%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM185^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 08:41:53 AM UTC 2026
% Result : Theorem 82.03s 13.06s
% Output : Refutation 82.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COM185^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.30 % Computer : n011.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue Feb 24 04:16:17 EST 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.40 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : COM185^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.40 % Domain : Computing Theory
% 0.16/0.40 % Problem : Grammars and languages 307
% 0.16/0.40 % Version : [Bla16] axioms : Especial.
% 0.16/0.40 % English :
% 0.16/0.40
% 0.16/0.40 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.16/0.40 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.16/0.40 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.16/0.40 % Source : [Bla16]
% 0.16/0.40 % Names : gram_lang__307.p [Bla16]
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % Rating : 0.67 v9.0.0, 1.00 v8.1.0, 0.75 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.16/0.40 % Syntax : Number of formulae : 322 ( 143 unt; 47 typ; 0 def)
% 0.16/0.40 % Number of atoms : 731 ( 375 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 7 ( 2 avg)
% 0.16/0.40 % Number of connectives : 4154 ( 82 ~; 10 |; 96 &;3652 @)
% 0.16/0.40 % ( 0 <=>; 314 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 21 ( 7 avg)
% 0.16/0.40 % Number of types : 4 ( 3 usr)
% 0.16/0.40 % Number of type conns : 293 ( 293 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 47 ( 44 usr; 4 con; 0-9 aty)
% 0.16/0.40 % Number of variables : 1282 ( 131 ^;1033 !; 71 ?;1282 :)
% 0.16/0.40 % ( 47 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.40 % SPC : TH1_THM_EQU_NAR
% 0.16/0.40
% 0.16/0.40 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.40 % 2016-07-13 14:42:04.312
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 %----Could-be-implicit typings (6)
% 0.16/0.40 thf(ty_t_Sum__Type_Osum,type,
% 0.16/0.40 sum_sum: $tType > $tType > $tType ).
% 0.16/0.40
% 0.16/0.40 thf(ty_t_DTree_Odtree,type,
% 0.16/0.40 dtree: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(ty_t_Set_Oset,type,
% 0.16/0.40 set: $tType > $tType ).
% 0.16/0.40
% 0.16/0.40 thf(ty_t_DTree_OT,type,
% 0.16/0.40 t: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(ty_t_DTree_ON,type,
% 0.16/0.40 n: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(ty_t_itself,type,
% 0.16/0.40 itself: $tType > $tType ).
% 0.16/0.40
% 0.16/0.40 %----Explicit typings (41)
% 0.16/0.40 thf(sy_cl_HOL_Otype,type,
% 0.16/0.40 type:
% 0.16/0.40 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_cl_Orderings_Obot,type,
% 0.16/0.40 bot:
% 0.16/0.40 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_cl_Complete__Lattices_OSup,type,
% 0.16/0.40 complete_Sup:
% 0.16/0.40 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_cl_Complete__Partial__Order_Occpo,type,
% 0.16/0.40 comple1141879883l_ccpo:
% 0.16/0.40 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 0.16/0.40 comple187826305attice:
% 0.16/0.40 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__lattice,type,
% 0.16/0.40 condit378418413attice:
% 0.16/0.40 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p,type,
% 0.16/0.40 bNF_Greatest_image2p:
% 0.16/0.40 !>[C: $tType,A: $tType,D: $tType,B: $tType] : ( ( C > A ) > ( D > B ) > ( C > D > $o ) > A > B > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Basic__BNFs_Osetl,type,
% 0.16/0.40 basic_setl:
% 0.16/0.40 !>[A: $tType,B: $tType] : ( ( sum_sum @ A @ B ) > ( set @ A ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Basic__BNFs_Osetr,type,
% 0.16/0.40 basic_setr:
% 0.16/0.40 !>[A: $tType,B: $tType] : ( ( sum_sum @ A @ B ) > ( set @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Complete__Lattices_OSup__class_OSup,type,
% 0.16/0.40 complete_Sup_Sup:
% 0.16/0.40 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_DTree_ONode,type,
% 0.16/0.40 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_DTree_Ocont,type,
% 0.16/0.40 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_DTree_Odtree_Oroot,type,
% 0.16/0.40 root: dtree > n ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFr,type,
% 0.16/0.40 gram_L861583724lle_Fr: ( set @ n ) > dtree > ( set @ t ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OItr,type,
% 0.16/0.40 gram_L1580978439le_Itr: ( set @ n ) > dtree > ( set @ n ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 0.16/0.40 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 0.16/0.40 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 0.16/0.40 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 0.16/0.40 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2,type,
% 0.16/0.40 gram_L1283001940subtr2: ( set @ n ) > dtree > dtree > $o ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_HOL_OThe,type,
% 0.16/0.40 the:
% 0.16/0.40 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_If,type,
% 0.16/0.40 if:
% 0.16/0.40 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Lifting_Orel__pred__comp,type,
% 0.16/0.40 rel_pred_comp:
% 0.16/0.40 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( B > $o ) > A > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.16/0.40 bot_bot:
% 0.16/0.40 !>[A: $tType] : A ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Pure_Otype,type,
% 0.16/0.40 type2:
% 0.16/0.40 !>[A: $tType] : ( itself @ A ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Set_OCollect,type,
% 0.16/0.40 collect:
% 0.16/0.40 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Set_Oimage,type,
% 0.16/0.40 image:
% 0.16/0.40 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Set_Oinsert,type,
% 0.16/0.40 insert:
% 0.16/0.40 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Set_Ois__empty,type,
% 0.16/0.40 is_empty:
% 0.16/0.40 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Set_Ois__singleton,type,
% 0.16/0.40 is_singleton:
% 0.16/0.40 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Set_Othe__elem,type,
% 0.16/0.40 the_elem:
% 0.16/0.40 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Set_Ovimage,type,
% 0.16/0.40 vimage:
% 0.16/0.40 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Sum__Type_OInl,type,
% 0.16/0.40 sum_Inl:
% 0.16/0.40 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Sum__Type_OInr,type,
% 0.16/0.40 sum_Inr:
% 0.16/0.40 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Sum__Type_OSuml,type,
% 0.16/0.40 sum_Suml:
% 0.16/0.40 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( sum_sum @ A @ B ) > C ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Sum__Type_Oold_Osum_Orec__set__sum,type,
% 0.16/0.40 sum_rec_set_sum:
% 0.16/0.40 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 0.16/0.40 sum_rec_sum:
% 0.16/0.40 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_Sum__Type_Osum_Ocase__sum,type,
% 0.16/0.40 sum_case_sum:
% 0.16/0.40 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( B > C ) > ( sum_sum @ A @ B ) > C ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_c_member,type,
% 0.16/0.40 member:
% 0.16/0.40 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.16/0.40
% 0.16/0.40 thf(sy_v_ns,type,
% 0.16/0.40 ns: set @ n ).
% 0.16/0.40
% 0.16/0.40 thf(sy_v_tr,type,
% 0.16/0.40 tr: dtree ).
% 0.16/0.40
% 0.16/0.40 %----Relevant facts (256)
% 0.16/0.40 thf(fact_0_inItr_OBase,axiom,
% 0.16/0.40 ! [Tr: dtree,Ns: set @ n] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inItr.Base
% 0.16/0.40 thf(fact_1_subtr_ORefl,axiom,
% 0.16/0.40 ! [Tr: dtree,Ns: set @ n] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr.Refl
% 0.16/0.40 thf(fact_2_inItr__subtr,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.16/0.40 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.16/0.40 => ? [Tr2: dtree] :
% 0.16/0.40 ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr )
% 0.16/0.40 & ( ( root @ Tr2 )
% 0.16/0.40 = N ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inItr_subtr
% 0.16/0.40 thf(fact_3_subtr__inItr,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr: dtree,N: n,Tr1: dtree] :
% 0.16/0.40 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.16/0.40 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.16/0.40 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr_inItr
% 0.16/0.40 thf(fact_4_subtr__trans,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 0.16/0.40 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.40 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 0.16/0.40 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr_trans
% 0.16/0.40 thf(fact_5_inItr__root__in,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.16/0.40 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.16/0.40 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.16/0.40
% 0.16/0.40 % inItr_root_in
% 0.16/0.40 thf(fact_6_subtr__rootL__in,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.40 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.40 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr_rootL_in
% 0.16/0.40 thf(fact_7_subtr__rootR__in,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.40 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.40 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr_rootR_in
% 0.16/0.40 thf(fact_8_Itr__def,axiom,
% 0.16/0.40 ( gram_L1580978439le_Itr
% 0.16/0.40 = ( ^ [Ns2: set @ n,Tr4: dtree] : ( collect @ n @ ( gram_L830233218_inItr @ Ns2 @ Tr4 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Itr_def
% 0.16/0.40 thf(fact_9_rel__pred__comp__def,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( rel_pred_comp @ A @ B )
% 0.16/0.40 = ( ^ [R: A > B > $o,P: B > $o,X: A] :
% 0.16/0.40 ? [Y: B] :
% 0.16/0.40 ( ( R @ X @ Y )
% 0.16/0.40 & ( P @ Y ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % rel_pred_comp_def
% 0.16/0.40 thf(fact_10_Itr__subtr,axiom,
% 0.16/0.40 ( gram_L1580978439le_Itr
% 0.16/0.40 = ( ^ [Ns2: set @ n,Tr4: dtree] :
% 0.16/0.40 ( complete_Sup_Sup @ ( set @ n )
% 0.16/0.40 @ ( collect @ ( set @ n )
% 0.16/0.40 @ ^ [Uu: set @ n] :
% 0.16/0.40 ? [Tr5: dtree] :
% 0.16/0.40 ( ( Uu
% 0.16/0.40 = ( gram_L1580978439le_Itr @ Ns2 @ Tr5 ) )
% 0.16/0.40 & ( gram_L716654942_subtr @ Ns2 @ Tr5 @ Tr4 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Itr_subtr
% 0.16/0.40 thf(fact_11_inFr2__root__in,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.16/0.40 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 0.16/0.40 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr2_root_in
% 0.16/0.40 thf(fact_12_Fr__subtr,axiom,
% 0.16/0.40 ( gram_L861583724lle_Fr
% 0.16/0.40 = ( ^ [Ns2: set @ n,Tr4: dtree] :
% 0.16/0.40 ( complete_Sup_Sup @ ( set @ t )
% 0.16/0.40 @ ( collect @ ( set @ t )
% 0.16/0.40 @ ^ [Uu: set @ t] :
% 0.16/0.40 ? [Tr5: dtree] :
% 0.16/0.40 ( ( Uu
% 0.16/0.40 = ( gram_L861583724lle_Fr @ Ns2 @ Tr5 ) )
% 0.16/0.40 & ( gram_L716654942_subtr @ Ns2 @ Tr5 @ Tr4 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Fr_subtr
% 0.16/0.40 thf(fact_13_subtr__inFr,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr: dtree,T2: t,Tr1: dtree] :
% 0.16/0.40 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.16/0.40 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.16/0.40 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr_inFr
% 0.16/0.40 thf(fact_14_subtr__subtr2,axiom,
% 0.16/0.40 gram_L716654942_subtr = gram_L1283001940subtr2 ).
% 0.16/0.40
% 0.16/0.40 % subtr_subtr2
% 0.16/0.40 thf(fact_15_inFr__root__in,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.16/0.40 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.16/0.40 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr_root_in
% 0.16/0.40 thf(fact_16_not__root__inFr,axiom,
% 0.16/0.40 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.16/0.40 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % not_root_inFr
% 0.16/0.40 thf(fact_17_subtr2_ORefl,axiom,
% 0.16/0.40 ! [Tr: dtree,Ns: set @ n] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ( gram_L1283001940subtr2 @ Ns @ Tr @ Tr ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr2.Refl
% 0.16/0.40 thf(fact_18_subtr2__rootL__in,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.40 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.16/0.40 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr2_rootL_in
% 0.16/0.40 thf(fact_19_subtr2__rootR__in,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.40 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.16/0.40 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr2_rootR_in
% 0.16/0.40 thf(fact_20_inFr__inFr2,axiom,
% 0.16/0.40 gram_L1333338417e_inFr = gram_L805317441_inFr2 ).
% 0.16/0.40
% 0.16/0.40 % inFr_inFr2
% 0.16/0.40 thf(fact_21_subtr2__trans,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 0.16/0.40 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.16/0.40 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 0.16/0.40 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr2_trans
% 0.16/0.40 thf(fact_22_Fr__def,axiom,
% 0.16/0.40 ( gram_L861583724lle_Fr
% 0.16/0.40 = ( ^ [Ns2: set @ n,Tr4: dtree] : ( collect @ t @ ( gram_L1333338417e_inFr @ Ns2 @ Tr4 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Fr_def
% 0.16/0.40 thf(fact_23_UN__ball__bex__simps_I3_J,axiom,
% 0.16/0.40 ! [D: $tType,A2: set @ ( set @ D ),P2: D > $o] :
% 0.16/0.40 ( ( ? [X: D] :
% 0.16/0.40 ( ( member @ D @ X @ ( complete_Sup_Sup @ ( set @ D ) @ A2 ) )
% 0.16/0.40 & ( P2 @ X ) ) )
% 0.16/0.40 = ( ? [X: set @ D] :
% 0.16/0.40 ( ( member @ ( set @ D ) @ X @ A2 )
% 0.16/0.40 & ? [Y: D] :
% 0.16/0.40 ( ( member @ D @ Y @ X )
% 0.16/0.40 & ( P2 @ Y ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_ball_bex_simps(3)
% 0.16/0.40 thf(fact_24_UN__ball__bex__simps_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ ( set @ A ),P2: A > $o] :
% 0.16/0.40 ( ( ! [X: A] :
% 0.16/0.40 ( ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ A2 ) )
% 0.16/0.40 => ( P2 @ X ) ) )
% 0.16/0.40 = ( ! [X: set @ A] :
% 0.16/0.40 ( ( member @ ( set @ A ) @ X @ A2 )
% 0.16/0.40 => ! [Y: A] :
% 0.16/0.40 ( ( member @ A @ Y @ X )
% 0.16/0.40 => ( P2 @ Y ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_ball_bex_simps(1)
% 0.16/0.40 thf(fact_25_UnionI,axiom,
% 0.16/0.40 ! [A: $tType,X2: set @ A,C2: set @ ( set @ A ),A2: A] :
% 0.16/0.40 ( ( member @ ( set @ A ) @ X2 @ C2 )
% 0.16/0.40 => ( ( member @ A @ A2 @ X2 )
% 0.16/0.40 => ( member @ A @ A2 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UnionI
% 0.16/0.40 thf(fact_26_Union__iff,axiom,
% 0.16/0.40 ! [A: $tType,A2: A,C2: set @ ( set @ A )] :
% 0.16/0.40 ( ( member @ A @ A2 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) )
% 0.16/0.40 = ( ? [X: set @ A] :
% 0.16/0.40 ( ( member @ ( set @ A ) @ X @ C2 )
% 0.16/0.40 & ( member @ A @ A2 @ X ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Union_iff
% 0.16/0.40 thf(fact_27_Union__SetCompr__eq,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: B > ( set @ A ),P2: B > $o] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( collect @ ( set @ A )
% 0.16/0.40 @ ^ [Uu: set @ A] :
% 0.16/0.40 ? [X: B] :
% 0.16/0.40 ( ( Uu
% 0.16/0.40 = ( F @ X ) )
% 0.16/0.40 & ( P2 @ X ) ) ) )
% 0.16/0.40 = ( collect @ A
% 0.16/0.40 @ ^ [A3: A] :
% 0.16/0.40 ? [X: B] :
% 0.16/0.40 ( ( P2 @ X )
% 0.16/0.40 & ( member @ A @ A3 @ ( F @ X ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Union_SetCompr_eq
% 0.16/0.40 thf(fact_28_UnionE,axiom,
% 0.16/0.40 ! [A: $tType,A2: A,C2: set @ ( set @ A )] :
% 0.16/0.40 ( ( member @ A @ A2 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) )
% 0.16/0.40 => ~ ! [X3: set @ A] :
% 0.16/0.40 ( ( member @ A @ A2 @ X3 )
% 0.16/0.40 => ~ ( member @ ( set @ A ) @ X3 @ C2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UnionE
% 0.16/0.40 thf(fact_29_not__root__Fr,axiom,
% 0.16/0.40 ! [Tr: dtree,Ns: set @ n] :
% 0.16/0.40 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ( ( gram_L861583724lle_Fr @ Ns @ Tr )
% 0.16/0.40 = ( bot_bot @ ( set @ t ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % not_root_Fr
% 0.16/0.40 thf(fact_30_Fr__subtr__cont,axiom,
% 0.16/0.40 ( gram_L861583724lle_Fr
% 0.16/0.40 = ( ^ [Ns2: set @ n,Tr4: dtree] :
% 0.16/0.40 ( complete_Sup_Sup @ ( set @ t )
% 0.16/0.40 @ ( collect @ ( set @ t )
% 0.16/0.40 @ ^ [Uu: set @ t] :
% 0.16/0.40 ? [Tr5: dtree] :
% 0.16/0.40 ( ( Uu
% 0.16/0.40 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr5 ) ) )
% 0.16/0.40 & ( gram_L716654942_subtr @ Ns2 @ Tr5 @ Tr4 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Fr_subtr_cont
% 0.16/0.40 thf(fact_31_image2p__def,axiom,
% 0.16/0.40 ! [D: $tType,B: $tType,A: $tType,C: $tType] :
% 0.16/0.40 ( ( bNF_Greatest_image2p @ C @ A @ D @ B )
% 0.16/0.40 = ( ^ [F2: C > A,G: D > B,R: C > D > $o,X: A,Y: B] :
% 0.16/0.40 ? [X4: C,Y2: D] :
% 0.16/0.40 ( ( R @ X4 @ Y2 )
% 0.16/0.40 & ( ( F2 @ X4 )
% 0.16/0.40 = X )
% 0.16/0.40 & ( ( G @ Y2 )
% 0.16/0.40 = Y ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image2p_def
% 0.16/0.40 thf(fact_32_root__Node,axiom,
% 0.16/0.40 ! [N: n,As: set @ ( sum_sum @ t @ dtree )] :
% 0.16/0.40 ( ( root @ ( node @ N @ As ) )
% 0.16/0.40 = N ) ).
% 0.16/0.40
% 0.16/0.40 % root_Node
% 0.16/0.40 thf(fact_33_Sup__bot__conv_I1_J,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [A2: set @ A] :
% 0.16/0.40 ( ( ( complete_Sup_Sup @ A @ A2 )
% 0.16/0.40 = ( bot_bot @ A ) )
% 0.16/0.40 = ( ! [X: A] :
% 0.16/0.40 ( ( member @ A @ X @ A2 )
% 0.16/0.40 => ( X
% 0.16/0.40 = ( bot_bot @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Sup_bot_conv(1)
% 0.16/0.40 thf(fact_34_Sup__bot__conv_I2_J,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [A2: set @ A] :
% 0.16/0.40 ( ( ( bot_bot @ A )
% 0.16/0.40 = ( complete_Sup_Sup @ A @ A2 ) )
% 0.16/0.40 = ( ! [X: A] :
% 0.16/0.40 ( ( member @ A @ X @ A2 )
% 0.16/0.40 => ( X
% 0.16/0.40 = ( bot_bot @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Sup_bot_conv(2)
% 0.16/0.40 thf(fact_35_Sup__empty,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 = ( bot_bot @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Sup_empty
% 0.16/0.40 thf(fact_36_Node__root__cont,axiom,
% 0.16/0.40 ! [Tr: dtree] :
% 0.16/0.40 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 0.16/0.40 = Tr ) ).
% 0.16/0.40
% 0.16/0.40 % Node_root_cont
% 0.16/0.40 thf(fact_37_Union__empty,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( set @ A ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Union_empty
% 0.16/0.40 thf(fact_38_image2pI,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,D: $tType,B: $tType,R2: A > B > $o,X5: A,Y3: B,F: A > C,G2: B > D] :
% 0.16/0.40 ( ( R2 @ X5 @ Y3 )
% 0.16/0.40 => ( bNF_Greatest_image2p @ A @ C @ B @ D @ F @ G2 @ R2 @ ( F @ X5 ) @ ( G2 @ Y3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image2pI
% 0.16/0.40 thf(fact_39_image2pE,axiom,
% 0.16/0.40 ! [D: $tType,B: $tType,A: $tType,C: $tType,F: A > B,G2: C > D,R2: A > C > $o,Fx: B,Gy: D] :
% 0.16/0.40 ( ( bNF_Greatest_image2p @ A @ B @ C @ D @ F @ G2 @ R2 @ Fx @ Gy )
% 0.16/0.40 => ~ ! [X6: A] :
% 0.16/0.40 ( ( Fx
% 0.16/0.40 = ( F @ X6 ) )
% 0.16/0.40 => ! [Y4: C] :
% 0.16/0.40 ( ( Gy
% 0.16/0.40 = ( G2 @ Y4 ) )
% 0.16/0.40 => ~ ( R2 @ X6 @ Y4 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image2pE
% 0.16/0.40 thf(fact_40_empty__Union__conv,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ ( set @ A )] :
% 0.16/0.40 ( ( ( bot_bot @ ( set @ A ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ A ) @ A2 ) )
% 0.16/0.40 = ( ! [X: set @ A] :
% 0.16/0.40 ( ( member @ ( set @ A ) @ X @ A2 )
% 0.16/0.40 => ( X
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % empty_Union_conv
% 0.16/0.40 thf(fact_41_Union__empty__conv,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ ( set @ A )] :
% 0.16/0.40 ( ( ( complete_Sup_Sup @ ( set @ A ) @ A2 )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 = ( ! [X: set @ A] :
% 0.16/0.40 ( ( member @ ( set @ A ) @ X @ A2 )
% 0.16/0.40 => ( X
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Union_empty_conv
% 0.16/0.40 thf(fact_42_dtree__cong,axiom,
% 0.16/0.40 ! [Tr: dtree,Tr6: dtree] :
% 0.16/0.40 ( ( ( root @ Tr )
% 0.16/0.40 = ( root @ Tr6 ) )
% 0.16/0.40 => ( ( ( cont @ Tr )
% 0.16/0.40 = ( cont @ Tr6 ) )
% 0.16/0.40 => ( Tr = Tr6 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % dtree_cong
% 0.16/0.40 thf(fact_43_inFr_OBase,axiom,
% 0.16/0.40 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.16/0.40 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr.Base
% 0.16/0.40 thf(fact_44_inFr2_OBase,axiom,
% 0.16/0.40 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.16/0.40 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr2.Base
% 0.16/0.40 thf(fact_45_mem__Collect__eq,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,P2: A > $o] :
% 0.16/0.40 ( ( member @ A @ A4 @ ( collect @ A @ P2 ) )
% 0.16/0.40 = ( P2 @ A4 ) ) ).
