_HOL_Obool___Orderings_Oord_15,axiom,
% 0.17/0.43 ord @ $o @ ( type2 @ $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(tcon_HOL_Obool___Orderings_Obot_16,axiom,
% 0.17/0.43 bot @ $o @ ( type2 @ $o ) ).
% 0.17/0.43
% 0.17/0.43 %----Conjectures (2)
% 0.17/0.43 thf(conj_0,hypothesis,
% 0.17/0.43 $true ).
% 0.17/0.43
% 0.17/0.43 thf(conj_1,conjecture,
% 0.17/0.43 ? [Tr6: dtree] :
% 0.17/0.43 ( ( ( bot_bot @ ( set @ t ) )
% 0.17/0.43 = ( gram_L861583724lle_Fr @ ns @ Tr6 ) )
% 0.17/0.43 & ( gram_L864798063lle_wf @ Tr6 )
% 0.17/0.43 & ( ( root @ Tr6 )
% 0.17/0.43 = n2 )
% 0.17/0.43 & ( gram_L646766332egular @ Tr6 ) ) ).
% 0.17/0.43
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 ------------------------
% 2.86/1.52 ---- Embedded in THF ---
% 2.86/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.86/1.53 %%% Generated on Tue Feb 24 04:17:34 EST 2026
% 2.86/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.86/1.53 %%% Logic specification used:
% 2.86/1.53 %%% thf(spec, logic, $$dhol).
% 2.86/1.53
% 2.86/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2DTF30331.p
% 2.86/1.53 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 2.86/1.53 thf(ty_t_DTree_Odtree, type, dtree: $tType).
% 2.86/1.53 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.86/1.53 thf(ty_t_DTree_OT, type, t: $tType).
% 2.86/1.53 thf(ty_t_DTree_ON, type, n: $tType).
% 2.86/1.53 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.86/1.53 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.86/1.53 thf(sy_c_DTree_ONode, type, node: (n > ((set @ ((sum_sum @ t) @ dtree)) > dtree))).
% 2.86/1.53 thf(sy_c_DTree_Ocorec, type, corec: (!> [A:$tType]: (((A > n) > ((A > (set @ ((sum_sum @ t) @ ((sum_sum @ dtree) @ A)))) > (A > dtree)))))).
% 2.86/1.53 thf(sy_c_DTree_Odtree_Oroot, type, root: (dtree > n)).
% 2.86/1.53 thf(sy_c_DTree_Ounfold, type, unfold: (!> [A:$tType]: (((A > n) > ((A > (set @ ((sum_sum @ t) @ A))) > (A > dtree)))))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFr, type, gram_L861583724lle_Fr: ((set @ n) > (dtree > (set @ t)))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH, type, gram_L1451583624elle_H: (dtree > (n > dtree))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c, type, gram_L1221482011le_H_c: (dtree > (n > (set @ ((sum_sum @ t) @ n))))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r, type, gram_L1221482026le_H_r: (dtree > (n > n))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OL, type, gram_L1451583628elle_L: ((set @ n) > (n > (set @ (set @ t))))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr, type, gram_L1231612515_deftr: (n > dtree)).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst, type, gram_L1004374585hsubst: (dtree > (dtree > dtree))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c, type, gram_L1905609002ubst_c: (dtree > (dtree > (set @ ((sum_sum @ t) @ dtree))))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r, type, gram_L1905609017ubst_r: (dtree > n)).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr, type, gram_L1333338417e_inFr: ((set @ n) > (dtree > (t > $o)))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr, type, gram_L830233218_inItr: ((set @ n) > (dtree > (n > $o)))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Opick, type, gram_L315592705e_pick: (dtree > (n > dtree))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Orcut, type, gram_L1828378864e_rcut: (dtree > dtree)).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oreg, type, gram_L1918716148le_reg: ((n > dtree) > (dtree > $o))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oregular, type, gram_L646766332egular: (dtree > $o)).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr, type, gram_L716654942_subtr: ((set @ n) > (dtree > (dtree > $o)))).
% 2.86/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf, type, gram_L864798063lle_wf: (dtree > $o)).
% 2.86/1.53 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.86/1.53 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 2.86/1.53 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.86/1.53 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.86/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.86/1.53 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.86/1.53 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.86/1.53 thf(sy_c_Relation_Oinv__imagep, type, inv_imagep: (!> [B:$tType,A:$tType]: (((B > (B > $o)) > ((A > B) > (A > (A > $o))))))).
% 2.86/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.86/1.53 thf(sy_c_Set_OPow, type, pow: (!> [A:$tType]: (((set @ A) > (set @ (set @ A)))))).
% 2.86/1.53 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.86/1.53 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.86/1.53 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.86/1.53 thf(sy_c_Set_Opairwise, type, pairwise: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.86/1.53 thf(sy_c_Set_Oremove, type, remove: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.86/1.53 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.86/1.53 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.86/1.53 thf(sy_v_n, type, n2: n).
% 2.86/1.53 thf(sy_v_ns, type, ns: (set @ n)).
% 2.86/1.53 thf(fact_0_assms, axiom, (~ ((((member @ n) @ n2) @ ns)))).
% 2.86/1.53 thf(fact_1_not__root__Fr, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((~ ((((member @ n) @ (root @ Tr)) @ Ns))) => (((gram_L861583724lle_Fr @ Ns) @ Tr) = (bot_bot @ (set @ t))))))).
% 2.86/1.53 thf(fact_2_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 2.86/1.53 thf(fact_3_all__not__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X:A]: ((~ ((((member @ A) @ X) @ A2))))) = (A2 = (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_4_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X:A]: ((~ ((P @ X))))))))).
% 2.86/1.53 thf(fact_5_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X:A]: ((~ ((P @ X))))))))).
% 2.86/1.53 thf(fact_6_bot__apply, axiom, (! [C2:$tType,D:$tType]: ((((bot @ C2) @ (type2 @ C2)) => ((bot_bot @ (D > C2)) = (^ [X:D]: ((bot_bot @ C2)))))))).
% 2.86/1.53 thf(fact_7_hsubst__r__def, axiom, (gram_L1905609017ubst_r = root)).
% 2.86/1.53 thf(fact_8_root__rcut, axiom, (! [Tr0:dtree]: (((root @ (gram_L1828378864e_rcut @ Tr0)) = (root @ Tr0))))).
% 2.86/1.53 thf(fact_9_regular__def2, axiom, (gram_L646766332egular = (^ [Tr2:dtree]: ((? [F:(n > dtree)]: ((((gram_L1918716148le_reg @ F) @ Tr2) & (! [N:n]: (((root @ (F @ N)) = N)))))))))).
% 2.86/1.53 thf(fact_10_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.86/1.53 thf(fact_11_equals0D, axiom, (! [A:$tType,A2:(set @ A),A3:A]: (((A2 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A3) @ A2))))))).
% 2.86/1.53 thf(fact_12_equals0I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [Y:A]: ((~ ((((member @ A) @ Y) @ A2))))) => (A2 = (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_13_ex__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((? [X:A]: ((((member @ A) @ X) @ A2))) = (A2 != (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_14_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.86/1.53 thf(fact_15_reg__root, axiom, (! [F2:(n > dtree),Tr:dtree]: ((((gram_L1918716148le_reg @ F2) @ Tr) => ((F2 @ (root @ Tr)) = Tr))))).
% 2.86/1.53 thf(fact_16_regular__def, axiom, (gram_L646766332egular = (^ [Tr2:dtree]: ((? [F:(n > dtree)]: (((gram_L1918716148le_reg @ F) @ Tr2))))))).
% 2.86/1.53 thf(fact_17_wf__rcut, axiom, (! [Tr0:dtree]: (((gram_L864798063lle_wf @ Tr0) => (gram_L864798063lle_wf @ (gram_L1828378864e_rcut @ Tr0)))))).
% 2.86/1.53 thf(fact_18_regular__rcut, axiom, (! [Tr0:dtree]: ((gram_L646766332egular @ (gram_L1828378864e_rcut @ Tr0))))).
% 2.86/1.53 thf(fact_19_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X:A]: ((bot_bot @ B)))))))).
% 2.86/1.53 thf(fact_20_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A4:(set @ A)]: ((A4 = (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_21_rcut__eq, axiom, (! [Tr0:dtree]: ((((gram_L1828378864e_rcut @ Tr0) = Tr0) = ((gram_L1918716148le_reg @ (gram_L1451583624elle_H @ Tr0)) @ Tr0))))).
% 2.86/1.53 thf(fact_22_rcut__reg, axiom, (! [Tr0:dtree]: ((((gram_L1918716148le_reg @ (gram_L1451583624elle_H @ Tr0)) @ Tr0) => ((gram_L1828378864e_rcut @ Tr0) = Tr0))))).
% 2.86/1.53 thf(fact_23_reg__rcut, axiom, (! [Tr0:dtree]: (((gram_L1918716148le_reg @ (gram_L1451583624elle_H @ Tr0)) @ (gram_L1828378864e_rcut @ Tr0))))).
% 2.86/1.53 thf(fact_24_rcut__def, axiom, (gram_L1828378864e_rcut = (^ [Tr02:dtree]: (((gram_L1451583624elle_H @ Tr02) @ (root @ Tr02)))))).
% 2.86/1.53 thf(fact_25_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.86/1.53 thf(fact_26_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_27_root__deftr, axiom, (! [N2:n]: (((root @ (gram_L1231612515_deftr @ N2)) = N2)))).
% 2.86/1.53 thf(fact_28_is__singletonI_H, axiom, (! [A:$tType,A2:(set @ A)]: (((A2 != (bot_bot @ (set @ A))) => ((! [X2:A,Y:A]: (((((member @ A) @ X2) @ A2) => ((((member @ A) @ Y) @ A2) => (X2 = Y))))) => ((is_singleton @ A) @ A2)))))).
% 2.86/1.53 thf(fact_29_reg__deftr, axiom, (! [N2:n]: (((gram_L1918716148le_reg @ gram_L1231612515_deftr) @ (gram_L1231612515_deftr @ N2))))).
% 2.86/1.53 thf(fact_30_reg__def2, axiom, (gram_L1918716148le_reg = (^ [F:(n > dtree),Tr2:dtree]: ((! [Ns2:(set @ n),Tr3:dtree]: (((((gram_L716654942_subtr @ Ns2) @ Tr3) @ Tr2) => (Tr3 = (F @ (root @ Tr3)))))))))).
% 2.86/1.53 thf(fact_31_subtr__trans, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Tr32:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((((gram_L716654942_subtr @ Ns) @ Tr22) @ Tr32) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr32)))))).
% 2.86/1.53 thf(fact_32_subtr__deftr, axiom, (! [Ns:(set @ n),Tr4:dtree,N2:n]: (((((gram_L716654942_subtr @ Ns) @ Tr4) @ (gram_L1231612515_deftr @ N2)) => (Tr4 = (gram_L1231612515_deftr @ (root @ Tr4))))))).
% 2.86/1.53 thf(fact_33_subtr_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L716654942_subtr @ Ns) @ Tr) @ Tr))))).
% 2.86/1.53 thf(fact_34_subtr__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 2.86/1.53 thf(fact_35_subtr__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr22)) @ Ns))))).
% 2.86/1.53 thf(fact_36_wf__subtr, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr:dtree]: (((gram_L864798063lle_wf @ Tr1) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (gram_L864798063lle_wf @ Tr)))))).
% 2.86/1.53 thf(fact_37_reg__subtr, axiom, (! [F2:(n > dtree),Tr:dtree,Ns:(set @ n),Tr4:dtree]: ((((gram_L1918716148le_reg @ F2) @ Tr) => ((((gram_L716654942_subtr @ Ns) @ Tr4) @ Tr) => ((gram_L1918716148le_reg @ F2) @ Tr4)))))).
% 2.86/1.53 thf(fact_38_regular__subtr, axiom, (! [Tr:dtree,Ns:(set @ n),Tr4:dtree]: (((gram_L646766332egular @ Tr) => ((((gram_L716654942_subtr @ Ns) @ Tr4) @ Tr) => (gram_L646766332egular @ Tr4)))))).
% 2.86/1.53 thf(fact_39_wf__deftr, axiom, (! [N2:n]: ((gram_L864798063lle_wf @ (gram_L1231612515_deftr @ N2))))).
% 2.86/1.53 thf(fact_40_root__H__pick, axiom, (! [Tr0:dtree,N2:n]: (((root @ ((gram_L1451583624elle_H @ Tr0) @ N2)) = (root @ ((gram_L315592705e_pick @ Tr0) @ N2)))))).
% 2.86/1.53 thf(fact_41_reg__def, axiom, (gram_L1918716148le_reg = (^ [F:(n > dtree),Tr2:dtree]: ((! [Tr3:dtree]: (((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr3) @ Tr2) => (Tr3 = (F @ (root @ Tr3)))))))))).
% 2.86/1.53 thf(fact_42_in__inv__imagep, axiom, (! [B:$tType,A:$tType]: ((((inv_imagep @ A) @ B) = (^ [R:(A > (A > $o)),F:(B > A),X:B,Y2:B]: (((R @ (F @ X)) @ (F @ Y2)))))))).
% 2.86/1.53 thf(fact_43_is__singletonI, axiom, (! [A:$tType,X3:A]: (((is_singleton @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_44_inItr__subtr, axiom, (! [Ns:(set @ n),Tr:dtree,N2:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N2) => (? [Tr5:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr5) @ Tr) & ((root @ Tr5) = N2)))))))).
% 2.86/1.53 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.86/1.53 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A2)))) = A2)))).
% 2.86/1.53 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.86/1.53 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G:(A > B)]: (((! [X2:A]: (((F2 @ X2) = (G @ X2)))) => (F2 = G))))).
% 2.86/1.53 thf(fact_49_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((? [X:A]: ((A4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))))))))))).
% 2.86/1.53 thf(fact_50_is__singletonE, axiom, (! [A:$tType,A2:(set @ A)]: ((((is_singleton @ A) @ A2) => (~ ((! [X2:A]: ((A2 != (((insert @ A) @ X2) @ (bot_bot @ (set @ A)))))))))))).
% 2.86/1.53 thf(fact_51_root__hsubst, axiom, (! [Tr0:dtree,Tr:dtree]: (((root @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) = (root @ Tr))))).
% 2.86/1.53 thf(fact_52_pairwise__empty, axiom, (! [A:$tType,P:(A > (A > $o))]: ((((pairwise @ A) @ P) @ (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_53_top__apply, axiom, (! [C2:$tType,D:$tType]: ((((top @ C2) @ (type2 @ C2)) => ((top_top @ (D > C2)) = (^ [X:D]: ((top_top @ C2)))))))).
% 2.86/1.53 thf(fact_54_UNIV__I, axiom, (! [A:$tType,X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))).
% 2.86/1.53 thf(fact_55_insert__absorb2, axiom, (! [A:$tType,X3:A,A2:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ X3) @ A2)) = (((insert @ A) @ X3) @ A2))))).
% 2.86/1.53 thf(fact_56_insert__iff, axiom, (! [A:$tType,A3:A,B2:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B2) @ A2)) = ((A3 = B2) | (((member @ A) @ A3) @ A2)))))).
% 2.86/1.53 thf(fact_57_insertCI, axiom, (! [A:$tType,A3:A,B3:(set @ A),B2:A]: ((((~ ((((member @ A) @ A3) @ B3))) => (A3 = B2)) => (((member @ A) @ A3) @ (((insert @ A) @ B2) @ B3)))))).
% 2.86/1.53 thf(fact_58_singletonI, axiom, (! [A:$tType,A3:A]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_59_root__H, axiom, (! [Tr0:dtree,N2:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N2) => ((root @ ((gram_L1451583624elle_H @ Tr0) @ N2)) = N2))))).
% 2.86/1.53 thf(fact_60_subtr__pick, axiom, (! [Tr0:dtree,N2:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N2) => (((gram_L716654942_subtr @ (top_top @ (set @ n))) @ ((gram_L315592705e_pick @ Tr0) @ N2)) @ Tr0))))).
% 2.86/1.53 thf(fact_61_pairwise__def, axiom, (! [A:$tType]: (((pairwise @ A) = (^ [R2:(A > (A > $o)),S:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ S) => (! [Y2:A]: (((((member @ A) @ Y2) @ S) => ((X != Y2) => ((R2 @ X) @ Y2)))))))))))))).
% 2.86/1.53 thf(fact_62_wf__pick, axiom, (! [Tr0:dtree,N2:n]: (((gram_L864798063lle_wf @ Tr0) => ((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N2) => (gram_L864798063lle_wf @ ((gram_L315592705e_pick @ Tr0) @ N2))))))).
% 2.86/1.53 thf(fact_63_root__pick, axiom, (! [Tr0:dtree,N2:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N2) => ((root @ ((gram_L315592705e_pick @ Tr0) @ N2)) = N2))))).
% 2.86/1.53 thf(fact_64_mk__disjoint__insert, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => (? [B4:(set @ A)]: (((A2 = (((insert @ A) @ A3) @ B4)) & (~ ((((member @ A) @ A3) @ B4)))))))))).
% 2.86/1.53 thf(fact_65_pairwise__insert, axiom, (! [A:$tType,R3:(A > (A > $o)),X3:A,S2:(set @ A)]: (((((pairwise @ A) @ R3) @ (((insert @ A) @ X3) @ S2)) = ((! [Y2:A]: ((((((member @ A) @ Y2) @ S2) & (Y2 != X3)) => (((R3 @ X3) @ Y2) & ((R3 @ Y2) @ X3))))) & (((pairwise @ A) @ R3) @ S2)))))).
% 2.86/1.53 thf(fact_66_insert__commute, axiom, (! [A:$tType,X3:A,Y3:A,A2:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ Y3) @ A2)) = (((insert @ A) @ Y3) @ (((insert @ A) @ X3) @ A2)))))).
% 2.86/1.53 thf(fact_67_insert__eq__iff, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:A,B3:(set @ A)]: (((~ ((((member @ A) @ A3) @ A2))) => ((~ ((((member @ A) @ B2) @ B3))) => (((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B2) @ B3)) = (((A3 = B2) => (A2 = B3)) & ((A3 != B2) => (? [C3:(set @ A)]: (((A2 = (((insert @ A) @ B2) @ C3)) & ((~ ((((member @ A) @ B2) @ C3))) & ((B3 = (((insert @ A) @ A3) @ C3)) & (~ ((((member @ A) @ A3) @ C3)))))))))))))))).
% 2.86/1.53 thf(fact_68_insert__absorb, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => ((((insert @ A) @ A3) @ A2) = A2))))).
% 2.86/1.53 thf(fact_69_insert__ident, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ X3) @ A2))) => ((~ ((((member @ A) @ X3) @ B3))) => (((((insert @ A) @ X3) @ A2) = (((insert @ A) @ X3) @ B3)) = (A2 = B3))))))).
% 2.86/1.53 thf(fact_70_UNIV__witness, axiom, (! [A:$tType]: ((? [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A)))))))).
% 2.86/1.53 thf(fact_71_insert__UNIV, axiom, (! [A:$tType,X3:A]: (((((insert @ A) @ X3) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.86/1.53 thf(fact_72_Set_Oset__insert, axiom, (! [A:$tType,X3:A,A2:(set @ A)]: (((((member @ A) @ X3) @ A2) => (~ ((! [B4:(set @ A)]: (((A2 = (((insert @ A) @ X3) @ B4)) => (((member @ A) @ X3) @ B4)))))))))).
% 2.86/1.53 thf(fact_73_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X2:A]: ((((member @ A) @ X2) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 2.86/1.53 thf(fact_74_insertI2, axiom, (! [A:$tType,A3:A,B3:(set @ A),B2:A]: (((((member @ A) @ A3) @ B3) => (((member @ A) @ A3) @ (((insert @ A) @ B2) @ B3)))))).
% 2.86/1.53 thf(fact_75_insertI1, axiom, (! [A:$tType,A3:A,B3:(set @ A)]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ B3))))).
% 2.86/1.53 thf(fact_76_insertE, axiom, (! [A:$tType,A3:A,B2:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B2) @ A2)) => ((A3 != B2) => (((member @ A) @ A3) @ A2)))))).
% 2.86/1.53 thf(fact_77_pairwise__singleton, axiom, (! [A:$tType,P:(A > (A > $o)),A2:A]: ((((pairwise @ A) @ P) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_78_pick, axiom, (! [Tr0:dtree,N2:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N2) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ ((gram_L315592705e_pick @ Tr0) @ N2)) @ Tr0) & ((root @ ((gram_L315592705e_pick @ Tr0) @ N2)) = N2)))))).
% 2.86/1.53 thf(fact_79_singleton__inject, axiom, (! [A:$tType,A3:A,B2:A]: ((((((insert @ A) @ A3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A3 = B2))))).
% 2.86/1.53 thf(fact_80_insert__not__empty, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((insert @ A) @ A3) @ A2) != (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_81_doubleton__eq__iff, axiom, (! [A:$tType,A3:A,B2:A,C:A,D2:A]: ((((((insert @ A) @ A3) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A3 = C) & (B2 = D2)) | ((A3 = D2) & (B2 = C))))))).
% 2.86/1.53 thf(fact_82_singleton__iff, axiom, (! [A:$tType,B2:A,A3:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = (B2 = A3))))).
% 2.86/1.53 thf(fact_83_singletonD, axiom, (! [A:$tType,B2:A,A3:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) => (B2 = A3))))).
% 2.86/1.53 thf(fact_84_empty__not__UNIV, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) != (top_top @ (set @ A)))))).
% 2.86/1.53 thf(fact_85_subtr__H, axiom, (! [Tr0:dtree,N2:n,Tr1:dtree]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N2) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr1) @ ((gram_L1451583624elle_H @ Tr0) @ N2)) => (? [N1:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N1) & (Tr1 = ((gram_L1451583624elle_H @ Tr0) @ N1)))))))))).
% 2.86/1.53 thf(fact_86_wf__H, axiom, (! [Tr0:dtree,N2:n]: (((gram_L864798063lle_wf @ Tr0) => ((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N2) => (gram_L864798063lle_wf @ ((gram_L1451583624elle_H @ Tr0) @ N2))))))).
% 2.86/1.53 thf(fact_87_inItr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,N2:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 2.86/1.53 thf(fact_88_inItr_OBase, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L830233218_inItr @ Ns) @ Tr) @ (root @ Tr)))))).
% 2.86/1.53 thf(fact_89_hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => (((gram_L1004374585hsubst @ Tr0) @ Tr) = ((gram_L1004374585hsubst @ Tr0) @ Tr0)))))).
% 2.86/1.53 thf(fact_90_subtr__inItr, axiom, (! [Ns:(set @ n),Tr:dtree,N2:n,Tr1:dtree]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N2) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (((gram_L830233218_inItr @ Ns) @ Tr1) @ N2)))))).
% 2.86/1.53 thf(fact_91_wf__hsubst, axiom, (! [Tr0:dtree,Tr:dtree]: (((gram_L864798063lle_wf @ Tr0) => ((gram_L864798063lle_wf @ Tr) => (gram_L864798063lle_wf @ ((gram_L1004374585hsubst @ Tr0) @ Tr))))))).
% 2.86/1.53 thf(fact_92_H__r__def, axiom, (gram_L1221482026le_H_r = (^ [Tr02:dtree,N:n]: ((root @ ((gram_L315592705e_pick @ Tr02) @ N)))))).
% 2.86/1.53 thf(fact_93_L__rec__notin, axiom, (! [N2:n,Ns:(set @ n)]: (((~ ((((member @ n) @ N2) @ Ns))) => (((gram_L1451583628elle_L @ Ns) @ N2) = (((insert @ (set @ t)) @ (bot_bot @ (set @ t))) @ (bot_bot @ (set @ (set @ t))))))))).
% 2.86/1.53 thf(fact_94_iso__tuple__UNIV__I, axiom, (! [A:$tType,X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))).
% 2.86/1.53 thf(fact_95_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((A4 = (((insert @ A) @ ((the_elem @ A) @ A4)) @ (bot_bot @ (set @ A)))))))))).
% 2.86/1.53 thf(fact_96_the__elem__eq, axiom, (! [A:$tType,X3:A]: ((((the_elem @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) = X3)))).
% 2.86/1.53 thf(fact_97_hsubst__def, axiom, (gram_L1004374585hsubst = (^ [Tr02:dtree]: ((((unfold @ dtree) @ gram_L1905609017ubst_r) @ (gram_L1905609002ubst_c @ Tr02)))))).
% 2.86/1.53 thf(fact_98_Fr__rcut, axiom, (! [Tr0:dtree]: ((((ord_less_eq @ (set @ t)) @ ((gram_L861583724lle_Fr @ (top_top @ (set @ n))) @ (gram_L1828378864e_rcut @ Tr0))) @ ((gram_L861583724lle_Fr @ (top_top @ (set @ n))) @ Tr0))))).
% 2.86/1.53 thf(fact_99_inFr__hsubst__notin, axiom, (! [Ns:(set @ n),Tr:dtree,T:t,Tr0:dtree]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T) => ((~ ((((member @ n) @ (root @ Tr0)) @ Ns))) => (((gram_L1333338417e_inFr @ Ns) @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) @ T)))))).
% 2.86/1.53 thf(fact_100_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 2.86/1.53 thf(fact_101_subsetI, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A2) => (((member @ A) @ X2) @ B3)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B3))))).
% 2.86/1.53 thf(fact_102_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ A2) => (A2 = B3)))))).
% 2.86/1.53 thf(fact_103_subset__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = (A2 = (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_104_empty__subsetI, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2)))).
% 2.86/1.53 thf(fact_105_insert__subset, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ A2)) @ B3) = ((((member @ A) @ X3) @ B3) & (((ord_less_eq @ (set @ A)) @ A2) @ B3)))))).
% 2.86/1.53 thf(fact_106_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A3:A,A2:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A3) @ A2)) = ((A3 = B2) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_107_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:A]: ((((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A3 = B2) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_108_set__mp, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B3)))))).
% 2.86/1.53 thf(fact_109_in__mono, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B3)))))).
% 2.86/1.53 thf(fact_110_subsetD, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B3)))))).
% 2.86/1.53 thf(fact_111_subsetCE, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B3)))))).
% 2.86/1.53 thf(fact_112_equalityE, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((A2 = B3) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (~ ((((ord_less_eq @ (set @ A)) @ B3) @ A2)))))))))).
% 2.86/1.53 thf(fact_113_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B5)))))))))).
% 2.86/1.53 thf(fact_114_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((A2 = B3) => (((ord_less_eq @ (set @ A)) @ A2) @ B3))))).
% 2.86/1.53 thf(fact_115_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((A2 = B3) => (((ord_less_eq @ (set @ A)) @ B3) @ A2))))).
% 2.86/1.53 thf(fact_116_set__rev__mp, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ X3) @ A2) => ((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((member @ A) @ X3) @ B3)))))).
% 2.86/1.53 thf(fact_117_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A4) => (((member @ A) @ T2) @ B5)))))))))).
% 2.86/1.53 thf(fact_118_rev__subsetD, axiom, (! [A:$tType,C:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C) @ A2) => ((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((member @ A) @ C) @ B3)))))).
% 2.86/1.53 thf(fact_119_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 2.86/1.53 thf(fact_120_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) => (Q @ X2)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.86/1.53 thf(fact_121_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ C4) => (((ord_less_eq @ (set @ A)) @ A2) @ C4)))))).
% 2.86/1.53 thf(fact_122_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F2:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G) => (((ord_less_eq @ B) @ (F2 @ X3)) @ (G @ X3))))))))).
% 2.86/1.53 thf(fact_123_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F2:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G) => (((ord_less_eq @ B) @ (F2 @ X3)) @ (G @ X3))))))))).
% 2.86/1.53 thf(fact_124_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F2:(A > B),G:(A > B)]: (((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G @ X2)))) => (((ord_less_eq @ (A > B)) @ F2) @ G)))))))).
% 2.86/1.53 thf(fact_125_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z:(set @ A)]: ((Y4 = Z))) = (^ [A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))).
% 2.86/1.53 thf(fact_126_contra__subsetD, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((~ ((((member @ A) @ C) @ B3))) => (~ ((((member @ A) @ C) @ A2)))))))).
% 2.86/1.53 thf(fact_127_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F:(A > B),G2:(A > B)]: ((! [X:A]: ((((ord_less_eq @ B) @ (F @ X)) @ (G2 @ X))))))))))).
% 2.86/1.53 thf(fact_128_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X:A]: (((P @ X) => (Q @ X)))))))).
% 2.86/1.53 thf(fact_129_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,F2:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A3) @ (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X2:B,Y:B]: (((((ord_less_eq @ B) @ X2) @ Y) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y))))) => (((ord_less_eq @ A) @ A3) @ (F2 @ C))))))))))).
% 2.86/1.53 thf(fact_130_order__subst2, axiom, (! [A:$tType,C2:$tType]: (((((order @ C2) @ (type2 @ C2)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,B2:A,F2:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ C2) @ (F2 @ B2)) @ C) => ((! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => (((ord_less_eq @ C2) @ (F2 @ X2)) @ (F2 @ Y))))) => (((ord_less_eq @ C2) @ (F2 @ A3)) @ C)))))))))).
% 2.86/1.53 thf(fact_131_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,F2:(B > A),B2:B,C:B]: (((A3 = (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X2:B,Y:B]: (((((ord_less_eq @ B) @ X2) @ Y) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y))))) => (((ord_less_eq @ A) @ A3) @ (F2 @ C))))))))))).
% 2.86/1.53 thf(fact_132_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,B2:A,F2:(A > B),C:B]: (((((ord_less_eq @ A) @ A3) @ B2) => (((F2 @ B2) = C) => ((! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => (((ord_less_eq @ B) @ (F2 @ X2)) @ (F2 @ Y))))) => (((ord_less_eq @ B) @ (F2 @ A3)) @ C)))))))))).
% 2.86/1.53 thf(fact_133_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) & (((ord_less_eq @ A) @ Y2) @ X))))))))).
% 2.86/1.53 thf(fact_134_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ X3) => (X3 = Y3))))))))).
% 2.86/1.53 thf(fact_135_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) | (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 2.86/1.53 thf(fact_136_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y3:A]: (((X3 = Y3) => (((ord_less_eq @ A) @ X3) @ Y3)))))))).
% 2.86/1.53 thf(fact_137_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y3:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y3))) => (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 2.86/1.53 thf(fact_138_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 2.86/1.53 thf(fact_139_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y3:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ Z2)))) => (((((ord_less_eq @ A) @ Y3) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y3)))) => (((((ord_less_eq @ A) @ Z2) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ X3)))) => (((((ord_less_eq @ A) @ Y3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y3))))))))))))))))).