% 0.16/0.40
% 0.16/0.40 % mem_Collect_eq
% 0.16/0.40 thf(fact_46_Collect__mem__eq,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ A] :
% 0.16/0.40 ( ( collect @ A
% 0.16/0.40 @ ^ [X: A] : ( member @ A @ X @ A2 ) )
% 0.16/0.40 = A2 ) ).
% 0.16/0.40
% 0.16/0.40 % Collect_mem_eq
% 0.16/0.40 thf(fact_47_Collect__cong,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.16/0.40 ( ! [X6: A] :
% 0.16/0.40 ( ( P2 @ X6 )
% 0.16/0.40 = ( Q @ X6 ) )
% 0.16/0.40 => ( ( collect @ A @ P2 )
% 0.16/0.40 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Collect_cong
% 0.16/0.40 thf(fact_48_ext,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.16/0.40 ( ! [X6: A] :
% 0.16/0.40 ( ( F @ X6 )
% 0.16/0.40 = ( G2 @ X6 ) )
% 0.16/0.40 => ( F = G2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % ext
% 0.16/0.40 thf(fact_49_inFr__subtr,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.16/0.40 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.16/0.40 => ? [Tr2: dtree] :
% 0.16/0.40 ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr )
% 0.16/0.40 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr_subtr
% 0.16/0.40 thf(fact_50_vimage__empty,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: A > B] :
% 0.16/0.40 ( ( vimage @ A @ B @ F @ ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_empty
% 0.16/0.40 thf(fact_51_vimage__Collect__eq,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: A > B,P2: B > $o] :
% 0.16/0.40 ( ( vimage @ A @ B @ F @ ( collect @ B @ P2 ) )
% 0.16/0.40 = ( collect @ A
% 0.16/0.40 @ ^ [Y: A] : ( P2 @ ( F @ Y ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_Collect_eq
% 0.16/0.40 thf(fact_52_vimage__ident,axiom,
% 0.16/0.40 ! [A: $tType,Y5: set @ A] :
% 0.16/0.40 ( ( vimage @ A @ A
% 0.16/0.40 @ ^ [X: A] : X
% 0.16/0.40 @ Y5 )
% 0.16/0.40 = Y5 ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_ident
% 0.16/0.40 thf(fact_53_vimage__eq,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A4: A,F: A > B,B2: set @ B] :
% 0.16/0.40 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ B2 ) )
% 0.16/0.40 = ( member @ B @ ( F @ A4 ) @ B2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_eq
% 0.16/0.40 thf(fact_54_vimageI,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: B > A,A4: B,B3: A,B2: set @ A] :
% 0.16/0.40 ( ( ( F @ A4 )
% 0.16/0.40 = B3 )
% 0.16/0.40 => ( ( member @ A @ B3 @ B2 )
% 0.16/0.40 => ( member @ B @ A4 @ ( vimage @ B @ A @ F @ B2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimageI
% 0.16/0.40 thf(fact_55_old_Osum_Oinject_I1_J,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,A4: A,A5: A] :
% 0.16/0.40 ( ( ( sum_Inl @ A @ B @ A4 )
% 0.16/0.40 = ( sum_Inl @ A @ B @ A5 ) )
% 0.16/0.40 = ( A4 = A5 ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.inject(1)
% 0.16/0.40 thf(fact_56_sum_Oinject_I1_J,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 0.16/0.40 ( ( ( sum_Inl @ A @ B @ X1 )
% 0.16/0.40 = ( sum_Inl @ A @ B @ Y1 ) )
% 0.16/0.40 = ( X1 = Y1 ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum.inject(1)
% 0.16/0.40 thf(fact_57_empty__Collect__eq,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o] :
% 0.16/0.40 ( ( ( bot_bot @ ( set @ A ) )
% 0.16/0.40 = ( collect @ A @ P2 ) )
% 0.16/0.40 = ( ! [X: A] :
% 0.16/0.40 ~ ( P2 @ X ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % empty_Collect_eq
% 0.16/0.40 thf(fact_58_Collect__empty__eq,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o] :
% 0.16/0.40 ( ( ( collect @ A @ P2 )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 = ( ! [X: A] :
% 0.16/0.40 ~ ( P2 @ X ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Collect_empty_eq
% 0.16/0.40 thf(fact_59_empty__iff,axiom,
% 0.16/0.40 ! [A: $tType,C3: A] :
% 0.16/0.40 ~ ( member @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % empty_iff
% 0.16/0.40 thf(fact_60_all__not__in__conv,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ A] :
% 0.16/0.40 ( ( ! [X: A] :
% 0.16/0.40 ~ ( member @ A @ X @ A2 ) )
% 0.16/0.40 = ( A2
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % all_not_in_conv
% 0.16/0.40 thf(fact_61_bot__set__def,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( bot_bot @ ( set @ A ) )
% 0.16/0.40 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % bot_set_def
% 0.16/0.40 thf(fact_62_emptyE,axiom,
% 0.16/0.40 ! [A: $tType,A4: A] :
% 0.16/0.40 ~ ( member @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % emptyE
% 0.16/0.40 thf(fact_63_equals0D,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ A,A4: A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 => ~ ( member @ A @ A4 @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % equals0D
% 0.16/0.40 thf(fact_64_equals0I,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ A] :
% 0.16/0.40 ( ! [Y4: A] :
% 0.16/0.40 ~ ( member @ A @ Y4 @ A2 )
% 0.16/0.40 => ( A2
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % equals0I
% 0.16/0.40 thf(fact_65_ex__in__conv,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ A] :
% 0.16/0.40 ( ( ? [X: A] : ( member @ A @ X @ A2 ) )
% 0.16/0.40 = ( A2
% 0.16/0.40 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % ex_in_conv
% 0.16/0.40 thf(fact_66_Inl__inject,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X5: A,Y3: A] :
% 0.16/0.40 ( ( ( sum_Inl @ A @ B @ X5 )
% 0.16/0.40 = ( sum_Inl @ A @ B @ Y3 ) )
% 0.16/0.40 => ( X5 = Y3 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Inl_inject
% 0.16/0.40 thf(fact_67_vimageD,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A4: A,F: A > B,A2: set @ B] :
% 0.16/0.40 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ A2 ) )
% 0.16/0.40 => ( member @ B @ ( F @ A4 ) @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimageD
% 0.16/0.40 thf(fact_68_vimageE,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A4: A,F: A > B,B2: set @ B] :
% 0.16/0.40 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ B2 ) )
% 0.16/0.40 => ( member @ B @ ( F @ A4 ) @ B2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimageE
% 0.16/0.40 thf(fact_69_vimageI2,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: B > A,A4: B,A2: set @ A] :
% 0.16/0.40 ( ( member @ A @ ( F @ A4 ) @ A2 )
% 0.16/0.40 => ( member @ B @ A4 @ ( vimage @ B @ A @ F @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimageI2
% 0.16/0.40 thf(fact_70_vimage__Collect,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,P2: B > $o,F: A > B,Q: A > $o] :
% 0.16/0.40 ( ! [X6: A] :
% 0.16/0.40 ( ( P2 @ ( F @ X6 ) )
% 0.16/0.40 = ( Q @ X6 ) )
% 0.16/0.40 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P2 ) )
% 0.16/0.40 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_Collect
% 0.16/0.40 thf(fact_71_empty__def,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( bot_bot @ ( set @ A ) )
% 0.16/0.40 = ( collect @ A
% 0.16/0.40 @ ^ [X: A] : $false ) ) ).
% 0.16/0.40
% 0.16/0.40 % empty_def
% 0.16/0.40 thf(fact_72_vimage__def,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( vimage @ A @ B )
% 0.16/0.40 = ( ^ [F2: A > B,B4: set @ B] :
% 0.16/0.40 ( collect @ A
% 0.16/0.40 @ ^ [X: A] : ( member @ B @ ( F2 @ X ) @ B4 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_def
% 0.16/0.40 thf(fact_73_bot__apply,axiom,
% 0.16/0.40 ! [C: $tType,D: $tType] :
% 0.16/0.40 ( ( bot @ C @ ( type2 @ C ) )
% 0.16/0.40 => ( ( bot_bot @ ( D > C ) )
% 0.16/0.40 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % bot_apply
% 0.16/0.40 thf(fact_74_old_Osum_Osimps_I7_J,axiom,
% 0.16/0.40 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A4: A] :
% 0.16/0.40 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A4 ) )
% 0.16/0.40 = ( F1 @ A4 ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.simps(7)
% 0.16/0.40 thf(fact_75_Set_Ois__empty__def,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( is_empty @ A )
% 0.16/0.40 = ( ^ [A6: set @ A] :
% 0.16/0.40 ( A6
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Set.is_empty_def
% 0.16/0.40 thf(fact_76_inFr_Ocases,axiom,
% 0.16/0.40 ! [A1: set @ n,A22: dtree,A32: t] :
% 0.16/0.40 ( ( gram_L1333338417e_inFr @ A1 @ A22 @ A32 )
% 0.16/0.40 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.40 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 0.16/0.40 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.40 => ! [Tr12: dtree] :
% 0.16/0.40 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 0.16/0.40 => ~ ( gram_L1333338417e_inFr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr.cases
% 0.16/0.40 thf(fact_77_inFr_Osimps,axiom,
% 0.16/0.40 ( gram_L1333338417e_inFr
% 0.16/0.40 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 0.16/0.40 ( ? [Tr4: dtree,Ns2: set @ n,T3: t] :
% 0.16/0.40 ( ( A12 = Ns2 )
% 0.16/0.40 & ( A23 = Tr4 )
% 0.16/0.40 & ( A33 = T3 )
% 0.16/0.40 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.40 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) ) )
% 0.16/0.40 | ? [Tr4: dtree,Ns2: set @ n,Tr13: dtree,T3: t] :
% 0.16/0.40 ( ( A12 = Ns2 )
% 0.16/0.40 & ( A23 = Tr4 )
% 0.16/0.40 & ( A33 = T3 )
% 0.16/0.40 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.40 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 0.16/0.40 & ( gram_L1333338417e_inFr @ Ns2 @ Tr13 @ T3 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr.simps
% 0.16/0.40 thf(fact_78_inFr_Oinducts,axiom,
% 0.16/0.40 ! [X1: set @ n,X22: dtree,X32: t,P2: ( set @ n ) > dtree > t > $o] :
% 0.16/0.40 ( ( gram_L1333338417e_inFr @ X1 @ X22 @ X32 )
% 0.16/0.40 => ( ! [Tr7: dtree,Ns3: set @ n,T4: t] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr7 ) )
% 0.16/0.40 => ( P2 @ Ns3 @ Tr7 @ T4 ) ) )
% 0.16/0.40 => ( ! [Tr7: dtree,Ns3: set @ n,Tr12: dtree,T4: t] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 0.16/0.40 => ( ( gram_L1333338417e_inFr @ Ns3 @ Tr12 @ T4 )
% 0.16/0.40 => ( ( P2 @ Ns3 @ Tr12 @ T4 )
% 0.16/0.40 => ( P2 @ Ns3 @ Tr7 @ T4 ) ) ) ) )
% 0.16/0.40 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr.inducts
% 0.16/0.40 thf(fact_79_Suml_Osimps,axiom,
% 0.16/0.40 ! [B: $tType,C: $tType,A: $tType,F: A > C,X5: A] :
% 0.16/0.40 ( ( sum_Suml @ A @ C @ B @ F @ ( sum_Inl @ A @ B @ X5 ) )
% 0.16/0.40 = ( F @ X5 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Suml.simps
% 0.16/0.40 thf(fact_80_sum_Oinject_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,X22: B,Y22: B] :
% 0.16/0.40 ( ( ( sum_Inr @ B @ A @ X22 )
% 0.16/0.40 = ( sum_Inr @ B @ A @ Y22 ) )
% 0.16/0.40 = ( X22 = Y22 ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum.inject(2)
% 0.16/0.40 thf(fact_81_old_Osum_Oinject_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,B3: B,B5: B] :
% 0.16/0.40 ( ( ( sum_Inr @ B @ A @ B3 )
% 0.16/0.40 = ( sum_Inr @ B @ A @ B5 ) )
% 0.16/0.40 = ( B3 = B5 ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.inject(2)
% 0.16/0.40 thf(fact_82_old_Osum_Osimps_I8_J,axiom,
% 0.16/0.40 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F22: B > T,B3: B] :
% 0.16/0.40 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ B3 ) )
% 0.16/0.40 = ( F22 @ B3 ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.simps(8)
% 0.16/0.40 thf(fact_83_Inr__inject,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,X5: B,Y3: B] :
% 0.16/0.40 ( ( ( sum_Inr @ B @ A @ X5 )
% 0.16/0.40 = ( sum_Inr @ B @ A @ Y3 ) )
% 0.16/0.40 => ( X5 = Y3 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Inr_inject
% 0.16/0.40 thf(fact_84_not__arg__cong__Inr,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X5: A,Y3: A] :
% 0.16/0.40 ( ( X5 != Y3 )
% 0.16/0.40 => ( ( sum_Inr @ A @ B @ X5 )
% 0.16/0.40 != ( sum_Inr @ A @ B @ Y3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % not_arg_cong_Inr
% 0.16/0.40 thf(fact_85_Suml__inject,axiom,
% 0.16/0.40 ! [B: $tType,C: $tType,A: $tType,F: A > C,G2: A > C] :
% 0.16/0.40 ( ( ( sum_Suml @ A @ C @ B @ F )
% 0.16/0.40 = ( sum_Suml @ A @ C @ B @ G2 ) )
% 0.16/0.40 => ( F = G2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Suml_inject
% 0.16/0.40 thf(fact_86_obj__sumE,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.16/0.40 ( ! [X6: A] :
% 0.16/0.40 ( S
% 0.16/0.40 != ( sum_Inl @ A @ B @ X6 ) )
% 0.16/0.40 => ~ ! [X6: B] :
% 0.16/0.40 ( S
% 0.16/0.40 != ( sum_Inr @ B @ A @ X6 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % obj_sumE
% 0.16/0.40 thf(fact_87_sum_Odistinct_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,X1: A,X22: B] :
% 0.16/0.40 ( ( sum_Inl @ A @ B @ X1 )
% 0.16/0.40 != ( sum_Inr @ B @ A @ X22 ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum.distinct(1)
% 0.16/0.40 thf(fact_88_old_Osum_Odistinct_I2_J,axiom,
% 0.16/0.40 ! [B6: $tType,A7: $tType,B7: B6,A8: A7] :
% 0.16/0.40 ( ( sum_Inr @ B6 @ A7 @ B7 )
% 0.16/0.40 != ( sum_Inl @ A7 @ B6 @ A8 ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.distinct(2)
% 0.16/0.40 thf(fact_89_old_Osum_Odistinct_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A4: A,B5: B] :
% 0.16/0.40 ( ( sum_Inl @ A @ B @ A4 )
% 0.16/0.40 != ( sum_Inr @ B @ A @ B5 ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.distinct(1)
% 0.16/0.40 thf(fact_90_sumE,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.16/0.40 ( ! [X6: A] :
% 0.16/0.40 ( S
% 0.16/0.40 != ( sum_Inl @ A @ B @ X6 ) )
% 0.16/0.40 => ~ ! [Y4: B] :
% 0.16/0.40 ( S
% 0.16/0.40 != ( sum_Inr @ B @ A @ Y4 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % sumE
% 0.16/0.40 thf(fact_91_Inr__not__Inl,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,B3: B,A4: A] :
% 0.16/0.40 ( ( sum_Inr @ B @ A @ B3 )
% 0.16/0.40 != ( sum_Inl @ A @ B @ A4 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Inr_not_Inl
% 0.16/0.40 thf(fact_92_split__sum__ex,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.16/0.40 ? [X7: sum_sum @ A @ B] : ( P3 @ X7 ) )
% 0.16/0.40 = ( ^ [P: ( sum_sum @ A @ B ) > $o] :
% 0.16/0.40 ( ? [X: A] : ( P @ ( sum_Inl @ A @ B @ X ) )
% 0.16/0.40 | ? [X: B] : ( P @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % split_sum_ex
% 0.16/0.40 thf(fact_93_split__sum__all,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.16/0.40 ! [X7: sum_sum @ A @ B] : ( P3 @ X7 ) )
% 0.16/0.40 = ( ^ [P: ( sum_sum @ A @ B ) > $o] :
% 0.16/0.40 ( ! [X: A] : ( P @ ( sum_Inl @ A @ B @ X ) )
% 0.16/0.40 & ! [X: B] : ( P @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % split_sum_all
% 0.16/0.40 thf(fact_94_old_Osum_Oexhaust,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,Y3: sum_sum @ A @ B] :
% 0.16/0.40 ( ! [A9: A] :
% 0.16/0.40 ( Y3
% 0.16/0.40 != ( sum_Inl @ A @ B @ A9 ) )
% 0.16/0.40 => ~ ! [B8: B] :
% 0.16/0.40 ( Y3
% 0.16/0.40 != ( sum_Inr @ B @ A @ B8 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.exhaust
% 0.16/0.40 thf(fact_95_old_Osum_Oinducts,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,P2: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 0.16/0.40 ( ! [A9: A] : ( P2 @ ( sum_Inl @ A @ B @ A9 ) )
% 0.16/0.40 => ( ! [B8: B] : ( P2 @ ( sum_Inr @ B @ A @ B8 ) )
% 0.16/0.40 => ( P2 @ Sum ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.inducts
% 0.16/0.40 thf(fact_96_subtr_OStep,axiom,
% 0.16/0.40 ! [Tr3: dtree,Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 0.16/0.40 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 0.16/0.40 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr.Step
% 0.16/0.40 thf(fact_97_subtr_Ocases,axiom,
% 0.16/0.40 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.16/0.40 ( ( gram_L716654942_subtr @ A1 @ A22 @ A32 )
% 0.16/0.40 => ( ( ( A32 = A22 )
% 0.16/0.40 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.16/0.40 => ~ ( ( member @ n @ ( root @ A32 ) @ A1 )
% 0.16/0.40 => ! [Tr23: dtree] :
% 0.16/0.40 ( ( gram_L716654942_subtr @ A1 @ A22 @ Tr23 )
% 0.16/0.40 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ A32 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr.cases
% 0.16/0.40 thf(fact_98_subtr_Osimps,axiom,
% 0.16/0.40 ( gram_L716654942_subtr
% 0.16/0.40 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.16/0.40 ( ? [Tr4: dtree,Ns2: set @ n] :
% 0.16/0.40 ( ( A12 = Ns2 )
% 0.16/0.40 & ( A23 = Tr4 )
% 0.16/0.40 & ( A33 = Tr4 )
% 0.16/0.40 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 0.16/0.40 | ? [Tr32: dtree,Ns2: set @ n,Tr13: dtree,Tr24: dtree] :
% 0.16/0.40 ( ( A12 = Ns2 )
% 0.16/0.40 & ( A23 = Tr13 )
% 0.16/0.40 & ( A33 = Tr32 )
% 0.16/0.40 & ( member @ n @ ( root @ Tr32 ) @ Ns2 )
% 0.16/0.40 & ( gram_L716654942_subtr @ Ns2 @ Tr13 @ Tr24 )
% 0.16/0.40 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr24 ) @ ( cont @ Tr32 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr.simps
% 0.16/0.40 thf(fact_99_subtr__StepL,axiom,
% 0.16/0.40 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.16/0.40 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 0.16/0.40 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr_StepL
% 0.16/0.40 thf(fact_100_subtr_Oinducts,axiom,
% 0.16/0.40 ! [X1: set @ n,X22: dtree,X32: dtree,P2: ( set @ n ) > dtree > dtree > $o] :
% 0.16/0.40 ( ( gram_L716654942_subtr @ X1 @ X22 @ X32 )
% 0.16/0.40 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.16/0.40 => ( P2 @ Ns3 @ Tr7 @ Tr7 ) )
% 0.16/0.40 => ( ! [Tr33: dtree,Ns3: set @ n,Tr12: dtree,Tr23: dtree] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr33 ) @ Ns3 )
% 0.16/0.40 => ( ( gram_L716654942_subtr @ Ns3 @ Tr12 @ Tr23 )
% 0.16/0.40 => ( ( P2 @ Ns3 @ Tr12 @ Tr23 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr33 ) )
% 0.16/0.40 => ( P2 @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 0.16/0.40 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr.inducts
% 0.16/0.40 thf(fact_101_subtr__inductL,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 0.16/0.40 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.40 => ( ! [Ns3: set @ n,Tr7: dtree] : ( Phi @ Ns3 @ Tr7 @ Tr7 )
% 0.16/0.40 => ( ! [Ns3: set @ n,Tr12: dtree,Tr23: dtree,Tr33: dtree] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr12 ) @ Ns3 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.16/0.40 => ( ( gram_L716654942_subtr @ Ns3 @ Tr23 @ Tr33 )
% 0.16/0.40 => ( ( Phi @ Ns3 @ Tr23 @ Tr33 )
% 0.16/0.40 => ( Phi @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 0.16/0.40 => ( Phi @ Ns @ Tr1 @ Tr22 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr_inductL
% 0.16/0.40 thf(fact_102_bot__fun__def,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( bot @ B @ ( type2 @ B ) )
% 0.16/0.40 => ( ( bot_bot @ ( A > B ) )
% 0.16/0.40 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % bot_fun_def
% 0.16/0.40 thf(fact_103_subtr2_Oinducts,axiom,
% 0.16/0.40 ! [X1: set @ n,X22: dtree,X32: dtree,P2: ( set @ n ) > dtree > dtree > $o] :
% 0.16/0.40 ( ( gram_L1283001940subtr2 @ X1 @ X22 @ X32 )
% 0.16/0.40 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.16/0.40 => ( P2 @ Ns3 @ Tr7 @ Tr7 ) )
% 0.16/0.40 => ( ! [Tr12: dtree,Ns3: set @ n,Tr23: dtree,Tr33: dtree] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr12 ) @ Ns3 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.16/0.40 => ( ( gram_L1283001940subtr2 @ Ns3 @ Tr23 @ Tr33 )
% 0.16/0.40 => ( ( P2 @ Ns3 @ Tr23 @ Tr33 )
% 0.16/0.40 => ( P2 @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 0.16/0.40 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr2.inducts
% 0.16/0.40 thf(fact_104_subtr2__StepR,axiom,
% 0.16/0.40 ! [Tr3: dtree,Ns: set @ n,Tr22: dtree,Tr1: dtree] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 0.16/0.40 => ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.16/0.40 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr2_StepR
% 0.16/0.40 thf(fact_105_subtr2_Osimps,axiom,
% 0.16/0.40 ( gram_L1283001940subtr2
% 0.16/0.40 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.16/0.40 ( ? [Tr4: dtree,Ns2: set @ n] :
% 0.16/0.40 ( ( A12 = Ns2 )
% 0.16/0.40 & ( A23 = Tr4 )
% 0.16/0.40 & ( A33 = Tr4 )
% 0.16/0.40 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 0.16/0.40 | ? [Tr13: dtree,Ns2: set @ n,Tr24: dtree,Tr32: dtree] :
% 0.16/0.40 ( ( A12 = Ns2 )
% 0.16/0.40 & ( A23 = Tr13 )
% 0.16/0.40 & ( A33 = Tr32 )
% 0.16/0.40 & ( member @ n @ ( root @ Tr13 ) @ Ns2 )
% 0.16/0.40 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr24 ) )
% 0.16/0.40 & ( gram_L1283001940subtr2 @ Ns2 @ Tr24 @ Tr32 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr2.simps
% 0.16/0.40 thf(fact_106_subtr2_Ocases,axiom,
% 0.16/0.40 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.16/0.40 ( ( gram_L1283001940subtr2 @ A1 @ A22 @ A32 )
% 0.16/0.40 => ( ( ( A32 = A22 )
% 0.16/0.40 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.16/0.40 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.40 => ! [Tr23: dtree] :
% 0.16/0.40 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A22 ) @ ( cont @ Tr23 ) )
% 0.16/0.40 => ~ ( gram_L1283001940subtr2 @ A1 @ Tr23 @ A32 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr2.cases
% 0.16/0.40 thf(fact_107_subtr2_OStep,axiom,
% 0.16/0.40 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.16/0.40 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 0.16/0.40 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % subtr2.Step
% 0.16/0.40 thf(fact_108_inFr_OInd,axiom,
% 0.16/0.40 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,T2: t] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.40 => ( ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 )
% 0.16/0.40 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr.Ind
% 0.16/0.40 thf(fact_109_inItr_OInd,axiom,
% 0.16/0.40 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N: n] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.40 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N )
% 0.16/0.40 => ( gram_L830233218_inItr @ Ns @ Tr @ N ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inItr.Ind
% 0.16/0.40 thf(fact_110_inItr_Ocases,axiom,
% 0.16/0.40 ! [A1: set @ n,A22: dtree,A32: n] :
% 0.16/0.40 ( ( gram_L830233218_inItr @ A1 @ A22 @ A32 )
% 0.16/0.40 => ( ( ( A32
% 0.16/0.40 = ( root @ A22 ) )
% 0.16/0.40 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.16/0.40 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.40 => ! [Tr12: dtree] :
% 0.16/0.40 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 0.16/0.40 => ~ ( gram_L830233218_inItr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inItr.cases
% 0.16/0.40 thf(fact_111_inItr_Osimps,axiom,
% 0.16/0.40 ( gram_L830233218_inItr
% 0.16/0.40 = ( ^ [A12: set @ n,A23: dtree,A33: n] :
% 0.16/0.40 ( ? [Tr4: dtree,Ns2: set @ n] :
% 0.16/0.40 ( ( A12 = Ns2 )
% 0.16/0.40 & ( A23 = Tr4 )
% 0.16/0.40 & ( A33
% 0.16/0.40 = ( root @ Tr4 ) )
% 0.16/0.40 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 0.16/0.40 | ? [Tr4: dtree,Ns2: set @ n,Tr13: dtree,N2: n] :
% 0.16/0.40 ( ( A12 = Ns2 )
% 0.16/0.40 & ( A23 = Tr4 )
% 0.16/0.40 & ( A33 = N2 )
% 0.16/0.40 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.40 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 0.16/0.40 & ( gram_L830233218_inItr @ Ns2 @ Tr13 @ N2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inItr.simps
% 0.16/0.40 thf(fact_112_inItr_Oinducts,axiom,
% 0.16/0.40 ! [X1: set @ n,X22: dtree,X32: n,P2: ( set @ n ) > dtree > n > $o] :
% 0.16/0.40 ( ( gram_L830233218_inItr @ X1 @ X22 @ X32 )
% 0.16/0.40 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.16/0.40 => ( P2 @ Ns3 @ Tr7 @ ( root @ Tr7 ) ) )
% 0.16/0.40 => ( ! [Tr7: dtree,Ns3: set @ n,Tr12: dtree,N3: n] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 0.16/0.40 => ( ( gram_L830233218_inItr @ Ns3 @ Tr12 @ N3 )
% 0.16/0.40 => ( ( P2 @ Ns3 @ Tr12 @ N3 )
% 0.16/0.40 => ( P2 @ Ns3 @ Tr7 @ N3 ) ) ) ) )
% 0.16/0.40 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inItr.inducts
% 0.16/0.40 thf(fact_113_inFr2__Ind,axiom,
% 0.16/0.40 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.16/0.40 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 0.16/0.40 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.40 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr2_Ind
% 0.16/0.40 thf(fact_114_Inl__Inr__False,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,X5: A,Y3: B] :
% 0.16/0.40 ( ( sum_Inl @ A @ B @ X5 )
% 0.16/0.40 != ( sum_Inr @ B @ A @ Y3 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Inl_Inr_False
% 0.16/0.40 thf(fact_115_Inr__Inl__False,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X5: B,Y3: A] :
% 0.16/0.40 ( ( sum_Inr @ B @ A @ X5 )
% 0.16/0.40 != ( sum_Inl @ A @ B @ Y3 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Inr_Inl_False
% 0.16/0.40 thf(fact_116_Inl__Inr__image__cong,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,A2: set @ ( sum_sum @ A @ B ),B2: set @ ( sum_sum @ A @ B )] :
% 0.16/0.40 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A2 )
% 0.16/0.40 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B2 ) )
% 0.16/0.40 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A2 )
% 0.16/0.40 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B2 ) )
% 0.16/0.40 => ( A2 = B2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Inl_Inr_image_cong
% 0.16/0.40 thf(fact_117_bot__empty__eq,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( bot_bot @ ( A > $o ) )
% 0.16/0.40 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % bot_empty_eq
% 0.16/0.40 thf(fact_118_Collect__empty__eq__bot,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o] :
% 0.16/0.40 ( ( ( collect @ A @ P2 )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 = ( P2
% 0.16/0.40 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Collect_empty_eq_bot
% 0.16/0.40 thf(fact_119_obj__sumE__f,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P2: $o] :
% 0.16/0.40 ( ! [X6: A] :
% 0.16/0.40 ( ( S
% 0.16/0.40 = ( F @ ( sum_Inl @ A @ C @ X6 ) ) )
% 0.16/0.40 => P2 )
% 0.16/0.40 => ( ! [X6: C] :
% 0.16/0.40 ( ( S
% 0.16/0.40 = ( F @ ( sum_Inr @ C @ A @ X6 ) ) )
% 0.16/0.40 => P2 )
% 0.16/0.40 => ! [X8: sum_sum @ A @ C] :
% 0.16/0.40 ( ( S
% 0.16/0.40 = ( F @ X8 ) )
% 0.16/0.40 => P2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % obj_sumE_f
% 0.16/0.40 thf(fact_120_inFr2_Oinducts,axiom,
% 0.16/0.40 ! [X1: set @ n,X22: dtree,X32: t,P2: ( set @ n ) > dtree > t > $o] :
% 0.16/0.40 ( ( gram_L805317441_inFr2 @ X1 @ X22 @ X32 )
% 0.16/0.40 => ( ! [Tr7: dtree,Ns3: set @ n,T4: t] :
% 0.16/0.40 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr7 ) )
% 0.16/0.40 => ( P2 @ Ns3 @ Tr7 @ T4 ) ) )
% 0.16/0.40 => ( ! [Tr12: dtree,Tr7: dtree,Ns1: set @ n,T4: t] :
% 0.16/0.40 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 0.16/0.40 => ( ( gram_L805317441_inFr2 @ Ns1 @ Tr12 @ T4 )
% 0.16/0.40 => ( ( P2 @ Ns1 @ Tr12 @ T4 )
% 0.16/0.40 => ( P2 @ ( insert @ n @ ( root @ Tr7 ) @ Ns1 ) @ Tr7 @ T4 ) ) ) )
% 0.16/0.40 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr2.inducts
% 0.16/0.40 thf(fact_121_inFr2_Osimps,axiom,
% 0.16/0.40 ( gram_L805317441_inFr2
% 0.16/0.40 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 0.16/0.40 ( ? [Tr4: dtree,Ns2: set @ n,T3: t] :
% 0.16/0.40 ( ( A12 = Ns2 )
% 0.16/0.40 & ( A23 = Tr4 )
% 0.16/0.40 & ( A33 = T3 )
% 0.16/0.40 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.40 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) ) )
% 0.16/0.40 | ? [Tr13: dtree,Tr4: dtree,Ns12: set @ n,T3: t] :
% 0.16/0.40 ( ( A12
% 0.16/0.40 = ( insert @ n @ ( root @ Tr4 ) @ Ns12 ) )
% 0.16/0.40 & ( A23 = Tr4 )
% 0.16/0.40 & ( A33 = T3 )
% 0.16/0.40 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 0.16/0.40 & ( gram_L805317441_inFr2 @ Ns12 @ Tr13 @ T3 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr2.simps
% 0.16/0.40 thf(fact_122_inFr2_Ocases,axiom,
% 0.16/0.40 ! [A1: set @ n,A22: dtree,A32: t] :
% 0.16/0.40 ( ( gram_L805317441_inFr2 @ A1 @ A22 @ A32 )
% 0.16/0.40 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.40 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 0.16/0.40 => ~ ! [Tr12: dtree,Tr7: dtree,Ns1: set @ n] :
% 0.16/0.40 ( ( A1
% 0.16/0.40 = ( insert @ n @ ( root @ Tr7 ) @ Ns1 ) )
% 0.16/0.40 => ( ( A22 = Tr7 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 0.16/0.40 => ~ ( gram_L805317441_inFr2 @ Ns1 @ Tr12 @ A32 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr2.cases
% 0.16/0.40 thf(fact_123_inFr2_OInd,axiom,
% 0.16/0.40 ! [Tr1: dtree,Tr: dtree,Ns13: set @ n,T2: t] :
% 0.16/0.40 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.40 => ( ( gram_L805317441_inFr2 @ Ns13 @ Tr1 @ T2 )
% 0.16/0.40 => ( gram_L805317441_inFr2 @ ( insert @ n @ ( root @ Tr ) @ Ns13 ) @ Tr @ T2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr2.Ind
% 0.16/0.40 thf(fact_124_insertCI,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,B2: set @ A,B3: A] :
% 0.16/0.40 ( ( ~ ( member @ A @ A4 @ B2 )
% 0.16/0.40 => ( A4 = B3 ) )
% 0.16/0.40 => ( member @ A @ A4 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insertCI
% 0.16/0.40 thf(fact_125_insert__iff,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,B3: A,A2: set @ A] :
% 0.16/0.40 ( ( member @ A @ A4 @ ( insert @ A @ B3 @ A2 ) )
% 0.16/0.40 = ( ( A4 = B3 )
% 0.16/0.40 | ( member @ A @ A4 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_iff
% 0.16/0.40 thf(fact_126_insert__absorb2,axiom,
% 0.16/0.40 ! [A: $tType,X5: A,A2: set @ A] :
% 0.16/0.40 ( ( insert @ A @ X5 @ ( insert @ A @ X5 @ A2 ) )
% 0.16/0.40 = ( insert @ A @ X5 @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_absorb2
% 0.16/0.40 thf(fact_127_singletonI,axiom,
% 0.16/0.40 ! [A: $tType,A4: A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % singletonI
% 0.16/0.40 thf(fact_128_singleton__conv2,axiom,
% 0.16/0.40 ! [A: $tType,A4: A] :
% 0.16/0.40 ( ( collect @ A
% 0.16/0.40 @ ( ^ [Y6: A,Z: A] : ( Y6 = Z )
% 0.16/0.40 @ A4 ) )
% 0.16/0.40 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % singleton_conv2
% 0.16/0.40 thf(fact_129_singleton__conv,axiom,
% 0.16/0.40 ! [A: $tType,A4: A] :
% 0.16/0.40 ( ( collect @ A
% 0.16/0.40 @ ^ [X: A] : ( X = A4 ) )
% 0.16/0.40 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % singleton_conv
% 0.16/0.40 thf(fact_130_singleton__inject,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,B3: A] :
% 0.16/0.40 ( ( ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 => ( A4 = B3 ) ) ).
% 0.16/0.40
% 0.16/0.40 % singleton_inject
% 0.16/0.40 thf(fact_131_insert__not__empty,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,A2: set @ A] :
% 0.16/0.40 ( ( insert @ A @ A4 @ A2 )
% 0.16/0.40 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_not_empty
% 0.16/0.40 thf(fact_132_doubleton__eq__iff,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,B3: A,C3: A,D2: A] :
% 0.16/0.40 ( ( ( insert @ A @ A4 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 = ( insert @ A @ C3 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.16/0.40 = ( ( ( A4 = C3 )
% 0.16/0.40 & ( B3 = D2 ) )
% 0.16/0.40 | ( ( A4 = D2 )
% 0.16/0.40 & ( B3 = C3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % doubleton_eq_iff
% 0.16/0.40 thf(fact_133_singleton__iff,axiom,
% 0.16/0.40 ! [A: $tType,B3: A,A4: A] :
% 0.16/0.40 ( ( member @ A @ B3 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 = ( B3 = A4 ) ) ).
% 0.16/0.40
% 0.16/0.40 % singleton_iff
% 0.16/0.40 thf(fact_134_singletonD,axiom,
% 0.16/0.40 ! [A: $tType,B3: A,A4: A] :
% 0.16/0.40 ( ( member @ A @ B3 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 => ( B3 = A4 ) ) ).
% 0.16/0.40
% 0.16/0.40 % singletonD
% 0.16/0.40 thf(fact_135_insertE,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,B3: A,A2: set @ A] :
% 0.16/0.40 ( ( member @ A @ A4 @ ( insert @ A @ B3 @ A2 ) )
% 0.16/0.40 => ( ( A4 != B3 )
% 0.16/0.40 => ( member @ A @ A4 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insertE
% 0.16/0.40 thf(fact_136_insertI1,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,B2: set @ A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ B2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % insertI1
% 0.16/0.40 thf(fact_137_insertI2,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,B2: set @ A,B3: A] :
% 0.16/0.40 ( ( member @ A @ A4 @ B2 )
% 0.16/0.40 => ( member @ A @ A4 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insertI2
% 0.16/0.40 thf(fact_138_Set_Oset__insert,axiom,
% 0.16/0.40 ! [A: $tType,X5: A,A2: set @ A] :
% 0.16/0.40 ( ( member @ A @ X5 @ A2 )
% 0.16/0.40 => ~ ! [B9: set @ A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( insert @ A @ X5 @ B9 ) )
% 0.16/0.40 => ( member @ A @ X5 @ B9 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Set.set_insert
% 0.16/0.40 thf(fact_139_insert__compr,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( insert @ A )
% 0.16/0.40 = ( ^ [A3: A,B4: set @ A] :
% 0.16/0.40 ( collect @ A
% 0.16/0.40 @ ^ [X: A] :
% 0.16/0.40 ( ( X = A3 )
% 0.16/0.40 | ( member @ A @ X @ B4 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_compr
% 0.16/0.40 thf(fact_140_insert__ident,axiom,
% 0.16/0.40 ! [A: $tType,X5: A,A2: set @ A,B2: set @ A] :
% 0.16/0.40 ( ~ ( member @ A @ X5 @ A2 )
% 0.16/0.40 => ( ~ ( member @ A @ X5 @ B2 )
% 0.16/0.40 => ( ( ( insert @ A @ X5 @ A2 )
% 0.16/0.40 = ( insert @ A @ X5 @ B2 ) )
% 0.16/0.40 = ( A2 = B2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_ident
% 0.16/0.40 thf(fact_141_insert__absorb,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,A2: set @ A] :
% 0.16/0.40 ( ( member @ A @ A4 @ A2 )
% 0.16/0.40 => ( ( insert @ A @ A4 @ A2 )
% 0.16/0.40 = A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_absorb
% 0.16/0.40 thf(fact_142_insert__eq__iff,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,A2: set @ A,B3: A,B2: set @ A] :
% 0.16/0.40 ( ~ ( member @ A @ A4 @ A2 )
% 0.16/0.40 => ( ~ ( member @ A @ B3 @ B2 )
% 0.16/0.40 => ( ( ( insert @ A @ A4 @ A2 )
% 0.16/0.40 = ( insert @ A @ B3 @ B2 ) )
% 0.16/0.40 = ( ( ( A4 = B3 )
% 0.16/0.40 => ( A2 = B2 ) )
% 0.16/0.40 & ( ( A4 != B3 )
% 0.16/0.40 => ? [C4: set @ A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( insert @ A @ B3 @ C4 ) )
% 0.16/0.40 & ~ ( member @ A @ B3 @ C4 )
% 0.16/0.40 & ( B2
% 0.16/0.40 = ( insert @ A @ A4 @ C4 ) )
% 0.16/0.40 & ~ ( member @ A @ A4 @ C4 ) ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_eq_iff
% 0.16/0.40 thf(fact_143_insert__Collect,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,P2: A > $o] :
% 0.16/0.40 ( ( insert @ A @ A4 @ ( collect @ A @ P2 ) )
% 0.16/0.40 = ( collect @ A
% 0.16/0.40 @ ^ [U: A] :
% 0.16/0.40 ( ( U != A4 )
% 0.16/0.40 => ( P2 @ U ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_Collect
% 0.16/0.40 thf(fact_144_insert__commute,axiom,
% 0.16/0.40 ! [A: $tType,X5: A,Y3: A,A2: set @ A] :
% 0.16/0.40 ( ( insert @ A @ X5 @ ( insert @ A @ Y3 @ A2 ) )
% 0.16/0.40 = ( insert @ A @ Y3 @ ( insert @ A @ X5 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_commute
% 0.16/0.40 thf(fact_145_mk__disjoint__insert,axiom,
% 0.16/0.40 ! [A: $tType,A4: A,A2: set @ A] :
% 0.16/0.40 ( ( member @ A @ A4 @ A2 )
% 0.16/0.40 => ? [B9: set @ A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( insert @ A @ A4 @ B9 ) )
% 0.16/0.40 & ~ ( member @ A @ A4 @ B9 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % mk_disjoint_insert
% 0.16/0.40 thf(fact_146_Collect__conv__if2,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o,A4: A] :
% 0.16/0.40 ( ( ( P2 @ A4 )
% 0.16/0.40 => ( ( collect @ A
% 0.16/0.40 @ ^ [X: A] :
% 0.16/0.40 ( ( A4 = X )
% 0.16/0.40 & ( P2 @ X ) ) )
% 0.16/0.40 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.16/0.40 & ( ~ ( P2 @ A4 )
% 0.16/0.40 => ( ( collect @ A
% 0.16/0.40 @ ^ [X: A] :
% 0.16/0.40 ( ( A4 = X )
% 0.16/0.40 & ( P2 @ X ) ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Collect_conv_if2
% 0.16/0.40 thf(fact_147_Collect__conv__if,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o,A4: A] :
% 0.16/0.40 ( ( ( P2 @ A4 )
% 0.16/0.40 => ( ( collect @ A
% 0.16/0.40 @ ^ [X: A] :
% 0.16/0.40 ( ( X = A4 )
% 0.16/0.40 & ( P2 @ X ) ) )
% 0.16/0.40 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.16/0.40 & ( ~ ( P2 @ A4 )
% 0.16/0.40 => ( ( collect @ A
% 0.16/0.40 @ ^ [X: A] :
% 0.16/0.40 ( ( X = A4 )
% 0.16/0.40 & ( P2 @ X ) ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Collect_conv_if
% 0.16/0.40 thf(fact_148_vimage__singleton__eq,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A4: A,F: A > B,B3: B] :
% 0.16/0.40 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ ( insert @ B @ B3 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 0.16/0.40 = ( ( F @ A4 )
% 0.16/0.40 = B3 ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_singleton_eq
% 0.16/0.40 thf(fact_149_inFr__Ind__minus,axiom,
% 0.16/0.40 ! [Ns13: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.16/0.40 ( ( gram_L1333338417e_inFr @ Ns13 @ Tr1 @ T2 )
% 0.16/0.40 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.40 => ( gram_L1333338417e_inFr @ ( insert @ n @ ( root @ Tr ) @ Ns13 ) @ Tr @ T2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % inFr_Ind_minus
% 0.16/0.40 thf(fact_150_ccpo__Sup__singleton,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( comple1141879883l_ccpo @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [X5: A] :
% 0.16/0.40 ( ( complete_Sup_Sup @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 = X5 ) ) ).
% 0.16/0.40
% 0.16/0.40 % ccpo_Sup_singleton
% 0.16/0.40 thf(fact_151_cSup__singleton,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( condit378418413attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [X5: A] :
% 0.16/0.40 ( ( complete_Sup_Sup @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 = X5 ) ) ).
% 0.16/0.40
% 0.16/0.40 % cSup_singleton
% 0.16/0.40 thf(fact_152_is__singletonI,axiom,
% 0.16/0.40 ! [A: $tType,X5: A] : ( is_singleton @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % is_singletonI
% 0.16/0.40 thf(fact_153_the__elem__eq,axiom,
% 0.16/0.40 ! [A: $tType,X5: A] :
% 0.16/0.40 ( ( the_elem @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 = X5 ) ).