% 2.86/1.53 thf(fact_140_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y3:A,X3:A]: (((((ord_less_eq @ A) @ Y3) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y3) = (X3 = Y3))))))))).
% 2.86/1.53 thf(fact_141_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A3:A,B2:A,C:A]: (((A3 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 2.86/1.53 thf(fact_142_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A3:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 2.86/1.53 thf(fact_143_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A,B2:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ A) @ B2) @ A3) => (A3 = B2))))))))).
% 2.86/1.53 thf(fact_144_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 2.86/1.53 thf(fact_145_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 2.86/1.53 thf(fact_146_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A3:A,B2:A]: (((! [A5:A,B6:A]: (((((ord_less_eq @ A) @ A5) @ B6) => ((P @ A5) @ B6)))) => ((! [A5:A,B6:A]: ((((P @ B6) @ A5) => ((P @ A5) @ B6)))) => ((P @ A3) @ B2))))))))).
% 2.86/1.53 thf(fact_147_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A3:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A3) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A3))))))))).
% 2.86/1.53 thf(fact_148_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A3:A]: (((((ord_less_eq @ A) @ B2) @ A3) => ((((ord_less_eq @ A) @ A3) @ B2) => (A3 = B2))))))))).
% 2.86/1.53 thf(fact_149_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.86/1.53 thf(fact_150_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A))))))))).
% 2.86/1.53 thf(fact_151_bot_Oextremum, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A3))))))).
% 2.86/1.53 thf(fact_152_bot_Oextremum__unique, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ A3) @ (bot_bot @ A)) = (A3 = (bot_bot @ A))))))))).
% 2.86/1.53 thf(fact_153_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ A3) @ (bot_bot @ A)) => (A3 = (bot_bot @ A))))))))).
% 2.86/1.53 thf(fact_154_top__greatest, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ (top_top @ A)))))))).
% 2.86/1.53 thf(fact_155_top_Oextremum__unique, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A3) = (A3 = (top_top @ A))))))))).
% 2.86/1.53 thf(fact_156_top_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A3) => (A3 = (top_top @ A))))))))).
% 2.86/1.53 thf(fact_157_subset__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (top_top @ (set @ A)))))).
% 2.86/1.53 thf(fact_158_insert__mono, axiom, (! [A:$tType,C4:(set @ A),D3:(set @ A),A3:A]: (((((ord_less_eq @ (set @ A)) @ C4) @ D3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A3) @ C4)) @ (((insert @ A) @ A3) @ D3)))))).
% 2.86/1.53 thf(fact_159_subset__insert, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ X3) @ A2))) => ((((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ B3)) = (((ord_less_eq @ (set @ A)) @ A2) @ B3)))))).
% 2.86/1.53 thf(fact_160_subset__insertI, axiom, (! [A:$tType,B3:(set @ A),A3:A]: ((((ord_less_eq @ (set @ A)) @ B3) @ (((insert @ A) @ A3) @ B3))))).
% 2.86/1.53 thf(fact_161_subset__insertI2, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ B3)))))).
% 2.86/1.53 thf(fact_162_inFr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T:t]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 2.86/1.53 thf(fact_163_not__root__inFr, axiom, (! [Tr:dtree,Ns:(set @ n),T:t]: (((~ ((((member @ n) @ (root @ Tr)) @ Ns))) => (~ ((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T))))))).
% 2.86/1.53 thf(fact_164_subtr__inFr, axiom, (! [Ns:(set @ n),Tr:dtree,T:t,Tr1:dtree]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (((gram_L1333338417e_inFr @ Ns) @ Tr1) @ T)))))).
% 2.86/1.53 thf(fact_165_pairwise__subset, axiom, (! [A:$tType,P:(A > (A > $o)),S3:(set @ A),T3:(set @ A)]: (((((pairwise @ A) @ P) @ S3) => ((((ord_less_eq @ (set @ A)) @ T3) @ S3) => (((pairwise @ A) @ P) @ T3)))))).
% 2.86/1.53 thf(fact_166_subset__singletonD, axiom, (! [A:$tType,A2:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) => ((A2 = (bot_bot @ (set @ A))) | (A2 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_167_subset__singleton__iff, axiom, (! [A:$tType,X4:(set @ A),A3:A]: (((((ord_less_eq @ (set @ A)) @ X4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = ((X4 = (bot_bot @ (set @ A))) | (X4 = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_168_unfold_I1_J, axiom, (! [A:$tType,Rt:(A > n),Ct:(A > (set @ ((sum_sum @ t) @ A))),B2:A]: (((root @ ((((unfold @ A) @ Rt) @ Ct) @ B2)) = (Rt @ B2))))).
% 2.86/1.53 thf(fact_169_insert__subsetI, axiom, (! [A:$tType,X3:A,A2:(set @ A),X4:(set @ A)]: (((((member @ A) @ X3) @ A2) => ((((ord_less_eq @ (set @ A)) @ X4) @ A2) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ X4)) @ A2)))))).
% 2.86/1.53 thf(fact_170_subset__emptyI, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X2:A]: ((~ ((((member @ A) @ X2) @ A2))))) => (((ord_less_eq @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_171_Pow__empty, axiom, (! [A:$tType]: ((((pow @ A) @ (bot_bot @ (set @ A))) = (((insert @ (set @ A)) @ (bot_bot @ (set @ A))) @ (bot_bot @ (set @ (set @ A)))))))).
% 2.86/1.53 thf(fact_172_Pow__singleton__iff, axiom, (! [A:$tType,X4:(set @ A),Y5:(set @ A)]: (((((pow @ A) @ X4) = (((insert @ (set @ A)) @ Y5) @ (bot_bot @ (set @ (set @ A))))) = ((X4 = (bot_bot @ (set @ A))) & (Y5 = (bot_bot @ (set @ A)))))))).
% 2.86/1.53 thf(fact_173_top1I, axiom, (! [A:$tType,X3:A]: (((top_top @ (A > $o)) @ X3)))).
% 2.86/1.53 thf(fact_174_Pow__iff, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((member @ (set @ A)) @ A2) @ ((pow @ A) @ B3)) = (((ord_less_eq @ (set @ A)) @ A2) @ B3))))).
% 2.86/1.53 thf(fact_175_PowI, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((member @ (set @ A)) @ A2) @ ((pow @ A) @ B3)))))).
% 2.86/1.53 thf(fact_176_Pow__UNIV, axiom, (! [A:$tType]: ((((pow @ A) @ (top_top @ (set @ A))) = (top_top @ (set @ (set @ A))))))).
% 2.86/1.53 thf(fact_177_Pow__top, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (set @ A)) @ A2) @ ((pow @ A) @ A2))))).
% 2.86/1.53 thf(fact_178_Pow__bottom, axiom, (! [A:$tType,B3:(set @ A)]: ((((member @ (set @ A)) @ (bot_bot @ (set @ A))) @ ((pow @ A) @ B3))))).
% 2.86/1.53 thf(fact_179_Pow__mono, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((ord_less_eq @ (set @ (set @ A))) @ ((pow @ A) @ A2)) @ ((pow @ A) @ B3)))))).
% 2.86/1.53 thf(fact_180_PowD, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((member @ (set @ A)) @ A2) @ ((pow @ A) @ B3)) => (((ord_less_eq @ (set @ A)) @ A2) @ B3))))).
% 2.86/1.53 thf(fact_181_subtr__mono, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Ns3:(set @ n)]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((((ord_less_eq @ (set @ n)) @ Ns) @ Ns3) => (((gram_L716654942_subtr @ Ns3) @ Tr1) @ Tr22)))))).
% 2.86/1.53 thf(fact_182_inFr__mono, axiom, (! [Ns:(set @ n),Tr:dtree,T:t,Ns3:(set @ n)]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T) => ((((ord_less_eq @ (set @ n)) @ Ns) @ Ns3) => (((gram_L1333338417e_inFr @ Ns3) @ Tr) @ T)))))).
% 2.86/1.53 thf(fact_183_inItr__mono, axiom, (! [Ns:(set @ n),Tr:dtree,N2:n,Ns3:(set @ n)]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N2) => ((((ord_less_eq @ (set @ n)) @ Ns) @ Ns3) => (((gram_L830233218_inItr @ Ns3) @ Tr) @ N2)))))).
% 2.86/1.53 thf(fact_184_Pow__not__empty, axiom, (! [A:$tType,A2:(set @ A)]: ((((pow @ A) @ A2) != (bot_bot @ (set @ (set @ A))))))).
% 2.86/1.53 thf(fact_185_H__def, axiom, (gram_L1451583624elle_H = (^ [Tr02:dtree]: ((((unfold @ n) @ (gram_L1221482026le_H_r @ Tr02)) @ (gram_L1221482011le_H_c @ Tr02)))))).
% 2.86/1.53 thf(fact_186_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X3:A]: (((P & ((top_top @ (A > $o)) @ X3)) = P)))).
% 2.86/1.53 thf(fact_187_top__conj_I1_J, axiom, (! [A:$tType,X3:A,P:$o]: (((((top_top @ (A > $o)) @ X3) & P) = P)))).
% 2.86/1.53 thf(fact_188_root__Node, axiom, (! [N2:n,As:(set @ ((sum_sum @ t) @ dtree))]: (((root @ ((node @ N2) @ As)) = N2)))).
% 2.86/1.53 thf(fact_189_subset__Compl__singleton, axiom, (! [A:$tType,A2:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ ((uminus_uminus @ (set @ A)) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))) = (~ ((((member @ A) @ B2) @ A2))))))).
% 2.86/1.53 thf(fact_190_Compl__eq__Compl__iff, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A2) = ((uminus_uminus @ (set @ A)) @ B3)) = (A2 = B3))))).
% 2.86/1.53 thf(fact_191_Compl__iff, axiom, (! [A:$tType,C:A,A2:(set @ A)]: (((((member @ A) @ C) @ ((uminus_uminus @ (set @ A)) @ A2)) = (~ ((((member @ A) @ C) @ A2))))))).
% 2.86/1.53 thf(fact_192_ComplI, axiom, (! [A:$tType,C:A,A2:(set @ A)]: (((~ ((((member @ A) @ C) @ A2))) => (((member @ A) @ C) @ ((uminus_uminus @ (set @ A)) @ A2)))))).
% 2.86/1.53 thf(fact_193_Compl__subset__Compl__iff, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) @ ((uminus_uminus @ (set @ A)) @ B3)) = (((ord_less_eq @ (set @ A)) @ B3) @ A2))))).
% 2.86/1.53 thf(fact_194_Compl__anti__mono, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ B3)) @ ((uminus_uminus @ (set @ A)) @ A2)))))).
% 2.86/1.53 thf(fact_195_subset__Compl__self__eq, axiom, (! [A:$tType,A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ ((uminus_uminus @ (set @ A)) @ A2)) = (A2 = (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_196_Compl__UNIV__eq, axiom, (! [A:$tType]: ((((uminus_uminus @ (set @ A)) @ (top_top @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_197_Compl__empty__eq, axiom, (! [A:$tType]: ((((uminus_uminus @ (set @ A)) @ (bot_bot @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.86/1.53 thf(fact_198_double__complement, axiom, (! [A:$tType,A2:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) = A2)))).
% 2.86/1.53 thf(fact_199_ComplD, axiom, (! [A:$tType,C:A,A2:(set @ A)]: (((((member @ A) @ C) @ ((uminus_uminus @ (set @ A)) @ A2)) => (~ ((((member @ A) @ C) @ A2))))))).
% 2.86/1.53 thf(fact_200_compl__bot__eq, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (((uminus_uminus @ A) @ (bot_bot @ A)) = (top_top @ A)))))).
% 2.86/1.53 thf(fact_201_compl__top__eq, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (((uminus_uminus @ A) @ (top_top @ A)) = (bot_bot @ A)))))).
% 2.86/1.53 thf(fact_202_compl__le__compl__iff, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X3)) @ ((uminus_uminus @ A) @ Y3)) = (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 2.86/1.53 thf(fact_203_compl__mono, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y3)) @ ((uminus_uminus @ A) @ X3))))))))).
% 2.86/1.53 thf(fact_204_compl__le__swap1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [Y3:A,X3:A]: (((((ord_less_eq @ A) @ Y3) @ ((uminus_uminus @ A) @ X3)) => (((ord_less_eq @ A) @ X3) @ ((uminus_uminus @ A) @ Y3))))))))).
% 2.86/1.53 thf(fact_205_compl__le__swap2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [Y3:A,X3:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y3)) @ X3) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X3)) @ Y3)))))))).
% 2.86/1.53 thf(fact_206_neg__le__iff__le, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B2:A,A3:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A3)) = (((ord_less_eq @ A) @ A3) @ B2)))))))).
% 2.86/1.53 thf(fact_207_le__minus__iff, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B2:A]: (((((ord_less_eq @ A) @ A3) @ ((uminus_uminus @ A) @ B2)) = (((ord_less_eq @ A) @ B2) @ ((uminus_uminus @ A) @ A3))))))))).
% 2.86/1.53 thf(fact_208_le__imp__neg__le, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B2:A]: (((((ord_less_eq @ A) @ A3) @ B2) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A3))))))))).
% 2.86/1.53 thf(fact_209_minus__le__iff, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B2:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ A3)) @ B2) = (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B2)) @ A3)))))))).
% 2.86/1.53 thf(fact_210_inFr__hsubst__minus, axiom, (! [Ns:(set @ n),Tr0:dtree,Tr:dtree,T:t]: (((((gram_L1333338417e_inFr @ (((minus_minus @ (set @ n)) @ Ns) @ (((insert @ n) @ (root @ Tr0)) @ (bot_bot @ (set @ n))))) @ Tr) @ T) => (((gram_L1333338417e_inFr @ Ns) @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) @ T))))).
% 2.86/1.53 thf(fact_211_corec_I1_J, axiom, (! [A:$tType,Rt:(A > n),Ct:(A > (set @ ((sum_sum @ t) @ ((sum_sum @ dtree) @ A)))),B2:A]: (((root @ ((((corec @ A) @ Rt) @ Ct) @ B2)) = (Rt @ B2))))).
% 2.86/1.53 thf(fact_212_DiffI, axiom, (! [A:$tType,C:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C) @ A2) => ((~ ((((member @ A) @ C) @ B3))) => (((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B3))))))).
% 2.86/1.53 thf(fact_213_Diff__iff, axiom, (! [A:$tType,C:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) = ((((member @ A) @ C) @ A2) & (~ ((((member @ A) @ C) @ B3)))))))).
% 2.86/1.53 thf(fact_214_Diff__idemp, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) @ B3) = (((minus_minus @ (set @ A)) @ A2) @ B3))))).
% 2.86/1.53 thf(fact_215_Diff__cancel, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ A2) = (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_216_empty__Diff, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2) = (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_217_Diff__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = A2)))).
% 2.86/1.53 thf(fact_218_insert__Diff1, axiom, (! [A:$tType,X3:A,B3:(set @ A),A2:(set @ A)]: (((((member @ A) @ X3) @ B3) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A2)) @ B3) = (((minus_minus @ (set @ A)) @ A2) @ B3)))))).
% 2.86/1.53 thf(fact_219_Diff__insert0, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ X3) @ A2))) => ((((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ B3)) = (((minus_minus @ (set @ A)) @ A2) @ B3)))))).
% 2.86/1.53 thf(fact_220_Diff__eq__empty__iff, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: ((((((minus_minus @ (set @ A)) @ A2) @ B3) = (bot_bot @ (set @ A))) = (((ord_less_eq @ (set @ A)) @ A2) @ B3))))).
% 2.86/1.53 thf(fact_221_Diff__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_222_insert__Diff__single, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((insert @ A) @ A3) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) = (((insert @ A) @ A3) @ A2))))).
% 2.86/1.53 thf(fact_223_diff__eq__diff__less__eq, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B2:A,C:A,D2:A]: ((((((minus_minus @ A) @ A3) @ B2) = (((minus_minus @ A) @ C) @ D2)) => ((((ord_less_eq @ A) @ A3) @ B2) = (((ord_less_eq @ A) @ C) @ D2))))))))).
% 2.86/1.53 thf(fact_224_diff__right__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A3) @ C)) @ (((minus_minus @ A) @ B2) @ C))))))))).
% 2.86/1.53 thf(fact_225_diff__left__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B2:A,A3:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A3) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C) @ A3)) @ (((minus_minus @ A) @ C) @ B2))))))))).
% 2.86/1.53 thf(fact_226_diff__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B2:A,D2:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ A) @ D2) @ C) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A3) @ C)) @ (((minus_minus @ A) @ B2) @ D2)))))))))).
% 2.86/1.53 thf(fact_227_insert__Diff__if, axiom, (! [A:$tType,X3:A,B3:(set @ A),A2:(set @ A)]: ((((((member @ A) @ X3) @ B3) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A2)) @ B3) = (((minus_minus @ (set @ A)) @ A2) @ B3))) & ((~ ((((member @ A) @ X3) @ B3))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A2)) @ B3) = (((insert @ A) @ X3) @ (((minus_minus @ (set @ A)) @ A2) @ B3)))))))).
% 2.86/1.53 thf(fact_228_DiffE, axiom, (! [A:$tType,C:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) => (~ (((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B3)))))))).
% 2.86/1.53 thf(fact_229_DiffD1, axiom, (! [A:$tType,C:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) => (((member @ A) @ C) @ A2))))).
% 2.86/1.53 thf(fact_230_DiffD2, axiom, (! [A:$tType,C:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) => (~ ((((member @ A) @ C) @ B3))))))).
% 2.86/1.53 thf(fact_231_subset__Diff__insert, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),X3:A,C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B3) @ (((insert @ A) @ X3) @ C4))) = ((((ord_less_eq @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B3) @ C4)) & (~ ((((member @ A) @ X3) @ A2)))))))).
% 2.86/1.53 thf(fact_232_Diff__insert__absorb, axiom, (! [A:$tType,X3:A,A2:(set @ A)]: (((~ ((((member @ A) @ X3) @ A2))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A2)) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) = A2))))).
% 2.86/1.53 thf(fact_233_Diff__insert2, axiom, (! [A:$tType,A2:(set @ A),A3:A,B3:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B3)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) @ B3))))).
% 2.86/1.53 thf(fact_234_insert__Diff, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => ((((insert @ A) @ A3) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) = A2))))).
% 2.86/1.53 thf(fact_235_Diff__insert, axiom, (! [A:$tType,A2:(set @ A),A3:A,B3:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B3)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.86/1.53 thf(fact_236_Diff__mono, axiom, (! [A:$tType,A2:(set @ A),C4:(set @ A),D3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C4) => ((((ord_less_eq @ (set @ A)) @ D3) @ B3) => (((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) @ (((minus_minus @ (set @ A)) @ C4) @ D3))))))).
% 2.86/1.53 thf(fact_237_Diff__subset, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) @ A2)))).
% 2.86/1.53 thf(fact_238_double__diff, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ C4) => ((((minus_minus @ (set @ A)) @ B3) @ (((minus_minus @ (set @ A)) @ C4) @ A2)) = A2)))))).
% 2.86/1.53 thf(fact_239_Compl__eq__Diff__UNIV, axiom, (! [A:$tType]: (((uminus_uminus @ (set @ A)) = ((minus_minus @ (set @ A)) @ (top_top @ (set @ A))))))).
% 2.86/1.53 thf(fact_240_Diff__single__insert, axiom, (! [A:$tType,A2:(set @ A),X3:A,B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))) @ B3) => (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ B3)))))).
% 2.86/1.53 thf(fact_241_subset__insert__iff, axiom, (! [A:$tType,A2:(set @ A),X3:A,B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ B3)) = (((((member @ A) @ X3) @ A2) => (((ord_less_eq @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))) @ B3)) & ((~ ((((member @ A) @ X3) @ A2))) => (((ord_less_eq @ (set @ A)) @ A2) @ B3))))))).
% 2.86/1.53 thf(fact_242_Compl__insert, axiom, (! [A:$tType,X3:A,A2:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ (((insert @ A) @ X3) @ A2)) = (((minus_minus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))))).
% 2.86/1.53 thf(fact_243_remove__def, axiom, (! [A:$tType]: (((remove @ A) = (^ [X:A,A4:(set @ A)]: ((((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))))))))).
% 2.86/1.53 thf(fact_244_psubset__insert__iff, axiom, (! [A:$tType,A2:(set @ A),X3:A,B3:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ B3)) = (((((member @ A) @ X3) @ B3) => (((ord_less @ (set @ A)) @ A2) @ B3)) & ((~ ((((member @ A) @ X3) @ B3))) => (((((member @ A) @ X3) @ A2) => (((ord_less @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))) @ B3)) & ((~ ((((member @ A) @ X3) @ A2))) => (((ord_less_eq @ (set @ A)) @ A2) @ B3))))))))).
% 2.86/1.53 thf(fact_245_member__remove, axiom, (! [A:$tType,X3:A,Y3:A,A2:(set @ A)]: (((((member @ A) @ X3) @ (((remove @ A) @ Y3) @ A2)) = ((((member @ A) @ X3) @ A2) & (X3 != Y3)))))).
% 2.86/1.53 thf(fact_246_psubsetI, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((A2 != B3) => (((ord_less @ (set @ A)) @ A2) @ B3)))))).
% 2.86/1.53 thf(fact_247_bot_Onot__eq__extremum, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: (((A3 != (bot_bot @ A)) = (((ord_less @ A) @ (bot_bot @ A)) @ A3)))))))).
% 2.86/1.53 thf(fact_248_bot_Oextremum__strict, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ (bot_bot @ A)))))))))).
% 2.86/1.53 thf(fact_249_not__psubset__empty, axiom, (! [A:$tType,A2:(set @ A)]: ((~ ((((ord_less @ (set @ A)) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.86/1.53 thf(fact_250_psubset__imp__ex__mem, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B3) => (? [B6:A]: ((((member @ A) @ B6) @ (((minus_minus @ (set @ A)) @ B3) @ A2)))))))).
% 2.86/1.53 thf(fact_251_leD, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y3:A,X3:A]: (((((ord_less_eq @ A) @ Y3) @ X3) => (~ ((((ord_less @ A) @ X3) @ Y3)))))))))).
% 2.86/1.53 thf(fact_252_leI, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y3:A]: (((~ ((((ord_less @ A) @ X3) @ Y3))) => (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 2.86/1.53 thf(fact_253_le__less, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) | (X = Y2))))))))).
% 2.86/1.53 thf(fact_254_less__le, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) & (X != Y2))))))))).
% 2.86/1.53 thf(fact_255_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,F2:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A3) @ (F2 @ B2)) => ((((ord_less @ B) @ B2) @ C) => ((! [X2:B,Y:B]: (((((ord_less @ B) @ X2) @ Y) => (((ord_less @ A) @ (F2 @ X2)) @ (F2 @ Y))))) => (((ord_less @ A) @ A3) @ (F2 @ C))))))))))).
% 2.86/1.53 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A6:$tType,A7:$tType]: ((((boolean_algebra @ A7) @ (type2 @ A7)) => ((boolean_algebra @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A6:$tType,A7:$tType]: ((((order_top @ A7) @ (type2 @ A7)) => ((order_top @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A6:$tType,A7:$tType]: ((((order_bot @ A7) @ (type2 @ A7)) => ((order_bot @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A6:$tType,A7:$tType]: ((((preorder @ A7) @ (type2 @ A7)) => ((preorder @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Oorder, axiom, (! [A6:$tType,A7:$tType]: ((((order @ A7) @ (type2 @ A7)) => ((order @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Otop, axiom, (! [A6:$tType,A7:$tType]: ((((top @ A7) @ (type2 @ A7)) => ((top @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: ((((ord @ A7) @ (type2 @ A7)) => ((ord @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Obot, axiom, (! [A6:$tType,A7:$tType]: ((((bot @ A7) @ (type2 @ A7)) => ((bot @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.86/1.53 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_1, axiom, (! [A6:$tType]: (((boolean_algebra @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oorder__top_2, axiom, (! [A6:$tType]: (((order_top @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oorder__bot_3, axiom, (! [A6:$tType]: (((order_bot @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Opreorder_4, axiom, (! [A6:$tType]: (((preorder @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oorder_5, axiom, (! [A6:$tType]: (((order @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Otop_6, axiom, (! [A6:$tType]: (((top @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oord_7, axiom, (! [A6:$tType]: (((ord @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Obot_8, axiom, (! [A6:$tType]: (((bot @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.86/1.53 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_9, axiom, ((boolean_algebra @ $o) @ (type2 @ $o))).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oorder__top_10, axiom, ((order_top @ $o) @ (type2 @ $o))).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oorder__bot_11, axiom, ((order_bot @ $o) @ (type2 @ $o))).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Opreorder_12, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_13, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Otop_14, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oord_15, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Obot_16, axiom, ((bot @ $o) @ (type2 @ $o))).
% 2.86/1.53 thf(conj_0, hypothesis, $true).
% 2.86/1.53 thf(conj_1, conjecture, (? [Tr6:dtree]: ((((bot_bot @ (set @ t)) = ((gram_L861583724lle_Fr @ ns) @ Tr6)) & ((gram_L864798063lle_wf @ Tr6) & (((root @ Tr6) = n2) & (gram_L646766332egular @ Tr6))))))).
% 2.86/1.53 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2DTF30331.p
% 2.86/1.53 ------------------------
% 2.86/1.57 ---- Cleaned THF ---
% 2.86/1.57 thf(ty_t_Sum__Type_Osum,type,
% 2.86/1.57 sum_sum: $tType > $tType > $tType ).
% 2.86/1.57
% 2.86/1.57 thf(ty_t_DTree_Odtree,type,
% 2.86/1.57 dtree: $tType ).
% 2.86/1.57
% 2.86/1.57 thf(ty_t_Set_Oset,type,
% 2.86/1.57 set: $tType > $tType ).
% 2.86/1.57
% 2.86/1.57 thf(ty_t_DTree_OT,type,
% 2.86/1.57 t: $tType ).
% 2.86/1.57
% 2.86/1.57 thf(ty_t_DTree_ON,type,
% 2.86/1.57 n: $tType ).
% 2.86/1.57
% 2.86/1.57 thf(ty_t_itself,type,
% 2.86/1.57 itself: $tType > $tType ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_HOL_Otype,type,
% 2.86/1.57 type:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Orderings_Obot,type,
% 2.86/1.57 bot:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Orderings_Oord,type,
% 2.86/1.57 ord:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Orderings_Otop,type,
% 2.86/1.57 top:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Orderings_Oorder,type,
% 2.86/1.57 order:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Orderings_Olinorder,type,
% 2.86/1.57 linorder:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Orderings_Opreorder,type,
% 2.86/1.57 preorder:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.86/1.57 order_bot:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Orderings_Oorder__top,type,
% 2.86/1.57 order_top:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 2.86/1.57 boolean_algebra:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.86/1.57 ordered_ab_group_add:
% 2.86/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_DTree_ONode,type,
% 2.86/1.57 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_DTree_Ocorec,type,
% 2.86/1.57 corec:
% 2.86/1.57 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ) ) > A > dtree ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_DTree_Odtree_Oroot,type,
% 2.86/1.57 root: dtree > n ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_DTree_Ounfold,type,
% 2.86/1.57 unfold:
% 2.86/1.57 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFr,type,
% 2.86/1.57 gram_L861583724lle_Fr: ( set @ n ) > dtree > ( set @ t ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH,type,
% 2.86/1.57 gram_L1451583624elle_H: dtree > n > dtree ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c,type,
% 2.86/1.57 gram_L1221482011le_H_c: dtree > n > ( set @ ( sum_sum @ t @ n ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r,type,
% 2.86/1.57 gram_L1221482026le_H_r: dtree > n > n ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OL,type,
% 2.86/1.57 gram_L1451583628elle_L: ( set @ n ) > n > ( set @ ( set @ t ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 2.86/1.57 gram_L1231612515_deftr: n > dtree ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 2.86/1.57 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 2.86/1.57 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 2.86/1.57 gram_L1905609017ubst_r: dtree > n ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 2.86/1.57 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 2.86/1.57 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Opick,type,
% 2.86/1.57 gram_L315592705e_pick: dtree > n > dtree ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Orcut,type,
% 2.86/1.57 gram_L1828378864e_rcut: dtree > dtree ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oreg,type,
% 2.86/1.57 gram_L1918716148le_reg: ( n > dtree ) > dtree > $o ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oregular,type,
% 2.86/1.57 gram_L646766332egular: dtree > $o ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 2.86/1.57 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 2.86/1.57 gram_L864798063lle_wf: dtree > $o ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.86/1.57 minus_minus:
% 2.86/1.57 !>[A: $tType] : ( A > A > A ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 2.86/1.57 uminus_uminus:
% 2.86/1.57 !>[A: $tType] : ( A > A ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.86/1.57 bot_bot:
% 2.86/1.57 !>[A: $tType] : A ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.86/1.57 ord_less:
% 2.86/1.57 !>[A: $tType] : ( A > A > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.86/1.57 ord_less_eq:
% 2.86/1.57 !>[A: $tType] : ( A > A > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.86/1.57 top_top:
% 2.86/1.57 !>[A: $tType] : A ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Pure_Otype,type,
% 2.86/1.57 type2:
% 2.86/1.57 !>[A: $tType] : ( itself @ A ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Relation_Oinv__imagep,type,
% 2.86/1.57 inv_imagep:
% 2.86/1.57 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Set_OCollect,type,
% 2.86/1.57 collect:
% 2.86/1.57 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Set_OPow,type,
% 2.86/1.57 pow:
% 2.86/1.57 !>[A: $tType] : ( ( set @ A ) > ( set @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Set_Oinsert,type,
% 2.86/1.57 insert:
% 2.86/1.57 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Set_Ois__empty,type,
% 2.86/1.57 is_empty:
% 2.86/1.57 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Set_Ois__singleton,type,
% 2.86/1.57 is_singleton:
% 2.86/1.57 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Set_Opairwise,type,
% 2.86/1.57 pairwise:
% 2.86/1.57 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Set_Oremove,type,
% 2.86/1.57 remove:
% 2.86/1.57 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_Set_Othe__elem,type,
% 2.86/1.57 the_elem:
% 2.86/1.57 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_c_member,type,
% 2.86/1.57 member:
% 2.86/1.57 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(sy_v_n,type,
% 2.86/1.57 n2: n ).
% 2.86/1.57
% 2.86/1.57 thf(sy_v_ns,type,
% 2.86/1.57 ns: set @ n ).