% 0.16/0.40
% 0.16/0.40 % the_elem_eq
% 0.16/0.40 thf(fact_154_is__singleton__the__elem,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( is_singleton @ A )
% 0.16/0.40 = ( ^ [A6: set @ A] :
% 0.16/0.40 ( A6
% 0.16/0.40 = ( insert @ A @ ( the_elem @ A @ A6 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % is_singleton_the_elem
% 0.16/0.40 thf(fact_155_is__singletonI_H,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 != ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 => ( ! [X6: A,Y4: A] :
% 0.16/0.40 ( ( member @ A @ X6 @ A2 )
% 0.16/0.40 => ( ( member @ A @ Y4 @ A2 )
% 0.16/0.40 => ( X6 = Y4 ) ) )
% 0.16/0.40 => ( is_singleton @ A @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % is_singletonI'
% 0.16/0.40 thf(fact_156_is__singleton__def,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( is_singleton @ A )
% 0.16/0.40 = ( ^ [A6: set @ A] :
% 0.16/0.40 ? [X: A] :
% 0.16/0.40 ( A6
% 0.16/0.40 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % is_singleton_def
% 0.16/0.40 thf(fact_157_is__singletonE,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ A] :
% 0.16/0.40 ( ( is_singleton @ A @ A2 )
% 0.16/0.40 => ~ ! [X6: A] :
% 0.16/0.40 ( A2
% 0.16/0.40 != ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % is_singletonE
% 0.16/0.40 thf(fact_158_sum__set__simps_I1_J,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X5: A] :
% 0.16/0.40 ( ( basic_setl @ A @ B @ ( sum_Inl @ A @ B @ X5 ) )
% 0.16/0.40 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum_set_simps(1)
% 0.16/0.40 thf(fact_159_sum__set__simps_I4_J,axiom,
% 0.16/0.40 ! [E: $tType,A: $tType,X5: A] :
% 0.16/0.40 ( ( basic_setr @ E @ A @ ( sum_Inr @ A @ E @ X5 ) )
% 0.16/0.40 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum_set_simps(4)
% 0.16/0.40 thf(fact_160_the__elem__def,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( the_elem @ A )
% 0.16/0.40 = ( ^ [X9: set @ A] :
% 0.16/0.40 ( the @ A
% 0.16/0.40 @ ^ [X: A] :
% 0.16/0.40 ( X9
% 0.16/0.40 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % the_elem_def
% 0.16/0.40 thf(fact_161_sum__set__simps_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,X5: A] :
% 0.16/0.40 ( ( basic_setl @ C @ A @ ( sum_Inr @ A @ C @ X5 ) )
% 0.16/0.40 = ( bot_bot @ ( set @ C ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum_set_simps(2)
% 0.16/0.40 thf(fact_162_sum__set__simps_I3_J,axiom,
% 0.16/0.40 ! [A: $tType,D: $tType,X5: A] :
% 0.16/0.40 ( ( basic_setr @ A @ D @ ( sum_Inl @ A @ D @ X5 ) )
% 0.16/0.40 = ( bot_bot @ ( set @ D ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum_set_simps(3)
% 0.16/0.40 thf(fact_163_old_Orec__sum__def,axiom,
% 0.16/0.40 ! [B: $tType,T: $tType,A: $tType] :
% 0.16/0.40 ( ( sum_rec_sum @ A @ T @ B )
% 0.16/0.40 = ( ^ [F12: A > T,F23: B > T,X: sum_sum @ A @ B] : ( the @ T @ ( sum_rec_set_sum @ A @ T @ B @ F12 @ F23 @ X ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.rec_sum_def
% 0.16/0.40 thf(fact_164_the__sym__eq__trivial,axiom,
% 0.16/0.40 ! [A: $tType,X5: A] :
% 0.16/0.40 ( ( the @ A
% 0.16/0.40 @ ( ^ [Y6: A,Z: A] : ( Y6 = Z )
% 0.16/0.40 @ X5 ) )
% 0.16/0.40 = X5 ) ).
% 0.16/0.40
% 0.16/0.40 % the_sym_eq_trivial
% 0.16/0.40 thf(fact_165_the__eq__trivial,axiom,
% 0.16/0.40 ! [A: $tType,A4: A] :
% 0.16/0.40 ( ( the @ A
% 0.16/0.40 @ ^ [X: A] : ( X = A4 ) )
% 0.16/0.40 = A4 ) ).
% 0.16/0.40
% 0.16/0.40 % the_eq_trivial
% 0.16/0.40 thf(fact_166_the__equality,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o,A4: A] :
% 0.16/0.40 ( ( P2 @ A4 )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( P2 @ X6 )
% 0.16/0.40 => ( X6 = A4 ) )
% 0.16/0.40 => ( ( the @ A @ P2 )
% 0.16/0.40 = A4 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % the_equality
% 0.16/0.40 thf(fact_167_theI,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o,A4: A] :
% 0.16/0.40 ( ( P2 @ A4 )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( P2 @ X6 )
% 0.16/0.40 => ( X6 = A4 ) )
% 0.16/0.40 => ( P2 @ ( the @ A @ P2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % theI
% 0.16/0.40 thf(fact_168_theI_H,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o] :
% 0.16/0.40 ( ? [X8: A] :
% 0.16/0.40 ( ( P2 @ X8 )
% 0.16/0.40 & ! [Y4: A] :
% 0.16/0.40 ( ( P2 @ Y4 )
% 0.16/0.40 => ( Y4 = X8 ) ) )
% 0.16/0.40 => ( P2 @ ( the @ A @ P2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % theI'
% 0.16/0.40 thf(fact_169_theI2,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o,A4: A,Q: A > $o] :
% 0.16/0.40 ( ( P2 @ A4 )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( P2 @ X6 )
% 0.16/0.40 => ( X6 = A4 ) )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( P2 @ X6 )
% 0.16/0.40 => ( Q @ X6 ) )
% 0.16/0.40 => ( Q @ ( the @ A @ P2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % theI2
% 0.16/0.40 thf(fact_170_If__def,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( if @ A )
% 0.16/0.40 = ( ^ [P: $o,X: A,Y: A] :
% 0.16/0.40 ( the @ A
% 0.16/0.40 @ ^ [Z2: A] :
% 0.16/0.40 ( ( P
% 0.16/0.40 => ( Z2 = X ) )
% 0.16/0.40 & ( ~ P
% 0.16/0.40 => ( Z2 = Y ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % If_def
% 0.16/0.40 thf(fact_171_the1I2,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.16/0.40 ( ? [X8: A] :
% 0.16/0.40 ( ( P2 @ X8 )
% 0.16/0.40 & ! [Y4: A] :
% 0.16/0.40 ( ( P2 @ Y4 )
% 0.16/0.40 => ( Y4 = X8 ) ) )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( P2 @ X6 )
% 0.16/0.40 => ( Q @ X6 ) )
% 0.16/0.40 => ( Q @ ( the @ A @ P2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % the1I2
% 0.16/0.40 thf(fact_172_the1__equality,axiom,
% 0.16/0.40 ! [A: $tType,P2: A > $o,A4: A] :
% 0.16/0.40 ( ? [X8: A] :
% 0.16/0.40 ( ( P2 @ X8 )
% 0.16/0.40 & ! [Y4: A] :
% 0.16/0.40 ( ( P2 @ Y4 )
% 0.16/0.40 => ( Y4 = X8 ) ) )
% 0.16/0.40 => ( ( P2 @ A4 )
% 0.16/0.40 => ( ( the @ A @ P2 )
% 0.16/0.40 = A4 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % the1_equality
% 0.16/0.40 thf(fact_173_setl_Oinducts,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X5: A,S: sum_sum @ A @ B,P2: A > $o] :
% 0.16/0.40 ( ( member @ A @ X5 @ ( basic_setl @ A @ B @ S ) )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( S
% 0.16/0.40 = ( sum_Inl @ A @ B @ X6 ) )
% 0.16/0.40 => ( P2 @ X6 ) )
% 0.16/0.40 => ( P2 @ X5 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % setl.inducts
% 0.16/0.40 thf(fact_174_setl_Ointros,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,S: sum_sum @ A @ B,X5: A] :
% 0.16/0.40 ( ( S
% 0.16/0.40 = ( sum_Inl @ A @ B @ X5 ) )
% 0.16/0.40 => ( member @ A @ X5 @ ( basic_setl @ A @ B @ S ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % setl.intros
% 0.16/0.40 thf(fact_175_setl_Osimps,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,A4: A,S: sum_sum @ A @ B] :
% 0.16/0.40 ( ( member @ A @ A4 @ ( basic_setl @ A @ B @ S ) )
% 0.16/0.40 = ( ? [X: A] :
% 0.16/0.40 ( ( A4 = X )
% 0.16/0.40 & ( S
% 0.16/0.40 = ( sum_Inl @ A @ B @ X ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % setl.simps
% 0.16/0.40 thf(fact_176_setr_Oinducts,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,X5: B,S: sum_sum @ A @ B,P2: B > $o] :
% 0.16/0.40 ( ( member @ B @ X5 @ ( basic_setr @ A @ B @ S ) )
% 0.16/0.40 => ( ! [X6: B] :
% 0.16/0.40 ( ( S
% 0.16/0.40 = ( sum_Inr @ B @ A @ X6 ) )
% 0.16/0.40 => ( P2 @ X6 ) )
% 0.16/0.40 => ( P2 @ X5 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % setr.inducts
% 0.16/0.40 thf(fact_177_setr_Ointros,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,S: sum_sum @ A @ B,X5: B] :
% 0.16/0.40 ( ( S
% 0.16/0.40 = ( sum_Inr @ B @ A @ X5 ) )
% 0.16/0.40 => ( member @ B @ X5 @ ( basic_setr @ A @ B @ S ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % setr.intros
% 0.16/0.40 thf(fact_178_setr_Osimps,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A4: B,S: sum_sum @ A @ B] :
% 0.16/0.40 ( ( member @ B @ A4 @ ( basic_setr @ A @ B @ S ) )
% 0.16/0.40 = ( ? [X: B] :
% 0.16/0.40 ( ( A4 = X )
% 0.16/0.40 & ( S
% 0.16/0.40 = ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % setr.simps
% 0.16/0.40 thf(fact_179_setr_Ocases,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A4: B,S: sum_sum @ A @ B] :
% 0.16/0.40 ( ( member @ B @ A4 @ ( basic_setr @ A @ B @ S ) )
% 0.16/0.40 => ( S
% 0.16/0.40 = ( sum_Inr @ B @ A @ A4 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % setr.cases
% 0.16/0.40 thf(fact_180_setl_Ocases,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,A4: A,S: sum_sum @ A @ B] :
% 0.16/0.40 ( ( member @ A @ A4 @ ( basic_setl @ A @ B @ S ) )
% 0.16/0.40 => ( S
% 0.16/0.40 = ( sum_Inl @ A @ B @ A4 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % setl.cases
% 0.16/0.40 thf(fact_181_vimage__eq__UN,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( vimage @ A @ B )
% 0.16/0.40 = ( ^ [F2: A > B,B4: set @ B] :
% 0.16/0.40 ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ B @ ( set @ A )
% 0.16/0.40 @ ^ [Y: B] : ( vimage @ A @ B @ F2 @ ( insert @ B @ Y @ ( bot_bot @ ( set @ B ) ) ) )
% 0.16/0.40 @ B4 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_eq_UN
% 0.16/0.40 thf(fact_182_sum__set__defs_I2_J,axiom,
% 0.16/0.40 ! [C: $tType,D: $tType] :
% 0.16/0.40 ( ( basic_setr @ C @ D )
% 0.16/0.40 = ( sum_case_sum @ C @ ( set @ D ) @ D
% 0.16/0.40 @ ^ [A3: C] : ( bot_bot @ ( set @ D ) )
% 0.16/0.40 @ ^ [Z2: D] : ( insert @ D @ Z2 @ ( bot_bot @ ( set @ D ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum_set_defs(2)
% 0.16/0.40 thf(fact_183_sum__set__defs_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType] :
% 0.16/0.40 ( ( basic_setl @ A @ B )
% 0.16/0.40 = ( sum_case_sum @ A @ ( set @ A ) @ B
% 0.16/0.40 @ ^ [Z2: A] : ( insert @ A @ Z2 @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 @ ^ [B10: B] : ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum_set_defs(1)
% 0.16/0.40 thf(fact_184_image__eqI,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,B3: A,F: B > A,X5: B,A2: set @ B] :
% 0.16/0.40 ( ( B3
% 0.16/0.40 = ( F @ X5 ) )
% 0.16/0.40 => ( ( member @ B @ X5 @ A2 )
% 0.16/0.40 => ( member @ A @ B3 @ ( image @ B @ A @ F @ A2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_eqI
% 0.16/0.40 thf(fact_185_image__ident,axiom,
% 0.16/0.40 ! [A: $tType,Y5: set @ A] :
% 0.16/0.40 ( ( image @ A @ A
% 0.16/0.40 @ ^ [X: A] : X
% 0.16/0.40 @ Y5 )
% 0.16/0.40 = Y5 ) ).
% 0.16/0.40
% 0.16/0.40 % image_ident
% 0.16/0.40 thf(fact_186_case__sum__KK,axiom,
% 0.16/0.40 ! [C: $tType,B: $tType,A: $tType,A4: C] :
% 0.16/0.40 ( ( sum_case_sum @ A @ C @ B
% 0.16/0.40 @ ^ [X: A] : A4
% 0.16/0.40 @ ^ [X: B] : A4 )
% 0.16/0.40 = ( ^ [X: sum_sum @ A @ B] : A4 ) ) ).
% 0.16/0.40
% 0.16/0.40 % case_sum_KK
% 0.16/0.40 thf(fact_187_image__is__empty,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: B > A,A2: set @ B] :
% 0.16/0.40 ( ( ( image @ B @ A @ F @ A2 )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 = ( A2
% 0.16/0.40 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_is_empty
% 0.16/0.40 thf(fact_188_empty__is__image,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: B > A,A2: set @ B] :
% 0.16/0.40 ( ( ( bot_bot @ ( set @ A ) )
% 0.16/0.40 = ( image @ B @ A @ F @ A2 ) )
% 0.16/0.40 = ( A2
% 0.16/0.40 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % empty_is_image
% 0.16/0.40 thf(fact_189_image__empty,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: B > A] :
% 0.16/0.40 ( ( image @ B @ A @ F @ ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_empty
% 0.16/0.40 thf(fact_190_insert__image,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X5: A,A2: set @ A,F: A > B] :
% 0.16/0.40 ( ( member @ A @ X5 @ A2 )
% 0.16/0.40 => ( ( insert @ B @ ( F @ X5 ) @ ( image @ A @ B @ F @ A2 ) )
% 0.16/0.40 = ( image @ A @ B @ F @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % insert_image
% 0.16/0.40 thf(fact_191_image__insert,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: B > A,A4: B,B2: set @ B] :
% 0.16/0.40 ( ( image @ B @ A @ F @ ( insert @ B @ A4 @ B2 ) )
% 0.16/0.40 = ( insert @ A @ ( F @ A4 ) @ ( image @ B @ A @ F @ B2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_insert
% 0.16/0.40 thf(fact_192_ball__UN,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,B2: B > ( set @ A ),A2: set @ B,P2: A > $o] :
% 0.16/0.40 ( ( ! [X: A] :
% 0.16/0.40 ( ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 0.16/0.40 => ( P2 @ X ) ) )
% 0.16/0.40 = ( ! [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 => ! [Y: A] :
% 0.16/0.40 ( ( member @ A @ Y @ ( B2 @ X ) )
% 0.16/0.40 => ( P2 @ Y ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % ball_UN
% 0.16/0.40 thf(fact_193_bex__UN,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,B2: B > ( set @ A ),A2: set @ B,P2: A > $o] :
% 0.16/0.40 ( ( ? [X: A] :
% 0.16/0.40 ( ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 0.16/0.40 & ( P2 @ X ) ) )
% 0.16/0.40 = ( ? [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 & ? [Y: A] :
% 0.16/0.40 ( ( member @ A @ Y @ ( B2 @ X ) )
% 0.16/0.40 & ( P2 @ Y ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % bex_UN
% 0.16/0.40 thf(fact_194_UN__ball__bex__simps_I2_J,axiom,
% 0.16/0.40 ! [C: $tType,B: $tType,B2: B > ( set @ C ),A2: set @ B,P2: C > $o] :
% 0.16/0.40 ( ( ! [X: C] :
% 0.16/0.40 ( ( member @ C @ X @ ( complete_Sup_Sup @ ( set @ C ) @ ( image @ B @ ( set @ C ) @ B2 @ A2 ) ) )
% 0.16/0.40 => ( P2 @ X ) ) )
% 0.16/0.40 = ( ! [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 => ! [Y: C] :
% 0.16/0.40 ( ( member @ C @ Y @ ( B2 @ X ) )
% 0.16/0.40 => ( P2 @ Y ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_ball_bex_simps(2)
% 0.16/0.40 thf(fact_195_UN__ball__bex__simps_I4_J,axiom,
% 0.16/0.40 ! [F3: $tType,E: $tType,B2: E > ( set @ F3 ),A2: set @ E,P2: F3 > $o] :
% 0.16/0.40 ( ( ? [X: F3] :
% 0.16/0.40 ( ( member @ F3 @ X @ ( complete_Sup_Sup @ ( set @ F3 ) @ ( image @ E @ ( set @ F3 ) @ B2 @ A2 ) ) )
% 0.16/0.40 & ( P2 @ X ) ) )
% 0.16/0.40 = ( ? [X: E] :
% 0.16/0.40 ( ( member @ E @ X @ A2 )
% 0.16/0.40 & ? [Y: F3] :
% 0.16/0.40 ( ( member @ F3 @ Y @ ( B2 @ X ) )
% 0.16/0.40 & ( P2 @ Y ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_ball_bex_simps(4)
% 0.16/0.40 thf(fact_196_SUP__identity__eq,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [A2: set @ A] :
% 0.16/0.40 ( ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ A @ A
% 0.16/0.40 @ ^ [X: A] : X
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( complete_Sup_Sup @ A @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_identity_eq
% 0.16/0.40 thf(fact_197_SUP__apply,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType] :
% 0.16/0.40 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [F: C > B > A,A2: set @ C,X5: B] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( B > A ) @ ( image @ C @ ( B > A ) @ F @ A2 ) @ X5 )
% 0.16/0.40 = ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ C @ A
% 0.16/0.40 @ ^ [Y: C] : ( F @ Y @ X5 )
% 0.16/0.40 @ A2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_apply
% 0.16/0.40 thf(fact_198_UN__I,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,A4: A,A2: set @ A,B3: B,B2: A > ( set @ B )] :
% 0.16/0.40 ( ( member @ A @ A4 @ A2 )
% 0.16/0.40 => ( ( member @ B @ B3 @ ( B2 @ A4 ) )
% 0.16/0.40 => ( member @ B @ B3 @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ A @ ( set @ B ) @ B2 @ A2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_I
% 0.16/0.40 thf(fact_199_UN__iff,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,B3: A,B2: B > ( set @ A ),A2: set @ B] :
% 0.16/0.40 ( ( member @ A @ B3 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 0.16/0.40 = ( ? [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 & ( member @ A @ B3 @ ( B2 @ X ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_iff
% 0.16/0.40 thf(fact_200_SUP__bot,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [A2: set @ B] :
% 0.16/0.40 ( ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ B @ A
% 0.16/0.40 @ ^ [X: B] : ( bot_bot @ A )
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( bot_bot @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_bot
% 0.16/0.40 thf(fact_201_SUP__bot__conv_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [B2: B > A,A2: set @ B] :
% 0.16/0.40 ( ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ B2 @ A2 ) )
% 0.16/0.40 = ( bot_bot @ A ) )
% 0.16/0.40 = ( ! [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 => ( ( B2 @ X )
% 0.16/0.40 = ( bot_bot @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_bot_conv(1)
% 0.16/0.40 thf(fact_202_SUP__bot__conv_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [B2: B > A,A2: set @ B] :
% 0.16/0.40 ( ( ( bot_bot @ A )
% 0.16/0.40 = ( complete_Sup_Sup @ A @ ( image @ B @ A @ B2 @ A2 ) ) )
% 0.16/0.40 = ( ! [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 => ( ( B2 @ X )
% 0.16/0.40 = ( bot_bot @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_bot_conv(2)
% 0.16/0.40 thf(fact_203_cSUP__const,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( condit378418413attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [A2: set @ B,C3: A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 != ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ B @ A
% 0.16/0.40 @ ^ [X: B] : C3
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = C3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % cSUP_const
% 0.16/0.40 thf(fact_204_SUP__const,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [A2: set @ B,F: A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 != ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ B @ A
% 0.16/0.40 @ ^ [I: B] : F
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = F ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_const
% 0.16/0.40 thf(fact_205_UN__constant,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,A2: set @ B,C3: set @ A] :
% 0.16/0.40 ( ( ( A2
% 0.16/0.40 = ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ B @ ( set @ A )
% 0.16/0.40 @ ^ [Y: B] : C3
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 & ( ( A2
% 0.16/0.40 != ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ B @ ( set @ A )
% 0.16/0.40 @ ^ [Y: B] : C3
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = C3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_constant
% 0.16/0.40 thf(fact_206_SUP__empty,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [F: B > A] :
% 0.16/0.40 ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ ( bot_bot @ ( set @ B ) ) ) )
% 0.16/0.40 = ( bot_bot @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_empty
% 0.16/0.40 thf(fact_207_UN__simps_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C2: set @ B,A4: A,B2: B > ( set @ A )] :
% 0.16/0.40 ( ( ( C2
% 0.16/0.40 = ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ B @ ( set @ A )
% 0.16/0.40 @ ^ [X: B] : ( insert @ A @ A4 @ ( B2 @ X ) )
% 0.16/0.40 @ C2 ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 & ( ( C2
% 0.16/0.40 != ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ B @ ( set @ A )
% 0.16/0.40 @ ^ [X: B] : ( insert @ A @ A4 @ ( B2 @ X ) )
% 0.16/0.40 @ C2 ) )
% 0.16/0.40 = ( insert @ A @ A4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ C2 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_simps(1)
% 0.16/0.40 thf(fact_208_UN__singleton,axiom,
% 0.16/0.40 ! [A: $tType,A2: set @ A] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ A @ ( set @ A )
% 0.16/0.40 @ ^ [X: A] : ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = A2 ) ).