% 2.86/1.57
% 2.86/1.57 thf(fact_0_assms,axiom,
% 2.86/1.57 ~ ( member @ n @ n2 @ ns ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_1_not__root__Fr,axiom,
% 2.86/1.57 ! [Tr: dtree,Ns: set @ n] :
% 2.86/1.57 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 2.86/1.57 => ( ( gram_L861583724lle_Fr @ Ns @ Tr )
% 2.86/1.57 = ( bot_bot @ ( set @ t ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_2_empty__iff,axiom,
% 2.86/1.57 ! [A: $tType,C: A] :
% 2.86/1.57 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_3_all__not__in__conv,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( ! [X: A] :
% 2.86/1.57 ~ ( member @ A @ X @ A2 ) )
% 2.86/1.57 = ( A2
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_4_Collect__empty__eq,axiom,
% 2.86/1.57 ! [A: $tType,P: A > $o] :
% 2.86/1.57 ( ( ( collect @ A @ P )
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 = ( ! [X: A] :
% 2.86/1.57 ~ ( P @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_5_empty__Collect__eq,axiom,
% 2.86/1.57 ! [A: $tType,P: A > $o] :
% 2.86/1.57 ( ( ( bot_bot @ ( set @ A ) )
% 2.86/1.57 = ( collect @ A @ P ) )
% 2.86/1.57 = ( ! [X: A] :
% 2.86/1.57 ~ ( P @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_6_bot__apply,axiom,
% 2.86/1.57 ! [C2: $tType,D: $tType] :
% 2.86/1.57 ( ( bot @ C2 @ ( type2 @ C2 ) )
% 2.86/1.57 => ( ( bot_bot @ ( D > C2 ) )
% 2.86/1.57 = ( ^ [X: D] : ( bot_bot @ C2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_7_hsubst__r__def,axiom,
% 2.86/1.57 gram_L1905609017ubst_r = root ).
% 2.86/1.57
% 2.86/1.57 thf(fact_8_root__rcut,axiom,
% 2.86/1.57 ! [Tr0: dtree] :
% 2.86/1.57 ( ( root @ ( gram_L1828378864e_rcut @ Tr0 ) )
% 2.86/1.57 = ( root @ Tr0 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_9_regular__def2,axiom,
% 2.86/1.57 ( gram_L646766332egular
% 2.86/1.57 = ( ^ [Tr2: dtree] :
% 2.86/1.57 ? [F: n > dtree] :
% 2.86/1.57 ( ( gram_L1918716148le_reg @ F @ Tr2 )
% 2.86/1.57 & ! [N: n] :
% 2.86/1.57 ( ( root @ ( F @ N ) )
% 2.86/1.57 = N ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_10_emptyE,axiom,
% 2.86/1.57 ! [A: $tType,A3: A] :
% 2.86/1.57 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_11_equals0D,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,A3: A] :
% 2.86/1.57 ( ( A2
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_12_equals0I,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ! [Y: A] :
% 2.86/1.57 ~ ( member @ A @ Y @ A2 )
% 2.86/1.57 => ( A2
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_13_ex__in__conv,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( ? [X: A] : ( member @ A @ X @ A2 ) )
% 2.86/1.57 = ( A2
% 2.86/1.57 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_14_bot__set__def,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( bot_bot @ ( set @ A ) )
% 2.86/1.57 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_15_reg__root,axiom,
% 2.86/1.57 ! [F2: n > dtree,Tr: dtree] :
% 2.86/1.57 ( ( gram_L1918716148le_reg @ F2 @ Tr )
% 2.86/1.57 => ( ( F2 @ ( root @ Tr ) )
% 2.86/1.57 = Tr ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_16_regular__def,axiom,
% 2.86/1.57 ( gram_L646766332egular
% 2.86/1.57 = ( ^ [Tr2: dtree] :
% 2.86/1.57 ? [F: n > dtree] : ( gram_L1918716148le_reg @ F @ Tr2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_17_wf__rcut,axiom,
% 2.86/1.57 ! [Tr0: dtree] :
% 2.86/1.57 ( ( gram_L864798063lle_wf @ Tr0 )
% 2.86/1.57 => ( gram_L864798063lle_wf @ ( gram_L1828378864e_rcut @ Tr0 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_18_regular__rcut,axiom,
% 2.86/1.57 ! [Tr0: dtree] : ( gram_L646766332egular @ ( gram_L1828378864e_rcut @ Tr0 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_19_bot__fun__def,axiom,
% 2.86/1.57 ! [B: $tType,A: $tType] :
% 2.86/1.57 ( ( bot @ B @ ( type2 @ B ) )
% 2.86/1.57 => ( ( bot_bot @ ( A > B ) )
% 2.86/1.57 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_20_Set_Ois__empty__def,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( is_empty @ A )
% 2.86/1.57 = ( ^ [A4: set @ A] :
% 2.86/1.57 ( A4
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_21_rcut__eq,axiom,
% 2.86/1.57 ! [Tr0: dtree] :
% 2.86/1.57 ( ( ( gram_L1828378864e_rcut @ Tr0 )
% 2.86/1.57 = Tr0 )
% 2.86/1.57 = ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ Tr0 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_22_rcut__reg,axiom,
% 2.86/1.57 ! [Tr0: dtree] :
% 2.86/1.57 ( ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ Tr0 )
% 2.86/1.57 => ( ( gram_L1828378864e_rcut @ Tr0 )
% 2.86/1.57 = Tr0 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_23_reg__rcut,axiom,
% 2.86/1.57 ! [Tr0: dtree] : ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ ( gram_L1828378864e_rcut @ Tr0 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_24_rcut__def,axiom,
% 2.86/1.57 ( gram_L1828378864e_rcut
% 2.86/1.57 = ( ^ [Tr02: dtree] : ( gram_L1451583624elle_H @ Tr02 @ ( root @ Tr02 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_25_Collect__empty__eq__bot,axiom,
% 2.86/1.57 ! [A: $tType,P: A > $o] :
% 2.86/1.57 ( ( ( collect @ A @ P )
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 = ( P
% 2.86/1.57 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_26_bot__empty__eq,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( bot_bot @ ( A > $o ) )
% 2.86/1.57 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_27_root__deftr,axiom,
% 2.86/1.57 ! [N2: n] :
% 2.86/1.57 ( ( root @ ( gram_L1231612515_deftr @ N2 ) )
% 2.86/1.57 = N2 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_28_is__singletonI_H,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( A2
% 2.86/1.57 != ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 => ( ! [X2: A,Y: A] :
% 2.86/1.57 ( ( member @ A @ X2 @ A2 )
% 2.86/1.57 => ( ( member @ A @ Y @ A2 )
% 2.86/1.57 => ( X2 = Y ) ) )
% 2.86/1.57 => ( is_singleton @ A @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_29_reg__deftr,axiom,
% 2.86/1.57 ! [N2: n] : ( gram_L1918716148le_reg @ gram_L1231612515_deftr @ ( gram_L1231612515_deftr @ N2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_30_reg__def2,axiom,
% 2.86/1.57 ( gram_L1918716148le_reg
% 2.86/1.57 = ( ^ [F: n > dtree,Tr2: dtree] :
% 2.86/1.57 ! [Ns2: set @ n,Tr3: dtree] :
% 2.86/1.57 ( ( gram_L716654942_subtr @ Ns2 @ Tr3 @ Tr2 )
% 2.86/1.57 => ( Tr3
% 2.86/1.57 = ( F @ ( root @ Tr3 ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_31_subtr__trans,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr32: dtree] :
% 2.86/1.57 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 2.86/1.57 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr32 )
% 2.86/1.57 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr32 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_32_subtr__deftr,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr4: dtree,N2: n] :
% 2.86/1.57 ( ( gram_L716654942_subtr @ Ns @ Tr4 @ ( gram_L1231612515_deftr @ N2 ) )
% 2.86/1.57 => ( Tr4
% 2.86/1.57 = ( gram_L1231612515_deftr @ ( root @ Tr4 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_33_subtr_ORefl,axiom,
% 2.86/1.57 ! [Tr: dtree,Ns: set @ n] :
% 2.86/1.57 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.86/1.57 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_34_subtr__rootL__in,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 2.86/1.57 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 2.86/1.57 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_35_subtr__rootR__in,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 2.86/1.57 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 2.86/1.57 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_36_wf__subtr,axiom,
% 2.86/1.57 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 2.86/1.57 ( ( gram_L864798063lle_wf @ Tr1 )
% 2.86/1.57 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 2.86/1.57 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_37_reg__subtr,axiom,
% 2.86/1.57 ! [F2: n > dtree,Tr: dtree,Ns: set @ n,Tr4: dtree] :
% 2.86/1.57 ( ( gram_L1918716148le_reg @ F2 @ Tr )
% 2.86/1.57 => ( ( gram_L716654942_subtr @ Ns @ Tr4 @ Tr )
% 2.86/1.57 => ( gram_L1918716148le_reg @ F2 @ Tr4 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_38_regular__subtr,axiom,
% 2.86/1.57 ! [Tr: dtree,Ns: set @ n,Tr4: dtree] :
% 2.86/1.57 ( ( gram_L646766332egular @ Tr )
% 2.86/1.57 => ( ( gram_L716654942_subtr @ Ns @ Tr4 @ Tr )
% 2.86/1.57 => ( gram_L646766332egular @ Tr4 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_39_wf__deftr,axiom,
% 2.86/1.57 ! [N2: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_40_root__H__pick,axiom,
% 2.86/1.57 ! [Tr0: dtree,N2: n] :
% 2.86/1.57 ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N2 ) )
% 2.86/1.57 = ( root @ ( gram_L315592705e_pick @ Tr0 @ N2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_41_reg__def,axiom,
% 2.86/1.57 ( gram_L1918716148le_reg
% 2.86/1.57 = ( ^ [F: n > dtree,Tr2: dtree] :
% 2.86/1.57 ! [Tr3: dtree] :
% 2.86/1.57 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr3 @ Tr2 )
% 2.86/1.57 => ( Tr3
% 2.86/1.57 = ( F @ ( root @ Tr3 ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_42_in__inv__imagep,axiom,
% 2.86/1.57 ! [B: $tType,A: $tType] :
% 2.86/1.57 ( ( inv_imagep @ A @ B )
% 2.86/1.57 = ( ^ [R: A > A > $o,F: B > A,X: B,Y2: B] : ( R @ ( F @ X ) @ ( F @ Y2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_43_is__singletonI,axiom,
% 2.86/1.57 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_44_inItr__subtr,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr: dtree,N2: n] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ Ns @ Tr @ N2 )
% 2.86/1.57 => ? [Tr5: dtree] :
% 2.86/1.57 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 2.86/1.57 & ( ( root @ Tr5 )
% 2.86/1.57 = N2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_45_mem__Collect__eq,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,P: A > $o] :
% 2.86/1.57 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.86/1.57 = ( P @ A3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_46_Collect__mem__eq,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( collect @ A
% 2.86/1.57 @ ^ [X: A] : ( member @ A @ X @ A2 ) )
% 2.86/1.57 = A2 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_47_Collect__cong,axiom,
% 2.86/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.86/1.57 ( ! [X2: A] :
% 2.86/1.57 ( ( P @ X2 )
% 2.86/1.57 = ( Q @ X2 ) )
% 2.86/1.57 => ( ( collect @ A @ P )
% 2.86/1.57 = ( collect @ A @ Q ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_48_ext,axiom,
% 2.86/1.57 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 2.86/1.57 ( ! [X2: A] :
% 2.86/1.57 ( ( F2 @ X2 )
% 2.86/1.57 = ( G @ X2 ) )
% 2.86/1.57 => ( F2 = G ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_49_is__singleton__def,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( is_singleton @ A )
% 2.86/1.57 = ( ^ [A4: set @ A] :
% 2.86/1.57 ? [X: A] :
% 2.86/1.57 ( A4
% 2.86/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_50_is__singletonE,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( is_singleton @ A @ A2 )
% 2.86/1.57 => ~ ! [X2: A] :
% 2.86/1.57 ( A2
% 2.86/1.57 != ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_51_root__hsubst,axiom,
% 2.86/1.57 ! [Tr0: dtree,Tr: dtree] :
% 2.86/1.57 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 2.86/1.57 = ( root @ Tr ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_52_pairwise__empty,axiom,
% 2.86/1.57 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_53_top__apply,axiom,
% 2.86/1.57 ! [C2: $tType,D: $tType] :
% 2.86/1.57 ( ( top @ C2 @ ( type2 @ C2 ) )
% 2.86/1.57 => ( ( top_top @ ( D > C2 ) )
% 2.86/1.57 = ( ^ [X: D] : ( top_top @ C2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_54_UNIV__I,axiom,
% 2.86/1.57 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_55_insert__absorb2,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A] :
% 2.86/1.57 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A2 ) )
% 2.86/1.57 = ( insert @ A @ X3 @ A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_56_insert__iff,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 2.86/1.57 = ( ( A3 = B2 )
% 2.86/1.57 | ( member @ A @ A3 @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_57_insertCI,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,B3: set @ A,B2: A] :
% 2.86/1.57 ( ( ~ ( member @ A @ A3 @ B3 )
% 2.86/1.57 => ( A3 = B2 ) )
% 2.86/1.57 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_58_singletonI,axiom,
% 2.86/1.57 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_59_root__H,axiom,
% 2.86/1.57 ! [Tr0: dtree,N2: n] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 2.86/1.57 => ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N2 ) )
% 2.86/1.57 = N2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_60_subtr__pick,axiom,
% 2.86/1.57 ! [Tr0: dtree,N2: n] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 2.86/1.57 => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N2 ) @ Tr0 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_61_pairwise__def,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( pairwise @ A )
% 2.86/1.57 = ( ^ [R2: A > A > $o,S: set @ A] :
% 2.86/1.57 ! [X: A] :
% 2.86/1.57 ( ( member @ A @ X @ S )
% 2.86/1.57 => ! [Y2: A] :
% 2.86/1.57 ( ( member @ A @ Y2 @ S )
% 2.86/1.57 => ( ( X != Y2 )
% 2.86/1.57 => ( R2 @ X @ Y2 ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_62_wf__pick,axiom,
% 2.86/1.57 ! [Tr0: dtree,N2: n] :
% 2.86/1.57 ( ( gram_L864798063lle_wf @ Tr0 )
% 2.86/1.57 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 2.86/1.57 => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ Tr0 @ N2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_63_root__pick,axiom,
% 2.86/1.57 ! [Tr0: dtree,N2: n] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 2.86/1.57 => ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N2 ) )
% 2.86/1.57 = N2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_64_mk__disjoint__insert,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ A3 @ A2 )
% 2.86/1.57 => ? [B4: set @ A] :
% 2.86/1.57 ( ( A2
% 2.86/1.57 = ( insert @ A @ A3 @ B4 ) )
% 2.86/1.57 & ~ ( member @ A @ A3 @ B4 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_65_pairwise__insert,axiom,
% 2.86/1.57 ! [A: $tType,R3: A > A > $o,X3: A,S2: set @ A] :
% 2.86/1.57 ( ( pairwise @ A @ R3 @ ( insert @ A @ X3 @ S2 ) )
% 2.86/1.57 = ( ! [Y2: A] :
% 2.86/1.57 ( ( ( member @ A @ Y2 @ S2 )
% 2.86/1.57 & ( Y2 != X3 ) )
% 2.86/1.57 => ( ( R3 @ X3 @ Y2 )
% 2.86/1.57 & ( R3 @ Y2 @ X3 ) ) )
% 2.86/1.57 & ( pairwise @ A @ R3 @ S2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_66_insert__commute,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,Y3: A,A2: set @ A] :
% 2.86/1.57 ( ( insert @ A @ X3 @ ( insert @ A @ Y3 @ A2 ) )
% 2.86/1.57 = ( insert @ A @ Y3 @ ( insert @ A @ X3 @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_67_insert__eq__iff,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,A2: set @ A,B2: A,B3: set @ A] :
% 2.86/1.57 ( ~ ( member @ A @ A3 @ A2 )
% 2.86/1.57 => ( ~ ( member @ A @ B2 @ B3 )
% 2.86/1.57 => ( ( ( insert @ A @ A3 @ A2 )
% 2.86/1.57 = ( insert @ A @ B2 @ B3 ) )
% 2.86/1.57 = ( ( ( A3 = B2 )
% 2.86/1.57 => ( A2 = B3 ) )
% 2.86/1.57 & ( ( A3 != B2 )
% 2.86/1.57 => ? [C3: set @ A] :
% 2.86/1.57 ( ( A2
% 2.86/1.57 = ( insert @ A @ B2 @ C3 ) )
% 2.86/1.57 & ~ ( member @ A @ B2 @ C3 )
% 2.86/1.57 & ( B3
% 2.86/1.57 = ( insert @ A @ A3 @ C3 ) )
% 2.86/1.57 & ~ ( member @ A @ A3 @ C3 ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_68_insert__absorb,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ A3 @ A2 )
% 2.86/1.57 => ( ( insert @ A @ A3 @ A2 )
% 2.86/1.57 = A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_69_insert__ident,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ~ ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ~ ( member @ A @ X3 @ B3 )
% 2.86/1.57 => ( ( ( insert @ A @ X3 @ A2 )
% 2.86/1.57 = ( insert @ A @ X3 @ B3 ) )
% 2.86/1.57 = ( A2 = B3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_70_UNIV__witness,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ? [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_71_insert__UNIV,axiom,
% 2.86/1.57 ! [A: $tType,X3: A] :
% 2.86/1.57 ( ( insert @ A @ X3 @ ( top_top @ ( set @ A ) ) )
% 2.86/1.57 = ( top_top @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_72_Set_Oset__insert,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ~ ! [B4: set @ A] :
% 2.86/1.57 ( ( A2
% 2.86/1.57 = ( insert @ A @ X3 @ B4 ) )
% 2.86/1.57 => ( member @ A @ X3 @ B4 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_73_UNIV__eq__I,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ! [X2: A] : ( member @ A @ X2 @ A2 )
% 2.86/1.57 => ( ( top_top @ ( set @ A ) )
% 2.86/1.57 = A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_74_insertI2,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,B3: set @ A,B2: A] :
% 2.86/1.57 ( ( member @ A @ A3 @ B3 )
% 2.86/1.57 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_75_insertI1,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,B3: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_76_insertE,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 2.86/1.57 => ( ( A3 != B2 )
% 2.86/1.57 => ( member @ A @ A3 @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_77_pairwise__singleton,axiom,
% 2.86/1.57 ! [A: $tType,P: A > A > $o,A2: A] : ( pairwise @ A @ P @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_78_pick,axiom,
% 2.86/1.57 ! [Tr0: dtree,N2: n] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 2.86/1.57 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N2 ) @ Tr0 )
% 2.86/1.57 & ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N2 ) )
% 2.86/1.57 = N2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_79_singleton__inject,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,B2: A] :
% 2.86/1.57 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.57 => ( A3 = B2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_80_insert__not__empty,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,A2: set @ A] :
% 2.86/1.57 ( ( insert @ A @ A3 @ A2 )
% 2.86/1.57 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_81_doubleton__eq__iff,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,B2: A,C: A,D2: A] :
% 2.86/1.57 ( ( ( insert @ A @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.57 = ( insert @ A @ C @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.86/1.57 = ( ( ( A3 = C )
% 2.86/1.57 & ( B2 = D2 ) )
% 2.86/1.57 | ( ( A3 = D2 )
% 2.86/1.57 & ( B2 = C ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_82_singleton__iff,axiom,
% 2.86/1.57 ! [A: $tType,B2: A,A3: A] :
% 2.86/1.57 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.57 = ( B2 = A3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_83_singletonD,axiom,
% 2.86/1.57 ! [A: $tType,B2: A,A3: A] :
% 2.86/1.57 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.57 => ( B2 = A3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_84_empty__not__UNIV,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( bot_bot @ ( set @ A ) )
% 2.86/1.57 != ( top_top @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_85_subtr__H,axiom,
% 2.86/1.57 ! [Tr0: dtree,N2: n,Tr1: dtree] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 2.86/1.57 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ ( gram_L1451583624elle_H @ Tr0 @ N2 ) )
% 2.86/1.57 => ? [N1: n] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N1 )
% 2.86/1.57 & ( Tr1
% 2.86/1.57 = ( gram_L1451583624elle_H @ Tr0 @ N1 ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_86_wf__H,axiom,
% 2.86/1.57 ! [Tr0: dtree,N2: n] :
% 2.86/1.57 ( ( gram_L864798063lle_wf @ Tr0 )
% 2.86/1.57 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N2 )
% 2.86/1.57 => ( gram_L864798063lle_wf @ ( gram_L1451583624elle_H @ Tr0 @ N2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_87_inItr__root__in,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr: dtree,N2: n] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ Ns @ Tr @ N2 )
% 2.86/1.57 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_88_inItr_OBase,axiom,
% 2.86/1.57 ! [Tr: dtree,Ns: set @ n] :
% 2.86/1.57 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.86/1.57 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_89_hsubst__eq,axiom,
% 2.86/1.57 ! [Tr: dtree,Tr0: dtree] :
% 2.86/1.57 ( ( ( root @ Tr )
% 2.86/1.57 = ( root @ Tr0 ) )
% 2.86/1.57 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 2.86/1.57 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_90_subtr__inItr,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr: dtree,N2: n,Tr1: dtree] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ Ns @ Tr @ N2 )
% 2.86/1.57 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 2.86/1.57 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_91_wf__hsubst,axiom,
% 2.86/1.57 ! [Tr0: dtree,Tr: dtree] :
% 2.86/1.57 ( ( gram_L864798063lle_wf @ Tr0 )
% 2.86/1.57 => ( ( gram_L864798063lle_wf @ Tr )
% 2.86/1.57 => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_92_H__r__def,axiom,
% 2.86/1.57 ( gram_L1221482026le_H_r
% 2.86/1.57 = ( ^ [Tr02: dtree,N: n] : ( root @ ( gram_L315592705e_pick @ Tr02 @ N ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_93_L__rec__notin,axiom,
% 2.86/1.57 ! [N2: n,Ns: set @ n] :
% 2.86/1.57 ( ~ ( member @ n @ N2 @ Ns )
% 2.86/1.57 => ( ( gram_L1451583628elle_L @ Ns @ N2 )
% 2.86/1.57 = ( insert @ ( set @ t ) @ ( bot_bot @ ( set @ t ) ) @ ( bot_bot @ ( set @ ( set @ t ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_94_iso__tuple__UNIV__I,axiom,
% 2.86/1.57 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_95_is__singleton__the__elem,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( is_singleton @ A )
% 2.86/1.57 = ( ^ [A4: set @ A] :
% 2.86/1.57 ( A4
% 2.86/1.57 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_96_the__elem__eq,axiom,
% 2.86/1.57 ! [A: $tType,X3: A] :
% 2.86/1.57 ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.57 = X3 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_97_hsubst__def,axiom,
% 2.86/1.57 ( gram_L1004374585hsubst
% 2.86/1.57 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_98_Fr__rcut,axiom,
% 2.86/1.57 ! [Tr0: dtree] : ( ord_less_eq @ ( set @ t ) @ ( gram_L861583724lle_Fr @ ( top_top @ ( set @ n ) ) @ ( gram_L1828378864e_rcut @ Tr0 ) ) @ ( gram_L861583724lle_Fr @ ( top_top @ ( set @ n ) ) @ Tr0 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_99_inFr__hsubst__notin,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr: dtree,T: t,Tr0: dtree] :
% 2.86/1.57 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T )
% 2.86/1.57 => ( ~ ( member @ n @ ( root @ Tr0 ) @ Ns )
% 2.86/1.57 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_100_order__refl,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_101_subsetI,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ! [X2: A] :
% 2.86/1.57 ( ( member @ A @ X2 @ A2 )
% 2.86/1.57 => ( member @ A @ X2 @ B3 ) )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_102_subset__antisym,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A2 )
% 2.86/1.57 => ( A2 = B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_103_subset__empty,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 = ( A2
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_104_empty__subsetI,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_105_insert__subset,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 2.86/1.57 = ( ( member @ A @ X3 @ B3 )
% 2.86/1.57 & ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_106_singleton__insert__inj__eq,axiom,
% 2.86/1.57 ! [A: $tType,B2: A,A3: A,A2: set @ A] :
% 2.86/1.57 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 = ( insert @ A @ A3 @ A2 ) )
% 2.86/1.57 = ( ( A3 = B2 )
% 2.86/1.57 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_107_singleton__insert__inj__eq_H,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,A2: set @ A,B2: A] :
% 2.86/1.57 ( ( ( insert @ A @ A3 @ A2 )
% 2.86/1.57 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.57 = ( ( A3 = B2 )
% 2.86/1.57 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_108_set__mp,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( member @ A @ X3 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_109_in__mono,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( member @ A @ X3 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_110_subsetD,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A,C: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ( member @ A @ C @ A2 )
% 2.86/1.57 => ( member @ A @ C @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_111_subsetCE,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A,C: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ( member @ A @ C @ A2 )
% 2.86/1.57 => ( member @ A @ C @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_112_equalityE,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( A2 = B3 )
% 2.86/1.57 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_113_subset__eq,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) )
% 2.86/1.57 = ( ^ [A4: set @ A,B5: set @ A] :
% 2.86/1.57 ! [X: A] :
% 2.86/1.57 ( ( member @ A @ X @ A4 )
% 2.86/1.57 => ( member @ A @ X @ B5 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_114_equalityD1,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( A2 = B3 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_115_equalityD2,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( A2 = B3 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_116_set__rev__mp,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( member @ A @ X3 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_117_subset__iff,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) )
% 2.86/1.57 = ( ^ [A4: set @ A,B5: set @ A] :
% 2.86/1.57 ! [T2: A] :
% 2.86/1.57 ( ( member @ A @ T2 @ A4 )
% 2.86/1.57 => ( member @ A @ T2 @ B5 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_118_rev__subsetD,axiom,
% 2.86/1.57 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( member @ A @ C @ A2 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( member @ A @ C @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_119_subset__refl,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_120_Collect__mono,axiom,
% 2.86/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.86/1.57 ( ! [X2: A] :
% 2.86/1.57 ( ( P @ X2 )
% 2.86/1.57 => ( Q @ X2 ) )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_121_subset__trans,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A,C4: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C4 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_122_le__funD,axiom,
% 2.86/1.57 ! [B: $tType,A: $tType] :
% 2.86/1.57 ( ( ord @ B @ ( type2 @ B ) )
% 2.86/1.57 => ! [F2: A > B,G: A > B,X3: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 2.86/1.57 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_123_le__funE,axiom,
% 2.86/1.57 ! [B: $tType,A: $tType] :
% 2.86/1.57 ( ( ord @ B @ ( type2 @ B ) )
% 2.86/1.57 => ! [F2: A > B,G: A > B,X3: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 2.86/1.57 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_124_le__funI,axiom,
% 2.86/1.57 ! [B: $tType,A: $tType] :
% 2.86/1.57 ( ( ord @ B @ ( type2 @ B ) )
% 2.86/1.57 => ! [F2: A > B,G: A > B] :
% 2.86/1.57 ( ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G @ X2 ) )
% 2.86/1.57 => ( ord_less_eq @ ( A > B ) @ F2 @ G ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_125_set__eq__subset,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 2.86/1.57 = ( ^ [A4: set @ A,B5: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.86/1.57 & ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_126_contra__subsetD,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A,C: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ~ ( member @ A @ C @ B3 )
% 2.86/1.57 => ~ ( member @ A @ C @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_127_le__fun__def,axiom,
% 2.86/1.57 ! [B: $tType,A: $tType] :
% 2.86/1.57 ( ( ord @ B @ ( type2 @ B ) )
% 2.86/1.57 => ( ( ord_less_eq @ ( A > B ) )
% 2.86/1.57 = ( ^ [F: A > B,G2: A > B] :
% 2.86/1.57 ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_128_Collect__mono__iff,axiom,
% 2.86/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.86/1.57 = ( ! [X: A] :
% 2.86/1.57 ( ( P @ X )
% 2.86/1.57 => ( Q @ X ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_129_order__subst1,axiom,
% 2.86/1.57 ! [A: $tType,B: $tType] :
% 2.86/1.57 ( ( ( order @ B @ ( type2 @ B ) )
% 2.86/1.57 & ( order @ A @ ( type2 @ A ) ) )
% 2.86/1.57 => ! [A3: A,F2: B > A,B2: B,C: B] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B2 ) )
% 2.86/1.57 => ( ( ord_less_eq @ B @ B2 @ C )
% 2.86/1.57 => ( ! [X2: B,Y: B] :
% 2.86/1.57 ( ( ord_less_eq @ B @ X2 @ Y )
% 2.86/1.57 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 2.86/1.57 => ( ord_less_eq @ A @ A3 @ ( F2 @ C ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_130_order__subst2,axiom,
% 2.86/1.57 ! [A: $tType,C2: $tType] :
% 2.86/1.57 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 2.86/1.57 & ( order @ A @ ( type2 @ A ) ) )
% 2.86/1.57 => ! [A3: A,B2: A,F2: A > C2,C: C2] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 => ( ( ord_less_eq @ C2 @ ( F2 @ B2 ) @ C )
% 2.86/1.57 => ( ! [X2: A,Y: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.86/1.57 => ( ord_less_eq @ C2 @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 2.86/1.57 => ( ord_less_eq @ C2 @ ( F2 @ A3 ) @ C ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_131_ord__eq__le__subst,axiom,
% 2.86/1.57 ! [A: $tType,B: $tType] :
% 2.86/1.57 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.86/1.57 & ( ord @ A @ ( type2 @ A ) ) )
% 2.86/1.57 => ! [A3: A,F2: B > A,B2: B,C: B] :
% 2.86/1.57 ( ( A3
% 2.86/1.57 = ( F2 @ B2 ) )
% 2.86/1.57 => ( ( ord_less_eq @ B @ B2 @ C )
% 2.86/1.57 => ( ! [X2: B,Y: B] :
% 2.86/1.57 ( ( ord_less_eq @ B @ X2 @ Y )
% 2.86/1.57 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 2.86/1.57 => ( ord_less_eq @ A @ A3 @ ( F2 @ C ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_132_ord__le__eq__subst,axiom,
% 2.86/1.57 ! [A: $tType,B: $tType] :
% 2.86/1.57 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.86/1.57 & ( ord @ A @ ( type2 @ A ) ) )
% 2.86/1.57 => ! [A3: A,B2: A,F2: A > B,C: B] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 => ( ( ( F2 @ B2 )
% 2.86/1.57 = C )
% 2.86/1.57 => ( ! [X2: A,Y: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.86/1.57 => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 2.86/1.57 => ( ord_less_eq @ B @ ( F2 @ A3 ) @ C ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_133_eq__iff,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.86/1.57 = ( ^ [X: A,Y2: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.86/1.57 & ( ord_less_eq @ A @ Y2 @ X ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_134_antisym,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A,Y3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.86/1.57 => ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.86/1.57 => ( X3 = Y3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_135_linear,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A,Y3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.86/1.57 | ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_136_eq__refl,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A,Y3: A] :
% 2.86/1.57 ( ( X3 = Y3 )
% 2.86/1.57 => ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_137_le__cases,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A,Y3: A] :
% 2.86/1.57 ( ~ ( ord_less_eq @ A @ X3 @ Y3 )
% 2.86/1.57 => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_138_order_Otrans,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A,C: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.86/1.57 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_139_le__cases3,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A,Y3: A,Z2: A] :
% 2.86/1.57 ( ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.86/1.57 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 2.86/1.57 => ( ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.86/1.57 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 2.86/1.57 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 2.86/1.57 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 2.86/1.57 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 2.86/1.57 => ~ ( ord_less_eq @ A @ Y3 @ X3 ) )
% 2.86/1.57 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 2.86/1.57 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 2.86/1.57 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 2.86/1.57 => ~ ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_140_antisym__conv,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [Y3: A,X3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.86/1.57 => ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.86/1.57 = ( X3 = Y3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_141_ord__eq__le__trans,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A,C: A] :
% 2.86/1.57 ( ( A3 = B2 )
% 2.86/1.57 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.86/1.57 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_142_ord__le__eq__trans,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A,C: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 => ( ( B2 = C )
% 2.86/1.57 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_143_order__class_Oorder_Oantisym,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 => ( ( ord_less_eq @ A @ B2 @ A3 )
% 2.86/1.57 => ( A3 = B2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_144_order__trans,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A,Y3: A,Z2: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.86/1.57 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 2.86/1.57 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_145_dual__order_Orefl,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_146_linorder__wlog,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [P: A > A > $o,A3: A,B2: A] :
% 2.86/1.57 ( ! [A5: A,B6: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A5 @ B6 )
% 2.86/1.57 => ( P @ A5 @ B6 ) )
% 2.86/1.57 => ( ! [A5: A,B6: A] :
% 2.86/1.57 ( ( P @ B6 @ A5 )
% 2.86/1.57 => ( P @ A5 @ B6 ) )
% 2.86/1.57 => ( P @ A3 @ B2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_147_dual__order_Otrans,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [B2: A,A3: A,C: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ B2 @ A3 )
% 2.86/1.57 => ( ( ord_less_eq @ A @ C @ B2 )
% 2.86/1.57 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_148_dual__order_Oantisym,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [B2: A,A3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ B2 @ A3 )
% 2.86/1.57 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 => ( A3 = B2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_149_top__set__def,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( top_top @ ( set @ A ) )
% 2.86/1.57 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_150_top__empty__eq,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( top_top @ ( A > $o ) )
% 2.86/1.57 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_151_bot_Oextremum,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_152_bot_Oextremum__unique,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 2.86/1.57 = ( A3
% 2.86/1.57 = ( bot_bot @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_153_bot_Oextremum__uniqueI,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 2.86/1.57 => ( A3
% 2.86/1.57 = ( bot_bot @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_154_top__greatest,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order_top @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ ( top_top @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_155_top_Oextremum__unique,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order_top @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 2.86/1.57 = ( A3
% 2.86/1.57 = ( top_top @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_156_top_Oextremum__uniqueI,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order_top @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 2.86/1.57 => ( A3
% 2.86/1.57 = ( top_top @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_157_subset__UNIV,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_158_insert__mono,axiom,
% 2.86/1.57 ! [A: $tType,C4: set @ A,D3: set @ A,A3: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A3 @ C4 ) @ ( insert @ A @ A3 @ D3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_159_subset__insert,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ~ ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 2.86/1.57 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_160_subset__insertI,axiom,
% 2.86/1.57 ! [A: $tType,B3: set @ A,A3: A] : ( ord_less_eq @ ( set @ A ) @ B3 @ ( insert @ A @ A3 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_161_subset__insertI2,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A,B2: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_162_inFr__root__in,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr: dtree,T: t] :
% 2.86/1.57 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T )
% 2.86/1.57 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_163_not__root__inFr,axiom,
% 2.86/1.57 ! [Tr: dtree,Ns: set @ n,T: t] :
% 2.86/1.57 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 2.86/1.57 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_164_subtr__inFr,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr: dtree,T: t,Tr1: dtree] :
% 2.86/1.57 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T )
% 2.86/1.57 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 2.86/1.57 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_165_pairwise__subset,axiom,
% 2.86/1.57 ! [A: $tType,P: A > A > $o,S3: set @ A,T3: set @ A] :
% 2.86/1.57 ( ( pairwise @ A @ P @ S3 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ A ) @ T3 @ S3 )
% 2.86/1.57 => ( pairwise @ A @ P @ T3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_166_subset__singletonD,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,X3: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.57 => ( ( A2
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 | ( A2
% 2.86/1.57 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_167_subset__singleton__iff,axiom,
% 2.86/1.57 ! [A: $tType,X4: set @ A,A3: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ X4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.57 = ( ( X4
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 | ( X4
% 2.86/1.57 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_168_unfold_I1_J,axiom,
% 2.86/1.57 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 2.86/1.57 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 2.86/1.57 = ( Rt @ B2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_169_insert__subsetI,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A,X4: set @ A] :
% 2.86/1.57 ( ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ A ) @ X4 @ A2 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X4 ) @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_170_subset__emptyI,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ! [X2: A] :
% 2.86/1.57 ~ ( member @ A @ X2 @ A2 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_171_Pow__empty,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( pow @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 = ( insert @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_172_Pow__singleton__iff,axiom,
% 2.86/1.57 ! [A: $tType,X4: set @ A,Y5: set @ A] :
% 2.86/1.57 ( ( ( pow @ A @ X4 )
% 2.86/1.57 = ( insert @ ( set @ A ) @ Y5 @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) )
% 2.86/1.57 = ( ( X4
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 & ( Y5
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_173_top1I,axiom,
% 2.86/1.57 ! [A: $tType,X3: A] : ( top_top @ ( A > $o ) @ X3 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_174_Pow__iff,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( member @ ( set @ A ) @ A2 @ ( pow @ A @ B3 ) )
% 2.86/1.57 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_175_PowI,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( member @ ( set @ A ) @ A2 @ ( pow @ A @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_176_Pow__UNIV,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( pow @ A @ ( top_top @ ( set @ A ) ) )
% 2.86/1.57 = ( top_top @ ( set @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_177_Pow__top,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] : ( member @ ( set @ A ) @ A2 @ ( pow @ A @ A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_178_Pow__bottom,axiom,
% 2.86/1.57 ! [A: $tType,B3: set @ A] : ( member @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ ( pow @ A @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_179_Pow__mono,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( pow @ A @ A2 ) @ ( pow @ A @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_180_PowD,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( member @ ( set @ A ) @ A2 @ ( pow @ A @ B3 ) )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_181_subtr__mono,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Ns3: set @ n] :
% 2.86/1.57 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 2.86/1.57 => ( gram_L716654942_subtr @ Ns3 @ Tr1 @ Tr22 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_182_inFr__mono,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr: dtree,T: t,Ns3: set @ n] :
% 2.86/1.57 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 2.86/1.57 => ( gram_L1333338417e_inFr @ Ns3 @ Tr @ T ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_183_inItr__mono,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr: dtree,N2: n,Ns3: set @ n] :
% 2.86/1.57 ( ( gram_L830233218_inItr @ Ns @ Tr @ N2 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 2.86/1.57 => ( gram_L830233218_inItr @ Ns3 @ Tr @ N2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_184_Pow__not__empty,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( pow @ A @ A2 )
% 2.86/1.57 != ( bot_bot @ ( set @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_185_H__def,axiom,
% 2.86/1.57 ( gram_L1451583624elle_H
% 2.86/1.57 = ( ^ [Tr02: dtree] : ( unfold @ n @ ( gram_L1221482026le_H_r @ Tr02 ) @ ( gram_L1221482011le_H_c @ Tr02 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_186_top__conj_I2_J,axiom,
% 2.86/1.57 ! [A: $tType,P: $o,X3: A] :
% 2.86/1.57 ( ( P
% 2.86/1.57 & ( top_top @ ( A > $o ) @ X3 ) )
% 2.86/1.57 = P ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_187_top__conj_I1_J,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,P: $o] :
% 2.86/1.57 ( ( ( top_top @ ( A > $o ) @ X3 )
% 2.86/1.57 & P )
% 2.86/1.57 = P ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_188_root__Node,axiom,
% 2.86/1.57 ! [N2: n,As: set @ ( sum_sum @ t @ dtree )] :
% 2.86/1.57 ( ( root @ ( node @ N2 @ As ) )
% 2.86/1.57 = N2 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_189_subset__Compl__singleton,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B2: A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.86/1.57 = ( ~ ( member @ A @ B2 @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_190_Compl__eq__Compl__iff,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ( uminus_uminus @ ( set @ A ) @ A2 )
% 2.86/1.57 = ( uminus_uminus @ ( set @ A ) @ B3 ) )
% 2.86/1.57 = ( A2 = B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_191_Compl__iff,axiom,
% 2.86/1.57 ! [A: $tType,C: A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 2.86/1.57 = ( ~ ( member @ A @ C @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_192_ComplI,axiom,
% 2.86/1.57 ! [A: $tType,C: A,A2: set @ A] :
% 2.86/1.57 ( ~ ( member @ A @ C @ A2 )
% 2.86/1.57 => ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_193_Compl__subset__Compl__iff,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( uminus_uminus @ ( set @ A ) @ B3 ) )
% 2.86/1.57 = ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_194_Compl__anti__mono,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B3 ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_195_subset__Compl__self__eq,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 2.86/1.57 = ( A2
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_196_Compl__UNIV__eq,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( uminus_uminus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) )
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_197_Compl__empty__eq,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( uminus_uminus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 = ( top_top @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_198_double__complement,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 2.86/1.57 = A2 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_199_ComplD,axiom,
% 2.86/1.57 ! [A: $tType,C: A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 2.86/1.57 => ~ ( member @ A @ C @ A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_200_compl__bot__eq,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.86/1.57 => ( ( uminus_uminus @ A @ ( bot_bot @ A ) )
% 2.86/1.57 = ( top_top @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_201_compl__top__eq,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.86/1.57 => ( ( uminus_uminus @ A @ ( top_top @ A ) )
% 2.86/1.57 = ( bot_bot @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_202_compl__le__compl__iff,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A,Y3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ ( uminus_uminus @ A @ Y3 ) )
% 2.86/1.57 = ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_203_compl__mono,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A,Y3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.86/1.57 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y3 ) @ ( uminus_uminus @ A @ X3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_204_compl__le__swap1,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [Y3: A,X3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ Y3 @ ( uminus_uminus @ A @ X3 ) )
% 2.86/1.57 => ( ord_less_eq @ A @ X3 @ ( uminus_uminus @ A @ Y3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_205_compl__le__swap2,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [Y3: A,X3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y3 ) @ X3 )
% 2.86/1.57 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ Y3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_206_neg__le__iff__le,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [B2: A,A3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A3 ) )
% 2.86/1.57 = ( ord_less_eq @ A @ A3 @ B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_207_le__minus__iff,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ ( uminus_uminus @ A @ B2 ) )
% 2.86/1.57 = ( ord_less_eq @ A @ B2 @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_208_le__imp__neg__le,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_209_minus__le__iff,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A3 ) @ B2 )
% 2.86/1.57 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ A3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_210_inFr__hsubst__minus,axiom,
% 2.86/1.57 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T: t] :
% 2.86/1.57 ( ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T )
% 2.86/1.57 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_211_corec_I1_J,axiom,
% 2.86/1.57 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ),B2: A] :
% 2.86/1.57 ( ( root @ ( corec @ A @ Rt @ Ct @ B2 ) )
% 2.86/1.57 = ( Rt @ B2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_212_DiffI,axiom,
% 2.86/1.57 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( member @ A @ C @ A2 )
% 2.86/1.57 => ( ~ ( member @ A @ C @ B3 )
% 2.86/1.57 => ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_213_Diff__iff,axiom,
% 2.86/1.57 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 2.86/1.57 = ( ( member @ A @ C @ A2 )
% 2.86/1.57 & ~ ( member @ A @ C @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_214_Diff__idemp,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ B3 )
% 2.86/1.57 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_215_Diff__cancel,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( minus_minus @ ( set @ A ) @ A2 @ A2 )
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_216_empty__Diff,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 )
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_217_Diff__empty,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( minus_minus @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 = A2 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_218_insert__Diff1,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,B3: set @ A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ X3 @ B3 )
% 2.86/1.57 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 2.86/1.57 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_219_Diff__insert0,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ~ ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 2.86/1.57 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_220_Diff__eq__empty__iff,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ( minus_minus @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.57 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_221_Diff__UNIV,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ( ( minus_minus @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 2.86/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_222_insert__Diff__single,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,A2: set @ A] :
% 2.86/1.57 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.86/1.57 = ( insert @ A @ A3 @ A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_223_diff__eq__diff__less__eq,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A,C: A,D2: A] :
% 2.86/1.57 ( ( ( minus_minus @ A @ A3 @ B2 )
% 2.86/1.57 = ( minus_minus @ A @ C @ D2 ) )
% 2.86/1.57 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 = ( ord_less_eq @ A @ C @ D2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_224_diff__right__mono,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A,C: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_225_diff__left__mono,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [B2: A,A3: A,C: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ B2 @ A3 )
% 2.86/1.57 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A3 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_226_diff__mono,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A,B2: A,D2: A,C: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.86/1.57 => ( ( ord_less_eq @ A @ D2 @ C )
% 2.86/1.57 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B2 @ D2 ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_227_insert__Diff__if,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,B3: set @ A,A2: set @ A] :
% 2.86/1.57 ( ( ( member @ A @ X3 @ B3 )
% 2.86/1.57 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 2.86/1.57 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) )
% 2.86/1.57 & ( ~ ( member @ A @ X3 @ B3 )
% 2.86/1.57 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 2.86/1.57 = ( insert @ A @ X3 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_228_DiffE,axiom,
% 2.86/1.57 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 2.86/1.57 => ~ ( ( member @ A @ C @ A2 )
% 2.86/1.57 => ( member @ A @ C @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_229_DiffD1,axiom,
% 2.86/1.57 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 2.86/1.57 => ( member @ A @ C @ A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_230_DiffD2,axiom,
% 2.86/1.57 ! [A: $tType,C: A,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 2.86/1.57 => ~ ( member @ A @ C @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_231_subset__Diff__insert,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A,C4: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B3 @ ( insert @ A @ X3 @ C4 ) ) )
% 2.86/1.57 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B3 @ C4 ) )
% 2.86/1.57 & ~ ( member @ A @ X3 @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_232_Diff__insert__absorb,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A] :
% 2.86/1.57 ( ~ ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.57 = A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_233_Diff__insert2,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,A3: A,B3: set @ A] :
% 2.86/1.57 ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B3 ) )
% 2.86/1.57 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_234_insert__Diff,axiom,
% 2.86/1.57 ! [A: $tType,A3: A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ A3 @ A2 )
% 2.86/1.57 => ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.86/1.57 = A2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_235_Diff__insert,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,A3: A,B3: set @ A] :
% 2.86/1.57 ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B3 ) )
% 2.86/1.57 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_236_Diff__mono,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,C4: set @ A,D3: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ A ) @ D3 @ B3 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ ( minus_minus @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_237_Diff__subset,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ A2 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_238_double__diff,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A,C4: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C4 )
% 2.86/1.57 => ( ( minus_minus @ ( set @ A ) @ B3 @ ( minus_minus @ ( set @ A ) @ C4 @ A2 ) )
% 2.86/1.57 = A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_239_Compl__eq__Diff__UNIV,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( uminus_uminus @ ( set @ A ) )
% 2.86/1.57 = ( minus_minus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_240_Diff__single__insert,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,X3: A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B3 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_241_subset__insert__iff,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,X3: A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 2.86/1.57 = ( ( ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B3 ) )
% 2.86/1.57 & ( ~ ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_242_Compl__insert,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,A2: set @ A] :
% 2.86/1.57 ( ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) )
% 2.86/1.57 = ( minus_minus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_243_remove__def,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( remove @ A )
% 2.86/1.57 = ( ^ [X: A,A4: set @ A] : ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_244_psubset__insert__iff,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,X3: A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 2.86/1.57 = ( ( ( member @ A @ X3 @ B3 )
% 2.86/1.57 => ( ord_less @ ( set @ A ) @ A2 @ B3 ) )
% 2.86/1.57 & ( ~ ( member @ A @ X3 @ B3 )
% 2.86/1.57 => ( ( ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ord_less @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B3 ) )
% 2.86/1.57 & ( ~ ( member @ A @ X3 @ A2 )
% 2.86/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_245_member__remove,axiom,
% 2.86/1.57 ! [A: $tType,X3: A,Y3: A,A2: set @ A] :
% 2.86/1.57 ( ( member @ A @ X3 @ ( remove @ A @ Y3 @ A2 ) )
% 2.86/1.57 = ( ( member @ A @ X3 @ A2 )
% 2.86/1.57 & ( X3 != Y3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_246_psubsetI,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ( ( A2 != B3 )
% 2.86/1.57 => ( ord_less @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_247_bot_Onot__eq__extremum,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A] :
% 2.86/1.57 ( ( A3
% 2.86/1.57 != ( bot_bot @ A ) )
% 2.86/1.57 = ( ord_less @ A @ ( bot_bot @ A ) @ A3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_248_bot_Oextremum__strict,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [A3: A] :
% 2.86/1.57 ~ ( ord_less @ A @ A3 @ ( bot_bot @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_249_not__psubset__empty,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A] :
% 2.86/1.57 ~ ( ord_less @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_250_psubset__imp__ex__mem,axiom,
% 2.86/1.57 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.86/1.57 ( ( ord_less @ ( set @ A ) @ A2 @ B3 )
% 2.86/1.57 => ? [B6: A] : ( member @ A @ B6 @ ( minus_minus @ ( set @ A ) @ B3 @ A2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_251_leD,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [Y3: A,X3: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.86/1.57 => ~ ( ord_less @ A @ X3 @ Y3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_252_leI,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.57 => ! [X3: A,Y3: A] :
% 2.86/1.57 ( ~ ( ord_less @ A @ X3 @ Y3 )
% 2.86/1.57 => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_253_le__less,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ( ( ord_less_eq @ A )
% 2.86/1.57 = ( ^ [X: A,Y2: A] :
% 2.86/1.57 ( ( ord_less @ A @ X @ Y2 )
% 2.86/1.57 | ( X = Y2 ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_254_less__le,axiom,
% 2.86/1.57 ! [A: $tType] :
% 2.86/1.57 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.57 => ( ( ord_less @ A )
% 2.86/1.57 = ( ^ [X: A,Y2: A] :
% 2.86/1.57 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.86/1.57 & ( X != Y2 ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_255_order__le__less__subst1,axiom,
% 2.86/1.57 ! [A: $tType,B: $tType] :
% 2.86/1.57 ( ( ( order @ B @ ( type2 @ B ) )
% 2.86/1.57 & ( order @ A @ ( type2 @ A ) ) )
% 2.86/1.57 => ! [A3: A,F2: B > A,B2: B,C: B] :
% 2.86/1.57 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B2 ) )
% 2.86/1.57 => ( ( ord_less @ B @ B2 @ C )
% 2.86/1.57 => ( ! [X2: B,Y: B] :
% 2.86/1.57 ( ( ord_less @ B @ X2 @ Y )
% 2.86/1.57 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 2.86/1.57 => ( ord_less @ A @ A3 @ ( F2 @ C ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 2.86/1.57 ! [A6: $tType,A7: $tType] :
% 2.86/1.57 ( ( boolean_algebra @ A7 @ ( type2 @ A7 ) )
% 2.86/1.57 => ( boolean_algebra @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 2.86/1.57 ! [A6: $tType,A7: $tType] :
% 2.86/1.57 ( ( order_top @ A7 @ ( type2 @ A7 ) )
% 2.86/1.57 => ( order_top @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.86/1.57 ! [A6: $tType,A7: $tType] :
% 2.86/1.57 ( ( order_bot @ A7 @ ( type2 @ A7 ) )
% 2.86/1.57 => ( order_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.86/1.57 ! [A6: $tType,A7: $tType] :
% 2.86/1.57 ( ( preorder @ A7 @ ( type2 @ A7 ) )
% 2.86/1.57 => ( preorder @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.86/1.57 ! [A6: $tType,A7: $tType] :
% 2.86/1.57 ( ( order @ A7 @ ( type2 @ A7 ) )
% 2.86/1.57 => ( order @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_fun___Orderings_Otop,axiom,
% 2.86/1.57 ! [A6: $tType,A7: $tType] :
% 2.86/1.57 ( ( top @ A7 @ ( type2 @ A7 ) )
% 2.86/1.57 => ( top @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_fun___Orderings_Oord,axiom,
% 2.86/1.57 ! [A6: $tType,A7: $tType] :
% 2.86/1.57 ( ( ord @ A7 @ ( type2 @ A7 ) )
% 2.86/1.57 => ( ord @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_fun___Orderings_Obot,axiom,
% 2.86/1.57 ! [A6: $tType,A7: $tType] :
% 2.86/1.57 ( ( bot @ A7 @ ( type2 @ A7 ) )
% 2.86/1.57 => ( bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_1,axiom,
% 2.86/1.57 ! [A6: $tType] : ( boolean_algebra @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_Set_Oset___Orderings_Oorder__top_2,axiom,
% 2.86/1.57 ! [A6: $tType] : ( order_top @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_Set_Oset___Orderings_Oorder__bot_3,axiom,
% 2.86/1.57 ! [A6: $tType] : ( order_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 2.86/1.57 ! [A6: $tType] : ( preorder @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 2.86/1.57 ! [A6: $tType] : ( order @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_Set_Oset___Orderings_Otop_6,axiom,
% 2.86/1.57 ! [A6: $tType] : ( top @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_Set_Oset___Orderings_Oord_7,axiom,
% 2.86/1.57 ! [A6: $tType] : ( ord @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_Set_Oset___Orderings_Obot_8,axiom,
% 2.86/1.57 ! [A6: $tType] : ( bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_9,axiom,
% 2.86/1.57 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_HOL_Obool___Orderings_Oorder__top_10,axiom,
% 2.86/1.57 order_top @ $o @ ( type2 @ $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_HOL_Obool___Orderings_Oorder__bot_11,axiom,
% 2.86/1.57 order_bot @ $o @ ( type2 @ $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 2.86/1.57 preorder @ $o @ ( type2 @ $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.86/1.57 linorder @ $o @ ( type2 @ $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_HOL_Obool___Orderings_Oorder_13,axiom,
% 2.86/1.57 order @ $o @ ( type2 @ $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_HOL_Obool___Orderings_Otop_14,axiom,
% 2.86/1.57 top @ $o @ ( type2 @ $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_HOL_Obool___Orderings_Oord_15,axiom,
% 2.86/1.57 ord @ $o @ ( type2 @ $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(tcon_HOL_Obool___Orderings_Obot_16,axiom,
% 2.86/1.57 bot @ $o @ ( type2 @ $o ) ).
% 2.86/1.57
% 2.86/1.57 thf(conj_0,hypothesis,
% 2.86/1.57 $true ).
% 2.86/1.57
% 2.86/1.57 thf(conj_1,conjecture,
% 2.86/1.57 ? [Tr6: dtree] :
% 2.86/1.57 ( ( ( bot_bot @ ( set @ t ) )
% 2.86/1.57 = ( gram_L861583724lle_Fr @ ns @ Tr6 ) )
% 2.86/1.57 & ( gram_L864798063lle_wf @ Tr6 )
% 2.86/1.57 & ( ( root @ Tr6 )
% 2.86/1.57 = n2 )
% 2.86/1.57 & ( gram_L646766332egular @ Tr6 ) ) ).
% 2.86/1.57 ------------------------
% 2.86/1.60 % (30435)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/183Mi)
% 2.93/1.60 % (30437)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_30331 for (2999ds/27Mi)
% 2.93/1.60 % (30438)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/2Mi)
% 2.93/1.60 % (30440)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_30331 for (2999ds/275Mi)
% 2.93/1.60 % (30439)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_30331 for (2999ds/2Mi)
% 2.93/1.60 % (30441)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/18Mi)
% 2.93/1.60 % (30436)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_30331 for (2999ds/4Mi)
% 2.93/1.60 % (30438)Instruction limit reached!
% 2.93/1.60 % (30438)------------------------------
% 2.93/1.60 % (30438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (30438)Termination reason: Unknown
% 2.93/1.60 % (30438)Termination phase: shuffling
% 2.93/1.60
% 2.93/1.60 % (30439)Instruction limit reached!
% 2.93/1.60 % (30439)------------------------------
% 2.93/1.60 % (30439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (30439)Termination reason: Unknown
% 2.93/1.60 % (30439)Termination phase: shuffling
% 2.93/1.60
% 2.93/1.60 % (30439)Memory used [KB]: 1279
% 2.93/1.60 % (30439)Time elapsed: 0.003 s
% 2.93/1.60 % (30439)Instructions burned: 3 (million)
% 2.93/1.60 % (30439)------------------------------
% 2.93/1.60 % (30439)------------------------------
% 2.93/1.60 % (30438)Memory used [KB]: 1279
% 2.93/1.60 % (30438)Time elapsed: 0.003 s
% 2.93/1.60 % (30438)Instructions burned: 3 (million)
% 2.93/1.60 % (30438)------------------------------
% 2.93/1.60 % (30438)------------------------------
% 2.93/1.60 % (30436)Instruction limit reached!
% 2.93/1.60 % (30436)------------------------------
% 2.93/1.60 % (30436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (30436)Termination reason: Unknown
% 2.93/1.60 % (30436)Termination phase: shuffling
% 2.93/1.60
% 2.93/1.60 % (30436)Memory used [KB]: 1279
% 2.93/1.60 % (30436)Time elapsed: 0.004 s
% 2.93/1.60 % (30436)Instructions burned: 5 (million)
% 2.93/1.60 % (30436)------------------------------
% 2.93/1.60 % (30436)------------------------------
% 2.93/1.61 % (30441)Instruction limit reached!
% 2.93/1.61 % (30441)------------------------------
% 2.93/1.61 % (30441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (30441)Termination reason: Unknown
% 2.93/1.61 % (30441)Termination phase: shuffling
% 2.93/1.61
% 2.93/1.61 % (30441)Memory used [KB]: 1663
% 2.93/1.61 % (30441)Time elapsed: 0.011 s
% 2.93/1.61 % (30441)Instructions burned: 18 (million)
% 2.93/1.61 % (30441)------------------------------
% 2.93/1.61 % (30441)------------------------------
% 2.93/1.61 % (30437)Instruction limit reached!
% 2.93/1.61 % (30437)------------------------------
% 2.93/1.61 % (30437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (30437)Termination reason: Unknown
% 2.93/1.61 % (30437)Termination phase: Property scanning
% 2.93/1.61
% 2.93/1.61 % (30437)Memory used [KB]: 1663
% 2.93/1.61 % (30437)Time elapsed: 0.015 s
% 2.93/1.61 % (30437)Instructions burned: 28 (million)
% 2.93/1.61 % (30437)------------------------------
% 2.93/1.61 % (30437)------------------------------
% 2.93/1.62 % (30443)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_30331 for (2999ds/37Mi)
% 2.93/1.62 % (30444)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_30331 for (2999ds/15Mi)
% 2.93/1.62 % (30442)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/3Mi)
% 2.93/1.62 % (30440)Refutation not found, incomplete strategy
% 2.93/1.62 % (30440)------------------------------
% 2.93/1.62 % (30440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (30440)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.62
% 2.93/1.62
% 2.93/1.62 % (30440)Memory used [KB]: 6268
% 2.93/1.62 % (30440)Time elapsed: 0.022 s
% 2.93/1.62 % (30440)Instructions burned: 42 (million)
% 2.93/1.62 % (30440)------------------------------
% 2.93/1.62 % (30440)------------------------------
% 2.93/1.62 % (30442)Instruction limit reached!
% 2.93/1.62 % (30442)------------------------------
% 2.93/1.62 % (30442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (30442)Termination reason: Unknown
% 2.93/1.62 % (30442)Termination phase: shuffling
% 2.93/1.62
% 2.93/1.62 % (30442)Memory used [KB]: 1279
% 2.93/1.62 % (30442)Time elapsed: 0.003 s
% 2.93/1.62 % (30442)Instructions burned: 3 (million)
% 2.93/1.62 % (30442)------------------------------
% 2.93/1.62 % (30442)------------------------------
% 2.93/1.63 % (30445)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_30331 for (2999ds/3Mi)
% 2.93/1.63 % (30444)Instruction limit reached!
% 2.93/1.63 % (30444)------------------------------
% 2.93/1.63 % (30444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (30444)Termination reason: Unknown
% 2.93/1.63 % (30444)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (30444)Memory used [KB]: 1535
% 2.93/1.63 % (30444)Time elapsed: 0.009 s
% 2.93/1.63 % (30444)Instructions burned: 15 (million)
% 2.93/1.63 % (30444)------------------------------
% 2.93/1.63 % (30444)------------------------------
% 2.93/1.63 % (30445)Instruction limit reached!
% 2.93/1.63 % (30445)------------------------------
% 2.93/1.63 % (30445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (30445)Termination reason: Unknown
% 2.93/1.63 % (30445)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (30445)Memory used [KB]: 1279
% 2.93/1.63 % (30445)Time elapsed: 0.003 s
% 2.93/1.63 % (30445)Instructions burned: 3 (million)
% 2.93/1.63 % (30445)------------------------------
% 2.93/1.63 % (30445)------------------------------
% 2.93/1.63 % (30446)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_30331 for (2999ds/1041Mi)
% 2.93/1.64 % (30443)Instruction limit reached!
% 2.93/1.64 % (30443)------------------------------
% 2.93/1.64 % (30443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.64 % (30443)Termination reason: Unknown
% 2.93/1.64 % (30443)Termination phase: Property scanning
% 2.93/1.64
% 2.93/1.64 % (30443)Memory used [KB]: 1918
% 2.93/1.64 % (30443)Time elapsed: 0.019 s
% 2.93/1.64 % (30443)Instructions burned: 39 (million)
% 2.93/1.64 % (30443)------------------------------
% 2.93/1.64 % (30443)------------------------------
% 2.93/1.64 % (30447)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/7Mi)
% 2.93/1.64 % (30448)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/16Mi)
% 2.93/1.64 % (30447)Instruction limit reached!