% 0.16/0.40
% 0.16/0.40 % UN_singleton
% 0.16/0.40 thf(fact_209_SUP__eq__const,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [I2: set @ B,F: B > A,X5: A] :
% 0.16/0.40 ( ( I2
% 0.16/0.40 != ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ! [I3: B] :
% 0.16/0.40 ( ( member @ B @ I3 @ I2 )
% 0.16/0.40 => ( ( F @ I3 )
% 0.16/0.40 = X5 ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ I2 ) )
% 0.16/0.40 = X5 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_eq_const
% 0.16/0.40 thf(fact_210_Sup_OSUP__cong,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A2: set @ B,B2: set @ B,C2: B > A,D3: B > A,Sup: ( set @ A ) > A] :
% 0.16/0.40 ( ( A2 = B2 )
% 0.16/0.40 => ( ! [X6: B] :
% 0.16/0.40 ( ( member @ B @ X6 @ B2 )
% 0.16/0.40 => ( ( C2 @ X6 )
% 0.16/0.40 = ( D3 @ X6 ) ) )
% 0.16/0.40 => ( ( Sup @ ( image @ B @ A @ C2 @ A2 ) )
% 0.16/0.40 = ( Sup @ ( image @ B @ A @ D3 @ B2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Sup.SUP_cong
% 0.16/0.40 thf(fact_211_Inf_OINF__cong,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A2: set @ B,B2: set @ B,C2: B > A,D3: B > A,Inf: ( set @ A ) > A] :
% 0.16/0.40 ( ( A2 = B2 )
% 0.16/0.40 => ( ! [X6: B] :
% 0.16/0.40 ( ( member @ B @ X6 @ B2 )
% 0.16/0.40 => ( ( C2 @ X6 )
% 0.16/0.40 = ( D3 @ X6 ) ) )
% 0.16/0.40 => ( ( Inf @ ( image @ B @ A @ C2 @ A2 ) )
% 0.16/0.40 = ( Inf @ ( image @ B @ A @ D3 @ B2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Inf.INF_cong
% 0.16/0.40 thf(fact_212_case__sum__inject,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,B: $tType,F1: A > C,F22: B > C,G1: A > C,G22: B > C] :
% 0.16/0.40 ( ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 )
% 0.16/0.40 = ( sum_case_sum @ A @ C @ B @ G1 @ G22 ) )
% 0.16/0.40 => ~ ( ( F1 = G1 )
% 0.16/0.40 => ( F22 != G22 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % case_sum_inject
% 0.16/0.40 thf(fact_213_rev__image__eqI,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X5: A,A2: set @ A,B3: B,F: A > B] :
% 0.16/0.40 ( ( member @ A @ X5 @ A2 )
% 0.16/0.40 => ( ( B3
% 0.16/0.40 = ( F @ X5 ) )
% 0.16/0.40 => ( member @ B @ B3 @ ( image @ A @ B @ F @ A2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % rev_image_eqI
% 0.16/0.40 thf(fact_214_ball__imageD,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P2: A > $o] :
% 0.16/0.40 ( ! [X6: A] :
% 0.16/0.40 ( ( member @ A @ X6 @ ( image @ B @ A @ F @ A2 ) )
% 0.16/0.40 => ( P2 @ X6 ) )
% 0.16/0.40 => ! [X8: B] :
% 0.16/0.40 ( ( member @ B @ X8 @ A2 )
% 0.16/0.40 => ( P2 @ ( F @ X8 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % ball_imageD
% 0.16/0.40 thf(fact_215_image__cong,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,M: set @ A,N4: set @ A,F: A > B,G2: A > B] :
% 0.16/0.40 ( ( M = N4 )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( member @ A @ X6 @ N4 )
% 0.16/0.40 => ( ( F @ X6 )
% 0.16/0.40 = ( G2 @ X6 ) ) )
% 0.16/0.40 => ( ( image @ A @ B @ F @ M )
% 0.16/0.40 = ( image @ A @ B @ G2 @ N4 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_cong
% 0.16/0.40 thf(fact_216_bex__imageD,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P2: A > $o] :
% 0.16/0.40 ( ? [X8: A] :
% 0.16/0.40 ( ( member @ A @ X8 @ ( image @ B @ A @ F @ A2 ) )
% 0.16/0.40 & ( P2 @ X8 ) )
% 0.16/0.40 => ? [X6: B] :
% 0.16/0.40 ( ( member @ B @ X6 @ A2 )
% 0.16/0.40 & ( P2 @ ( F @ X6 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % bex_imageD
% 0.16/0.40 thf(fact_217_image__iff,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,Z3: A,F: B > A,A2: set @ B] :
% 0.16/0.40 ( ( member @ A @ Z3 @ ( image @ B @ A @ F @ A2 ) )
% 0.16/0.40 = ( ? [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 & ( Z3
% 0.16/0.40 = ( F @ X ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_iff
% 0.16/0.40 thf(fact_218_imageI,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X5: A,A2: set @ A,F: A > B] :
% 0.16/0.40 ( ( member @ A @ X5 @ A2 )
% 0.16/0.40 => ( member @ B @ ( F @ X5 ) @ ( image @ A @ B @ F @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % imageI
% 0.16/0.40 thf(fact_219_SUP__cong,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType] :
% 0.16/0.40 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [A2: set @ B,B2: set @ B,C2: B > A,D3: B > A] :
% 0.16/0.40 ( ( A2 = B2 )
% 0.16/0.40 => ( ! [X6: B] :
% 0.16/0.40 ( ( member @ B @ X6 @ B2 )
% 0.16/0.40 => ( ( C2 @ X6 )
% 0.16/0.40 = ( D3 @ X6 ) ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ C2 @ A2 ) )
% 0.16/0.40 = ( complete_Sup_Sup @ A @ ( image @ B @ A @ D3 @ B2 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_cong
% 0.16/0.40 thf(fact_220_Sup__SUP__eq,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( A > $o ) )
% 0.16/0.40 = ( ^ [S2: set @ ( A > $o ),X: A] : ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ ( A > $o ) @ ( set @ A ) @ ( collect @ A ) @ S2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Sup_SUP_eq
% 0.16/0.40 thf(fact_221_case__sum__step_I1_J,axiom,
% 0.16/0.40 ! [D: $tType,A: $tType,C: $tType,B: $tType,F4: B > A,G3: C > A,G2: D > A,P4: sum_sum @ B @ C] :
% 0.16/0.40 ( ( sum_case_sum @ ( sum_sum @ B @ C ) @ A @ D @ ( sum_case_sum @ B @ A @ C @ F4 @ G3 ) @ G2 @ ( sum_Inl @ ( sum_sum @ B @ C ) @ D @ P4 ) )
% 0.16/0.40 = ( sum_case_sum @ B @ A @ C @ F4 @ G3 @ P4 ) ) ).
% 0.16/0.40
% 0.16/0.40 % case_sum_step(1)
% 0.16/0.40 thf(fact_222_case__sum__step_I2_J,axiom,
% 0.16/0.40 ! [E: $tType,A: $tType,C: $tType,B: $tType,F: E > A,F4: B > A,G3: C > A,P4: sum_sum @ B @ C] :
% 0.16/0.40 ( ( sum_case_sum @ E @ A @ ( sum_sum @ B @ C ) @ F @ ( sum_case_sum @ B @ A @ C @ F4 @ G3 ) @ ( sum_Inr @ ( sum_sum @ B @ C ) @ E @ P4 ) )
% 0.16/0.40 = ( sum_case_sum @ B @ A @ C @ F4 @ G3 @ P4 ) ) ).
% 0.16/0.40
% 0.16/0.40 % case_sum_step(2)
% 0.16/0.40 thf(fact_223_old_Osum_Osimps_I5_J,axiom,
% 0.16/0.40 ! [B: $tType,C: $tType,A: $tType,F1: A > C,F22: B > C,X1: A] :
% 0.16/0.40 ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ X1 ) )
% 0.16/0.40 = ( F1 @ X1 ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.simps(5)
% 0.16/0.40 thf(fact_224_old_Osum_Osimps_I6_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,B: $tType,F1: A > C,F22: B > C,X22: B] :
% 0.16/0.40 ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ X22 ) )
% 0.16/0.40 = ( F22 @ X22 ) ) ).
% 0.16/0.40
% 0.16/0.40 % old.sum.simps(6)
% 0.16/0.40 thf(fact_225_setcompr__eq__image,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: B > A,P2: B > $o] :
% 0.16/0.40 ( ( collect @ A
% 0.16/0.40 @ ^ [Uu: A] :
% 0.16/0.40 ? [X: B] :
% 0.16/0.40 ( ( Uu
% 0.16/0.40 = ( F @ X ) )
% 0.16/0.40 & ( P2 @ X ) ) )
% 0.16/0.40 = ( image @ B @ A @ F @ ( collect @ B @ P2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % setcompr_eq_image
% 0.16/0.40 thf(fact_226_Setcompr__eq__image,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: B > A,A2: set @ B] :
% 0.16/0.40 ( ( collect @ A
% 0.16/0.40 @ ^ [Uu: A] :
% 0.16/0.40 ? [X: B] :
% 0.16/0.40 ( ( Uu
% 0.16/0.40 = ( F @ X ) )
% 0.16/0.40 & ( member @ B @ X @ A2 ) ) )
% 0.16/0.40 = ( image @ B @ A @ F @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Setcompr_eq_image
% 0.16/0.40 thf(fact_227_SUP__commute,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [F: B > C > A,B2: set @ C,A2: set @ B] :
% 0.16/0.40 ( ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ B @ A
% 0.16/0.40 @ ^ [I: B] : ( complete_Sup_Sup @ A @ ( image @ C @ A @ ( F @ I ) @ B2 ) )
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ C @ A
% 0.16/0.40 @ ^ [J: C] :
% 0.16/0.40 ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ B @ A
% 0.16/0.40 @ ^ [I: B] : ( F @ I @ J )
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 @ B2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_commute
% 0.16/0.40 thf(fact_228_UN__extend__simps_I9_J,axiom,
% 0.16/0.40 ! [S3: $tType,R3: $tType,Q2: $tType,C2: R3 > ( set @ S3 ),B2: Q2 > ( set @ R3 ),A2: set @ Q2] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( set @ S3 )
% 0.16/0.40 @ ( image @ Q2 @ ( set @ S3 )
% 0.16/0.40 @ ^ [X: Q2] : ( complete_Sup_Sup @ ( set @ S3 ) @ ( image @ R3 @ ( set @ S3 ) @ C2 @ ( B2 @ X ) ) )
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ S3 ) @ ( image @ R3 @ ( set @ S3 ) @ C2 @ ( complete_Sup_Sup @ ( set @ R3 ) @ ( image @ Q2 @ ( set @ R3 ) @ B2 @ A2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_extend_simps(9)
% 0.16/0.40 thf(fact_229_UN__E,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,B3: A,B2: B > ( set @ A ),A2: set @ B] :
% 0.16/0.40 ( ( member @ A @ B3 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 0.16/0.40 => ~ ! [X6: B] :
% 0.16/0.40 ( ( member @ B @ X6 @ A2 )
% 0.16/0.40 => ~ ( member @ A @ B3 @ ( B2 @ X6 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_E
% 0.16/0.40 thf(fact_230_UN__UN__flatten,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType,C2: B > ( set @ A ),B2: C > ( set @ B ),A2: set @ C] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ C2 @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ C @ ( set @ B ) @ B2 @ A2 ) ) ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ C @ ( set @ A )
% 0.16/0.40 @ ^ [Y: C] : ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ C2 @ ( B2 @ Y ) ) )
% 0.16/0.40 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_UN_flatten
% 0.16/0.40 thf(fact_231_SUP__UNION,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [F: B > A,G2: C > ( set @ B ),A2: set @ C] :
% 0.16/0.40 ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ C @ ( set @ B ) @ G2 @ A2 ) ) ) )
% 0.16/0.40 = ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ C @ A
% 0.16/0.40 @ ^ [Y: C] : ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ ( G2 @ Y ) ) )
% 0.16/0.40 @ A2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_UNION
% 0.16/0.40 thf(fact_232_imageE,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,B3: A,F: B > A,A2: set @ B] :
% 0.16/0.40 ( ( member @ A @ B3 @ ( image @ B @ A @ F @ A2 ) )
% 0.16/0.40 => ~ ! [X6: B] :
% 0.16/0.40 ( ( B3
% 0.16/0.40 = ( F @ X6 ) )
% 0.16/0.40 => ~ ( member @ B @ X6 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % imageE
% 0.16/0.40 thf(fact_233_image__image,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType,F: B > A,G2: C > B,A2: set @ C] :
% 0.16/0.40 ( ( image @ B @ A @ F @ ( image @ C @ B @ G2 @ A2 ) )
% 0.16/0.40 = ( image @ C @ A
% 0.16/0.40 @ ^ [X: C] : ( F @ ( G2 @ X ) )
% 0.16/0.40 @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_image
% 0.16/0.40 thf(fact_234_Compr__image__eq,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P2: A > $o] :
% 0.16/0.40 ( ( collect @ A
% 0.16/0.40 @ ^ [X: A] :
% 0.16/0.40 ( ( member @ A @ X @ ( image @ B @ A @ F @ A2 ) )
% 0.16/0.40 & ( P2 @ X ) ) )
% 0.16/0.40 = ( image @ B @ A @ F
% 0.16/0.40 @ ( collect @ B
% 0.16/0.40 @ ^ [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % Compr_image_eq
% 0.16/0.40 thf(fact_235_sum_Ocase__distrib,axiom,
% 0.16/0.40 ! [D: $tType,C: $tType,B: $tType,A: $tType,H: C > D,F1: A > C,F22: B > C,Sum: sum_sum @ A @ B] :
% 0.16/0.40 ( ( H @ ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ Sum ) )
% 0.16/0.40 = ( sum_case_sum @ A @ D @ B
% 0.16/0.40 @ ^ [X: A] : ( H @ ( F1 @ X ) )
% 0.16/0.40 @ ^ [X: B] : ( H @ ( F22 @ X ) )
% 0.16/0.40 @ Sum ) ) ).
% 0.16/0.40
% 0.16/0.40 % sum.case_distrib
% 0.16/0.40 thf(fact_236_image__UN,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType,F: B > A,B2: C > ( set @ B ),A2: set @ C] :
% 0.16/0.40 ( ( image @ B @ A @ F @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ C @ ( set @ B ) @ B2 @ A2 ) ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ C @ ( set @ A )
% 0.16/0.40 @ ^ [X: C] : ( image @ B @ A @ F @ ( B2 @ X ) )
% 0.16/0.40 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_UN
% 0.16/0.40 thf(fact_237_UN__extend__simps_I10_J,axiom,
% 0.16/0.40 ! [V: $tType,U2: $tType,T: $tType,B2: U2 > ( set @ V ),F: T > U2,A2: set @ T] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( set @ V )
% 0.16/0.40 @ ( image @ T @ ( set @ V )
% 0.16/0.40 @ ^ [A3: T] : ( B2 @ ( F @ A3 ) )
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ V ) @ ( image @ U2 @ ( set @ V ) @ B2 @ ( image @ T @ U2 @ F @ A2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_extend_simps(10)
% 0.16/0.40 thf(fact_238_image__Union,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: B > A,S4: set @ ( set @ B )] :
% 0.16/0.40 ( ( image @ B @ A @ F @ ( complete_Sup_Sup @ ( set @ B ) @ S4 ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ A ) @ ( image @ ( set @ B ) @ ( set @ A ) @ ( image @ B @ A @ F ) @ S4 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_Union
% 0.16/0.40 thf(fact_239_UN__extend__simps_I8_J,axiom,
% 0.16/0.40 ! [P5: $tType,O: $tType,B2: O > ( set @ P5 ),A2: set @ ( set @ O )] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( set @ P5 )
% 0.16/0.40 @ ( image @ ( set @ O ) @ ( set @ P5 )
% 0.16/0.40 @ ^ [Y: set @ O] : ( complete_Sup_Sup @ ( set @ P5 ) @ ( image @ O @ ( set @ P5 ) @ B2 @ Y ) )
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ P5 ) @ ( image @ O @ ( set @ P5 ) @ B2 @ ( complete_Sup_Sup @ ( set @ O ) @ A2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_extend_simps(8)
% 0.16/0.40 thf(fact_240_Inf_OINF__identity__eq,axiom,
% 0.16/0.40 ! [A: $tType,Inf: ( set @ A ) > A,A2: set @ A] :
% 0.16/0.40 ( ( Inf
% 0.16/0.40 @ ( image @ A @ A
% 0.16/0.40 @ ^ [X: A] : X
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( Inf @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Inf.INF_identity_eq
% 0.16/0.40 thf(fact_241_Sup_OSUP__identity__eq,axiom,
% 0.16/0.40 ! [A: $tType,Sup: ( set @ A ) > A,A2: set @ A] :
% 0.16/0.40 ( ( Sup
% 0.16/0.40 @ ( image @ A @ A
% 0.16/0.40 @ ^ [X: A] : X
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( Sup @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % Sup.SUP_identity_eq
% 0.16/0.40 thf(fact_242_the__elem__image__unique,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,A2: set @ A,F: A > B,X5: A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 != ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 => ( ! [Y4: A] :
% 0.16/0.40 ( ( member @ A @ Y4 @ A2 )
% 0.16/0.40 => ( ( F @ Y4 )
% 0.16/0.40 = ( F @ X5 ) ) )
% 0.16/0.40 => ( ( the_elem @ B @ ( image @ A @ B @ F @ A2 ) )
% 0.16/0.40 = ( F @ X5 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % the_elem_image_unique
% 0.16/0.40 thf(fact_243_image__constant__conv,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,A2: set @ B,C3: A] :
% 0.16/0.40 ( ( ( A2
% 0.16/0.40 = ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( image @ B @ A
% 0.16/0.40 @ ^ [X: B] : C3
% 0.16/0.40 @ A2 )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.40 & ( ( A2
% 0.16/0.40 != ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( image @ B @ A
% 0.16/0.40 @ ^ [X: B] : C3
% 0.16/0.40 @ A2 )
% 0.16/0.40 = ( insert @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_constant_conv
% 0.16/0.40 thf(fact_244_image__constant,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,X5: A,A2: set @ A,C3: B] :
% 0.16/0.40 ( ( member @ A @ X5 @ A2 )
% 0.16/0.40 => ( ( image @ A @ B
% 0.16/0.40 @ ^ [X: A] : C3
% 0.16/0.40 @ A2 )
% 0.16/0.40 = ( insert @ B @ C3 @ ( bot_bot @ ( set @ B ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % image_constant
% 0.16/0.40 thf(fact_245_UN__empty2,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,A2: set @ B] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ B @ ( set @ A )
% 0.16/0.40 @ ^ [X: B] : ( bot_bot @ ( set @ A ) )
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_empty2
% 0.16/0.40 thf(fact_246_UN__empty,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,B2: B > ( set @ A )] :
% 0.16/0.40 ( ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ ( bot_bot @ ( set @ B ) ) ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_empty
% 0.16/0.40 thf(fact_247_UNION__empty__conv_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,B2: B > ( set @ A ),A2: set @ B] :
% 0.16/0.40 ( ( ( bot_bot @ ( set @ A ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 0.16/0.40 = ( ! [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 => ( ( B2 @ X )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UNION_empty_conv(1)
% 0.16/0.40 thf(fact_248_UNION__empty__conv_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,B2: B > ( set @ A ),A2: set @ B] :
% 0.16/0.40 ( ( ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.40 = ( ! [X: B] :
% 0.16/0.40 ( ( member @ B @ X @ A2 )
% 0.16/0.40 => ( ( B2 @ X )
% 0.16/0.40 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UNION_empty_conv(2)
% 0.16/0.40 thf(fact_249_UN__insert__distrib,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,U3: A,A2: set @ A,A4: B,B2: A > ( set @ B )] :
% 0.16/0.40 ( ( member @ A @ U3 @ A2 )
% 0.16/0.40 => ( ( complete_Sup_Sup @ ( set @ B )
% 0.16/0.40 @ ( image @ A @ ( set @ B )
% 0.16/0.40 @ ^ [X: A] : ( insert @ B @ A4 @ ( B2 @ X ) )
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( insert @ B @ A4 @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ A @ ( set @ B ) @ B2 @ A2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_insert_distrib
% 0.16/0.40 thf(fact_250_vimage__UN,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType,F: A > B,B2: C > ( set @ B ),A2: set @ C] :
% 0.16/0.40 ( ( vimage @ A @ B @ F @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ C @ ( set @ B ) @ B2 @ A2 ) ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ C @ ( set @ A )
% 0.16/0.40 @ ^ [X: C] : ( vimage @ A @ B @ F @ ( B2 @ X ) )
% 0.16/0.40 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_UN
% 0.16/0.40 thf(fact_251_vimage__Union,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: A > B,A2: set @ ( set @ B )] :
% 0.16/0.40 ( ( vimage @ A @ B @ F @ ( complete_Sup_Sup @ ( set @ B ) @ A2 ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ A ) @ ( image @ ( set @ B ) @ ( set @ A ) @ ( vimage @ A @ B @ F ) @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % vimage_Union
% 0.16/0.40 thf(fact_252_case__sum__if,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,C: $tType,P4: $o,F: B > A,G2: C > A,X5: B,Y3: C] :
% 0.16/0.40 ( ( P4
% 0.16/0.40 => ( ( sum_case_sum @ B @ A @ C @ F @ G2 @ ( if @ ( sum_sum @ B @ C ) @ P4 @ ( sum_Inl @ B @ C @ X5 ) @ ( sum_Inr @ C @ B @ Y3 ) ) )
% 0.16/0.40 = ( F @ X5 ) ) )
% 0.16/0.40 & ( ~ P4
% 0.16/0.40 => ( ( sum_case_sum @ B @ A @ C @ F @ G2 @ ( if @ ( sum_sum @ B @ C ) @ P4 @ ( sum_Inl @ B @ C @ X5 ) @ ( sum_Inr @ C @ B @ Y3 ) ) )
% 0.16/0.40 = ( G2 @ Y3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % case_sum_if
% 0.16/0.40 thf(fact_253_surjective__sum,axiom,
% 0.16/0.40 ! [C: $tType,B: $tType,A: $tType,F: ( sum_sum @ A @ B ) > C] :
% 0.16/0.40 ( ( sum_case_sum @ A @ C @ B
% 0.16/0.40 @ ^ [X: A] : ( F @ ( sum_Inl @ A @ B @ X ) )
% 0.16/0.40 @ ^ [Y: B] : ( F @ ( sum_Inr @ B @ A @ Y ) ) )
% 0.16/0.40 = F ) ).
% 0.16/0.40
% 0.16/0.40 % surjective_sum
% 0.16/0.40 thf(fact_254_SUP__constant,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.16/0.40 => ! [A2: set @ B,C3: A] :
% 0.16/0.40 ( ( ( A2
% 0.16/0.40 = ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ B @ A
% 0.16/0.40 @ ^ [Y: B] : C3
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = ( bot_bot @ A ) ) )
% 0.16/0.40 & ( ( A2
% 0.16/0.40 != ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( complete_Sup_Sup @ A
% 0.16/0.40 @ ( image @ B @ A
% 0.16/0.40 @ ^ [Y: B] : C3
% 0.16/0.40 @ A2 ) )
% 0.16/0.40 = C3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % SUP_constant
% 0.16/0.40 thf(fact_255_UN__extend__simps_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C2: set @ B,A4: A,B2: B > ( set @ A )] :
% 0.16/0.40 ( ( ( C2
% 0.16/0.40 = ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( insert @ A @ A4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ C2 ) ) )
% 0.16/0.40 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.16/0.40 & ( ( C2
% 0.16/0.40 != ( bot_bot @ ( set @ B ) ) )
% 0.16/0.40 => ( ( insert @ A @ A4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ C2 ) ) )
% 0.16/0.40 = ( complete_Sup_Sup @ ( set @ A )
% 0.16/0.40 @ ( image @ B @ ( set @ A )
% 0.16/0.40 @ ^ [X: B] : ( insert @ A @ A4 @ ( B2 @ X ) )
% 0.16/0.40 @ C2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % UN_extend_simps(1)
% 0.16/0.40
% 0.16/0.40 %----Type constructors (15)
% 0.16/0.40 thf(tcon_fun___Conditionally__Complete__Lattices_Oconditionally__complete__lattice,axiom,
% 0.16/0.40 ! [A7: $tType,A10: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A10 @ ( type2 @ A10 ) )
% 0.16/0.40 => ( condit378418413attice @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 0.16/0.40 ! [A7: $tType,A10: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A10 @ ( type2 @ A10 ) )
% 0.16/0.40 => ( comple187826305attice @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_fun___Complete__Partial__Order_Occpo,axiom,
% 0.16/0.40 ! [A7: $tType,A10: $tType] :
% 0.16/0.40 ( ( comple187826305attice @ A10 @ ( type2 @ A10 ) )
% 0.16/0.40 => ( comple1141879883l_ccpo @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_fun___Complete__Lattices_OSup,axiom,
% 0.16/0.40 ! [A7: $tType,A10: $tType] :
% 0.16/0.40 ( ( complete_Sup @ A10 @ ( type2 @ A10 ) )
% 0.16/0.40 => ( complete_Sup @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_fun___Orderings_Obot,axiom,
% 0.16/0.40 ! [A7: $tType,A10: $tType] :
% 0.16/0.40 ( ( bot @ A10 @ ( type2 @ A10 ) )
% 0.16/0.40 => ( bot @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_Set_Oset___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_1,axiom,
% 0.16/0.40 ! [A7: $tType] : ( condit378418413attice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_2,axiom,
% 0.16/0.40 ! [A7: $tType] : ( comple187826305attice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_Set_Oset___Complete__Partial__Order_Occpo_3,axiom,
% 0.16/0.40 ! [A7: $tType] : ( comple1141879883l_ccpo @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_Set_Oset___Complete__Lattices_OSup_4,axiom,
% 0.16/0.40 ! [A7: $tType] : ( complete_Sup @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_Set_Oset___Orderings_Obot_5,axiom,
% 0.16/0.40 ! [A7: $tType] : ( bot @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(tcon_HOL_Obool___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_6,axiom,
% 0.16/0.41 condit378418413attice @ $o @ ( type2 @ $o ) ).