% 2.93/1.64 % (30447)------------------------------
% 2.93/1.64 % (30447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.64 % (30447)Termination reason: Unknown
% 2.93/1.64 % (30447)Termination phase: shuffling
% 2.93/1.64
% 2.93/1.64 % (30447)Memory used [KB]: 1407
% 2.93/1.64 % (30447)Time elapsed: 0.005 s
% 2.93/1.64 % (30447)Instructions burned: 8 (million)
% 2.93/1.64 % (30447)------------------------------
% 2.93/1.64 % (30447)------------------------------
% 2.93/1.64 % (30449)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_30331 for (2999ds/3Mi)
% 2.93/1.64 % (30450)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_30331 for (2999ds/3Mi)
% 2.93/1.65 % (30449)Instruction limit reached!
% 2.93/1.65 % (30449)------------------------------
% 2.93/1.65 % (30449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (30449)Termination reason: Unknown
% 2.93/1.65 % (30449)Termination phase: shuffling
% 2.93/1.65
% 2.93/1.65 % (30449)Memory used [KB]: 1279
% 2.93/1.65 % (30449)Time elapsed: 0.003 s
% 2.93/1.65 % (30449)Instructions burned: 4 (million)
% 2.93/1.65 % (30449)------------------------------
% 2.93/1.65 % (30449)------------------------------
% 2.93/1.65 % (30450)Instruction limit reached!
% 2.93/1.65 % (30450)------------------------------
% 2.93/1.65 % (30450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (30450)Termination reason: Unknown
% 2.93/1.65 % (30450)Termination phase: shuffling
% 2.93/1.65
% 2.93/1.65 % (30450)Memory used [KB]: 1279
% 2.93/1.65 % (30450)Time elapsed: 0.003 s
% 2.93/1.65 % (30450)Instructions burned: 3 (million)
% 2.93/1.65 % (30450)------------------------------
% 2.93/1.65 % (30450)------------------------------
% 2.93/1.65 % (30448)Instruction limit reached!
% 2.93/1.65 % (30448)------------------------------
% 2.93/1.65 % (30448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (30448)Termination reason: Unknown
% 2.93/1.65 % (30448)Termination phase: shuffling
% 2.93/1.65
% 2.93/1.65 % (30448)Memory used [KB]: 1535
% 2.93/1.65 % (30448)Time elapsed: 0.009 s
% 2.93/1.65 % (30448)Instructions burned: 16 (million)
% 2.93/1.65 % (30448)------------------------------
% 2.93/1.65 % (30448)------------------------------
% 2.93/1.65 % (30435)Instruction limit reached!
% 2.93/1.65 % (30435)------------------------------
% 2.93/1.65 % (30435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (30435)Termination reason: Unknown
% 2.93/1.65 % (30435)Termination phase: Saturation
% 2.93/1.65
% 2.93/1.65 % (30435)Memory used [KB]: 6908
% 2.93/1.65 % (30435)Time elapsed: 0.057 s
% 2.93/1.65 % (30435)Instructions burned: 183 (million)
% 2.93/1.65 % (30435)------------------------------
% 2.93/1.65 % (30435)------------------------------
% 2.93/1.65 % (30451)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/7Mi)
% 2.93/1.66 % (30451)Instruction limit reached!
% 2.93/1.66 % (30451)------------------------------
% 2.93/1.66 % (30451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (30451)Termination reason: Unknown
% 2.93/1.66 % (30451)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (30451)Memory used [KB]: 1407
% 2.93/1.66 % (30451)Time elapsed: 0.005 s
% 2.93/1.66 % (30451)Instructions burned: 7 (million)
% 2.93/1.66 % (30451)------------------------------
% 2.93/1.66 % (30451)------------------------------
% 2.93/1.66 % (30452)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/3Mi)
% 2.93/1.66 % (30454)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/18Mi)
% 2.93/1.66 % (30452)Instruction limit reached!
% 2.93/1.66 % (30452)------------------------------
% 2.93/1.66 % (30452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (30452)Termination reason: Unknown
% 2.93/1.66 % (30452)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (30452)Memory used [KB]: 1279
% 2.93/1.66 % (30452)Time elapsed: 0.003 s
% 2.93/1.66 % (30452)Instructions burned: 4 (million)
% 2.93/1.66 % (30452)------------------------------
% 2.93/1.66 % (30452)------------------------------
% 2.93/1.66 % (30453)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/4Mi)
% 2.93/1.66 % (30455)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/710Mi)
% 2.93/1.66 % (30453)Instruction limit reached!
% 2.93/1.66 % (30453)------------------------------
% 2.93/1.66 % (30453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (30453)Termination reason: Unknown
% 2.93/1.66 % (30453)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (30453)Memory used [KB]: 1279
% 2.93/1.66 % (30453)Time elapsed: 0.003 s
% 2.93/1.66 % (30453)Instructions burned: 4 (million)
% 2.93/1.66 % (30453)------------------------------
% 2.93/1.66 % (30453)------------------------------
% 2.93/1.66 % (30456)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/6Mi)
% 2.93/1.67 % (30454)Instruction limit reached!
% 2.93/1.67 % (30454)------------------------------
% 2.93/1.67 % (30454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.67 % (30454)Termination reason: Unknown
% 2.93/1.67 % (30454)Termination phase: Property scanning
% 2.93/1.67
% 2.93/1.67 % (30454)Memory used [KB]: 1663
% 2.93/1.67 % (30454)Time elapsed: 0.008 s
% 2.93/1.67 % (30454)Instructions burned: 21 (million)
% 2.93/1.67 % (30454)------------------------------
% 2.93/1.67 % (30454)------------------------------
% 2.93/1.67 % (30456)Instruction limit reached!
% 2.93/1.67 % (30456)------------------------------
% 2.93/1.67 % (30456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.67 % (30456)Termination reason: Unknown
% 2.93/1.67 % (30456)Termination phase: shuffling
% 2.93/1.67
% 2.93/1.67 % (30456)Memory used [KB]: 1407
% 2.93/1.67 % (30456)Time elapsed: 0.005 s
% 2.93/1.67 % (30456)Instructions burned: 6 (million)
% 2.93/1.67 % (30456)------------------------------
% 2.93/1.67 % (30456)------------------------------
% 2.93/1.67 % (30461)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_30331 for (2999ds/6Mi)
% 2.93/1.68 % (30458)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_30331 for (2999ds/902Mi)
% 2.93/1.68 % (30459)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_30331 for (2999ds/21Mi)
% 2.93/1.68 % (30461)Instruction limit reached!
% 2.93/1.68 % (30461)------------------------------
% 2.93/1.68 % (30461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.68 % (30461)Termination reason: Unknown
% 2.93/1.68 % (30461)Termination phase: shuffling
% 2.93/1.68
% 2.93/1.68 % (30461)Memory used [KB]: 1407
% 2.93/1.68 % (30461)Time elapsed: 0.003 s
% 2.93/1.68 % (30461)Instructions burned: 8 (million)
% 2.93/1.68 % (30461)------------------------------
% 2.93/1.68 % (30461)------------------------------
% 2.93/1.68 % (30460)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/5Mi)
% 2.93/1.68 % (30460)Instruction limit reached!
% 2.93/1.68 % (30460)------------------------------
% 2.93/1.68 % (30460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.68 % (30460)Termination reason: Unknown
% 2.93/1.68 % (30460)Termination phase: shuffling
% 2.93/1.68
% 2.93/1.68 % (30460)Memory used [KB]: 1407
% 2.93/1.68 % (30460)Time elapsed: 0.004 s
% 2.93/1.68 % (30460)Instructions burned: 6 (million)
% 2.93/1.68 % (30460)------------------------------
% 2.93/1.68 % (30460)------------------------------
% 2.93/1.68 % (30462)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/377Mi)
% 2.93/1.69 % (30463)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_30331 for (2998ds/779Mi)
% 2.93/1.69 % (30459)Instruction limit reached!
% 2.93/1.69 % (30459)------------------------------
% 2.93/1.69 % (30459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.69 % (30459)Termination reason: Unknown
% 2.93/1.69 % (30459)Termination phase: Property scanning
% 2.93/1.69
% 2.93/1.69 % (30459)Memory used [KB]: 1663
% 2.93/1.69 % (30459)Time elapsed: 0.012 s
% 2.93/1.69 % (30459)Instructions burned: 21 (million)
% 2.93/1.69 % (30459)------------------------------
% 2.93/1.69 % (30459)------------------------------
% 2.93/1.70 % (30464)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_30331 for (2998ds/19Mi)
% 2.93/1.70 % (30465)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30331 for (2998ds/879Mi)
% 2.93/1.71 % (30464)Instruction limit reached!
% 2.93/1.71 % (30464)------------------------------
% 2.93/1.71 % (30464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.71 % (30464)Termination reason: Unknown
% 2.93/1.71 % (30464)Termination phase: shuffling
% 2.93/1.71
% 2.93/1.71 % (30464)Memory used [KB]: 1663
% 2.93/1.71 % (30464)Time elapsed: 0.010 s
% 2.93/1.71 % (30464)Instructions burned: 19 (million)
% 2.93/1.71 % (30464)------------------------------
% 2.93/1.71 % (30464)------------------------------
% 2.93/1.72 % (30458)Refutation not found, incomplete strategy
% 2.93/1.72 % (30458)------------------------------
% 2.93/1.72 % (30458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.72 % (30458)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.72
% 2.93/1.72
% 2.93/1.72 % (30458)Memory used [KB]: 6780
% 2.93/1.72 % (30458)Time elapsed: 0.047 s
% 2.93/1.72 % (30458)Instructions burned: 95 (million)
% 2.93/1.72 % (30458)------------------------------
% 2.93/1.72 % (30458)------------------------------
% 2.93/1.73 % (30466)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30331 for (2998ds/17Mi)
% 2.93/1.73 % (30466)Instruction limit reached!
% 2.93/1.73 % (30466)------------------------------
% 2.93/1.73 % (30466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.73 % (30466)Termination reason: Unknown
% 2.93/1.74 % (30466)Termination phase: shuffling
% 2.93/1.74
% 2.93/1.74 % (30466)Memory used [KB]: 1535
% 2.93/1.74 % (30466)Time elapsed: 0.010 s
% 2.93/1.74 % (30466)Instructions burned: 17 (million)
% 2.93/1.74 % (30466)------------------------------
% 2.93/1.74 % (30466)------------------------------
% 2.93/1.74 % (30467)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30331 for (2998ds/3Mi)
% 2.93/1.74 % (30467)Instruction limit reached!
% 2.93/1.74 % (30467)------------------------------
% 2.93/1.74 % (30467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.74 % (30467)Termination reason: Unknown
% 2.93/1.74 % (30467)Termination phase: shuffling
% 2.93/1.74
% 2.93/1.74 % (30467)Memory used [KB]: 1279
% 2.93/1.74 % (30467)Time elapsed: 0.003 s
% 2.93/1.74 % (30467)Instructions burned: 3 (million)
% 2.93/1.74 % (30467)------------------------------
% 2.93/1.74 % (30467)------------------------------
% 2.93/1.75 % (30468)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_30331 for (2998ds/30Mi)
% 2.93/1.76 % (30469)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_30331 for (2998ds/127Mi)
% 2.93/1.77 % (30468)Instruction limit reached!
% 2.93/1.77 % (30468)------------------------------
% 2.93/1.77 % (30468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.77 % (30468)Termination reason: Unknown
% 2.93/1.77 % (30468)Termination phase: Property scanning
% 2.93/1.77
% 2.93/1.77 % (30468)Memory used [KB]: 1663
% 2.93/1.77 % (30468)Time elapsed: 0.016 s
% 2.93/1.77 % (30468)Instructions burned: 30 (million)
% 2.93/1.77 % (30468)------------------------------
% 2.93/1.77 % (30468)------------------------------
% 2.93/1.78 % (30470)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_30331 for (2998ds/100Mi)
% 2.93/1.82 % (30469)Instruction limit reached!
% 2.93/1.82 % (30469)------------------------------
% 2.93/1.82 % (30469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.82 % (30469)Termination reason: Unknown
% 2.93/1.82 % (30469)Termination phase: Saturation
% 2.93/1.82
% 2.93/1.82 % (30469)Memory used [KB]: 6780
% 2.93/1.82 % (30469)Time elapsed: 0.064 s
% 2.93/1.82 % (30469)Instructions burned: 128 (million)
% 2.93/1.82 % (30469)------------------------------
% 2.93/1.82 % (30469)------------------------------
% 2.93/1.83 % (30470)Instruction limit reached!
% 2.93/1.83 % (30470)------------------------------
% 2.93/1.83 % (30470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.83 % (30470)Termination reason: Unknown
% 2.93/1.83 % (30470)Termination phase: Property scanning
% 2.93/1.83
% 2.93/1.83 % (30470)Memory used [KB]: 2046
% 2.93/1.83 % (30470)Time elapsed: 0.047 s
% 2.93/1.83 % (30470)Instructions burned: 100 (million)
% 2.93/1.83 % (30470)------------------------------
% 2.93/1.83 % (30470)------------------------------
% 2.93/1.84 % (30471)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_30331 for (2997ds/3Mi)
% 2.93/1.84 % (30472)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_30331 for (2997ds/20Mi)
% 2.93/1.85 % (30471)Instruction limit reached!
% 2.93/1.85 % (30471)------------------------------
% 2.93/1.85 % (30471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.85 % (30471)Termination reason: Unknown
% 2.93/1.85 % (30471)Termination phase: shuffling
% 2.93/1.85
% 2.93/1.85 % (30471)Memory used [KB]: 1279
% 2.93/1.85 % (30471)Time elapsed: 0.003 s
% 2.93/1.85 % (30471)Instructions burned: 3 (million)
% 2.93/1.85 % (30471)------------------------------
% 2.93/1.85 % (30471)------------------------------
% 2.93/1.85 % (30472)Instruction limit reached!
% 2.93/1.85 % (30472)------------------------------
% 2.93/1.85 % (30472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.85 % (30472)Termination reason: Unknown
% 2.93/1.85 % (30472)Termination phase: Property scanning
% 2.93/1.85
% 2.93/1.85 % (30472)Memory used [KB]: 1663
% 2.93/1.85 % (30472)Time elapsed: 0.012 s
% 2.93/1.85 % (30472)Instructions burned: 20 (million)
% 2.93/1.85 % (30472)------------------------------
% 2.93/1.85 % (30472)------------------------------
% 2.93/1.86 % (30473)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_30331 for (2997ds/86Mi)
% 2.93/1.86 % (30474)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_30331 for (2997ds/107Mi)
% 2.93/1.87 % (30462)Instruction limit reached!
% 2.93/1.87 % (30462)------------------------------
% 2.93/1.87 % (30462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.87 % (30462)Termination reason: Unknown
% 2.93/1.87 % (30462)Termination phase: Saturation
% 2.93/1.87
% 2.93/1.87 % (30462)Memory used [KB]: 7547
% 2.93/1.87 % (30462)Time elapsed: 0.194 s
% 2.93/1.87 % (30462)Instructions burned: 378 (million)
% 2.93/1.87 % (30462)------------------------------
% 2.93/1.87 % (30462)------------------------------
% 2.93/1.89 % (30475)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_30331 for (2997ds/39Mi)
% 2.93/1.90 % (30474)Instruction limit reached!
% 2.93/1.90 % (30474)------------------------------
% 2.93/1.90 % (30474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.90 % (30474)Termination reason: Unknown
% 2.93/1.90 % (30474)Termination phase: Saturation
% 2.93/1.90
% 2.93/1.90 % (30474)Memory used [KB]: 6524
% 2.93/1.90 % (30474)Time elapsed: 0.033 s
% 2.93/1.90 % (30474)Instructions burned: 107 (million)
% 2.93/1.90 % (30474)------------------------------
% 2.93/1.90 % (30474)------------------------------
% 2.93/1.90 % (30473)Instruction limit reached!
% 2.93/1.90 % (30473)------------------------------
% 2.93/1.90 % (30473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.90 % (30473)Termination reason: Unknown
% 2.93/1.90 % (30473)Termination phase: Saturation
% 2.93/1.90
% 2.93/1.90 % (30473)Memory used [KB]: 6524
% 2.93/1.90 % (30473)Time elapsed: 0.042 s
% 2.93/1.90 % (30473)Instructions burned: 86 (million)
% 2.93/1.90 % (30473)------------------------------
% 2.93/1.90 % (30473)------------------------------
% 2.93/1.91 % (30476)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_30331 for (2996ds/448Mi)
% 2.93/1.91 % (30475)Instruction limit reached!
% 2.93/1.91 % (30475)------------------------------
% 2.93/1.91 % (30475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.91 % (30475)Termination reason: Unknown
% 2.93/1.91 % (30475)Termination phase: Property scanning
% 2.93/1.91
% 2.93/1.91 % (30475)Memory used [KB]: 2046
% 2.93/1.91 % (30475)Time elapsed: 0.020 s
% 2.93/1.91 % (30475)Instructions burned: 39 (million)
% 2.93/1.91 % (30475)------------------------------
% 2.93/1.91 % (30475)------------------------------
% 2.93/1.93 % (30478)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_30331 for (2996ds/98Mi)
% 2.93/1.93 % (30477)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_30331 for (2996ds/46Mi)
% 2.93/1.95 % (30477)Instruction limit reached!
% 2.93/1.95 % (30477)------------------------------
% 2.93/1.95 % (30477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.95 % (30477)Termination reason: Unknown
% 2.93/1.95 % (30477)Termination phase: Property scanning
% 2.93/1.95
% 2.93/1.95 % (30477)Memory used [KB]: 1918
% 2.93/1.95 % (30477)Time elapsed: 0.016 s
% 2.93/1.95 % (30477)Instructions burned: 47 (million)
% 2.93/1.95 % (30477)------------------------------
% 2.93/1.95 % (30477)------------------------------
% 2.93/1.96 % (30479)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_30331 for (2996ds/507Mi)
% 2.93/1.96 % (30463)Instruction limit reached!
% 2.93/1.96 % (30463)------------------------------
% 2.93/1.96 % (30463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.96 % (30463)Termination reason: Unknown
% 2.93/1.96 % (30463)Termination phase: Saturation
% 2.93/1.96
% 2.93/1.96 % (30463)Memory used [KB]: 7547
% 2.93/1.96 % (30463)Time elapsed: 0.276 s
% 2.93/1.96 % (30463)Instructions burned: 779 (million)
% 2.93/1.96 % (30463)------------------------------
% 2.93/1.96 % (30463)------------------------------
% 2.93/1.97 % (30478)Instruction limit reached!
% 2.93/1.97 % (30478)------------------------------
% 2.93/1.97 % (30478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.97 % (30478)Termination reason: Unknown
% 2.93/1.97 % (30478)Termination phase: Property scanning
% 2.93/1.97
% 2.93/1.97 % (30478)Memory used [KB]: 2174
% 2.93/1.97 % (30478)Time elapsed: 0.046 s
% 2.93/1.97 % (30478)Instructions burned: 98 (million)
% 2.93/1.97 % (30478)------------------------------
% 2.93/1.97 % (30478)------------------------------
% 2.93/1.97 % (30480)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_30331 for (2996ds/149Mi)
% 2.93/1.99 % (30481)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_30331 for (2995ds/39Mi)
% 2.93/2.01 % (30455)Instruction limit reached!
% 2.93/2.01 % (30455)------------------------------
% 2.93/2.01 % (30455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/2.01 % (30455)Termination reason: Unknown
% 2.93/2.01 % (30455)Termination phase: Saturation
% 2.93/2.01
% 2.93/2.01 % (30455)Memory used [KB]: 7931
% 2.93/2.01 % (30455)Time elapsed: 0.344 s
% 2.93/2.01 % (30455)Instructions burned: 710 (million)
% 2.93/2.01 % (30455)------------------------------
% 2.93/2.01 % (30455)------------------------------
% 2.93/2.01 % (30481)Instruction limit reached!
% 2.93/2.01 % (30481)------------------------------
% 2.93/2.01 % (30481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/2.01 % (30481)Termination reason: Unknown
% 2.93/2.01 % (30481)Termination phase: Clausification
% 2.93/2.01
% 2.93/2.01 % (30481)Memory used [KB]: 1918
% 2.93/2.01 % (30481)Time elapsed: 0.021 s
% 2.93/2.01 % (30481)Instructions burned: 39 (million)
% 2.93/2.01 % (30481)------------------------------
% 2.93/2.01 % (30481)------------------------------
% 2.93/2.02 % (30480)Instruction limit reached!
% 2.93/2.02 % (30480)------------------------------
% 2.93/2.02 % (30480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/2.02 % (30480)Termination reason: Unknown
% 2.93/2.02 % (30480)Termination phase: Saturation
% 2.93/2.02
% 2.93/2.02 % (30480)Memory used [KB]: 6780
% 2.93/2.02 % (30480)Time elapsed: 0.047 s
% 2.93/2.02 % (30480)Instructions burned: 150 (million)
% 2.93/2.02 % (30480)------------------------------
% 2.93/2.02 % (30480)------------------------------
% 2.93/2.02 % (30483)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_30331 for (2995ds/1087Mi)
% 2.93/2.02 % (30482)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_30331 for (2995ds/6Mi)
% 5.87/2.03 % (30484)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_30331 for (2995ds/47Mi)
% 5.87/2.03 % (30482)Instruction limit reached!
% 5.87/2.03 % (30482)------------------------------
% 5.87/2.03 % (30482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.03 % (30482)Termination reason: Unknown
% 5.87/2.03 % (30482)Termination phase: shuffling
% 5.87/2.03
% 5.87/2.03 % (30482)Memory used [KB]: 1407
% 5.87/2.03 % (30482)Time elapsed: 0.005 s
% 5.87/2.03 % (30482)Instructions burned: 7 (million)
% 5.87/2.03 % (30482)------------------------------
% 5.87/2.03 % (30482)------------------------------
% 5.87/2.04 % (30484)Instruction limit reached!
% 5.87/2.04 % (30484)------------------------------
% 5.87/2.04 % (30484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.04 % (30484)Termination reason: Unknown
% 5.87/2.04 % (30484)Termination phase: Property scanning
% 5.87/2.04
% 5.87/2.04 % (30484)Memory used [KB]: 1918
% 5.87/2.04 % (30484)Time elapsed: 0.016 s
% 5.87/2.04 % (30484)Instructions burned: 49 (million)
% 5.87/2.04 % (30484)------------------------------
% 5.87/2.04 % (30484)------------------------------
% 5.87/2.04 % (30485)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_30331 for (2995ds/44Mi)
% 5.87/2.05 % (30486)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_30331 for (2995ds/432Mi)
% 5.87/2.06 % (30485)Instruction limit reached!
% 5.87/2.06 % (30485)------------------------------
% 5.87/2.06 % (30485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.06 % (30485)Termination reason: Unknown
% 5.87/2.06 % (30485)Termination phase: Property scanning
% 5.87/2.06
% 5.87/2.06 % (30485)Memory used [KB]: 2046
% 5.87/2.06 % (30485)Time elapsed: 0.022 s
% 5.87/2.06 % (30485)Instructions burned: 45 (million)
% 5.87/2.06 % (30485)------------------------------
% 5.87/2.06 % (30485)------------------------------
% 5.87/2.08 % (30487)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_30331 for (2995ds/62Mi)
% 5.87/2.09 % (30487)Instruction limit reached!
% 5.87/2.09 % (30487)------------------------------
% 5.87/2.09 % (30487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.09 % (30487)Termination reason: Unknown
% 5.87/2.09 % (30487)Termination phase: Property scanning
% 5.87/2.09
% 5.87/2.09 % (30487)Memory used [KB]: 2174
% 5.87/2.09 % (30487)Time elapsed: 0.019 s
% 5.87/2.09 % (30487)Instructions burned: 64 (million)
% 5.87/2.09 % (30487)------------------------------
% 5.87/2.09 % (30487)------------------------------
% 5.87/2.10 % (30488)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_30331 for (2994ds/31Mi)
% 5.87/2.11 % (30488)Instruction limit reached!
% 5.87/2.11 % (30488)------------------------------
% 5.87/2.11 % (30488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.11 % (30488)Termination reason: Unknown
% 5.87/2.11 % (30488)Termination phase: Preprocessing 2
% 5.87/2.11
% 5.87/2.11 % (30488)Memory used [KB]: 1663
% 5.87/2.11 % (30488)Time elapsed: 0.011 s
% 5.87/2.11 % (30488)Instructions burned: 32 (million)
% 5.87/2.11 % (30488)------------------------------
% 5.87/2.11 % (30488)------------------------------
% 5.87/2.12 % (30476)Instruction limit reached!
% 5.87/2.12 % (30476)------------------------------
% 5.87/2.12 % (30476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.12 % (30476)Termination reason: Unknown
% 5.87/2.12 % (30476)Termination phase: Saturation
% 5.87/2.12
% 5.87/2.12 % (30476)Memory used [KB]: 7675
% 5.87/2.12 % (30476)Time elapsed: 0.212 s
% 5.87/2.12 % (30476)Instructions burned: 449 (million)
% 5.87/2.12 % (30476)------------------------------
% 5.87/2.12 % (30476)------------------------------
% 5.87/2.12 % (30489)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_30331 for (2994ds/96Mi)
% 6.41/2.13 % (30465)Instruction limit reached!
% 6.41/2.13 % (30465)------------------------------
% 6.41/2.13 % (30465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.13 % (30465)Termination reason: Unknown
% 6.41/2.13 % (30465)Termination phase: Saturation
% 6.41/2.13
% 6.41/2.13 % (30465)Memory used [KB]: 8059
% 6.41/2.13 % (30465)Time elapsed: 0.430 s
% 6.41/2.13 % (30465)Instructions burned: 880 (million)
% 6.41/2.13 % (30465)------------------------------
% 6.41/2.13 % (30465)------------------------------
% 6.41/2.13 % (30490)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_30331 for (2994ds/453Mi)
% 6.41/2.14 % (30446)Instruction limit reached!
% 6.41/2.14 % (30446)------------------------------
% 6.41/2.14 % (30446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.14 % (30446)Termination reason: Unknown
% 6.41/2.14 % (30446)Termination phase: Saturation
% 6.41/2.14
% 6.41/2.14 % (30446)Memory used [KB]: 9722
% 6.41/2.14 % (30446)Time elapsed: 0.509 s
% 6.41/2.14 % (30446)Instructions burned: 1042 (million)
% 6.41/2.14 % (30446)------------------------------
% 6.41/2.14 % (30446)------------------------------
% 6.41/2.15 % (30491)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_30331 for (2994ds/71Mi)
% 6.41/2.15 % (30489)Instruction limit reached!
% 6.41/2.15 % (30489)------------------------------
% 6.41/2.15 % (30489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.15 % (30489)Termination reason: Unknown
% 6.41/2.15 % (30489)Termination phase: Saturation
% 6.41/2.15
% 6.41/2.15 % (30489)Memory used [KB]: 6524
% 6.41/2.15 % (30489)Time elapsed: 0.032 s
% 6.41/2.15 % (30489)Instructions burned: 98 (million)
% 6.41/2.15 % (30489)------------------------------
% 6.41/2.15 % (30489)------------------------------
% 6.41/2.15 % (30492)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_30331 for (2994ds/83Mi)
% 6.41/2.17 % (30493)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_30331 for (2994ds/11Mi)
% 6.41/2.17 % (30493)Instruction limit reached!
% 6.41/2.17 % (30493)------------------------------
% 6.41/2.17 % (30493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.17 % (30493)Termination reason: Unknown
% 6.41/2.17 % (30493)Termination phase: shuffling
% 6.41/2.17
% 6.41/2.17 % (30493)Memory used [KB]: 1535
% 6.41/2.17 % (30493)Time elapsed: 0.007 s
% 6.41/2.17 % (30493)Instructions burned: 13 (million)
% 6.41/2.17 % (30493)------------------------------
% 6.41/2.17 % (30493)------------------------------
% 6.41/2.18 % (30491)Instruction limit reached!
% 6.41/2.18 % (30491)------------------------------
% 6.41/2.18 % (30491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.18 % (30491)Termination reason: Unknown
% 6.41/2.18 % (30491)Termination phase: Saturation
% 6.41/2.18
% 6.41/2.18 % (30491)Memory used [KB]: 6396
% 6.41/2.18 % (30491)Time elapsed: 0.035 s
% 6.41/2.18 % (30491)Instructions burned: 71 (million)
% 6.41/2.18 % (30491)------------------------------
% 6.41/2.18 % (30491)------------------------------
% 6.41/2.20 % (30492)Instruction limit reached!
% 6.41/2.20 % (30492)------------------------------
% 6.41/2.20 % (30492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.20 % (30492)Termination reason: Unknown
% 6.41/2.20 % (30492)Termination phase: Saturation
% 6.41/2.20
% 6.41/2.20 % (30492)Memory used [KB]: 6524
% 6.41/2.20 % (30492)Time elapsed: 0.042 s
% 6.41/2.20 % (30492)Instructions burned: 83 (million)
% 6.41/2.20 % (30492)------------------------------
% 6.41/2.20 % (30492)------------------------------
% 6.69/2.20 % (30495)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30331 for (2993ds/6Mi)
% 6.69/2.20 % (30494)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_30331 for (2993ds/41Mi)
% 6.69/2.20 % (30495)Instruction limit reached!
% 6.69/2.20 % (30495)------------------------------
% 6.69/2.20 % (30495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.20 % (30495)Termination reason: Unknown
% 6.69/2.20 % (30495)Termination phase: shuffling
% 6.69/2.20
% 6.69/2.20 % (30495)Memory used [KB]: 1407
% 6.69/2.20 % (30495)Time elapsed: 0.005 s
% 6.69/2.20 % (30495)Instructions burned: 7 (million)
% 6.69/2.20 % (30495)------------------------------
% 6.69/2.20 % (30495)------------------------------
% 6.69/2.21 % (30479)Instruction limit reached!
% 6.69/2.21 % (30479)------------------------------
% 6.69/2.21 % (30479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.21 % (30479)Termination reason: Unknown
% 6.69/2.21 % (30479)Termination phase: Saturation
% 6.69/2.21
% 6.69/2.21 % (30479)Memory used [KB]: 7931
% 6.69/2.21 % (30479)Time elapsed: 0.269 s
% 6.69/2.21 % (30479)Instructions burned: 507 (million)
% 6.69/2.21 % (30479)------------------------------
% 6.69/2.21 % (30479)------------------------------
% 6.69/2.21 % (30497)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_30331 for (2993ds/343Mi)
% 6.69/2.21 % (30496)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_30331 for (2993ds/150Mi)
% 6.69/2.22 % (30494)Instruction limit reached!
% 6.69/2.22 % (30494)------------------------------
% 6.69/2.22 % (30494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.22 % (30494)Termination reason: Unknown
% 6.69/2.22 % (30494)Termination phase: Property scanning
% 6.69/2.22
% 6.69/2.22 % (30494)Memory used [KB]: 1918
% 6.69/2.22 % (30494)Time elapsed: 0.021 s
% 6.69/2.22 % (30494)Instructions burned: 43 (million)
% 6.69/2.22 % (30494)------------------------------
% 6.69/2.22 % (30494)------------------------------
% 6.69/2.22 % (30498)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_30331 for (2993ds/109Mi)
% 6.69/2.23 % (30499)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_30331 for (2993ds/253Mi)
% 6.69/2.25 % (30486)Instruction limit reached!
% 6.69/2.25 % (30486)------------------------------
% 6.69/2.25 % (30486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.25 % (30486)Termination reason: Unknown
% 6.69/2.25 % (30486)Termination phase: Saturation
% 6.69/2.25
% 6.69/2.25 % (30486)Memory used [KB]: 3326
% 6.69/2.25 % (30486)Time elapsed: 0.203 s
% 6.69/2.25 % (30486)Instructions burned: 432 (million)
% 6.69/2.25 % (30486)------------------------------
% 6.69/2.25 % (30486)------------------------------
% 6.69/2.27 % (30501)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_30331 for (2993ds/140Mi)
% 6.69/2.27 % (30498)Instruction limit reached!
% 6.69/2.27 % (30498)------------------------------
% 6.69/2.27 % (30498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.27 % (30498)Termination reason: Unknown
% 6.69/2.27 % (30498)Termination phase: Saturation
% 6.69/2.27
% 6.69/2.27 % (30498)Memory used [KB]: 6652
% 6.69/2.27 % (30498)Time elapsed: 0.053 s
% 6.69/2.27 % (30498)Instructions burned: 110 (million)
% 6.69/2.27 % (30498)------------------------------
% 6.69/2.27 % (30498)------------------------------
% 6.69/2.29 % (30496)Instruction limit reached!
% 6.69/2.29 % (30496)------------------------------
% 6.69/2.29 % (30496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.29 % (30496)Termination reason: Unknown
% 6.69/2.29 % (30496)Termination phase: Saturation
% 6.69/2.29
% 6.69/2.29 % (30496)Memory used [KB]: 6908
% 6.69/2.29 % (30496)Time elapsed: 0.077 s
% 6.69/2.29 % (30496)Instructions burned: 150 (million)
% 6.69/2.29 % (30496)------------------------------
% 6.69/2.29 % (30496)------------------------------
% 6.69/2.29 % (30502)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_30331 for (2993ds/614Mi)
% 7.13/2.30 % (30503)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_30331 for (2992ds/202Mi)
% 7.13/2.32 % (30503)Refutation not found, incomplete strategy
% 7.13/2.32 % (30503)------------------------------
% 7.13/2.32 % (30503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.32 % (30503)Termination reason: Refutation not found, incomplete strategy
% 7.13/2.32
% 7.13/2.32
% 7.13/2.32 % (30503)Memory used [KB]: 6268
% 7.13/2.32 % (30503)Time elapsed: 0.020 s
% 7.13/2.32 % (30503)Instructions burned: 45 (million)
% 7.13/2.32 % (30503)------------------------------
% 7.13/2.32 % (30503)------------------------------
% 7.13/2.32 % (30490)Instruction limit reached!
% 7.13/2.32 % (30490)------------------------------
% 7.13/2.32 % (30490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.32 % (30490)Termination reason: Unknown
% 7.13/2.32 % (30490)Termination phase: Saturation
% 7.13/2.32
% 7.13/2.32 % (30490)Memory used [KB]: 7675
% 7.13/2.32 % (30490)Time elapsed: 0.189 s
% 7.13/2.32 % (30490)Instructions burned: 454 (million)
% 7.13/2.32 % (30490)------------------------------
% 7.13/2.32 % (30490)------------------------------
% 7.13/2.33 % (30504)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_30331 for (2992ds/339Mi)
% 7.13/2.34 % (30505)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_30331 for (2992ds/283Mi)
% 7.13/2.34 % (30501)Instruction limit reached!
% 7.13/2.34 % (30501)------------------------------
% 7.13/2.34 % (30501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.34 % (30501)Termination reason: Unknown
% 7.13/2.34 % (30501)Termination phase: Saturation
% 7.13/2.34
% 7.13/2.34 % (30501)Memory used [KB]: 6780
% 7.13/2.34 % (30501)Time elapsed: 0.071 s
% 7.13/2.34 % (30501)Instructions burned: 141 (million)
% 7.13/2.34 % (30501)------------------------------
% 7.13/2.34 % (30501)------------------------------
% 7.13/2.35 % (30497)Instruction limit reached!
% 7.13/2.35 % (30497)------------------------------
% 7.13/2.35 % (30497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.35 % (30497)Termination reason: Unknown
% 7.13/2.35 % (30497)Termination phase: Saturation
% 7.13/2.35
% 7.13/2.35 % (30497)Memory used [KB]: 7291
% 7.13/2.35 % (30497)Time elapsed: 0.141 s
% 7.13/2.35 % (30497)Instructions burned: 344 (million)
% 7.13/2.35 % (30497)------------------------------
% 7.13/2.35 % (30497)------------------------------
% 7.13/2.35 % (30506)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_30331 for (2992ds/134Mi)
% 7.13/2.36 % (30499)Instruction limit reached!
% 7.13/2.36 % (30499)------------------------------
% 7.13/2.36 % (30499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.36 % (30499)Termination reason: Unknown
% 7.13/2.36 % (30499)Termination phase: Saturation
% 7.13/2.36
% 7.13/2.36 % (30499)Memory used [KB]: 6908
% 7.13/2.36 % (30499)Time elapsed: 0.127 s
% 7.13/2.36 % (30499)Instructions burned: 253 (million)
% 7.13/2.36 % (30499)------------------------------
% 7.13/2.36 % (30499)------------------------------
% 7.13/2.36 % (30507)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_30331 for (2992ds/298Mi)
% 7.13/2.39 % (30509)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_30331 for (2992ds/192Mi)
% 7.74/2.42 % (30506)Instruction limit reached!
% 7.74/2.42 % (30506)------------------------------
% 7.74/2.42 % (30506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.42 % (30506)Termination reason: Unknown
% 7.74/2.42 % (30506)Termination phase: Saturation
% 7.74/2.42
% 7.74/2.42 % (30506)Memory used [KB]: 6780
% 7.74/2.42 % (30506)Time elapsed: 0.066 s
% 7.74/2.42 % (30506)Instructions burned: 134 (million)
% 7.74/2.42 % (30506)------------------------------
% 7.74/2.42 % (30506)------------------------------
% 7.74/2.44 % (30510)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_30331 for (2991ds/258Mi)
% 7.74/2.45 % (30507)Instruction limit reached!
% 7.74/2.45 % (30507)------------------------------
% 7.74/2.45 % (30507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.45 % (30507)Termination reason: Unknown
% 7.74/2.45 % (30507)Termination phase: Saturation
% 7.74/2.45
% 7.74/2.45 % (30507)Memory used [KB]: 7803
% 7.74/2.45 % (30507)Time elapsed: 0.089 s
% 7.74/2.45 % (30507)Instructions burned: 299 (million)
% 7.74/2.45 % (30507)------------------------------
% 7.74/2.45 % (30507)------------------------------
% 7.74/2.46 % (30511)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_30331 for (2991ds/90Mi)
% 7.74/2.47 % (30504)Instruction limit reached!
% 7.74/2.47 % (30504)------------------------------
% 7.74/2.47 % (30504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.47 % (30504)Termination reason: Unknown
% 7.74/2.47 % (30504)Termination phase: Saturation
% 7.74/2.47
% 7.74/2.47 % (30504)Memory used [KB]: 7419
% 7.74/2.47 % (30504)Time elapsed: 0.146 s
% 7.74/2.47 % (30504)Instructions burned: 340 (million)
% 7.74/2.47 % (30504)------------------------------
% 7.74/2.47 % (30504)------------------------------
% 7.74/2.48 % (30505)Instruction limit reached!
% 7.74/2.48 % (30505)------------------------------
% 7.74/2.48 % (30505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.48 % (30505)Termination reason: Unknown
% 7.74/2.48 % (30505)Termination phase: Saturation
% 7.74/2.48
% 7.74/2.48 % (30505)Memory used [KB]: 7419
% 7.74/2.48 % (30505)Time elapsed: 0.142 s
% 7.74/2.48 % (30505)Instructions burned: 284 (million)
% 7.74/2.48 % (30505)------------------------------
% 7.74/2.48 % (30505)------------------------------
% 7.74/2.48 % (30509)Instruction limit reached!
% 7.74/2.48 % (30509)------------------------------
% 7.74/2.48 % (30509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.48 % (30509)Termination reason: Unknown
% 7.74/2.48 % (30509)Termination phase: Saturation
% 7.74/2.48
% 7.74/2.48 % (30509)Memory used [KB]: 7547
% 7.74/2.48 % (30509)Time elapsed: 0.126 s
% 7.74/2.48 % (30509)Instructions burned: 193 (million)
% 7.74/2.48 % (30509)------------------------------
% 7.74/2.48 % (30509)------------------------------
% 7.74/2.49 % (30512)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_30331 for (2991ds/231Mi)
% 7.74/2.49 % (30511)Instruction limit reached!
% 7.74/2.49 % (30511)------------------------------
% 7.74/2.49 % (30511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.49 % (30511)Termination reason: Unknown
% 7.74/2.49 % (30511)Termination phase: Saturation
% 7.74/2.49
% 7.74/2.49 % (30511)Memory used [KB]: 6524
% 7.74/2.49 % (30511)Time elapsed: 0.037 s
% 7.74/2.49 % (30511)Instructions burned: 91 (million)
% 7.74/2.49 % (30511)------------------------------
% 7.74/2.49 % (30511)------------------------------
% 7.74/2.49 % (30513)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_30331 for (2991ds/458Mi)
% 8.38/2.50 % (30514)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_30331 for (2990ds/31Mi)
% 8.38/2.51 % (30515)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_30331 for (2990ds/297Mi)
% 8.38/2.52 % (30514)Instruction limit reached!
% 8.38/2.52 % (30514)------------------------------
% 8.38/2.52 % (30514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.38/2.52 % (30514)Termination reason: Unknown
% 8.38/2.52 % (30514)Termination phase: Preprocessing 2
% 8.38/2.52
% 8.38/2.52 % (30514)Memory used [KB]: 1663
% 8.38/2.52 % (30514)Time elapsed: 0.017 s
% 8.38/2.52 % (30514)Instructions burned: 32 (million)
% 8.38/2.52 % (30514)------------------------------
% 8.38/2.52 % (30514)------------------------------
% 8.38/2.53 % (30510)Instruction limit reached!
% 8.38/2.53 % (30510)------------------------------
% 8.38/2.53 % (30510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.38/2.53 % (30510)Termination reason: Unknown
% 8.38/2.53 % (30510)Termination phase: Saturation
% 8.38/2.53
% 8.38/2.53 % (30510)Memory used [KB]: 7291
% 8.38/2.53 % (30510)Time elapsed: 0.095 s
% 8.38/2.53 % (30510)Instructions burned: 260 (million)
% 8.38/2.53 % (30510)------------------------------
% 8.38/2.53 % (30510)------------------------------
% 8.38/2.54 % (30516)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_30331 for (2990ds/987Mi)
% 8.38/2.55 % (30517)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_30331 for (2990ds/182Mi)
% 8.38/2.56 % (30483)Instruction limit reached!
% 8.38/2.56 % (30483)------------------------------
% 8.38/2.56 % (30483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.38/2.56 % (30483)Termination reason: Unknown
% 8.38/2.56 % (30483)Termination phase: Saturation
% 8.38/2.56
% 8.38/2.56 % (30483)Memory used [KB]: 7675
% 8.38/2.56 % (30483)Time elapsed: 0.537 s
% 8.38/2.56 % (30483)Instructions burned: 1088 (million)
% 8.38/2.56 % (30483)------------------------------
% 8.38/2.56 % (30483)------------------------------
% 8.38/2.58 % (30518)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_30331 for (2990ds/182Mi)
% 8.38/2.59 % (30502)Instruction limit reached!
% 8.38/2.59 % (30502)------------------------------
% 8.38/2.59 % (30502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.38/2.59 % (30502)Termination reason: Unknown
% 8.38/2.59 % (30502)Termination phase: Saturation
% 8.38/2.59
% 8.38/2.59 % (30502)Memory used [KB]: 8187
% 8.38/2.59 % (30502)Time elapsed: 0.301 s
% 8.38/2.59 % (30502)Instructions burned: 615 (million)
% 8.38/2.59 % (30502)------------------------------
% 8.38/2.59 % (30502)------------------------------
% 8.38/2.59 % (30512)Instruction limit reached!
% 8.38/2.59 % (30512)------------------------------
% 8.38/2.59 % (30512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.38/2.59 % (30512)Termination reason: Unknown
% 8.38/2.59 % (30512)Termination phase: Saturation
% 8.38/2.59
% 8.38/2.59 % (30512)Memory used [KB]: 7036
% 8.38/2.59 % (30512)Time elapsed: 0.108 s
% 8.38/2.59 % (30512)Instructions burned: 231 (million)
% 8.38/2.59 % (30512)------------------------------
% 8.38/2.59 % (30512)------------------------------
% 9.52/2.61 % (30519)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_30331 for (2989ds/154Mi)
% 9.52/2.61 % (30520)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_30331 for (2989ds/79Mi)
% 9.52/2.63 % (30517)Instruction limit reached!
% 9.52/2.63 % (30517)------------------------------
% 9.52/2.63 % (30517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.63 % (30517)Termination reason: Unknown
% 9.52/2.63 % (30517)Termination phase: Saturation
% 9.52/2.63
% 9.52/2.63 % (30517)Memory used [KB]: 7036
% 9.52/2.63 % (30517)Time elapsed: 0.090 s
% 9.52/2.63 % (30517)Instructions burned: 182 (million)
% 9.52/2.63 % (30517)------------------------------
% 9.52/2.63 % (30517)------------------------------
% 9.52/2.64 % (30520)Instruction limit reached!
% 9.52/2.64 % (30520)------------------------------
% 9.52/2.64 % (30520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.64 % (30520)Termination reason: Unknown
% 9.52/2.64 % (30520)Termination phase: Saturation
% 9.52/2.64
% 9.52/2.64 % (30520)Memory used [KB]: 6524
% 9.52/2.64 % (30520)Time elapsed: 0.025 s
% 9.52/2.64 % (30520)Instructions burned: 80 (million)
% 9.52/2.64 % (30520)------------------------------
% 9.52/2.64 % (30520)------------------------------
% 9.52/2.64 % (30522)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_30331 for (2989ds/114Mi)
% 9.52/2.65 % (30521)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_30331 for (2989ds/216Mi)
% 9.52/2.66 % (30515)Instruction limit reached!
% 9.52/2.66 % (30515)------------------------------
% 9.52/2.66 % (30515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.66 % (30515)Termination reason: Unknown
% 9.52/2.66 % (30515)Termination phase: Saturation
% 9.52/2.66
% 9.52/2.66 % (30515)Memory used [KB]: 7419
% 9.52/2.66 % (30515)Time elapsed: 0.164 s
% 9.52/2.66 % (30515)Instructions burned: 297 (million)
% 9.52/2.66 % (30515)------------------------------
% 9.52/2.66 % (30515)------------------------------
% 9.52/2.67 % (30523)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_30331 for (2989ds/922Mi)
% 9.52/2.68 % (30519)Instruction limit reached!
% 9.52/2.68 % (30519)------------------------------
% 9.52/2.68 % (30519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.68 % (30519)Termination reason: Unknown
% 9.52/2.68 % (30519)Termination phase: Saturation
% 9.52/2.68
% 9.52/2.68 % (30519)Memory used [KB]: 2558
% 9.52/2.68 % (30519)Time elapsed: 0.071 s
% 9.52/2.68 % (30519)Instructions burned: 154 (million)
% 9.52/2.68 % (30519)------------------------------
% 9.52/2.68 % (30519)------------------------------
% 9.52/2.68 % (30518)Instruction limit reached!
% 9.52/2.68 % (30518)------------------------------
% 9.52/2.68 % (30518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.68 % (30518)Termination reason: Unknown
% 9.52/2.68 % (30518)Termination phase: Saturation
% 9.52/2.68
% 9.52/2.68 % (30518)Memory used [KB]: 6908
% 9.52/2.68 % (30518)Time elapsed: 0.123 s
% 9.52/2.68 % (30518)Instructions burned: 182 (million)
% 9.52/2.68 % (30518)------------------------------
% 9.52/2.68 % (30518)------------------------------
% 9.52/2.68 % (30522)Instruction limit reached!
% 9.52/2.68 % (30522)------------------------------
% 9.52/2.68 % (30522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.68 % (30522)Termination reason: Unknown
% 9.52/2.68 % (30522)Termination phase: Saturation
% 9.52/2.68
% 9.52/2.68 % (30522)Memory used [KB]: 6652
% 9.52/2.68 % (30522)Time elapsed: 0.035 s
% 9.52/2.68 % (30522)Instructions burned: 116 (million)
% 9.52/2.68 % (30522)------------------------------
% 9.52/2.68 % (30522)------------------------------
% 9.52/2.69 % (30526)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_30331 for (2988ds/50Mi)
% 9.52/2.69 % (30524)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_30331 for (2988ds/182Mi)
% 9.52/2.69 % (30525)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_30331 for (2988ds/164Mi)
% 10.06/2.70 % (30526)Instruction limit reached!
% 10.06/2.70 % (30526)------------------------------
% 10.06/2.70 % (30526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.06/2.70 % (30526)Termination reason: Unknown
% 10.06/2.70 % (30526)Termination phase: Preprocessing 1
% 10.06/2.70
% 10.06/2.70 % (30526)Memory used [KB]: 1918
% 10.06/2.70 % (30526)Time elapsed: 0.015 s
% 10.06/2.70 % (30526)Instructions burned: 53 (million)
% 10.06/2.70 % (30526)------------------------------
% 10.06/2.70 % (30526)------------------------------
% 10.06/2.71 % (30527)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_30331 for (2988ds/368Mi)
% 10.06/2.72 % (30513)Instruction limit reached!
% 10.06/2.72 % (30513)------------------------------
% 10.06/2.72 % (30513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.06/2.72 % (30513)Termination reason: Unknown
% 10.06/2.72 % (30513)Termination phase: Saturation
% 10.06/2.72
% 10.06/2.72 % (30513)Memory used [KB]: 7803
% 10.06/2.72 % (30513)Time elapsed: 0.251 s
% 10.06/2.72 % (30513)Instructions burned: 459 (million)
% 10.06/2.72 % (30513)------------------------------
% 10.06/2.72 % (30513)------------------------------
% 10.06/2.74 % (30528)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_30331 for (2988ds/1021Mi)
% 10.06/2.75 % (30521)Instruction limit reached!
% 10.06/2.75 % (30521)------------------------------
% 10.06/2.75 % (30521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.06/2.75 % (30521)Termination reason: Unknown
% 10.06/2.75 % (30521)Termination phase: Saturation
% 10.06/2.75
% 10.06/2.75 % (30521)Memory used [KB]: 7291
% 10.06/2.75 % (30521)Time elapsed: 0.103 s
% 10.06/2.75 % (30521)Instructions burned: 217 (million)
% 10.06/2.75 % (30521)------------------------------
% 10.06/2.75 % (30521)------------------------------
% 10.06/2.77 % (30525)Instruction limit reached!
% 10.06/2.77 % (30525)------------------------------
% 10.06/2.77 % (30525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.06/2.77 % (30525)Termination reason: Unknown
% 10.06/2.77 % (30525)Termination phase: Saturation
% 10.06/2.77
% 10.06/2.77 % (30525)Memory used [KB]: 2302
% 10.06/2.77 % (30525)Time elapsed: 0.077 s
% 10.06/2.77 % (30525)Instructions burned: 165 (million)
% 10.06/2.77 % (30525)------------------------------
% 10.06/2.77 % (30525)------------------------------
% 10.06/2.77 % (30529)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_30331 for (2988ds/267Mi)
% 10.06/2.77 % (30524)Instruction limit reached!
% 10.06/2.77 % (30524)------------------------------
% 10.06/2.77 % (30524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.06/2.77 % (30524)Termination reason: Unknown
% 10.06/2.77 % (30524)Termination phase: Saturation
% 10.06/2.77
% 10.06/2.77 % (30524)Memory used [KB]: 6908
% 10.06/2.77 % (30524)Time elapsed: 0.084 s
% 10.06/2.77 % (30524)Instructions burned: 183 (million)
% 10.06/2.77 % (30524)------------------------------
% 10.06/2.77 % (30524)------------------------------
% 10.06/2.78 % (30530)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_30331 for (2988ds/204Mi)
% 10.06/2.79 % (30531)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_30331 for (2987ds/26Mi)
% 10.64/2.80 % (30531)Instruction limit reached!
% 10.64/2.80 % (30531)------------------------------
% 10.64/2.80 % (30531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/2.80 % (30531)Termination reason: Unknown
% 10.64/2.80 % (30531)Termination phase: shuffling
% 10.64/2.80
% 10.64/2.80 % (30531)Memory used [KB]: 1791
% 10.64/2.80 % (30531)Time elapsed: 0.013 s
% 10.64/2.80 % (30531)Instructions burned: 26 (million)
% 10.64/2.80 % (30531)------------------------------
% 10.64/2.80 % (30531)------------------------------
% 10.64/2.81 % (30527)Instruction limit reached!
% 10.64/2.81 % (30527)------------------------------
% 10.64/2.81 % (30527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/2.81 % (30527)Termination reason: Unknown
% 10.64/2.81 % (30527)Termination phase: Saturation
% 10.64/2.81
% 10.64/2.81 % (30527)Memory used [KB]: 7803
% 10.64/2.81 % (30527)Time elapsed: 0.100 s
% 10.64/2.81 % (30527)Instructions burned: 370 (million)
% 10.64/2.81 % (30527)------------------------------
% 10.64/2.81 % (30527)------------------------------
% 10.64/2.82 % (30532)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_30331 for (2987ds/53Mi)
% 10.64/2.83 % (30533)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_30331 for (2987ds/4436Mi)
% 10.64/2.84 % (30532)Instruction limit reached!
% 10.64/2.84 % (30532)------------------------------
% 10.64/2.84 % (30532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/2.84 % (30532)Termination reason: Unknown
% 10.64/2.84 % (30532)Termination phase: Property scanning
% 10.64/2.84
% 10.64/2.84 % (30532)Memory used [KB]: 2046
% 10.64/2.84 % (30532)Time elapsed: 0.026 s
% 10.64/2.84 % (30532)Instructions burned: 53 (million)
% 10.64/2.84 % (30532)------------------------------
% 10.64/2.84 % (30532)------------------------------
% 10.64/2.86 % (30534)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_30331 for (2987ds/1539Mi)
% 10.64/2.89 % (30530)Instruction limit reached!
% 10.64/2.89 % (30530)------------------------------
% 10.64/2.89 % (30530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/2.89 % (30530)Termination reason: Unknown
% 10.64/2.89 % (30530)Termination phase: Saturation
% 10.64/2.89
% 10.64/2.89 % (30530)Memory used [KB]: 7164
% 10.64/2.89 % (30530)Time elapsed: 0.104 s
% 10.64/2.89 % (30530)Instructions burned: 204 (million)
% 10.64/2.89 % (30530)------------------------------
% 10.64/2.89 % (30530)------------------------------
% 10.94/2.90 % (30529)Instruction limit reached!
% 10.94/2.90 % (30529)------------------------------
% 10.94/2.90 % (30529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.94/2.90 % (30529)Termination reason: Unknown
% 10.94/2.90 % (30529)Termination phase: Saturation
% 10.94/2.90
% 10.94/2.90 % (30529)Memory used [KB]: 7419
% 10.94/2.90 % (30529)Time elapsed: 0.133 s
% 10.94/2.90 % (30529)Instructions burned: 268 (million)
% 10.94/2.90 % (30529)------------------------------
% 10.94/2.90 % (30529)------------------------------
% 10.94/2.91 % (30535)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_30331 for (2986ds/408Mi)
% 10.94/2.92 % (30536)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_30331 for (2986ds/5205Mi)
% 10.94/2.97 % (30535)Refutation not found, incomplete strategy
% 10.94/2.97 % (30535)------------------------------
% 10.94/2.97 % (30535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.94/2.97 % (30535)Termination reason: Refutation not found, incomplete strategy
% 10.94/2.97
% 10.94/2.97
% 10.94/2.97 % (30535)Memory used [KB]: 7036
% 10.94/2.97 % (30535)Time elapsed: 0.088 s
% 10.94/2.97 % (30535)Instructions burned: 105 (million)
% 10.94/2.97 % (30535)------------------------------
% 10.94/2.97 % (30535)------------------------------
% 10.94/2.98 % (30516)Instruction limit reached!
% 10.94/2.98 % (30516)------------------------------
% 10.94/2.98 % (30516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.94/2.98 % (30516)Termination reason: Unknown
% 10.94/2.98 % (30516)Termination phase: Saturation
% 10.94/2.98
% 10.94/2.98 % (30516)Memory used [KB]: 8571
% 10.94/2.98 % (30516)Time elapsed: 0.476 s
% 10.94/2.98 % (30516)Instructions burned: 987 (million)
% 10.94/2.98 % (30516)------------------------------
% 10.94/2.98 % (30516)------------------------------
% 10.94/3.00 % (30539)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_30331 for (2985ds/4350Mi)
% 10.94/3.00 % (30538)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_30331 for (2985ds/1913Mi)
% 10.94/3.02 % (30539)Refutation not found, incomplete strategy
% 10.94/3.02 % (30539)------------------------------
% 10.94/3.02 % (30539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.94/3.02 % (30539)Termination reason: Refutation not found, incomplete strategy
% 10.94/3.02
% 10.94/3.02
% 10.94/3.02 % (30539)Memory used [KB]: 6396
% 10.94/3.02 % (30539)Time elapsed: 0.025 s
% 10.94/3.02 % (30539)Instructions burned: 47 (million)
% 10.94/3.02 % (30539)------------------------------
% 10.94/3.02 % (30539)------------------------------
% 12.75/3.04 % (30541)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_30331 for (2985ds/68Mi)
% 12.75/3.07 % (30541)Instruction limit reached!
% 12.75/3.07 % (30541)------------------------------
% 12.75/3.07 % (30541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.75/3.07 % (30541)Termination reason: Unknown
% 12.75/3.07 % (30541)Termination phase: Property scanning
% 12.75/3.07
% 12.75/3.07 % (30541)Memory used [KB]: 1918
% 12.75/3.07 % (30541)Time elapsed: 0.035 s
% 12.75/3.07 % (30541)Instructions burned: 70 (million)
% 12.75/3.07 % (30541)------------------------------
% 12.75/3.07 % (30541)------------------------------
% 12.75/3.09 % (30542)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_30331 for (2985ds/358Mi)
% 13.39/3.13 % (30528)Instruction limit reached!
% 13.39/3.13 % (30528)------------------------------
% 13.39/3.13 % (30528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.13 % (30528)Termination reason: Unknown
% 13.39/3.13 % (30528)Termination phase: Saturation
% 13.39/3.13
% 13.39/3.13 % (30528)Memory used [KB]: 8187
% 13.39/3.13 % (30528)Time elapsed: 0.398 s
% 13.39/3.13 % (30528)Instructions burned: 1021 (million)
% 13.39/3.13 % (30528)------------------------------
% 13.39/3.13 % (30528)------------------------------
% 13.39/3.13 % (30523)Instruction limit reached!
% 13.39/3.13 % (30523)------------------------------
% 13.39/3.13 % (30523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.13 % (30523)Termination reason: Unknown
% 13.39/3.13 % (30523)Termination phase: Saturation
% 13.39/3.13
% 13.39/3.13 % (30523)Memory used [KB]: 7803
% 13.39/3.13 % (30523)Time elapsed: 0.463 s
% 13.39/3.13 % (30523)Instructions burned: 922 (million)
% 13.39/3.13 % (30523)------------------------------
% 13.39/3.13 % (30523)------------------------------
% 13.39/3.14 % (30543)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_30331 for (2984ds/31Mi)
% 13.39/3.15 % (30544)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_30331 for (2984ds/279Mi)
% 13.39/3.16 % (30543)Instruction limit reached!
% 13.39/3.16 % (30543)------------------------------
% 13.39/3.16 % (30543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.16 % (30543)Termination reason: Unknown
% 13.39/3.16 % (30543)Termination phase: Preprocessing 1
% 13.39/3.16
% 13.39/3.16 % (30543)Memory used [KB]: 1663
% 13.39/3.16 % (30543)Time elapsed: 0.017 s
% 13.39/3.16 % (30543)Instructions burned: 31 (million)
% 13.39/3.16 % (30543)------------------------------
% 13.39/3.16 % (30543)------------------------------
% 13.39/3.18 % (30545)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_30331 for (2984ds/258Mi)
% 13.76/3.21 % (30544)Refutation not found, incomplete strategy
% 13.76/3.21 % (30544)------------------------------
% 13.76/3.21 % (30544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/3.21 % (30544)Termination reason: Refutation not found, incomplete strategy
% 13.76/3.21
% 13.76/3.21
% 13.76/3.21 % (30544)Memory used [KB]: 6908
% 13.76/3.21 % (30544)Time elapsed: 0.064 s
% 13.76/3.21 % (30544)Instructions burned: 136 (million)
% 13.76/3.21 % (30544)------------------------------
% 13.76/3.21 % (30544)------------------------------
% 13.76/3.23 % (30546)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_30331 for (2983ds/26Mi)
% 13.76/3.24 % (30546)Instruction limit reached!
% 13.76/3.24 % (30546)------------------------------
% 13.76/3.24 % (30546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/3.24 % (30546)Termination reason: Unknown
% 13.76/3.24 % (30546)Termination phase: shuffling
% 13.76/3.24
% 13.76/3.24 % (30546)Memory used [KB]: 1791
% 13.76/3.24 % (30546)Time elapsed: 0.014 s
% 13.76/3.24 % (30546)Instructions burned: 27 (million)
% 13.76/3.24 % (30546)------------------------------
% 13.76/3.24 % (30546)------------------------------
% 13.76/3.26 % (30547)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_30331 for (2983ds/995Mi)
% 13.76/3.27 % (30542)Instruction limit reached!