% 0.16/0.41
% 0.16/0.41 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_7,axiom,
% 0.16/0.41 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 0.16/0.41
% 0.16/0.41 thf(tcon_HOL_Obool___Complete__Partial__Order_Occpo_8,axiom,
% 0.16/0.41 comple1141879883l_ccpo @ $o @ ( type2 @ $o ) ).
% 0.16/0.41
% 0.16/0.41 thf(tcon_HOL_Obool___Complete__Lattices_OSup_9,axiom,
% 0.16/0.41 complete_Sup @ $o @ ( type2 @ $o ) ).
% 0.16/0.41
% 0.16/0.41 thf(tcon_HOL_Obool___Orderings_Obot_10,axiom,
% 0.16/0.41 bot @ $o @ ( type2 @ $o ) ).
% 0.16/0.41
% 0.16/0.41 %----Helper facts (3)
% 0.16/0.41 thf(help_If_3_1_T,axiom,
% 0.16/0.41 ! [P2: $o] :
% 0.16/0.41 ( ( P2 = $true )
% 0.16/0.41 | ( P2 = $false ) ) ).
% 0.16/0.41
% 0.16/0.41 thf(help_If_2_1_T,axiom,
% 0.16/0.41 ! [A: $tType,X5: A,Y3: A] :
% 0.16/0.41 ( ( if @ A @ $false @ X5 @ Y3 )
% 0.16/0.41 = Y3 ) ).
% 0.16/0.41
% 0.16/0.41 thf(help_If_1_1_T,axiom,
% 0.16/0.41 ! [A: $tType,X5: A,Y3: A] :
% 0.16/0.41 ( ( if @ A @ $true @ X5 @ Y3 )
% 0.16/0.41 = X5 ) ).
% 0.16/0.41
% 0.16/0.41 %----Conjectures (1)
% 0.16/0.41 thf(conj_0,conjecture,
% 0.16/0.41 ( ( collect @ n @ ( gram_L830233218_inItr @ ns @ tr ) )
% 0.16/0.41 = ( collect @ n
% 0.16/0.41 @ ^ [Uu: n] :
% 0.16/0.41 ? [Tr5: dtree] :
% 0.16/0.41 ( ( Uu
% 0.16/0.41 = ( root @ Tr5 ) )
% 0.16/0.41 & ( gram_L716654942_subtr @ ns @ Tr5 @ tr ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 2.95/1.70 ---- Embedded in THF ---
% 3.26/1.70 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.26/1.70 %%% Generated on Tue Feb 24 04:16:18 EST 2026
% 3.26/1.70 %%% using '$$dhol' embedding, version 1.3.0.
% 3.26/1.70 %%% Logic specification used:
% 3.26/1.70 %%% thf(spec, logic, $$dhol).
% 3.26/1.70
% 3.26/1.70 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.40Ab8elA6V/DTF2DTF21337.p
% 3.26/1.70 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 3.26/1.70 thf(ty_t_DTree_Odtree, type, dtree: $tType).
% 3.26/1.70 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.26/1.70 thf(ty_t_DTree_OT, type, t: $tType).
% 3.26/1.70 thf(ty_t_DTree_ON, type, n: $tType).
% 3.26/1.70 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 3.26/1.70 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.26/1.70 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.26/1.70 thf(sy_cl_Complete__Lattices_OSup, type, complete_Sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.26/1.70 thf(sy_cl_Complete__Partial__Order_Occpo, type, comple1141879883l_ccpo: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.26/1.70 thf(sy_cl_Complete__Lattices_Ocomplete__lattice, type, comple187826305attice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.26/1.70 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__lattice, type, condit378418413attice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.26/1.70 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p, type, bNF_Greatest_image2p: (!> [C:$tType,A:$tType,D:$tType,B:$tType]: (((C > A) > ((D > B) > ((C > (D > $o)) > (A > (B > $o)))))))).
% 3.26/1.70 thf(sy_c_Basic__BNFs_Osetl, type, basic_setl: (!> [A:$tType,B:$tType]: ((((sum_sum @ A) @ B) > (set @ A))))).
% 3.26/1.70 thf(sy_c_Basic__BNFs_Osetr, type, basic_setr: (!> [A:$tType,B:$tType]: ((((sum_sum @ A) @ B) > (set @ B))))).
% 3.26/1.70 thf(sy_c_Complete__Lattices_OSup__class_OSup, type, complete_Sup_Sup: (!> [A:$tType]: (((set @ A) > A)))).
% 3.26/1.70 thf(sy_c_DTree_ONode, type, node: (n > ((set @ ((sum_sum @ t) @ dtree)) > dtree))).
% 3.26/1.70 thf(sy_c_DTree_Ocont, type, cont: (dtree > (set @ ((sum_sum @ t) @ dtree)))).
% 3.26/1.70 thf(sy_c_DTree_Odtree_Oroot, type, root: (dtree > n)).
% 3.26/1.70 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFr, type, gram_L861583724lle_Fr: ((set @ n) > (dtree > (set @ t)))).
% 3.26/1.70 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OItr, type, gram_L1580978439le_Itr: ((set @ n) > (dtree > (set @ n)))).
% 3.26/1.70 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr, type, gram_L1333338417e_inFr: ((set @ n) > (dtree > (t > $o)))).
% 3.26/1.70 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2, type, gram_L805317441_inFr2: ((set @ n) > (dtree > (t > $o)))).
% 3.26/1.70 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr, type, gram_L830233218_inItr: ((set @ n) > (dtree > (n > $o)))).
% 3.26/1.70 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr, type, gram_L716654942_subtr: ((set @ n) > (dtree > (dtree > $o)))).
% 3.26/1.70 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2, type, gram_L1283001940subtr2: ((set @ n) > (dtree > (dtree > $o)))).
% 3.26/1.70 thf(sy_c_HOL_OThe, type, the: (!> [A:$tType]: (((A > $o) > A)))).
% 3.26/1.70 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.26/1.70 thf(sy_c_Lifting_Orel__pred__comp, type, rel_pred_comp: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((B > $o) > (A > $o)))))).
% 3.26/1.70 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 3.26/1.70 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 3.26/1.70 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.26/1.70 thf(sy_c_Set_Oimage, type, image: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > (set @ B)))))).
% 3.26/1.70 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 3.26/1.70 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.26/1.70 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.26/1.70 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 3.26/1.70 thf(sy_c_Set_Ovimage, type, vimage: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ B) > (set @ A)))))).
% 3.26/1.70 thf(sy_c_Sum__Type_OInl, type, sum_Inl: (!> [A:$tType,B:$tType]: ((A > ((sum_sum @ A) @ B))))).
% 3.26/1.70 thf(sy_c_Sum__Type_OInr, type, sum_Inr: (!> [B:$tType,A:$tType]: ((B > ((sum_sum @ A) @ B))))).
% 3.26/1.70 thf(sy_c_Sum__Type_OSuml, type, sum_Suml: (!> [A:$tType,C:$tType,B:$tType]: (((A > C) > (((sum_sum @ A) @ B) > C))))).
% 3.26/1.70 thf(sy_c_Sum__Type_Oold_Osum_Orec__set__sum, type, sum_rec_set_sum: (!> [A:$tType,T:$tType,B:$tType]: (((A > T) > ((B > T) > (((sum_sum @ A) @ B) > (T > $o))))))).
% 3.26/1.70 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum, type, sum_rec_sum: (!> [A:$tType,T:$tType,B:$tType]: (((A > T) > ((B > T) > (((sum_sum @ A) @ B) > T)))))).
% 3.26/1.70 thf(sy_c_Sum__Type_Osum_Ocase__sum, type, sum_case_sum: (!> [A:$tType,C:$tType,B:$tType]: (((A > C) > ((B > C) > (((sum_sum @ A) @ B) > C)))))).
% 3.26/1.70 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.26/1.70 thf(sy_v_ns, type, ns: (set @ n)).
% 3.26/1.70 thf(sy_v_tr, type, tr: dtree).
% 3.26/1.70 thf(fact_0_inItr_OBase, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L830233218_inItr @ Ns) @ Tr) @ (root @ Tr)))))).
% 3.26/1.70 thf(fact_1_subtr_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L716654942_subtr @ Ns) @ Tr) @ Tr))))).
% 3.26/1.70 thf(fact_2_inItr__subtr, axiom, (! [Ns:(set @ n),Tr:dtree,N:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => (? [Tr2:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr2) @ Tr) & ((root @ Tr2) = N)))))))).
% 3.26/1.70 thf(fact_3_subtr__inItr, axiom, (! [Ns:(set @ n),Tr:dtree,N:n,Tr1:dtree]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (((gram_L830233218_inItr @ Ns) @ Tr1) @ N)))))).
% 3.26/1.70 thf(fact_4_subtr__trans, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Tr3:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((((gram_L716654942_subtr @ Ns) @ Tr22) @ Tr3) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr3)))))).
% 3.26/1.70 thf(fact_5_inItr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,N:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 3.26/1.70 thf(fact_6_subtr__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 3.26/1.70 thf(fact_7_subtr__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr22)) @ Ns))))).
% 3.26/1.70 thf(fact_8_Itr__def, axiom, (gram_L1580978439le_Itr = (^ [Ns2:(set @ n),Tr4:dtree]: (((collect @ n) @ ((gram_L830233218_inItr @ Ns2) @ Tr4)))))).
% 3.26/1.70 thf(fact_9_rel__pred__comp__def, axiom, (! [B:$tType,A:$tType]: ((((rel_pred_comp @ A) @ B) = (^ [R:(A > (B > $o)),P:(B > $o),X:A]: ((? [Y:B]: ((((R @ X) @ Y) & (P @ Y)))))))))).
% 3.26/1.70 thf(fact_10_Itr__subtr, axiom, (gram_L1580978439le_Itr = (^ [Ns2:(set @ n),Tr4:dtree]: (((complete_Sup_Sup @ (set @ n)) @ ((collect @ (set @ n)) @ (^ [Uu:(set @ n)]: ((? [Tr5:dtree]: (((Uu = ((gram_L1580978439le_Itr @ Ns2) @ Tr5)) & (((gram_L716654942_subtr @ Ns2) @ Tr5) @ Tr4)))))))))))).
% 3.26/1.70 thf(fact_11_inFr2__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 3.26/1.70 thf(fact_12_Fr__subtr, axiom, (gram_L861583724lle_Fr = (^ [Ns2:(set @ n),Tr4:dtree]: (((complete_Sup_Sup @ (set @ t)) @ ((collect @ (set @ t)) @ (^ [Uu:(set @ t)]: ((? [Tr5:dtree]: (((Uu = ((gram_L861583724lle_Fr @ Ns2) @ Tr5)) & (((gram_L716654942_subtr @ Ns2) @ Tr5) @ Tr4)))))))))))).
% 3.26/1.70 thf(fact_13_subtr__inFr, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t,Tr1:dtree]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (((gram_L1333338417e_inFr @ Ns) @ Tr1) @ T2)))))).
% 3.26/1.70 thf(fact_14_subtr__subtr2, axiom, (gram_L716654942_subtr = gram_L1283001940subtr2)).
% 3.26/1.70 thf(fact_15_inFr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 3.26/1.70 thf(fact_16_not__root__inFr, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((~ ((((member @ n) @ (root @ Tr)) @ Ns))) => (~ ((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2))))))).
% 3.26/1.70 thf(fact_17_subtr2_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L1283001940subtr2 @ Ns) @ Tr) @ Tr))))).
% 3.26/1.70 thf(fact_18_subtr2__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 3.26/1.70 thf(fact_19_subtr2__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr22)) @ Ns))))).
% 3.26/1.70 thf(fact_20_inFr__inFr2, axiom, (gram_L1333338417e_inFr = gram_L805317441_inFr2)).
% 3.26/1.70 thf(fact_21_subtr2__trans, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Tr3:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => ((((gram_L1283001940subtr2 @ Ns) @ Tr22) @ Tr3) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr3)))))).
% 3.26/1.70 thf(fact_22_Fr__def, axiom, (gram_L861583724lle_Fr = (^ [Ns2:(set @ n),Tr4:dtree]: (((collect @ t) @ ((gram_L1333338417e_inFr @ Ns2) @ Tr4)))))).
% 3.26/1.70 thf(fact_23_UN__ball__bex__simps_I3_J, axiom, (! [D:$tType,A2:(set @ (set @ D)),P2:(D > $o)]: (((? [X:D]: (((((member @ D) @ X) @ ((complete_Sup_Sup @ (set @ D)) @ A2)) & (P2 @ X)))) = (? [X:(set @ D)]: (((((member @ (set @ D)) @ X) @ A2) & (? [Y:D]: (((((member @ D) @ Y) @ X) & (P2 @ Y))))))))))).
% 3.26/1.70 thf(fact_24_UN__ball__bex__simps_I1_J, axiom, (! [A:$tType,A2:(set @ (set @ A)),P2:(A > $o)]: (((! [X:A]: (((((member @ A) @ X) @ ((complete_Sup_Sup @ (set @ A)) @ A2)) => (P2 @ X)))) = (! [X:(set @ A)]: (((((member @ (set @ A)) @ X) @ A2) => (! [Y:A]: (((((member @ A) @ Y) @ X) => (P2 @ Y))))))))))).
% 3.26/1.70 thf(fact_25_UnionI, axiom, (! [A:$tType,X2:(set @ A),C2:(set @ (set @ A)),A2:A]: (((((member @ (set @ A)) @ X2) @ C2) => ((((member @ A) @ A2) @ X2) => (((member @ A) @ A2) @ ((complete_Sup_Sup @ (set @ A)) @ C2))))))).
% 3.26/1.70 thf(fact_26_Union__iff, axiom, (! [A:$tType,A2:A,C2:(set @ (set @ A))]: (((((member @ A) @ A2) @ ((complete_Sup_Sup @ (set @ A)) @ C2)) = (? [X:(set @ A)]: (((((member @ (set @ A)) @ X) @ C2) & (((member @ A) @ A2) @ X)))))))).
% 3.26/1.70 thf(fact_27_Union__SetCompr__eq, axiom, (! [B:$tType,A:$tType,F:(B > (set @ A)),P2:(B > $o)]: ((((complete_Sup_Sup @ (set @ A)) @ ((collect @ (set @ A)) @ (^ [Uu:(set @ A)]: ((? [X:B]: (((Uu = (F @ X)) & (P2 @ X)))))))) = ((collect @ A) @ (^ [A3:A]: ((? [X:B]: (((P2 @ X) & (((member @ A) @ A3) @ (F @ X)))))))))))).
% 3.26/1.70 thf(fact_28_UnionE, axiom, (! [A:$tType,A2:A,C2:(set @ (set @ A))]: (((((member @ A) @ A2) @ ((complete_Sup_Sup @ (set @ A)) @ C2)) => (~ ((! [X3:(set @ A)]: (((((member @ A) @ A2) @ X3) => (~ ((((member @ (set @ A)) @ X3) @ C2)))))))))))).
% 3.26/1.70 thf(fact_29_not__root__Fr, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((~ ((((member @ n) @ (root @ Tr)) @ Ns))) => (((gram_L861583724lle_Fr @ Ns) @ Tr) = (bot_bot @ (set @ t))))))).
% 3.26/1.70 thf(fact_30_Fr__subtr__cont, axiom, (gram_L861583724lle_Fr = (^ [Ns2:(set @ n),Tr4:dtree]: (((complete_Sup_Sup @ (set @ t)) @ ((collect @ (set @ t)) @ (^ [Uu:(set @ t)]: ((? [Tr5:dtree]: (((Uu = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ Tr5))) & (((gram_L716654942_subtr @ Ns2) @ Tr5) @ Tr4)))))))))))).
% 3.26/1.70 thf(fact_31_image2p__def, axiom, (! [D:$tType,B:$tType,A:$tType,C:$tType]: ((((((bNF_Greatest_image2p @ C) @ A) @ D) @ B) = (^ [F2:(C > A),G:(D > B),R:(C > (D > $o)),X:A,Y:B]: ((? [X4:C,Y2:D]: ((((R @ X4) @ Y2) & (((F2 @ X4) = X) & ((G @ Y2) = Y))))))))))).
% 3.26/1.70 thf(fact_32_root__Node, axiom, (! [N:n,As:(set @ ((sum_sum @ t) @ dtree))]: (((root @ ((node @ N) @ As)) = N)))).
% 3.26/1.70 thf(fact_33_Sup__bot__conv_I1_J, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A2:(set @ A)]: (((((complete_Sup_Sup @ A) @ A2) = (bot_bot @ A)) = (! [X:A]: (((((member @ A) @ X) @ A2) => (X = (bot_bot @ A)))))))))))).
% 3.26/1.70 thf(fact_34_Sup__bot__conv_I2_J, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A2:(set @ A)]: ((((bot_bot @ A) = ((complete_Sup_Sup @ A) @ A2)) = (! [X:A]: (((((member @ A) @ X) @ A2) => (X = (bot_bot @ A)))))))))))).
% 3.26/1.70 thf(fact_35_Sup__empty, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (((complete_Sup_Sup @ A) @ (bot_bot @ (set @ A))) = (bot_bot @ A)))))).
% 3.26/1.70 thf(fact_36_Node__root__cont, axiom, (! [Tr:dtree]: ((((node @ (root @ Tr)) @ (cont @ Tr)) = Tr)))).
% 3.26/1.70 thf(fact_37_Union__empty, axiom, (! [A:$tType]: ((((complete_Sup_Sup @ (set @ A)) @ (bot_bot @ (set @ (set @ A)))) = (bot_bot @ (set @ A)))))).
% 3.26/1.70 thf(fact_38_image2pI, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R2:(A > (B > $o)),X5:A,Y3:B,F:(A > C),G2:(B > D)]: ((((R2 @ X5) @ Y3) => (((((((((bNF_Greatest_image2p @ A) @ C) @ B) @ D) @ F) @ G2) @ R2) @ (F @ X5)) @ (G2 @ Y3)))))).
% 3.26/1.70 thf(fact_39_image2pE, axiom, (! [D:$tType,B:$tType,A:$tType,C:$tType,F:(A > B),G2:(C > D),R2:(A > (C > $o)),Fx:B,Gy:D]: (((((((((((bNF_Greatest_image2p @ A) @ B) @ C) @ D) @ F) @ G2) @ R2) @ Fx) @ Gy) => (~ ((! [X6:A]: (((Fx = (F @ X6)) => (! [Y4:C]: (((Gy = (G2 @ Y4)) => (~ (((R2 @ X6) @ Y4))))))))))))))).
% 3.26/1.70 thf(fact_40_empty__Union__conv, axiom, (! [A:$tType,A2:(set @ (set @ A))]: ((((bot_bot @ (set @ A)) = ((complete_Sup_Sup @ (set @ A)) @ A2)) = (! [X:(set @ A)]: (((((member @ (set @ A)) @ X) @ A2) => (X = (bot_bot @ (set @ A)))))))))).
% 3.26/1.70 thf(fact_41_Union__empty__conv, axiom, (! [A:$tType,A2:(set @ (set @ A))]: (((((complete_Sup_Sup @ (set @ A)) @ A2) = (bot_bot @ (set @ A))) = (! [X:(set @ A)]: (((((member @ (set @ A)) @ X) @ A2) => (X = (bot_bot @ (set @ A)))))))))).
% 3.26/1.70 thf(fact_42_dtree__cong, axiom, (! [Tr:dtree,Tr6:dtree]: ((((root @ Tr) = (root @ Tr6)) => (((cont @ Tr) = (cont @ Tr6)) => (Tr = Tr6)))))).
% 3.26/1.70 thf(fact_43_inFr_OBase, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T2)) @ (cont @ Tr)) => (((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2)))))).
% 3.26/1.70 thf(fact_44_inFr2_OBase, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T2)) @ (cont @ Tr)) => (((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2)))))).
% 3.26/1.70 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P2:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P2)) = (P2 @ A4))))).
% 3.26/1.70 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A2)))) = A2)))).
% 3.26/1.70 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X6:A]: (((P2 @ X6) = (Q @ X6)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 3.26/1.70 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G2:(A > B)]: (((! [X6:A]: (((F @ X6) = (G2 @ X6)))) => (F = G2))))).
% 3.26/1.70 thf(fact_49_inFr__subtr, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => (? [Tr2:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr2) @ Tr) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T2)) @ (cont @ Tr2))))))))).
% 3.26/1.70 thf(fact_50_vimage__empty, axiom, (! [B:$tType,A:$tType,F:(A > B)]: ((((((vimage @ A) @ B) @ F) @ (bot_bot @ (set @ B))) = (bot_bot @ (set @ A)))))).
% 3.26/1.70 thf(fact_51_vimage__Collect__eq, axiom, (! [B:$tType,A:$tType,F:(A > B),P2:(B > $o)]: ((((((vimage @ A) @ B) @ F) @ ((collect @ B) @ P2)) = ((collect @ A) @ (^ [Y:A]: ((P2 @ (F @ Y))))))))).
% 3.26/1.70 thf(fact_52_vimage__ident, axiom, (! [A:$tType,Y5:(set @ A)]: ((((((vimage @ A) @ A) @ (^ [X:A]: (X))) @ Y5) = Y5)))).