% 13.76/3.27 % (30542)------------------------------
% 13.76/3.27 % (30542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/3.27 % (30542)Termination reason: Unknown
% 13.76/3.27 % (30542)Termination phase: Saturation
% 13.76/3.27
% 13.76/3.27 % (30542)Memory used [KB]: 7291
% 13.76/3.27 % (30542)Time elapsed: 0.181 s
% 13.76/3.27 % (30542)Instructions burned: 358 (million)
% 13.76/3.27 % (30542)------------------------------
% 13.76/3.27 % (30542)------------------------------
% 13.76/3.29 % (30548)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_30331 for (2983ds/373Mi)
% 14.46/3.31 % (30545)Instruction limit reached!
% 14.46/3.31 % (30545)------------------------------
% 14.46/3.31 % (30545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.31 % (30545)Termination reason: Unknown
% 14.46/3.31 % (30545)Termination phase: Saturation
% 14.46/3.31
% 14.46/3.31 % (30545)Memory used [KB]: 7036
% 14.46/3.31 % (30545)Time elapsed: 0.129 s
% 14.46/3.31 % (30545)Instructions burned: 258 (million)
% 14.46/3.31 % (30545)------------------------------
% 14.46/3.31 % (30545)------------------------------
% 14.46/3.33 % (30549)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_30331 for (2982ds/253Mi)
% 15.00/3.45 % (30549)Instruction limit reached!
% 15.00/3.45 % (30549)------------------------------
% 15.00/3.45 % (30549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.00/3.45 % (30549)Termination reason: Unknown
% 15.00/3.45 % (30549)Termination phase: Saturation
% 15.00/3.45
% 15.00/3.45 % (30549)Memory used [KB]: 7547
% 15.00/3.45 % (30549)Time elapsed: 0.121 s
% 15.00/3.45 % (30549)Instructions burned: 254 (million)
% 15.00/3.45 % (30549)------------------------------
% 15.00/3.45 % (30549)------------------------------
% 15.00/3.46 % (30548)Instruction limit reached!
% 15.00/3.46 % (30548)------------------------------
% 15.00/3.46 % (30548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.00/3.46 % (30548)Termination reason: Unknown
% 15.00/3.46 % (30548)Termination phase: Saturation
% 15.00/3.46
% 15.00/3.46 % (30548)Memory used [KB]: 7419
% 15.00/3.46 % (30548)Time elapsed: 0.178 s
% 15.00/3.46 % (30548)Instructions burned: 374 (million)
% 15.00/3.46 % (30548)------------------------------
% 15.00/3.46 % (30548)------------------------------
% 15.00/3.46 % (30550)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_30331 for (2981ds/832Mi)
% 15.00/3.48 % (30551)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_30331 for (2981ds/668Mi)
% 15.73/3.52 % (30550)Refutation not found, incomplete strategy
% 15.73/3.52 % (30550)------------------------------
% 15.73/3.52 % (30550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.73/3.52 % (30550)Termination reason: Refutation not found, incomplete strategy
% 15.73/3.52
% 15.73/3.52
% 15.73/3.52 % (30550)Memory used [KB]: 7036
% 15.73/3.52 % (30550)Time elapsed: 0.053 s
% 15.73/3.52 % (30550)Instructions burned: 105 (million)
% 15.73/3.52 % (30550)------------------------------
% 15.73/3.52 % (30550)------------------------------
% 15.73/3.53 % (30552)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_30331 for (2980ds/40Mi)
% 15.73/3.55 % (30552)Instruction limit reached!
% 15.73/3.55 % (30552)------------------------------
% 15.73/3.55 % (30552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.73/3.55 % (30552)Termination reason: Unknown
% 15.73/3.55 % (30552)Termination phase: Property scanning
% 15.73/3.55
% 15.73/3.55 % (30552)Memory used [KB]: 1918
% 15.73/3.55 % (30552)Time elapsed: 0.021 s
% 15.73/3.55 % (30552)Instructions burned: 42 (million)
% 15.73/3.55 % (30552)------------------------------
% 15.73/3.55 % (30552)------------------------------
% 15.73/3.57 % (30553)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_30331 for (2980ds/294Mi)
% 15.73/3.59 % (30534)Instruction limit reached!
% 15.73/3.59 % (30534)------------------------------
% 15.73/3.59 % (30534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.73/3.59 % (30534)Termination reason: Unknown
% 15.73/3.59 % (30534)Termination phase: Saturation
% 15.73/3.59
% 15.73/3.59 % (30534)Memory used [KB]: 9850
% 15.73/3.59 % (30534)Time elapsed: 0.731 s
% 15.73/3.59 % (30534)Instructions burned: 1539 (million)
% 15.73/3.59 % (30534)------------------------------
% 15.73/3.59 % (30534)------------------------------
% 16.23/3.61 % (30554)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_30331 for (2979ds/187Mi)
% 16.23/3.68 % (30554)Instruction limit reached!
% 16.23/3.68 % (30554)------------------------------
% 16.23/3.68 % (30554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.23/3.68 % (30554)Termination reason: Unknown
% 16.23/3.68 % (30554)Termination phase: Saturation
% 16.23/3.68
% 16.23/3.68 % (30554)Memory used [KB]: 7291
% 16.23/3.68 % (30554)Time elapsed: 0.094 s
% 16.23/3.68 % (30554)Instructions burned: 188 (million)
% 16.23/3.68 % (30554)------------------------------
% 16.23/3.68 % (30554)------------------------------
% 16.23/3.69 % (30555)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_30331 for (2979ds/371Mi)
% 16.62/3.71 % (30553)Instruction limit reached!
% 16.62/3.71 % (30553)------------------------------
% 16.62/3.71 % (30553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.62/3.71 % (30553)Termination reason: Unknown
% 16.62/3.71 % (30553)Termination phase: Saturation
% 16.62/3.71
% 16.62/3.71 % (30553)Memory used [KB]: 7291
% 16.62/3.71 % (30553)Time elapsed: 0.161 s
% 16.62/3.71 % (30553)Instructions burned: 295 (million)
% 16.62/3.71 % (30553)------------------------------
% 16.62/3.71 % (30553)------------------------------
% 16.62/3.72 % (30547)Instruction limit reached!
% 16.62/3.72 % (30547)------------------------------
% 16.62/3.72 % (30547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.62/3.72 % (30547)Termination reason: Unknown
% 16.62/3.72 % (30547)Termination phase: Saturation
% 16.62/3.72
% 16.62/3.72 % (30547)Memory used [KB]: 9210
% 16.62/3.72 % (30547)Time elapsed: 0.460 s
% 16.62/3.72 % (30547)Instructions burned: 997 (million)
% 16.62/3.72 % (30547)------------------------------
% 16.62/3.72 % (30547)------------------------------
% 16.62/3.72 % (30556)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_30331 for (2978ds/1827Mi)
% 16.62/3.73 % (30557)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_30331 for (2978ds/70Mi)
% 16.62/3.77 % (30557)Instruction limit reached!
% 16.62/3.77 % (30557)------------------------------
% 16.62/3.77 % (30557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.62/3.77 % (30557)Termination reason: Unknown
% 16.62/3.77 % (30557)Termination phase: Property scanning
% 16.62/3.77
% 16.62/3.77 % (30557)Memory used [KB]: 2174
% 16.62/3.77 % (30557)Time elapsed: 0.033 s
% 16.62/3.77 % (30557)Instructions burned: 70 (million)
% 16.62/3.77 % (30557)------------------------------
% 16.62/3.77 % (30557)------------------------------
% 16.62/3.79 % (30558)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_30331 for (2978ds/316Mi)
% 17.58/3.80 % (30551)Instruction limit reached!
% 17.58/3.80 % (30551)------------------------------
% 17.58/3.80 % (30551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.58/3.80 % (30551)Termination reason: Unknown
% 17.58/3.80 % (30551)Termination phase: Saturation
% 17.58/3.80
% 17.58/3.80 % (30551)Memory used [KB]: 13688
% 17.58/3.80 % (30551)Time elapsed: 0.324 s
% 17.58/3.80 % (30551)Instructions burned: 669 (million)
% 17.58/3.80 % (30551)------------------------------
% 17.58/3.80 % (30551)------------------------------
% 17.58/3.82 % (30559)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_30331 for (2977ds/932Mi)
% 17.58/3.85 % (30538)Instruction limit reached!
% 17.58/3.85 % (30538)------------------------------
% 17.58/3.85 % (30538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.58/3.85 % (30538)Termination reason: Unknown
% 17.58/3.85 % (30538)Termination phase: Saturation
% 17.58/3.85
% 17.58/3.85 % (30538)Memory used [KB]: 2942
% 17.58/3.85 % (30538)Time elapsed: 0.872 s
% 17.58/3.85 % (30538)Instructions burned: 1913 (million)
% 17.58/3.85 % (30538)------------------------------
% 17.58/3.85 % (30538)------------------------------
% 17.58/3.86 % (30555)Instruction limit reached!
% 17.58/3.86 % (30555)------------------------------
% 17.58/3.86 % (30555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.58/3.86 % (30555)Termination reason: Unknown
% 17.58/3.86 % (30555)Termination phase: Saturation
% 17.58/3.86
% 17.58/3.86 % (30555)Memory used [KB]: 7419
% 17.58/3.86 % (30555)Time elapsed: 0.194 s
% 17.58/3.86 % (30555)Instructions burned: 372 (million)
% 17.58/3.86 % (30555)------------------------------
% 17.58/3.86 % (30555)------------------------------
% 17.58/3.87 % (30560)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_30331 for (2977ds/4714Mi)
% 17.58/3.87 % (30561)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_30331 for (2977ds/8250Mi)
% 17.58/3.88 % (30558)Refutation not found, incomplete strategy
% 17.58/3.88 % (30558)------------------------------
% 17.58/3.88 % (30558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.58/3.88 % (30558)Termination reason: Refutation not found, incomplete strategy
% 17.58/3.88
% 17.58/3.88
% 17.58/3.88 % (30558)Memory used [KB]: 7419
% 17.58/3.88 % (30558)Time elapsed: 0.116 s
% 17.58/3.88 % (30558)Instructions burned: 192 (million)
% 17.58/3.88 % (30558)------------------------------
% 17.58/3.88 % (30558)------------------------------
% 18.46/3.90 % (30562)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_30331 for (2976ds/770Mi)
% 18.46/3.92 % (30560)Refutation not found, incomplete strategy
% 18.46/3.92 % (30560)------------------------------
% 18.46/3.92 % (30560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.46/3.92 % (30560)Termination reason: Refutation not found, incomplete strategy
% 18.46/3.92
% 18.46/3.92
% 18.46/3.92 % (30560)Memory used [KB]: 7547
% 18.46/3.92 % (30560)Time elapsed: 0.056 s
% 18.46/3.92 % (30560)Instructions burned: 196 (million)
% 18.46/3.92 % (30560)------------------------------
% 18.46/3.92 % (30560)------------------------------
% 18.46/3.93 % (30563)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_30331 for (2976ds/794Mi)
% 20.88/4.22 % (30562)Instruction limit reached!
% 20.88/4.22 % (30562)------------------------------
% 20.88/4.22 % (30562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.88/4.22 % (30562)Termination reason: Unknown
% 20.88/4.22 % (30562)Termination phase: Saturation
% 20.88/4.22
% 20.88/4.22 % (30562)Memory used [KB]: 7547
% 20.88/4.22 % (30562)Time elapsed: 0.319 s
% 20.88/4.22 % (30562)Instructions burned: 770 (million)
% 20.88/4.22 % (30562)------------------------------
% 20.88/4.22 % (30562)------------------------------
% 20.88/4.24 % (30565)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_30331 for (2973ds/464Mi)
% 20.88/4.27 % (30559)Instruction limit reached!
% 20.88/4.27 % (30559)------------------------------
% 20.88/4.27 % (30559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.88/4.27 % (30559)Termination reason: Unknown
% 20.88/4.27 % (30559)Termination phase: Saturation
% 20.88/4.27
% 20.88/4.27 % (30559)Memory used [KB]: 9338
% 20.88/4.27 % (30559)Time elapsed: 0.454 s
% 20.88/4.27 % (30559)Instructions burned: 932 (million)
% 20.88/4.27 % (30559)------------------------------
% 20.88/4.27 % (30559)------------------------------
% 20.88/4.29 % (30566)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_30331 for (2972ds/1376Mi)
% 21.49/4.30 % (30563)Instruction limit reached!
% 21.49/4.30 % (30563)------------------------------
% 21.49/4.30 % (30563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.30 % (30563)Termination reason: Unknown
% 21.49/4.30 % (30563)Termination phase: Saturation
% 21.49/4.30
% 21.49/4.30 % (30563)Memory used [KB]: 4477
% 21.49/4.30 % (30563)Time elapsed: 0.365 s
% 21.49/4.30 % (30563)Instructions burned: 794 (million)
% 21.49/4.30 % (30563)------------------------------
% 21.49/4.30 % (30563)------------------------------
% 21.49/4.32 % (30567)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_30331 for (2972ds/906Mi)
% 21.90/4.40 % (30565)Instruction limit reached!
% 21.90/4.40 % (30565)------------------------------
% 21.90/4.40 % (30565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.90/4.40 % (30565)Termination reason: Unknown
% 21.90/4.40 % (30565)Termination phase: Saturation
% 21.90/4.40
% 21.90/4.40 % (30565)Memory used [KB]: 7419
% 21.90/4.40 % (30565)Time elapsed: 0.165 s
% 21.90/4.40 % (30565)Instructions burned: 464 (million)
% 21.90/4.40 % (30565)------------------------------
% 21.90/4.40 % (30565)------------------------------
% 21.90/4.42 % (30568)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_30331 for (2971ds/434Mi)
% 21.90/4.45 % (30568)Refutation not found, incomplete strategy
% 21.90/4.45 % (30568)------------------------------
% 21.90/4.45 % (30568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.90/4.45 % (30568)Termination reason: Refutation not found, incomplete strategy
% 21.90/4.45
% 21.90/4.45
% 21.90/4.45 % (30568)Memory used [KB]: 6524
% 21.90/4.45 % (30568)Time elapsed: 0.034 s
% 21.90/4.45 % (30568)Instructions burned: 66 (million)
% 21.90/4.45 % (30568)------------------------------
% 21.90/4.45 % (30568)------------------------------
% 21.90/4.47 % (30569)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_30331 for (2971ds/865Mi)
% 22.54/4.57 % (30556)Instruction limit reached!
% 22.54/4.57 % (30556)------------------------------
% 22.54/4.57 % (30556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.54/4.57 % (30556)Termination reason: Unknown
% 22.54/4.57 % (30556)Termination phase: Saturation
% 22.54/4.57
% 22.54/4.57 % (30556)Memory used [KB]: 10490
% 22.54/4.57 % (30556)Time elapsed: 0.861 s
% 22.54/4.57 % (30556)Instructions burned: 1827 (million)
% 22.54/4.57 % (30556)------------------------------
% 22.54/4.57 % (30556)------------------------------
% 22.54/4.58 % (30570)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_30331 for (2970ds/593Mi)
% 22.92/4.64 % (30567)Instruction limit reached!
% 22.92/4.64 % (30567)------------------------------
% 22.92/4.64 % (30567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.92/4.64 % (30567)Termination reason: Unknown
% 22.92/4.64 % (30567)Termination phase: Saturation
% 22.92/4.64
% 22.92/4.64 % (30567)Memory used [KB]: 10362
% 22.92/4.64 % (30567)Time elapsed: 0.326 s
% 22.92/4.64 % (30567)Instructions burned: 906 (million)
% 22.92/4.64 % (30567)------------------------------
% 22.92/4.64 % (30567)------------------------------
% 22.92/4.65 % (30571)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_30331 for (2969ds/443Mi)
% 23.56/4.77 % (30571)Instruction limit reached!
% 23.56/4.77 % (30571)------------------------------
% 23.56/4.77 % (30571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.77 % (30571)Termination reason: Unknown
% 23.56/4.77 % (30571)Termination phase: Saturation
% 23.56/4.77
% 23.56/4.77 % (30571)Memory used [KB]: 8187
% 23.56/4.77 % (30571)Time elapsed: 0.121 s
% 23.56/4.77 % (30571)Instructions burned: 445 (million)
% 23.56/4.77 % (30571)------------------------------
% 23.56/4.77 % (30571)------------------------------
% 23.56/4.78 % (30572)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_30331 for (2967ds/594Mi)
% 23.99/4.84 % (30569)Instruction limit reached!
% 23.99/4.84 % (30569)------------------------------
% 23.99/4.84 % (30569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.99/4.84 % (30569)Termination reason: Unknown
% 23.99/4.84 % (30569)Termination phase: Saturation
% 23.99/4.84
% 23.99/4.84 % (30569)Memory used [KB]: 11129
% 23.99/4.84 % (30569)Time elapsed: 0.373 s
% 23.99/4.84 % (30569)Instructions burned: 867 (million)
% 23.99/4.84 % (30569)------------------------------
% 23.99/4.84 % (30569)------------------------------
% 23.99/4.85 % (30574)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_30331 for (2967ds/327Mi)
% 23.99/4.87 % (30570)Instruction limit reached!
% 23.99/4.87 % (30570)------------------------------
% 23.99/4.87 % (30570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.99/4.87 % (30570)Termination reason: Unknown
% 23.99/4.87 % (30570)Termination phase: Saturation
% 23.99/4.87
% 23.99/4.87 % (30570)Memory used [KB]: 8187
% 23.99/4.87 % (30570)Time elapsed: 0.292 s
% 23.99/4.87 % (30570)Instructions burned: 593 (million)
% 23.99/4.87 % (30570)------------------------------
% 23.99/4.87 % (30570)------------------------------
% 23.99/4.89 % (30575)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_30331 for (2966ds/5411Mi)
% 24.99/4.91 % (30575)Refutation not found, incomplete strategy
% 24.99/4.91 % (30575)------------------------------
% 24.99/4.91 % (30575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/4.91 % (30575)Termination reason: Refutation not found, incomplete strategy
% 24.99/4.91
% 24.99/4.91
% 24.99/4.91 % (30575)Memory used [KB]: 6268
% 24.99/4.91 % (30575)Time elapsed: 0.023 s
% 24.99/4.91 % (30575)Instructions burned: 42 (million)
% 24.99/4.91 % (30575)------------------------------
% 24.99/4.91 % (30575)------------------------------
% 24.99/4.93 % (30566)Instruction limit reached!
% 24.99/4.93 % (30566)------------------------------
% 24.99/4.93 % (30566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/4.93 % (30566)Termination reason: Unknown
% 24.99/4.93 % (30566)Termination phase: Saturation
% 24.99/4.93
% 24.99/4.93 % (30566)Memory used [KB]: 12792
% 24.99/4.93 % (30566)Time elapsed: 0.640 s
% 24.99/4.93 % (30566)Instructions burned: 1379 (million)
% 24.99/4.93 % (30566)------------------------------
% 24.99/4.93 % (30566)------------------------------
% 24.99/4.93 % (30576)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_30331 for (2966ds/1762Mi)
% 24.99/4.94 % (30577)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_30331 for (2966ds/96Mi)
% 24.99/4.96 % (30577)Instruction limit reached!
% 24.99/4.96 % (30577)------------------------------
% 24.99/4.96 % (30577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/4.96 % (30577)Termination reason: Unknown
% 24.99/4.96 % (30577)Termination phase: Property scanning
% 24.99/4.96
% 24.99/4.96 % (30577)Memory used [KB]: 2174
% 24.99/4.96 % (30577)Time elapsed: 0.028 s
% 24.99/4.96 % (30577)Instructions burned: 98 (million)
% 24.99/4.96 % (30577)------------------------------
% 24.99/4.96 % (30577)------------------------------
% 24.99/4.97 % (30579)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_30331 for (2966ds/503Mi)
% 24.99/4.99 % (30533)Instruction limit reached!
% 24.99/4.99 % (30533)------------------------------
% 24.99/4.99 % (30533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/4.99 % (30533)Termination reason: Unknown
% 24.99/4.99 % (30533)Termination phase: Saturation
% 24.99/4.99
% 24.99/4.99 % (30533)Memory used [KB]: 9210
% 24.99/4.99 % (30533)Time elapsed: 2.161 s
% 24.99/4.99 % (30533)Instructions burned: 4436 (million)
% 24.99/4.99 % (30533)------------------------------
% 24.99/4.99 % (30533)------------------------------
% 24.99/5.01 % (30580)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_30331 for (2965ds/90Mi)
% 24.99/5.02 % (30574)Instruction limit reached!
% 24.99/5.02 % (30574)------------------------------
% 24.99/5.02 % (30574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/5.02 % (30574)Termination reason: Unknown
% 24.99/5.02 % (30574)Termination phase: Saturation
% 24.99/5.02
% 24.99/5.02 % (30574)Memory used [KB]: 7291
% 24.99/5.02 % (30574)Time elapsed: 0.170 s
% 24.99/5.02 % (30574)Instructions burned: 328 (million)
% 24.99/5.02 % (30574)------------------------------
% 24.99/5.02 % (30574)------------------------------
% 26.67/5.03 % (30580)Instruction limit reached!
% 26.67/5.03 % (30580)------------------------------
% 26.67/5.03 % (30580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.67/5.03 % (30580)Termination reason: Unknown
% 26.67/5.03 % (30580)Termination phase: Saturation
% 26.67/5.03
% 26.67/5.03 % (30580)Memory used [KB]: 6524
% 26.67/5.03 % (30580)Time elapsed: 0.028 s
% 26.67/5.03 % (30580)Instructions burned: 91 (million)
% 26.67/5.03 % (30580)------------------------------
% 26.67/5.03 % (30580)------------------------------
% 26.67/5.04 % (30581)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_30331 for (2965ds/593Mi)
% 26.67/5.04 % (30582)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_30331 for (2965ds/1512Mi)
% 26.67/5.07 % (30572)Instruction limit reached!
% 26.67/5.07 % (30572)------------------------------
% 26.67/5.07 % (30572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.67/5.07 % (30572)Termination reason: Unknown
% 26.67/5.07 % (30572)Termination phase: Saturation
% 26.67/5.07
% 26.67/5.07 % (30572)Memory used [KB]: 7419
% 26.67/5.07 % (30572)Time elapsed: 0.295 s
% 26.67/5.07 % (30572)Instructions burned: 594 (million)
% 26.67/5.07 % (30572)------------------------------
% 26.67/5.07 % (30572)------------------------------
% 26.67/5.08 % (30582)Refutation not found, incomplete strategy
% 26.67/5.08 % (30582)------------------------------
% 26.67/5.08 % (30582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.67/5.08 % (30582)Termination reason: Refutation not found, incomplete strategy
% 26.67/5.08
% 26.67/5.08
% 26.67/5.08 % (30582)Memory used [KB]: 6908
% 26.67/5.08 % (30582)Time elapsed: 0.040 s
% 26.67/5.08 % (30582)Instructions burned: 107 (million)
% 26.67/5.08 % (30582)------------------------------
% 26.67/5.08 % (30582)------------------------------
% 26.67/5.09 % (30583)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_30331 for (2965ds/569Mi)
% 26.67/5.10 % (30584)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_30331 for (2964ds/501Mi)
% 27.19/5.20 % (30579)Instruction limit reached!
% 27.19/5.20 % (30579)------------------------------
% 27.19/5.20 % (30579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.19/5.20 % (30579)Termination reason: Unknown
% 27.19/5.20 % (30579)Termination phase: Saturation
% 27.19/5.20
% 27.19/5.20 % (30579)Memory used [KB]: 7803
% 27.19/5.20 % (30579)Time elapsed: 0.223 s
% 27.19/5.20 % (30579)Instructions burned: 503 (million)
% 27.19/5.20 % (30579)------------------------------
% 27.19/5.20 % (30579)------------------------------
% 27.25/5.21 % (30585)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_30331 for (2963ds/562Mi)
% 27.25/5.21 % (30536)Instruction limit reached!
% 27.25/5.21 % (30536)------------------------------
% 27.25/5.21 % (30536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.25/5.21 % (30536)Termination reason: Unknown
% 27.25/5.21 % (30536)Termination phase: Saturation
% 27.25/5.21
% 27.25/5.21 % (30536)Memory used [KB]: 15479
% 27.25/5.21 % (30536)Time elapsed: 2.298 s
% 27.25/5.21 % (30536)Instructions burned: 5205 (million)
% 27.25/5.21 % (30536)------------------------------
% 27.25/5.21 % (30536)------------------------------
% 27.25/5.23 % (30586)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_30331 for (2963ds/406Mi)
% 27.25/5.29 % (30584)Instruction limit reached!
% 27.25/5.29 % (30584)------------------------------
% 27.25/5.29 % (30584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.25/5.29 % (30584)Termination reason: Unknown
% 27.25/5.29 % (30584)Termination phase: Saturation
% 27.25/5.29
% 27.25/5.29 % (30584)Memory used [KB]: 7419
% 27.25/5.29 % (30584)Time elapsed: 0.190 s
% 27.25/5.29 % (30584)Instructions burned: 501 (million)
% 27.25/5.29 % (30584)------------------------------
% 27.25/5.29 % (30584)------------------------------
% 27.93/5.30 % (30587)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_30331 for (2962ds/582Mi)
% 27.93/5.31 % (30581)Instruction limit reached!
% 27.93/5.31 % (30581)------------------------------
% 27.93/5.31 % (30581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.31 % (30581)Termination reason: Unknown
% 27.93/5.31 % (30581)Termination phase: Saturation
% 27.93/5.31
% 27.93/5.31 % (30581)Memory used [KB]: 8955
% 27.93/5.31 % (30581)Time elapsed: 0.276 s
% 27.93/5.31 % (30581)Instructions burned: 594 (million)
% 27.93/5.31 % (30581)------------------------------
% 27.93/5.31 % (30581)------------------------------
% 27.93/5.33 % (30588)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_30331 for (2962ds/456Mi)
% 27.93/5.36 % (30583)Instruction limit reached!
% 27.93/5.36 % (30583)------------------------------
% 27.93/5.36 % (30583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.36 % (30583)Termination reason: Unknown
% 27.93/5.36 % (30583)Termination phase: Saturation
% 27.93/5.36
% 27.93/5.36 % (30583)Memory used [KB]: 7931
% 27.93/5.36 % (30583)Time elapsed: 0.274 s
% 27.93/5.36 % (30583)Instructions burned: 569 (million)
% 27.93/5.36 % (30583)------------------------------
% 27.93/5.36 % (30583)------------------------------
% 27.93/5.37 % (30585)Instruction limit reached!
% 27.93/5.37 % (30585)------------------------------
% 27.93/5.37 % (30585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.37 % (30585)Termination reason: Unknown
% 27.93/5.37 % (30585)Termination phase: Saturation
% 27.93/5.37
% 27.93/5.37 % (30585)Memory used [KB]: 7931
% 27.93/5.37 % (30585)Time elapsed: 0.169 s
% 27.93/5.37 % (30585)Instructions burned: 564 (million)
% 27.93/5.37 % (30585)------------------------------
% 27.93/5.37 % (30585)------------------------------
% 27.93/5.38 % (30589)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_30331 for (2962ds/393Mi)
% 27.93/5.38 % (30590)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_30331 for (2962ds/1335Mi)
% 28.88/5.40 % (30588)First to succeed.
% 28.88/5.41 % (30588)Refutation found. Thanks to Tanya!
% 28.88/5.41 % SZS status Theorem for DTF2THF_30331
% 28.88/5.41 % SZS output start Proof for DTF2THF_30331
% 28.88/5.41 thf(type_def_5, type, itself: ($tType) > $tType).
% 28.88/5.41 thf(type_def_7, type, n: $tType).
% 28.88/5.41 thf(type_def_8, type, t: $tType).
% 28.88/5.41 thf(type_def_9, type, dtree: $tType).
% 28.88/5.41 thf(type_def_10, type, sum_sum: ($tType * $tType) > $tType).
% 28.88/5.41 thf(type_def_11, type, set: ($tType) > $tType).
% 28.88/5.41 thf(func_def_0, type, sum_sum: ($tType * $tType) > $tType).
% 28.88/5.41 thf(func_def_1, type, dtree: $tType).
% 28.88/5.41 thf(func_def_2, type, set: ($tType) > $tType).
% 28.88/5.41 thf(func_def_3, type, t: $tType).
% 28.88/5.41 thf(func_def_4, type, n: $tType).
% 28.88/5.41 thf(func_def_5, type, itself: ($tType) > $tType).
% 28.88/5.41 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_7, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_8, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_9, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_10, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_11, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_12, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_13, type, order_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_14, type, order_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_15, type, boolean_algebra: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_16, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 28.88/5.41 thf(func_def_17, type, node: n > set @ sum_sum @ t @ dtree > dtree).
% 28.88/5.41 thf(func_def_18, type, corec: !>[X0: $tType]:((X0 > n) > (X0 > set @ sum_sum @ t @ sum_sum @ dtree @ X0) > X0 > dtree)).
% 28.88/5.41 thf(func_def_19, type, root: dtree > n).
% 28.88/5.41 thf(func_def_20, type, unfold: !>[X0: $tType]:((X0 > n) > (X0 > set @ sum_sum @ t @ X0) > X0 > dtree)).
% 28.88/5.41 thf(func_def_21, type, gram_L861583724lle_Fr: set @ n > dtree > set @ t).
% 28.88/5.41 thf(func_def_22, type, gram_L1451583624elle_H: dtree > n > dtree).
% 28.88/5.41 thf(func_def_23, type, gram_L1221482011le_H_c: dtree > n > set @ sum_sum @ t @ n).
% 28.88/5.41 thf(func_def_24, type, gram_L1221482026le_H_r: dtree > n > n).
% 28.88/5.41 thf(func_def_25, type, gram_L1451583628elle_L: set @ n > n > set @ set @ t).
% 28.88/5.41 thf(func_def_26, type, gram_L1231612515_deftr: n > dtree).
% 28.88/5.41 thf(func_def_27, type, gram_L1004374585hsubst: dtree > dtree > dtree).
% 28.88/5.41 thf(func_def_28, type, gram_L1905609002ubst_c: dtree > dtree > set @ sum_sum @ t @ dtree).
% 28.88/5.41 thf(func_def_29, type, gram_L1905609017ubst_r: dtree > n).
% 28.88/5.41 thf(func_def_30, type, gram_L1333338417e_inFr: set @ n > dtree > t > $o).
% 28.88/5.41 thf(func_def_31, type, gram_L830233218_inItr: set @ n > dtree > n > $o).