% 3.26/1.70 thf(fact_53_vimage__eq, axiom, (! [A:$tType,B:$tType,A4:A,F:(A > B),B2:(set @ B)]: (((((member @ A) @ A4) @ ((((vimage @ A) @ B) @ F) @ B2)) = (((member @ B) @ (F @ A4)) @ B2))))).
% 3.26/1.70 thf(fact_54_vimageI, axiom, (! [B:$tType,A:$tType,F:(B > A),A4:B,B3:A,B2:(set @ A)]: ((((F @ A4) = B3) => ((((member @ A) @ B3) @ B2) => (((member @ B) @ A4) @ ((((vimage @ B) @ A) @ F) @ B2))))))).
% 3.26/1.70 thf(fact_55_old_Osum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,A4:A,A5:A]: ((((((sum_Inl @ A) @ B) @ A4) = (((sum_Inl @ A) @ B) @ A5)) = (A4 = A5))))).
% 3.26/1.70 thf(fact_56_sum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,X1:A,Y1:A]: ((((((sum_Inl @ A) @ B) @ X1) = (((sum_Inl @ A) @ B) @ Y1)) = (X1 = Y1))))).
% 3.26/1.70 thf(fact_57_empty__Collect__eq, axiom, (! [A:$tType,P2:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P2)) = (! [X:A]: ((~ ((P2 @ X))))))))).
% 3.26/1.70 thf(fact_58_Collect__empty__eq, axiom, (! [A:$tType,P2:(A > $o)]: (((((collect @ A) @ P2) = (bot_bot @ (set @ A))) = (! [X:A]: ((~ ((P2 @ X))))))))).
% 3.26/1.70 thf(fact_59_empty__iff, axiom, (! [A:$tType,C3:A]: ((~ ((((member @ A) @ C3) @ (bot_bot @ (set @ A)))))))).
% 3.26/1.70 thf(fact_60_all__not__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X:A]: ((~ ((((member @ A) @ X) @ A2))))) = (A2 = (bot_bot @ (set @ A))))))).
% 3.26/1.70 thf(fact_61_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 3.26/1.70 thf(fact_62_emptyE, axiom, (! [A:$tType,A4:A]: ((~ ((((member @ A) @ A4) @ (bot_bot @ (set @ A)))))))).
% 3.26/1.70 thf(fact_63_equals0D, axiom, (! [A:$tType,A2:(set @ A),A4:A]: (((A2 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A4) @ A2))))))).
% 3.26/1.70 thf(fact_64_equals0I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [Y4:A]: ((~ ((((member @ A) @ Y4) @ A2))))) => (A2 = (bot_bot @ (set @ A))))))).
% 3.26/1.70 thf(fact_65_ex__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((? [X:A]: ((((member @ A) @ X) @ A2))) = (A2 != (bot_bot @ (set @ A))))))).
% 3.26/1.70 thf(fact_66_Inl__inject, axiom, (! [B:$tType,A:$tType,X5:A,Y3:A]: ((((((sum_Inl @ A) @ B) @ X5) = (((sum_Inl @ A) @ B) @ Y3)) => (X5 = Y3))))).
% 3.26/1.70 thf(fact_67_vimageD, axiom, (! [A:$tType,B:$tType,A4:A,F:(A > B),A2:(set @ B)]: (((((member @ A) @ A4) @ ((((vimage @ A) @ B) @ F) @ A2)) => (((member @ B) @ (F @ A4)) @ A2))))).
% 3.26/1.70 thf(fact_68_vimageE, axiom, (! [A:$tType,B:$tType,A4:A,F:(A > B),B2:(set @ B)]: (((((member @ A) @ A4) @ ((((vimage @ A) @ B) @ F) @ B2)) => (((member @ B) @ (F @ A4)) @ B2))))).
% 3.26/1.70 thf(fact_69_vimageI2, axiom, (! [B:$tType,A:$tType,F:(B > A),A4:B,A2:(set @ A)]: (((((member @ A) @ (F @ A4)) @ A2) => (((member @ B) @ A4) @ ((((vimage @ B) @ A) @ F) @ A2)))))).
% 3.26/1.70 thf(fact_70_vimage__Collect, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F:(A > B),Q:(A > $o)]: (((! [X6:A]: (((P2 @ (F @ X6)) = (Q @ X6)))) => (((((vimage @ A) @ B) @ F) @ ((collect @ B) @ P2)) = ((collect @ A) @ Q)))))).
% 3.26/1.70 thf(fact_71_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X:A]: ($false))))))).
% 3.26/1.70 thf(fact_72_vimage__def, axiom, (! [B:$tType,A:$tType]: ((((vimage @ A) @ B) = (^ [F2:(A > B),B4:(set @ B)]: (((collect @ A) @ (^ [X:A]: ((((member @ B) @ (F2 @ X)) @ B4)))))))))).
% 3.26/1.70 thf(fact_73_bot__apply, axiom, (! [C:$tType,D:$tType]: ((((bot @ C) @ (type2 @ C)) => ((bot_bot @ (D > C)) = (^ [X:D]: ((bot_bot @ C)))))))).
% 3.26/1.70 thf(fact_74_old_Osum_Osimps_I7_J, axiom, (! [B:$tType,T:$tType,A:$tType,F1:(A > T),F22:(B > T),A4:A]: ((((((((sum_rec_sum @ A) @ T) @ B) @ F1) @ F22) @ (((sum_Inl @ A) @ B) @ A4)) = (F1 @ A4))))).
% 3.26/1.70 thf(fact_75_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A6:(set @ A)]: ((A6 = (bot_bot @ (set @ A))))))))).
% 3.26/1.70 thf(fact_76_inFr_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:t]: (((((gram_L1333338417e_inFr @ A1) @ A22) @ A32) => (((((member @ n) @ (root @ A22)) @ A1) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ A32)) @ (cont @ A22))))) => (~ (((((member @ n) @ (root @ A22)) @ A1) => (! [Tr12:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ A22)) => (~ ((((gram_L1333338417e_inFr @ A1) @ Tr12) @ A32)))))))))))))).
% 3.26/1.70 thf(fact_77_inFr_Osimps, axiom, (gram_L1333338417e_inFr = (^ [A12:(set @ n),A23:dtree,A33:t]: (((? [Tr4:dtree,Ns2:(set @ n),T3:t]: (((A12 = Ns2) & ((A23 = Tr4) & ((A33 = T3) & ((((member @ n) @ (root @ Tr4)) @ Ns2) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T3)) @ (cont @ Tr4)))))))) | (? [Tr4:dtree,Ns2:(set @ n),Tr13:dtree,T3:t]: (((A12 = Ns2) & ((A23 = Tr4) & ((A33 = T3) & ((((member @ n) @ (root @ Tr4)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr4)) & (((gram_L1333338417e_inFr @ Ns2) @ Tr13) @ T3))))))))))))).
% 3.26/1.70 thf(fact_78_inFr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:t,P2:((set @ n) > (dtree > (t > $o)))]: (((((gram_L1333338417e_inFr @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns3:(set @ n),T4:t]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T4)) @ (cont @ Tr7)) => (((P2 @ Ns3) @ Tr7) @ T4))))) => ((! [Tr7:dtree,Ns3:(set @ n),Tr12:dtree,T4:t]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr7)) => ((((gram_L1333338417e_inFr @ Ns3) @ Tr12) @ T4) => ((((P2 @ Ns3) @ Tr12) @ T4) => (((P2 @ Ns3) @ Tr7) @ T4))))))) => (((P2 @ X1) @ X22) @ X32))))))).
% 3.26/1.70 thf(fact_79_Suml_Osimps, axiom, (! [B:$tType,C:$tType,A:$tType,F:(A > C),X5:A]: (((((((sum_Suml @ A) @ C) @ B) @ F) @ (((sum_Inl @ A) @ B) @ X5)) = (F @ X5))))).
% 3.26/1.70 thf(fact_80_sum_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,X22:B,Y22:B]: ((((((sum_Inr @ B) @ A) @ X22) = (((sum_Inr @ B) @ A) @ Y22)) = (X22 = Y22))))).
% 3.26/1.70 thf(fact_81_old_Osum_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,B3:B,B5:B]: ((((((sum_Inr @ B) @ A) @ B3) = (((sum_Inr @ B) @ A) @ B5)) = (B3 = B5))))).
% 3.26/1.70 thf(fact_82_old_Osum_Osimps_I8_J, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > T),F22:(B > T),B3:B]: ((((((((sum_rec_sum @ A) @ T) @ B) @ F1) @ F22) @ (((sum_Inr @ B) @ A) @ B3)) = (F22 @ B3))))).
% 3.26/1.70 thf(fact_83_Inr__inject, axiom, (! [A:$tType,B:$tType,X5:B,Y3:B]: ((((((sum_Inr @ B) @ A) @ X5) = (((sum_Inr @ B) @ A) @ Y3)) => (X5 = Y3))))).
% 3.26/1.70 thf(fact_84_not__arg__cong__Inr, axiom, (! [B:$tType,A:$tType,X5:A,Y3:A]: (((X5 != Y3) => ((((sum_Inr @ A) @ B) @ X5) != (((sum_Inr @ A) @ B) @ Y3)))))).
% 3.26/1.70 thf(fact_85_Suml__inject, axiom, (! [B:$tType,C:$tType,A:$tType,F:(A > C),G2:(A > C)]: (((((((sum_Suml @ A) @ C) @ B) @ F) = ((((sum_Suml @ A) @ C) @ B) @ G2)) => (F = G2))))).
% 3.26/1.70 thf(fact_86_obj__sumE, axiom, (! [A:$tType,B:$tType,S:((sum_sum @ A) @ B)]: (((! [X6:A]: ((S != (((sum_Inl @ A) @ B) @ X6)))) => (~ ((! [X6:B]: ((S != (((sum_Inr @ B) @ A) @ X6)))))))))).
% 3.26/1.70 thf(fact_87_sum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,X1:A,X22:B]: (((((sum_Inl @ A) @ B) @ X1) != (((sum_Inr @ B) @ A) @ X22))))).
% 3.26/1.70 thf(fact_88_old_Osum_Odistinct_I2_J, axiom, (! [B6:$tType,A7:$tType,B7:B6,A8:A7]: (((((sum_Inr @ B6) @ A7) @ B7) != (((sum_Inl @ A7) @ B6) @ A8))))).
% 3.26/1.70 thf(fact_89_old_Osum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,A4:A,B5:B]: (((((sum_Inl @ A) @ B) @ A4) != (((sum_Inr @ B) @ A) @ B5))))).
% 3.26/1.70 thf(fact_90_sumE, axiom, (! [A:$tType,B:$tType,S:((sum_sum @ A) @ B)]: (((! [X6:A]: ((S != (((sum_Inl @ A) @ B) @ X6)))) => (~ ((! [Y4:B]: ((S != (((sum_Inr @ B) @ A) @ Y4)))))))))).
% 3.26/1.70 thf(fact_91_Inr__not__Inl, axiom, (! [B:$tType,A:$tType,B3:B,A4:A]: (((((sum_Inr @ B) @ A) @ B3) != (((sum_Inl @ A) @ B) @ A4))))).
% 3.26/1.70 thf(fact_92_split__sum__ex, axiom, (! [B:$tType,A:$tType]: (((^ [P3:(((sum_sum @ A) @ B) > $o)]: ((? [X7:((sum_sum @ A) @ B)]: ((P3 @ X7))))) = (^ [P:(((sum_sum @ A) @ B) > $o)]: (((? [X:A]: ((P @ (((sum_Inl @ A) @ B) @ X)))) | (? [X:B]: ((P @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 3.26/1.70 thf(fact_93_split__sum__all, axiom, (! [B:$tType,A:$tType]: (((^ [P3:(((sum_sum @ A) @ B) > $o)]: ((! [X7:((sum_sum @ A) @ B)]: ((P3 @ X7))))) = (^ [P:(((sum_sum @ A) @ B) > $o)]: (((! [X:A]: ((P @ (((sum_Inl @ A) @ B) @ X)))) & (! [X:B]: ((P @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 3.26/1.70 thf(fact_94_old_Osum_Oexhaust, axiom, (! [A:$tType,B:$tType,Y3:((sum_sum @ A) @ B)]: (((! [A9:A]: ((Y3 != (((sum_Inl @ A) @ B) @ A9)))) => (~ ((! [B8:B]: ((Y3 != (((sum_Inr @ B) @ A) @ B8)))))))))).
% 3.26/1.70 thf(fact_95_old_Osum_Oinducts, axiom, (! [B:$tType,A:$tType,P2:(((sum_sum @ A) @ B) > $o),Sum:((sum_sum @ A) @ B)]: (((! [A9:A]: ((P2 @ (((sum_Inl @ A) @ B) @ A9)))) => ((! [B8:B]: ((P2 @ (((sum_Inr @ B) @ A) @ B8)))) => (P2 @ Sum)))))).
% 3.26/1.70 thf(fact_96_subtr_OStep, axiom, (! [Tr3:dtree,Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((member @ n) @ (root @ Tr3)) @ Ns) => ((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr3)) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr3))))))).
% 3.26/1.70 thf(fact_97_subtr_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:dtree]: (((((gram_L716654942_subtr @ A1) @ A22) @ A32) => (((A32 = A22) => (~ ((((member @ n) @ (root @ A22)) @ A1)))) => (~ (((((member @ n) @ (root @ A32)) @ A1) => (! [Tr23:dtree]: (((((gram_L716654942_subtr @ A1) @ A22) @ Tr23) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr23)) @ (cont @ A32))))))))))))))).
% 3.26/1.70 thf(fact_98_subtr_Osimps, axiom, (gram_L716654942_subtr = (^ [A12:(set @ n),A23:dtree,A33:dtree]: (((? [Tr4:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A23 = Tr4) & ((A33 = Tr4) & (((member @ n) @ (root @ Tr4)) @ Ns2)))))) | (? [Tr32:dtree,Ns2:(set @ n),Tr13:dtree,Tr24:dtree]: (((A12 = Ns2) & ((A23 = Tr13) & ((A33 = Tr32) & ((((member @ n) @ (root @ Tr32)) @ Ns2) & ((((gram_L716654942_subtr @ Ns2) @ Tr13) @ Tr24) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr24)) @ (cont @ Tr32)))))))))))))).
% 3.26/1.70 thf(fact_99_subtr__StepL, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr22:dtree,Tr3:dtree]: (((((member @ n) @ (root @ Tr1)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr22)) => ((((gram_L716654942_subtr @ Ns) @ Tr22) @ Tr3) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr3))))))).
% 3.26/1.70 thf(fact_100_subtr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:dtree,P2:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns3:(set @ n)]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => (((P2 @ Ns3) @ Tr7) @ Tr7)))) => ((! [Tr33:dtree,Ns3:(set @ n),Tr12:dtree,Tr23:dtree]: (((((member @ n) @ (root @ Tr33)) @ Ns3) => ((((gram_L716654942_subtr @ Ns3) @ Tr12) @ Tr23) => ((((P2 @ Ns3) @ Tr12) @ Tr23) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr23)) @ (cont @ Tr33)) => (((P2 @ Ns3) @ Tr12) @ Tr33))))))) => (((P2 @ X1) @ X22) @ X32))))))).
% 3.26/1.70 thf(fact_101_subtr__inductL, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Phi:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((! [Ns3:(set @ n),Tr7:dtree]: ((((Phi @ Ns3) @ Tr7) @ Tr7))) => ((! [Ns3:(set @ n),Tr12:dtree,Tr23:dtree,Tr33:dtree]: (((((member @ n) @ (root @ Tr12)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L716654942_subtr @ Ns3) @ Tr23) @ Tr33) => ((((Phi @ Ns3) @ Tr23) @ Tr33) => (((Phi @ Ns3) @ Tr12) @ Tr33))))))) => (((Phi @ Ns) @ Tr1) @ Tr22))))))).
% 3.26/1.70 thf(fact_102_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X:A]: ((bot_bot @ B)))))))).
% 3.26/1.70 thf(fact_103_subtr2_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:dtree,P2:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L1283001940subtr2 @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns3:(set @ n)]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => (((P2 @ Ns3) @ Tr7) @ Tr7)))) => ((! [Tr12:dtree,Ns3:(set @ n),Tr23:dtree,Tr33:dtree]: (((((member @ n) @ (root @ Tr12)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L1283001940subtr2 @ Ns3) @ Tr23) @ Tr33) => ((((P2 @ Ns3) @ Tr23) @ Tr33) => (((P2 @ Ns3) @ Tr12) @ Tr33))))))) => (((P2 @ X1) @ X22) @ X32))))))).
% 3.26/1.70 thf(fact_104_subtr2__StepR, axiom, (! [Tr3:dtree,Ns:(set @ n),Tr22:dtree,Tr1:dtree]: (((((member @ n) @ (root @ Tr3)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr3)) => ((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr3))))))).
% 3.26/1.70 thf(fact_105_subtr2_Osimps, axiom, (gram_L1283001940subtr2 = (^ [A12:(set @ n),A23:dtree,A33:dtree]: (((? [Tr4:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A23 = Tr4) & ((A33 = Tr4) & (((member @ n) @ (root @ Tr4)) @ Ns2)))))) | (? [Tr13:dtree,Ns2:(set @ n),Tr24:dtree,Tr32:dtree]: (((A12 = Ns2) & ((A23 = Tr13) & ((A33 = Tr32) & ((((member @ n) @ (root @ Tr13)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr24)) & (((gram_L1283001940subtr2 @ Ns2) @ Tr24) @ Tr32))))))))))))).
% 3.26/1.70 thf(fact_106_subtr2_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:dtree]: (((((gram_L1283001940subtr2 @ A1) @ A22) @ A32) => (((A32 = A22) => (~ ((((member @ n) @ (root @ A22)) @ A1)))) => (~ (((((member @ n) @ (root @ A22)) @ A1) => (! [Tr23:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ A22)) @ (cont @ Tr23)) => (~ ((((gram_L1283001940subtr2 @ A1) @ Tr23) @ A32)))))))))))))).
% 3.26/1.70 thf(fact_107_subtr2_OStep, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr22:dtree,Tr3:dtree]: (((((member @ n) @ (root @ Tr1)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr22)) => ((((gram_L1283001940subtr2 @ Ns) @ Tr22) @ Tr3) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr3))))))).
% 3.26/1.70 thf(fact_108_inFr_OInd, axiom, (! [Tr:dtree,Ns:(set @ n),Tr1:dtree,T2:t]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L1333338417e_inFr @ Ns) @ Tr1) @ T2) => (((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2))))))).
% 3.26/1.70 thf(fact_109_inItr_OInd, axiom, (! [Tr:dtree,Ns:(set @ n),Tr1:dtree,N:n]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L830233218_inItr @ Ns) @ Tr1) @ N) => (((gram_L830233218_inItr @ Ns) @ Tr) @ N))))))).
% 3.26/1.70 thf(fact_110_inItr_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:n]: (((((gram_L830233218_inItr @ A1) @ A22) @ A32) => (((A32 = (root @ A22)) => (~ ((((member @ n) @ (root @ A22)) @ A1)))) => (~ (((((member @ n) @ (root @ A22)) @ A1) => (! [Tr12:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ A22)) => (~ ((((gram_L830233218_inItr @ A1) @ Tr12) @ A32)))))))))))))).
% 3.26/1.70 thf(fact_111_inItr_Osimps, axiom, (gram_L830233218_inItr = (^ [A12:(set @ n),A23:dtree,A33:n]: (((? [Tr4:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A23 = Tr4) & ((A33 = (root @ Tr4)) & (((member @ n) @ (root @ Tr4)) @ Ns2)))))) | (? [Tr4:dtree,Ns2:(set @ n),Tr13:dtree,N2:n]: (((A12 = Ns2) & ((A23 = Tr4) & ((A33 = N2) & ((((member @ n) @ (root @ Tr4)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr4)) & (((gram_L830233218_inItr @ Ns2) @ Tr13) @ N2))))))))))))).
% 3.26/1.70 thf(fact_112_inItr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:n,P2:((set @ n) > (dtree > (n > $o)))]: (((((gram_L830233218_inItr @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns3:(set @ n)]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => (((P2 @ Ns3) @ Tr7) @ (root @ Tr7))))) => ((! [Tr7:dtree,Ns3:(set @ n),Tr12:dtree,N3:n]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr7)) => ((((gram_L830233218_inItr @ Ns3) @ Tr12) @ N3) => ((((P2 @ Ns3) @ Tr12) @ N3) => (((P2 @ Ns3) @ Tr7) @ N3))))))) => (((P2 @ X1) @ X22) @ X32))))))).
% 3.26/1.70 thf(fact_113_inFr2__Ind, axiom, (! [Ns:(set @ n),Tr1:dtree,T2:t,Tr:dtree]: (((((gram_L805317441_inFr2 @ Ns) @ Tr1) @ T2) => ((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => (((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2))))))).
% 3.26/1.70 thf(fact_114_Inl__Inr__False, axiom, (! [A:$tType,B:$tType,X5:A,Y3:B]: (((((sum_Inl @ A) @ B) @ X5) != (((sum_Inr @ B) @ A) @ Y3))))).
% 3.26/1.70 thf(fact_115_Inr__Inl__False, axiom, (! [B:$tType,A:$tType,X5:B,Y3:A]: (((((sum_Inr @ B) @ A) @ X5) != (((sum_Inl @ A) @ B) @ Y3))))).
% 3.26/1.70 thf(fact_116_Inl__Inr__image__cong, axiom, (! [B:$tType,A:$tType,A2:(set @ ((sum_sum @ A) @ B)),B2:(set @ ((sum_sum @ A) @ B))]: (((((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ A2) = ((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ B2)) => ((((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ A2) = ((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ B2)) => (A2 = B2)))))).
% 3.26/1.70 thf(fact_117_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (bot_bot @ (set @ A))))))))).
% 3.26/1.70 thf(fact_118_Collect__empty__eq__bot, axiom, (! [A:$tType,P2:(A > $o)]: (((((collect @ A) @ P2) = (bot_bot @ (set @ A))) = (P2 = (bot_bot @ (A > $o))))))).
% 3.26/1.70 thf(fact_119_obj__sumE__f, axiom, (! [A:$tType,C:$tType,B:$tType,S:B,F:(((sum_sum @ A) @ C) > B),P2:$o]: (((! [X6:A]: (((S = (F @ (((sum_Inl @ A) @ C) @ X6))) => P2))) => ((! [X6:C]: (((S = (F @ (((sum_Inr @ C) @ A) @ X6))) => P2))) => (! [X8:((sum_sum @ A) @ C)]: (((S = (F @ X8)) => P2)))))))).