% 28.88/5.41 thf(func_def_32, type, gram_L315592705e_pick: dtree > n > dtree).
% 28.88/5.41 thf(func_def_33, type, gram_L1828378864e_rcut: dtree > dtree).
% 28.88/5.41 thf(func_def_34, type, gram_L1918716148le_reg: (n > dtree) > dtree > $o).
% 28.88/5.41 thf(func_def_35, type, gram_L646766332egular: dtree > $o).
% 28.88/5.41 thf(func_def_36, type, gram_L716654942_subtr: set @ n > dtree > dtree > $o).
% 28.88/5.41 thf(func_def_37, type, gram_L864798063lle_wf: dtree > $o).
% 28.88/5.41 thf(func_def_38, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 28.88/5.41 thf(func_def_39, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 28.88/5.41 thf(func_def_40, type, bot_bot: !>[X0: $tType]:(X0)).
% 28.88/5.41 thf(func_def_41, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 28.88/5.41 thf(func_def_42, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 28.88/5.41 thf(func_def_43, type, top_top: !>[X0: $tType]:(X0)).
% 28.88/5.41 thf(func_def_44, type, type2: !>[X0: $tType]:(itself @ X0)).
% 28.88/5.41 thf(func_def_45, type, inv_imagep: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o)).
% 28.88/5.41 thf(func_def_46, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 28.88/5.41 thf(func_def_47, type, pow: !>[X0: $tType]:(set @ X0 > set @ set @ X0)).
% 28.88/5.41 thf(func_def_48, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 28.88/5.41 thf(func_def_49, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 28.88/5.41 thf(func_def_50, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 28.88/5.41 thf(func_def_51, type, pairwise: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 28.88/5.41 thf(func_def_52, type, remove: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 28.88/5.41 thf(func_def_53, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 28.88/5.41 thf(func_def_54, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 28.88/5.41 thf(func_def_55, type, n2: n).
% 28.88/5.41 thf(func_def_56, type, ns: set @ n).
% 28.88/5.41 thf(func_def_72, type, sK0: !>[X0: $tType]:(set @ X0 > X0)).
% 28.88/5.41 thf(func_def_73, type, sK1: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 28.88/5.41 thf(func_def_74, type, sK2: n > dtree > set @ n > dtree).
% 28.88/5.41 thf(func_def_75, type, sK3: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 28.88/5.41 thf(func_def_76, type, sK4: !>[X0: $tType]:(set @ X0 > X0)).
% 28.88/5.41 thf(func_def_77, type, sK5: !>[X0: $tType]:(set @ X0 > X0)).
% 28.88/5.41 thf(func_def_78, type, sK6: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 28.88/5.41 thf(func_def_79, type, sK7: dtree > dtree > n).
% 28.88/5.41 thf(func_def_80, type, sK8: !>[X0: $tType]:(X0)).
% 28.88/5.41 thf(func_def_81, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 28.88/5.41 thf(func_def_83, type, ph11: !>[X0: $tType]:(X0)).
% 28.88/5.41 thf(func_def_84, type, sK12: (n > dtree) > dtree > dtree).
% 28.88/5.41 thf(func_def_85, type, sK13: dtree > (n > dtree) > dtree).
% 28.88/5.41 thf(func_def_86, type, sK14: dtree > (n > dtree) > dtree).
% 28.88/5.41 thf(func_def_87, type, sK15: dtree > (n > dtree) > dtree).
% 28.88/5.41 thf(func_def_88, type, sK16: dtree > (n > dtree) > n > dtree).
% 28.88/5.41 thf(func_def_89, type, sK17: dtree > dtree).
% 28.88/5.41 thf(func_def_90, type, sK18: dtree > dtree).
% 28.88/5.41 thf(func_def_91, type, sK19: dtree > dtree).
% 28.88/5.41 thf(f1405,plain,(
% 28.88/5.41 $false),
% 28.88/5.41 inference(trivial_inequality_removal,[status(thm)],[f1378])).
% 28.88/5.41 thf(f1378,plain,(
% 28.88/5.41 (n2 != n2) | ($true != $true)),
% 28.88/5.41 inference(superposition,[status(thm)],[f1031,f1329])).
% 28.88/5.41 thf(f1329,plain,(
% 28.88/5.41 ( ! [X0 : n] : (($true = (member @ n @ X0 @ ns)) | (n2 != X0)) )),
% 28.88/5.41 inference(forward_demodulation,[status(thm)],[f1328,f1165])).
% 28.88/5.41 thf(f1165,plain,(
% 28.88/5.41 ( ! [X0 : n] : (((gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X0)) = X0)) )),
% 28.88/5.41 inference(definition_unfolding,[status(thm)],[f1039,f1111])).
% 28.88/5.41 thf(f1111,plain,(
% 28.88/5.41 (root = gram_L1905609017ubst_r)),
% 28.88/5.41 inference(cnf_transformation,[status(thm)],[f8])).
% 28.88/5.41 thf(f8,axiom,(
% 28.88/5.41 (root = gram_L1905609017ubst_r)),
% 28.88/5.41 file('/export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2THF_30331.p',fact_7_hsubst__r__def)).
% 28.88/5.41 thf(f1039,plain,(
% 28.88/5.41 ( ! [X0 : n] : (((root @ (gram_L1231612515_deftr @ X0)) = X0)) )),
% 28.88/5.41 inference(cnf_transformation,[status(thm)],[f782])).
% 28.88/5.41 thf(f782,plain,(
% 28.88/5.41 ! [X0 : n] : ((root @ (gram_L1231612515_deftr @ X0)) = X0)),
% 28.88/5.41 inference(rectify,[status(thm)],[f28])).
% 28.88/5.41 thf(f28,axiom,(
% 28.88/5.41 ! [X19 : n] : ((root @ (gram_L1231612515_deftr @ X19)) = X19)),
% 28.88/5.41 file('/export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2THF_30331.p',fact_27_root__deftr)).
% 28.88/5.41 thf(f1328,plain,(
% 28.88/5.41 ( ! [X0 : n] : (($true = (member @ n @ (gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X0)) @ ns)) | (n2 != X0)) )),
% 28.88/5.41 inference(trivial_inequality_removal,[status(thm)],[f1322])).
% 28.88/5.41 thf(f1322,plain,(
% 28.88/5.41 ( ! [X0 : n] : ((n2 != X0) | ($true = (member @ n @ (gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X0)) @ ns)) | (bot_bot @ set @ t != bot_bot @ set @ t)) )),
% 28.88/5.41 inference(superposition,[status(thm)],[f1318,f1186])).
% 28.88/5.41 thf(f1186,plain,(
% 28.88/5.41 ( ! [X0 : dtree,X1 : set @ n] : ((bot_bot @ set @ t = (gram_L861583724lle_Fr @ X1 @ X0)) | ($true = (member @ n @ (gram_L1905609017ubst_r @ X0) @ X1))) )),
% 28.88/5.41 inference(definition_unfolding,[status(thm)],[f1127,f1111])).
% 28.88/5.41 thf(f1127,plain,(
% 28.88/5.41 ( ! [X0 : dtree,X1 : set @ n] : (($true = (member @ n @ (root @ X0) @ X1)) | (bot_bot @ set @ t = (gram_L861583724lle_Fr @ X1 @ X0))) )),
% 28.88/5.41 inference(cnf_transformation,[status(thm)],[f876])).
% 28.88/5.41 thf(f876,plain,(
% 28.88/5.41 ! [X0 : dtree,X1 : set @ n] : (($true = (member @ n @ (root @ X0) @ X1)) | (bot_bot @ set @ t = (gram_L861583724lle_Fr @ X1 @ X0)))),
% 28.88/5.41 inference(ennf_transformation,[status(thm)],[f773])).
% 28.88/5.41 thf(f773,plain,(
% 28.88/5.41 ! [X0 : dtree,X1 : set @ n] : (($true != (member @ n @ (root @ X0) @ X1)) => (bot_bot @ set @ t = (gram_L861583724lle_Fr @ X1 @ X0)))),
% 28.88/5.41 inference(flattening,[status(thm)],[f595])).
% 28.88/5.41 thf(f595,plain,(
% 28.88/5.41 ! [X0 : dtree,X1 : set @ n] : (~($true = (member @ n @ (root @ X0) @ X1)) => (bot_bot @ set @ t = (gram_L861583724lle_Fr @ X1 @ X0)))),
% 28.88/5.41 inference(fool_elimination,[status(thm)],[f594])).
% 28.88/5.41 thf(f594,plain,(
% 28.88/5.41 ! [X0 : dtree,X1 : set @ n] : (~(member @ n @ (root @ X0) @ X1) => (bot_bot @ set @ t = (gram_L861583724lle_Fr @ X1 @ X0)))),
% 28.88/5.41 inference(rectify,[status(thm)],[f2])).
% 28.88/5.41 thf(f2,axiom,(
% 28.88/5.41 ! [X2 : dtree,X3 : set @ n] : (~(member @ n @ (root @ X2) @ X3) => ((gram_L861583724lle_Fr @ X3 @ X2) = bot_bot @ set @ t))),
% 28.88/5.41 file('/export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2THF_30331.p',fact_1_not__root__Fr)).
% 28.88/5.41 thf(f1318,plain,(
% 28.88/5.41 ( ! [X0 : n] : ((bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X0))) | (n2 != X0)) )),
% 28.88/5.41 inference(duplicate_literal_removal,[status(thm)],[f1317])).
% 28.88/5.41 thf(f1317,plain,(
% 28.88/5.41 ( ! [X0 : n] : ((bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X0))) | (n2 != X0) | (n2 != X0)) )),
% 28.88/5.41 inference(forward_demodulation,[status(thm)],[f1316,f1165])).
% 28.88/5.41 thf(f1316,plain,(
% 28.88/5.41 ( ! [X0 : n] : ((n2 != (gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X0))) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X0))) | (n2 != X0)) )),
% 28.88/5.41 inference(subsumption_resolution,[status(thm)],[f1310,f1101])).
% 28.88/5.41 thf(f1101,plain,(
% 28.88/5.41 ( ! [X0 : n] : (($true = (gram_L864798063lle_wf @ (gram_L1231612515_deftr @ X0)))) )),
% 28.88/5.41 inference(cnf_transformation,[status(thm)],[f391])).
% 28.88/5.41 thf(f391,plain,(
% 28.88/5.41 ! [X0 : n] : ($true = (gram_L864798063lle_wf @ (gram_L1231612515_deftr @ X0)))),
% 28.88/5.41 inference(fool_elimination,[status(thm)],[f390])).
% 28.88/5.41 thf(f390,plain,(
% 28.88/5.41 ! [X0 : n] : (gram_L864798063lle_wf @ (gram_L1231612515_deftr @ X0))),
% 28.88/5.41 inference(rectify,[status(thm)],[f40])).
% 28.88/5.41 thf(f40,axiom,(
% 28.88/5.41 ! [X19 : n] : (gram_L864798063lle_wf @ (gram_L1231612515_deftr @ X19))),
% 28.88/5.41 file('/export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2THF_30331.p',fact_39_wf__deftr)).
% 28.88/5.41 thf(f1310,plain,(
% 28.88/5.41 ( ! [X0 : n] : ((bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X0))) | ($true != (gram_L864798063lle_wf @ (gram_L1231612515_deftr @ X0))) | (n2 != (gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X0))) | (n2 != X0)) )),
% 28.88/5.41 inference(trivial_inequality_removal,[status(thm)],[f1309])).
% 28.88/5.41 thf(f1309,plain,(
% 28.88/5.41 ( ! [X0 : n] : (($true != (gram_L864798063lle_wf @ (gram_L1231612515_deftr @ X0))) | (n2 != (gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X0))) | ((sK12 @ gram_L1231612515_deftr @ (gram_L1231612515_deftr @ X0)) != (sK12 @ gram_L1231612515_deftr @ (gram_L1231612515_deftr @ X0))) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X0))) | (n2 != X0)) )),
% 28.88/5.41 inference(duplicate_literal_removal,[status(thm)],[f1308])).
% 28.88/5.41 thf(f1308,plain,(
% 28.88/5.41 ( ! [X0 : n] : ((bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X0))) | ($true != (gram_L864798063lle_wf @ (gram_L1231612515_deftr @ X0))) | ((sK12 @ gram_L1231612515_deftr @ (gram_L1231612515_deftr @ X0)) != (sK12 @ gram_L1231612515_deftr @ (gram_L1231612515_deftr @ X0))) | (n2 != X0) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X0))) | (n2 != (gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X0)))) )),
% 28.88/5.41 inference(superposition,[status(thm)],[f1231,f1300])).
% 28.88/5.41 thf(f1300,plain,(
% 28.88/5.41 ( ! [X0 : n > dtree,X1 : n] : (((sK12 @ X0 @ (gram_L1231612515_deftr @ X1)) = (gram_L1231612515_deftr @ (gram_L1905609017ubst_r @ (sK12 @ X0 @ (gram_L1231612515_deftr @ X1))))) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X1))) | (n2 != X1)) )),
% 28.88/5.41 inference(forward_demodulation,[status(thm)],[f1299,f1165])).
% 28.88/5.41 thf(f1299,plain,(
% 28.88/5.41 ( ! [X0 : n > dtree,X1 : n] : ((n2 != (gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X1))) | ((sK12 @ X0 @ (gram_L1231612515_deftr @ X1)) = (gram_L1231612515_deftr @ (gram_L1905609017ubst_r @ (sK12 @ X0 @ (gram_L1231612515_deftr @ X1))))) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X1)))) )),
% 28.88/5.41 inference(subsumption_resolution,[status(thm)],[f1256,f1101])).
% 28.88/5.41 thf(f1256,plain,(
% 28.88/5.41 ( ! [X0 : n > dtree,X1 : n] : ((bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X1))) | ((sK12 @ X0 @ (gram_L1231612515_deftr @ X1)) = (gram_L1231612515_deftr @ (gram_L1905609017ubst_r @ (sK12 @ X0 @ (gram_L1231612515_deftr @ X1))))) | ($true != (gram_L864798063lle_wf @ (gram_L1231612515_deftr @ X1))) | (n2 != (gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X1)))) )),
% 28.88/5.41 inference(trivial_inequality_removal,[status(thm)],[f1255])).
% 28.88/5.41 thf(f1255,plain,(
% 28.88/5.41 ( ! [X0 : n > dtree,X1 : n] : ((bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ (gram_L1231612515_deftr @ X1))) | (n2 != (gram_L1905609017ubst_r @ (gram_L1231612515_deftr @ X1))) | ((sK12 @ X0 @ (gram_L1231612515_deftr @ X1)) = (gram_L1231612515_deftr @ (gram_L1905609017ubst_r @ (sK12 @ X0 @ (gram_L1231612515_deftr @ X1))))) | ($true != (gram_L864798063lle_wf @ (gram_L1231612515_deftr @ X1))) | ($true != $true)) )),
% 28.88/5.41 inference(superposition,[status(thm)],[f1162,f1230])).
% 28.88/5.41 thf(f1230,plain,(
% 28.88/5.41 ( ! [X0 : dtree,X1 : n > dtree] : (($true = (gram_L716654942_subtr @ top_top @ set @ n @ (sK12 @ X1 @ X0) @ X0)) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0)) | (n2 != (gram_L1905609017ubst_r @ X0)) | ($true != (gram_L864798063lle_wf @ X0))) )),
% 28.88/5.41 inference(binary_proxy_clausification,[status(thm)],[f1228])).
% 28.88/5.41 thf(f1228,plain,(
% 28.88/5.41 ( ! [X0 : dtree,X1 : n > dtree] : ((n2 != (gram_L1905609017ubst_r @ X0)) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0)) | ($false = ((gram_L716654942_subtr @ top_top @ set @ n @ (sK12 @ X1 @ X0) @ X0) => ((X1 @ (gram_L1905609017ubst_r @ (sK12 @ X1 @ X0))) = (sK12 @ X1 @ X0)))) | ($true != (gram_L864798063lle_wf @ X0))) )),
% 28.88/5.41 inference(beta_eta_normalization,[status(thm)],[f1227])).
% 28.88/5.41 thf(f1227,plain,(
% 28.88/5.41 ( ! [X0 : dtree,X1 : n > dtree] : (($true != (gram_L864798063lle_wf @ X0)) | ($false = ((^[Y0 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y0 @ X0) => ((X1 @ (gram_L1905609017ubst_r @ Y0)) = Y0))) @ (sK12 @ X1 @ X0))) | (n2 != (gram_L1905609017ubst_r @ X0)) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0))) )),
% 28.88/5.41 inference(sigma_clausification,[status(thm)],[f1226])).
% 28.88/5.41 thf(f1226,plain,(
% 28.88/5.41 ( ! [X0 : dtree,X1 : n > dtree] : (($true != (gram_L864798063lle_wf @ X0)) | (n2 != (gram_L1905609017ubst_r @ X0)) | ($false = (!! @ dtree @ (^[Y0 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y0 @ X0) => ((X1 @ (gram_L1905609017ubst_r @ Y0)) = Y0))))) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0))) )),
% 28.88/5.41 inference(beta_eta_normalization,[status(thm)],[f1225])).
% 28.88/5.41 thf(f1225,plain,(
% 28.88/5.41 ( ! [X0 : dtree,X1 : n > dtree] : (($true != (gram_L864798063lle_wf @ X0)) | ($false = ((^[Y0 : n > dtree]: (!! @ dtree @ (^[Y1 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y1 @ X0) => ((Y0 @ (gram_L1905609017ubst_r @ Y1)) = Y1))))) @ X1)) | (n2 != (gram_L1905609017ubst_r @ X0)) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0))) )),
% 28.88/5.41 inference(pi_clausification,[status(thm)],[f1224])).
% 28.88/5.41 thf(f1224,plain,(
% 28.88/5.41 ( ! [X0 : dtree] : (($true != (?? @ (n > dtree) @ (^[Y0 : n > dtree]: (!! @ dtree @ (^[Y1 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y1 @ X0) => ((Y0 @ (gram_L1905609017ubst_r @ Y1)) = Y1))))))) | ($true != (gram_L864798063lle_wf @ X0)) | (n2 != (gram_L1905609017ubst_r @ X0)) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0))) )),
% 28.88/5.41 inference(beta_eta_normalization,[status(thm)],[f1185])).
% 28.88/5.41 thf(f1185,plain,(
% 28.88/5.41 ( ! [X0 : dtree] : (($true != (gram_L864798063lle_wf @ X0)) | (n2 != (gram_L1905609017ubst_r @ X0)) | ($true != ((^[Y0 : dtree]: (?? @ (n > dtree) @ (^[Y1 : n > dtree]: ((^[Y2 : n > dtree]: ((^[Y3 : dtree]: (!! @ dtree @ (^[Y4 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y4 @ Y3) => ((Y2 @ (gram_L1905609017ubst_r @ Y4)) = Y4))))))) @ Y1 @ Y0)))) @ X0)) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0))) )),
% 28.88/5.41 inference(definition_unfolding,[status(thm)],[f1120,f1148,f1111])).
% 28.88/5.41 thf(f1148,plain,(
% 28.88/5.41 (gram_L646766332egular = (^[Y0 : dtree]: (?? @ (n > dtree) @ (^[Y1 : n > dtree]: ((^[Y2 : n > dtree]: ((^[Y3 : dtree]: (!! @ dtree @ (^[Y4 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y4 @ Y3) => ((Y2 @ (gram_L1905609017ubst_r @ Y4)) = Y4))))))) @ Y1 @ Y0)))))),
% 28.88/5.41 inference(definition_unfolding,[status(thm)],[f1129,f1147])).
% 28.88/5.41 thf(f1147,plain,(
% 28.88/5.41 (gram_L1918716148le_reg = (^[Y0 : n > dtree]: ((^[Y1 : dtree]: (!! @ dtree @ (^[Y2 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y2 @ Y1) => ((Y0 @ (gram_L1905609017ubst_r @ Y2)) = Y2))))))))),
% 28.88/5.41 inference(definition_unfolding,[status(thm)],[f988,f1111])).
% 28.88/5.41 thf(f988,plain,(
% 28.88/5.41 (gram_L1918716148le_reg = (^[Y0 : n > dtree]: ((^[Y1 : dtree]: (!! @ dtree @ (^[Y2 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y2 @ Y1) => ((Y0 @ (root @ Y2)) = Y2))))))))),
% 28.88/5.41 inference(cnf_transformation,[status(thm)],[f465])).
% 28.88/5.41 thf(f465,plain,(
% 28.88/5.41 (gram_L1918716148le_reg = (^[Y0 : n > dtree]: ((^[Y1 : dtree]: (!! @ dtree @ (^[Y2 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y2 @ Y1) => ((Y0 @ (root @ Y2)) = Y2))))))))),
% 28.88/5.41 inference(fool_elimination,[status(thm)],[f464])).
% 28.88/5.41 thf(f464,plain,(
% 28.88/5.41 ((^[X0 : n > dtree, X1 : dtree] : (! [X2 : dtree] : ((gram_L716654942_subtr @ top_top @ set @ n @ X2 @ X1) => ((X0 @ (root @ X2)) = X2)))) = gram_L1918716148le_reg)),
% 28.88/5.41 inference(rectify,[status(thm)],[f42])).
% 28.88/5.41 thf(f42,axiom,(
% 28.88/5.41 ((^[X12 : n > dtree, X11 : dtree] : (! [X22 : dtree] : ((gram_L716654942_subtr @ top_top @ set @ n @ X22 @ X11) => ((X12 @ (root @ X22)) = X22)))) = gram_L1918716148le_reg)),
% 28.88/5.41 file('/export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2THF_30331.p',fact_41_reg__def)).
% 28.88/5.41 thf(f1129,plain,(
% 28.88/5.41 (gram_L646766332egular = (^[Y0 : dtree]: (?? @ (n > dtree) @ (^[Y1 : n > dtree]: (gram_L1918716148le_reg @ Y1 @ Y0)))))),
% 28.88/5.41 inference(cnf_transformation,[status(thm)],[f501])).
% 28.88/5.41 thf(f501,plain,(
% 28.88/5.41 (gram_L646766332egular = (^[Y0 : dtree]: (?? @ (n > dtree) @ (^[Y1 : n > dtree]: (gram_L1918716148le_reg @ Y1 @ Y0)))))),
% 28.88/5.41 inference(fool_elimination,[status(thm)],[f500])).
% 28.88/5.41 thf(f500,plain,(
% 28.88/5.41 ((^[X0 : dtree] : (? [X1 : n > dtree] : (gram_L1918716148le_reg @ X1 @ X0))) = gram_L646766332egular)),
% 28.88/5.41 inference(rectify,[status(thm)],[f17])).
% 28.88/5.41 thf(f17,axiom,(
% 28.88/5.41 ((^[X11 : dtree] : (? [X12 : n > dtree] : (gram_L1918716148le_reg @ X12 @ X11))) = gram_L646766332egular)),
% 28.88/5.41 file('/export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2THF_30331.p',fact_16_regular__def)).
% 28.88/5.41 thf(f1120,plain,(
% 28.88/5.41 ( ! [X0 : dtree] : (($true != (gram_L864798063lle_wf @ X0)) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0)) | ($true != (gram_L646766332egular @ X0)) | (n2 != (root @ X0))) )),
% 28.88/5.41 inference(cnf_transformation,[status(thm)],[f826])).
% 28.88/5.41 thf(f826,plain,(
% 28.88/5.41 ! [X0 : dtree] : (($true != (gram_L864798063lle_wf @ X0)) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0)) | ($true != (gram_L646766332egular @ X0)) | (n2 != (root @ X0)))),
% 28.88/5.41 inference(ennf_transformation,[status(thm)],[f711])).
% 28.88/5.41 thf(f711,plain,(
% 28.88/5.41 ~? [X0 : dtree] : (($true = (gram_L864798063lle_wf @ X0)) & (bot_bot @ set @ t = (gram_L861583724lle_Fr @ ns @ X0)) & ($true = (gram_L646766332egular @ X0)) & (n2 = (root @ X0)))),
% 28.88/5.41 inference(fool_elimination,[status(thm)],[f710])).
% 28.88/5.41 thf(f710,plain,(
% 28.88/5.41 ~? [X0 : dtree] : ((bot_bot @ set @ t = (gram_L861583724lle_Fr @ ns @ X0)) & (gram_L864798063lle_wf @ X0) & (n2 = (root @ X0)) & (gram_L646766332egular @ X0))),
% 28.88/5.41 inference(rectify,[status(thm)],[f284])).
% 28.88/5.41 thf(f284,negated_conjecture,(
% 28.88/5.41 ~? [X65 : dtree] : ((bot_bot @ set @ t = (gram_L861583724lle_Fr @ ns @ X65)) & (gram_L864798063lle_wf @ X65) & (n2 = (root @ X65)) & (gram_L646766332egular @ X65))),
% 28.88/5.41 inference(negated_conjecture,[status(cth)],[f283])).
% 28.88/5.41 thf(f283,conjecture,(
% 28.88/5.41 ? [X65 : dtree] : ((bot_bot @ set @ t = (gram_L861583724lle_Fr @ ns @ X65)) & (gram_L864798063lle_wf @ X65) & (n2 = (root @ X65)) & (gram_L646766332egular @ X65))),
% 28.88/5.41 file('/export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2THF_30331.p',conj_1)).
% 28.88/5.41 thf(f1162,plain,(
% 28.88/5.41 ( ! [X2 : n,X0 : set @ n,X1 : dtree] : (((gram_L1231612515_deftr @ (gram_L1905609017ubst_r @ X1)) = X1) | ($true != (gram_L716654942_subtr @ X0 @ X1 @ (gram_L1231612515_deftr @ X2)))) )),
% 28.88/5.41 inference(definition_unfolding,[status(thm)],[f1009,f1111])).
% 28.88/5.41 thf(f1009,plain,(
% 28.88/5.41 ( ! [X2 : n,X0 : set @ n,X1 : dtree] : (((gram_L1231612515_deftr @ (root @ X1)) = X1) | ($true != (gram_L716654942_subtr @ X0 @ X1 @ (gram_L1231612515_deftr @ X2)))) )),
% 28.88/5.41 inference(cnf_transformation,[status(thm)],[f854])).
% 28.88/5.41 thf(f854,plain,(
% 28.88/5.41 ! [X0 : set @ n,X1 : dtree,X2 : n] : (((gram_L1231612515_deftr @ (root @ X1)) = X1) | ($true != (gram_L716654942_subtr @ X0 @ X1 @ (gram_L1231612515_deftr @ X2))))),
% 28.88/5.41 inference(ennf_transformation,[status(thm)],[f289])).
% 28.88/5.41 thf(f289,plain,(
% 28.88/5.41 ! [X0 : set @ n,X1 : dtree,X2 : n] : (($true = (gram_L716654942_subtr @ X0 @ X1 @ (gram_L1231612515_deftr @ X2))) => ((gram_L1231612515_deftr @ (root @ X1)) = X1))),
% 28.88/5.41 inference(fool_elimination,[status(thm)],[f288])).
% 28.88/5.41 thf(f288,plain,(
% 28.88/5.41 ! [X0 : set @ n,X1 : dtree,X2 : n] : ((gram_L716654942_subtr @ X0 @ X1 @ (gram_L1231612515_deftr @ X2)) => ((gram_L1231612515_deftr @ (root @ X1)) = X1))),
% 28.88/5.41 inference(rectify,[status(thm)],[f33])).
% 28.88/5.41 thf(f33,axiom,(
% 28.88/5.41 ! [X3 : set @ n,X26 : dtree,X19 : n] : ((gram_L716654942_subtr @ X3 @ X26 @ (gram_L1231612515_deftr @ X19)) => ((gram_L1231612515_deftr @ (root @ X26)) = X26))),
% 28.88/5.41 file('/export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2THF_30331.p',fact_32_subtr__deftr)).
% 28.88/5.41 thf(f1231,plain,(
% 28.88/5.41 ( ! [X0 : dtree,X1 : n > dtree] : (((X1 @ (gram_L1905609017ubst_r @ (sK12 @ X1 @ X0))) != (sK12 @ X1 @ X0)) | (n2 != (gram_L1905609017ubst_r @ X0)) | ($true != (gram_L864798063lle_wf @ X0)) | (bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0))) )),
% 28.88/5.41 inference(equality_proxy_clausification,[status(thm)],[f1229])).
% 28.88/5.41 thf(f1229,plain,(
% 28.88/5.41 ( ! [X0 : dtree,X1 : n > dtree] : ((bot_bot @ set @ t != (gram_L861583724lle_Fr @ ns @ X0)) | ($true != (gram_L864798063lle_wf @ X0)) | ($false = ((X1 @ (gram_L1905609017ubst_r @ (sK12 @ X1 @ X0))) = (sK12 @ X1 @ X0))) | (n2 != (gram_L1905609017ubst_r @ X0))) )),
% 28.88/5.41 inference(binary_proxy_clausification,[status(thm)],[f1228])).
% 28.88/5.41 thf(f1031,plain,(
% 28.88/5.41 ((member @ n @ n2 @ ns) != $true)),
% 28.88/5.41 inference(cnf_transformation,[status(thm)],[f789])).
% 28.88/5.41 thf(f789,plain,(
% 28.88/5.41 ((member @ n @ n2 @ ns) != $true)),
% 28.88/5.41 inference(flattening,[status(thm)],[f663])).
% 28.88/5.41 thf(f663,plain,(
% 28.88/5.41 ~((member @ n @ n2 @ ns) = $true)),
% 28.88/5.41 inference(fool_elimination,[status(thm)],[f662])).
% 28.88/5.41 thf(f662,plain,(
% 28.88/5.41 ~(member @ n @ n2 @ ns)),
% 28.88/5.41 inference(rectify,[status(thm)],[f1])).
% 28.88/5.41 thf(f1,axiom,(
% 28.88/5.41 ~(member @ n @ n2 @ ns)),
% 28.88/5.41 file('/export/starexec/sandbox/tmp/tmp.EAA2zNteYe/DTF2THF_30331.p',fact_0_assms)).
% 28.88/5.41 % SZS output end Proof for DTF2THF_30331
% 28.88/5.41 % (30588)------------------------------
% 28.88/5.41 % (30588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.88/5.41 % (30588)Termination reason: Refutation
% 28.88/5.41
% 28.88/5.41 % (30588)Memory used [KB]: 7164
% 28.88/5.41 % (30588)Time elapsed: 0.076 s
% 28.88/5.41 % (30588)Instructions burned: 143 (million)
% 28.88/5.41 % (30588)------------------------------
% 28.88/5.41 % (30588)------------------------------
% 28.88/5.41 % (30434)Success in time 3.827 s
%------------------------------------------------------------------------------