% 3.26/1.70 thf(fact_120_inFr2_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:t,P2:((set @ n) > (dtree > (t > $o)))]: (((((gram_L805317441_inFr2 @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns3:(set @ n),T4:t]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T4)) @ (cont @ Tr7)) => (((P2 @ Ns3) @ Tr7) @ T4))))) => ((! [Tr12:dtree,Tr7:dtree,Ns1:(set @ n),T4:t]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr7)) => ((((gram_L805317441_inFr2 @ Ns1) @ Tr12) @ T4) => ((((P2 @ Ns1) @ Tr12) @ T4) => (((P2 @ (((insert @ n) @ (root @ Tr7)) @ Ns1)) @ Tr7) @ T4)))))) => (((P2 @ X1) @ X22) @ X32))))))).
% 3.26/1.70 thf(fact_121_inFr2_Osimps, axiom, (gram_L805317441_inFr2 = (^ [A12:(set @ n),A23:dtree,A33:t]: (((? [Tr4:dtree,Ns2:(set @ n),T3:t]: (((A12 = Ns2) & ((A23 = Tr4) & ((A33 = T3) & ((((member @ n) @ (root @ Tr4)) @ Ns2) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T3)) @ (cont @ Tr4)))))))) | (? [Tr13:dtree,Tr4:dtree,Ns12:(set @ n),T3:t]: (((A12 = (((insert @ n) @ (root @ Tr4)) @ Ns12)) & ((A23 = Tr4) & ((A33 = T3) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr4)) & (((gram_L805317441_inFr2 @ Ns12) @ Tr13) @ T3)))))))))))).
% 3.26/1.70 thf(fact_122_inFr2_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:t]: (((((gram_L805317441_inFr2 @ A1) @ A22) @ A32) => (((((member @ n) @ (root @ A22)) @ A1) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ A32)) @ (cont @ A22))))) => (~ ((! [Tr12:dtree,Tr7:dtree,Ns1:(set @ n)]: (((A1 = (((insert @ n) @ (root @ Tr7)) @ Ns1)) => ((A22 = Tr7) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr7)) => (~ ((((gram_L805317441_inFr2 @ Ns1) @ Tr12) @ A32))))))))))))))).
% 3.26/1.70 thf(fact_123_inFr2_OInd, axiom, (! [Tr1:dtree,Tr:dtree,Ns13:(set @ n),T2:t]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L805317441_inFr2 @ Ns13) @ Tr1) @ T2) => (((gram_L805317441_inFr2 @ (((insert @ n) @ (root @ Tr)) @ Ns13)) @ Tr) @ T2)))))).
% 3.26/1.70 thf(fact_124_insertCI, axiom, (! [A:$tType,A4:A,B2:(set @ A),B3:A]: ((((~ ((((member @ A) @ A4) @ B2))) => (A4 = B3)) => (((member @ A) @ A4) @ (((insert @ A) @ B3) @ B2)))))).
% 3.26/1.70 thf(fact_125_insert__iff, axiom, (! [A:$tType,A4:A,B3:A,A2:(set @ A)]: (((((member @ A) @ A4) @ (((insert @ A) @ B3) @ A2)) = ((A4 = B3) | (((member @ A) @ A4) @ A2)))))).
% 3.26/1.70 thf(fact_126_insert__absorb2, axiom, (! [A:$tType,X5:A,A2:(set @ A)]: (((((insert @ A) @ X5) @ (((insert @ A) @ X5) @ A2)) = (((insert @ A) @ X5) @ A2))))).
% 3.26/1.70 thf(fact_127_singletonI, axiom, (! [A:$tType,A4:A]: ((((member @ A) @ A4) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))))).
% 3.26/1.70 thf(fact_128_singleton__conv2, axiom, (! [A:$tType,A4:A]: ((((collect @ A) @ ((^ [Y6:A,Z:A]: ((Y6 = Z))) @ A4)) = (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))))).
% 3.26/1.70 thf(fact_129_singleton__conv, axiom, (! [A:$tType,A4:A]: ((((collect @ A) @ (^ [X:A]: ((X = A4)))) = (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))))).
% 3.26/1.70 thf(fact_130_singleton__inject, axiom, (! [A:$tType,A4:A,B3:A]: ((((((insert @ A) @ A4) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) => (A4 = B3))))).
% 3.26/1.70 thf(fact_131_insert__not__empty, axiom, (! [A:$tType,A4:A,A2:(set @ A)]: (((((insert @ A) @ A4) @ A2) != (bot_bot @ (set @ A)))))).
% 3.26/1.70 thf(fact_132_doubleton__eq__iff, axiom, (! [A:$tType,A4:A,B3:A,C3:A,D2:A]: ((((((insert @ A) @ A4) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C3) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A4 = C3) & (B3 = D2)) | ((A4 = D2) & (B3 = C3))))))).
% 3.26/1.70 thf(fact_133_singleton__iff, axiom, (! [A:$tType,B3:A,A4:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A)))) = (B3 = A4))))).
% 3.26/1.70 thf(fact_134_singletonD, axiom, (! [A:$tType,B3:A,A4:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A)))) => (B3 = A4))))).
% 3.26/1.70 thf(fact_135_insertE, axiom, (! [A:$tType,A4:A,B3:A,A2:(set @ A)]: (((((member @ A) @ A4) @ (((insert @ A) @ B3) @ A2)) => ((A4 != B3) => (((member @ A) @ A4) @ A2)))))).
% 3.26/1.70 thf(fact_136_insertI1, axiom, (! [A:$tType,A4:A,B2:(set @ A)]: ((((member @ A) @ A4) @ (((insert @ A) @ A4) @ B2))))).
% 3.26/1.70 thf(fact_137_insertI2, axiom, (! [A:$tType,A4:A,B2:(set @ A),B3:A]: (((((member @ A) @ A4) @ B2) => (((member @ A) @ A4) @ (((insert @ A) @ B3) @ B2)))))).
% 3.26/1.70 thf(fact_138_Set_Oset__insert, axiom, (! [A:$tType,X5:A,A2:(set @ A)]: (((((member @ A) @ X5) @ A2) => (~ ((! [B9:(set @ A)]: (((A2 = (((insert @ A) @ X5) @ B9)) => (((member @ A) @ X5) @ B9)))))))))).
% 3.26/1.70 thf(fact_139_insert__compr, axiom, (! [A:$tType]: (((insert @ A) = (^ [A3:A,B4:(set @ A)]: (((collect @ A) @ (^ [X:A]: (((X = A3) | (((member @ A) @ X) @ B4))))))))))).
% 3.26/1.70 thf(fact_140_insert__ident, axiom, (! [A:$tType,X5:A,A2:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X5) @ A2))) => ((~ ((((member @ A) @ X5) @ B2))) => (((((insert @ A) @ X5) @ A2) = (((insert @ A) @ X5) @ B2)) = (A2 = B2))))))).
% 3.26/1.70 thf(fact_141_insert__absorb, axiom, (! [A:$tType,A4:A,A2:(set @ A)]: (((((member @ A) @ A4) @ A2) => ((((insert @ A) @ A4) @ A2) = A2))))).
% 3.26/1.70 thf(fact_142_insert__eq__iff, axiom, (! [A:$tType,A4:A,A2:(set @ A),B3:A,B2:(set @ A)]: (((~ ((((member @ A) @ A4) @ A2))) => ((~ ((((member @ A) @ B3) @ B2))) => (((((insert @ A) @ A4) @ A2) = (((insert @ A) @ B3) @ B2)) = (((A4 = B3) => (A2 = B2)) & ((A4 != B3) => (? [C4:(set @ A)]: (((A2 = (((insert @ A) @ B3) @ C4)) & ((~ ((((member @ A) @ B3) @ C4))) & ((B2 = (((insert @ A) @ A4) @ C4)) & (~ ((((member @ A) @ A4) @ C4)))))))))))))))).
% 3.26/1.70 thf(fact_143_insert__Collect, axiom, (! [A:$tType,A4:A,P2:(A > $o)]: (((((insert @ A) @ A4) @ ((collect @ A) @ P2)) = ((collect @ A) @ (^ [U:A]: (((U != A4) => (P2 @ U))))))))).
% 3.26/1.70 thf(fact_144_insert__commute, axiom, (! [A:$tType,X5:A,Y3:A,A2:(set @ A)]: (((((insert @ A) @ X5) @ (((insert @ A) @ Y3) @ A2)) = (((insert @ A) @ Y3) @ (((insert @ A) @ X5) @ A2)))))).
% 3.26/1.70 thf(fact_145_mk__disjoint__insert, axiom, (! [A:$tType,A4:A,A2:(set @ A)]: (((((member @ A) @ A4) @ A2) => (? [B9:(set @ A)]: (((A2 = (((insert @ A) @ A4) @ B9)) & (~ ((((member @ A) @ A4) @ B9)))))))))).
% 3.26/1.70 thf(fact_146_Collect__conv__if2, axiom, (! [A:$tType,P2:(A > $o),A4:A]: ((((P2 @ A4) => (((collect @ A) @ (^ [X:A]: (((A4 = X) & (P2 @ X))))) = (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))) & ((~ ((P2 @ A4))) => (((collect @ A) @ (^ [X:A]: (((A4 = X) & (P2 @ X))))) = (bot_bot @ (set @ A)))))))).
% 3.26/1.70 thf(fact_147_Collect__conv__if, axiom, (! [A:$tType,P2:(A > $o),A4:A]: ((((P2 @ A4) => (((collect @ A) @ (^ [X:A]: (((X = A4) & (P2 @ X))))) = (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))) & ((~ ((P2 @ A4))) => (((collect @ A) @ (^ [X:A]: (((X = A4) & (P2 @ X))))) = (bot_bot @ (set @ A)))))))).
% 3.26/1.70 thf(fact_148_vimage__singleton__eq, axiom, (! [A:$tType,B:$tType,A4:A,F:(A > B),B3:B]: (((((member @ A) @ A4) @ ((((vimage @ A) @ B) @ F) @ (((insert @ B) @ B3) @ (bot_bot @ (set @ B))))) = ((F @ A4) = B3))))).
% 3.26/1.70 thf(fact_149_inFr__Ind__minus, axiom, (! [Ns13:(set @ n),Tr1:dtree,T2:t,Tr:dtree]: (((((gram_L1333338417e_inFr @ Ns13) @ Tr1) @ T2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => (((gram_L1333338417e_inFr @ (((insert @ n) @ (root @ Tr)) @ Ns13)) @ Tr) @ T2)))))).
% 3.26/1.70 thf(fact_150_ccpo__Sup__singleton, axiom, (! [A:$tType]: ((((comple1141879883l_ccpo @ A) @ (type2 @ A)) => (! [X5:A]: ((((complete_Sup_Sup @ A) @ (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))) = X5))))))).
% 3.26/1.70 thf(fact_151_cSup__singleton, axiom, (! [A:$tType]: ((((condit378418413attice @ A) @ (type2 @ A)) => (! [X5:A]: ((((complete_Sup_Sup @ A) @ (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))) = X5))))))).
% 3.26/1.70 thf(fact_152_is__singletonI, axiom, (! [A:$tType,X5:A]: (((is_singleton @ A) @ (((insert @ A) @ X5) @ (bot_bot @ (set @ A))))))).
% 3.26/1.70 thf(fact_153_the__elem__eq, axiom, (! [A:$tType,X5:A]: ((((the_elem @ A) @ (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))) = X5)))).
% 3.26/1.70 thf(fact_154_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A6:(set @ A)]: ((A6 = (((insert @ A) @ ((the_elem @ A) @ A6)) @ (bot_bot @ (set @ A)))))))))).
% 3.26/1.70 thf(fact_155_is__singletonI_H, axiom, (! [A:$tType,A2:(set @ A)]: (((A2 != (bot_bot @ (set @ A))) => ((! [X6:A,Y4:A]: (((((member @ A) @ X6) @ A2) => ((((member @ A) @ Y4) @ A2) => (X6 = Y4))))) => ((is_singleton @ A) @ A2)))))).
% 3.26/1.70 thf(fact_156_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A6:(set @ A)]: ((? [X:A]: ((A6 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))))))))))).
% 3.26/1.70 thf(fact_157_is__singletonE, axiom, (! [A:$tType,A2:(set @ A)]: ((((is_singleton @ A) @ A2) => (~ ((! [X6:A]: ((A2 != (((insert @ A) @ X6) @ (bot_bot @ (set @ A)))))))))))).
% 3.26/1.70 thf(fact_158_sum__set__simps_I1_J, axiom, (! [B:$tType,A:$tType,X5:A]: (((((basic_setl @ A) @ B) @ (((sum_Inl @ A) @ B) @ X5)) = (((insert @ A) @ X5) @ (bot_bot @ (set @ A))))))).
% 3.26/1.70 thf(fact_159_sum__set__simps_I4_J, axiom, (! [E:$tType,A:$tType,X5:A]: (((((basic_setr @ E) @ A) @ (((sum_Inr @ A) @ E) @ X5)) = (((insert @ A) @ X5) @ (bot_bot @ (set @ A))))))).
% 3.26/1.70 thf(fact_160_the__elem__def, axiom, (! [A:$tType]: (((the_elem @ A) = (^ [X9:(set @ A)]: (((the @ A) @ (^ [X:A]: ((X9 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))))).
% 3.26/1.70 thf(fact_161_sum__set__simps_I2_J, axiom, (! [A:$tType,C:$tType,X5:A]: (((((basic_setl @ C) @ A) @ (((sum_Inr @ A) @ C) @ X5)) = (bot_bot @ (set @ C)))))).
% 3.26/1.70 thf(fact_162_sum__set__simps_I3_J, axiom, (! [A:$tType,D:$tType,X5:A]: (((((basic_setr @ A) @ D) @ (((sum_Inl @ A) @ D) @ X5)) = (bot_bot @ (set @ D)))))).
% 3.26/1.70 thf(fact_163_old_Orec__sum__def, axiom, (! [B:$tType,T:$tType,A:$tType]: (((((sum_rec_sum @ A) @ T) @ B) = (^ [F12:(A > T),F23:(B > T),X:((sum_sum @ A) @ B)]: (((the @ T) @ ((((((sum_rec_set_sum @ A) @ T) @ B) @ F12) @ F23) @ X)))))))).
% 3.26/1.70 thf(fact_164_the__sym__eq__trivial, axiom, (! [A:$tType,X5:A]: ((((the @ A) @ ((^ [Y6:A,Z:A]: ((Y6 = Z))) @ X5)) = X5)))).
% 3.26/1.70 thf(fact_165_the__eq__trivial, axiom, (! [A:$tType,A4:A]: ((((the @ A) @ (^ [X:A]: ((X = A4)))) = A4)))).
% 3.26/1.70 thf(fact_166_the__equality, axiom, (! [A:$tType,P2:(A > $o),A4:A]: (((P2 @ A4) => ((! [X6:A]: (((P2 @ X6) => (X6 = A4)))) => (((the @ A) @ P2) = A4)))))).
% 3.26/1.70 thf(fact_167_theI, axiom, (! [A:$tType,P2:(A > $o),A4:A]: (((P2 @ A4) => ((! [X6:A]: (((P2 @ X6) => (X6 = A4)))) => (P2 @ ((the @ A) @ P2))))))).
% 3.26/1.70 thf(fact_168_theI_H, axiom, (! [A:$tType,P2:(A > $o)]: (((? [X8:A]: (((P2 @ X8) & (! [Y4:A]: (((P2 @ Y4) => (Y4 = X8))))))) => (P2 @ ((the @ A) @ P2)))))).
% 3.26/1.70 thf(fact_169_theI2, axiom, (! [A:$tType,P2:(A > $o),A4:A,Q:(A > $o)]: (((P2 @ A4) => ((! [X6:A]: (((P2 @ X6) => (X6 = A4)))) => ((! [X6:A]: (((P2 @ X6) => (Q @ X6)))) => (Q @ ((the @ A) @ P2)))))))).
% 3.26/1.70 thf(fact_170_If__def, axiom, (! [A:$tType]: (((if @ A) = (^ [P:$o,X:A,Y:A]: (((the @ A) @ (^ [Z2:A]: (((P => (Z2 = X)) & ((~ (P)) => (Z2 = Y)))))))))))).
% 3.26/1.70 thf(fact_171_the1I2, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((? [X8:A]: (((P2 @ X8) & (! [Y4:A]: (((P2 @ Y4) => (Y4 = X8))))))) => ((! [X6:A]: (((P2 @ X6) => (Q @ X6)))) => (Q @ ((the @ A) @ P2))))))).
% 3.26/1.70 thf(fact_172_the1__equality, axiom, (! [A:$tType,P2:(A > $o),A4:A]: (((? [X8:A]: (((P2 @ X8) & (! [Y4:A]: (((P2 @ Y4) => (Y4 = X8))))))) => ((P2 @ A4) => (((the @ A) @ P2) = A4)))))).
% 3.26/1.70 thf(fact_173_setl_Oinducts, axiom, (! [B:$tType,A:$tType,X5:A,S:((sum_sum @ A) @ B),P2:(A > $o)]: (((((member @ A) @ X5) @ (((basic_setl @ A) @ B) @ S)) => ((! [X6:A]: (((S = (((sum_Inl @ A) @ B) @ X6)) => (P2 @ X6)))) => (P2 @ X5)))))).
% 3.26/1.70 thf(fact_174_setl_Ointros, axiom, (! [B:$tType,A:$tType,S:((sum_sum @ A) @ B),X5:A]: (((S = (((sum_Inl @ A) @ B) @ X5)) => (((member @ A) @ X5) @ (((basic_setl @ A) @ B) @ S)))))).
% 3.26/1.70 thf(fact_175_setl_Osimps, axiom, (! [B:$tType,A:$tType,A4:A,S:((sum_sum @ A) @ B)]: (((((member @ A) @ A4) @ (((basic_setl @ A) @ B) @ S)) = (? [X:A]: (((A4 = X) & (S = (((sum_Inl @ A) @ B) @ X))))))))).
% 3.26/1.70 thf(fact_176_setr_Oinducts, axiom, (! [A:$tType,B:$tType,X5:B,S:((sum_sum @ A) @ B),P2:(B > $o)]: (((((member @ B) @ X5) @ (((basic_setr @ A) @ B) @ S)) => ((! [X6:B]: (((S = (((sum_Inr @ B) @ A) @ X6)) => (P2 @ X6)))) => (P2 @ X5)))))).
% 3.26/1.70 thf(fact_177_setr_Ointros, axiom, (! [B:$tType,A:$tType,S:((sum_sum @ A) @ B),X5:B]: (((S = (((sum_Inr @ B) @ A) @ X5)) => (((member @ B) @ X5) @ (((basic_setr @ A) @ B) @ S)))))).
% 3.26/1.70 thf(fact_178_setr_Osimps, axiom, (! [A:$tType,B:$tType,A4:B,S:((sum_sum @ A) @ B)]: (((((member @ B) @ A4) @ (((basic_setr @ A) @ B) @ S)) = (? [X:B]: (((A4 = X) & (S = (((sum_Inr @ B) @ A) @ X))))))))).
% 3.26/1.70 thf(fact_179_setr_Ocases, axiom, (! [A:$tType,B:$tType,A4:B,S:((sum_sum @ A) @ B)]: (((((member @ B) @ A4) @ (((basic_setr @ A) @ B) @ S)) => (S = (((sum_Inr @ B) @ A) @ A4)))))).
% 3.26/1.70 thf(fact_180_setl_Ocases, axiom, (! [B:$tType,A:$tType,A4:A,S:((sum_sum @ A) @ B)]: (((((member @ A) @ A4) @ (((basic_setl @ A) @ B) @ S)) => (S = (((sum_Inl @ A) @ B) @ A4)))))).
% 3.26/1.70 thf(fact_181_vimage__eq__UN, axiom, (! [B:$tType,A:$tType]: ((((vimage @ A) @ B) = (^ [F2:(A > B),B4:(set @ B)]: (((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ (^ [Y:B]: (((((vimage @ A) @ B) @ F2) @ (((insert @ B) @ Y) @ (bot_bot @ (set @ B))))))) @ B4)))))))).
% 3.26/1.70 thf(fact_182_sum__set__defs_I2_J, axiom, (! [C:$tType,D:$tType]: ((((basic_setr @ C) @ D) = (((((sum_case_sum @ C) @ (set @ D)) @ D) @ (^ [A3:C]: ((bot_bot @ (set @ D))))) @ (^ [Z2:D]: ((((insert @ D) @ Z2) @ (bot_bot @ (set @ D)))))))))).
% 3.26/1.70 thf(fact_183_sum__set__defs_I1_J, axiom, (! [A:$tType,B:$tType]: ((((basic_setl @ A) @ B) = (((((sum_case_sum @ A) @ (set @ A)) @ B) @ (^ [Z2:A]: ((((insert @ A) @ Z2) @ (bot_bot @ (set @ A)))))) @ (^ [B10:B]: ((bot_bot @ (set @ A))))))))).
% 3.26/1.70 thf(fact_184_image__eqI, axiom, (! [A:$tType,B:$tType,B3:A,F:(B > A),X5:B,A2:(set @ B)]: (((B3 = (F @ X5)) => ((((member @ B) @ X5) @ A2) => (((member @ A) @ B3) @ ((((image @ B) @ A) @ F) @ A2))))))).
% 3.26/1.70 thf(fact_185_image__ident, axiom, (! [A:$tType,Y5:(set @ A)]: ((((((image @ A) @ A) @ (^ [X:A]: (X))) @ Y5) = Y5)))).
% 3.26/1.70 thf(fact_186_case__sum__KK, axiom, (! [C:$tType,B:$tType,A:$tType,A4:C]: (((((((sum_case_sum @ A) @ C) @ B) @ (^ [X:A]: (A4))) @ (^ [X:B]: (A4))) = (^ [X:((sum_sum @ A) @ B)]: (A4)))))).
% 3.26/1.70 thf(fact_187_image__is__empty, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:(set @ B)]: (((((((image @ B) @ A) @ F) @ A2) = (bot_bot @ (set @ A))) = (A2 = (bot_bot @ (set @ B))))))).
% 3.26/1.70 thf(fact_188_empty__is__image, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:(set @ B)]: ((((bot_bot @ (set @ A)) = ((((image @ B) @ A) @ F) @ A2)) = (A2 = (bot_bot @ (set @ B))))))).
% 3.26/1.70 thf(fact_189_image__empty, axiom, (! [B:$tType,A:$tType,F:(B > A)]: ((((((image @ B) @ A) @ F) @ (bot_bot @ (set @ B))) = (bot_bot @ (set @ A)))))).
% 3.26/1.70 thf(fact_190_insert__image, axiom, (! [B:$tType,A:$tType,X5:A,A2:(set @ A),F:(A > B)]: (((((member @ A) @ X5) @ A2) => ((((insert @ B) @ (F @ X5)) @ ((((image @ A) @ B) @ F) @ A2)) = ((((image @ A) @ B) @ F) @ A2)))))).
% 3.26/1.70 thf(fact_191_image__insert, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:B,B2:(set @ B)]: ((((((image @ B) @ A) @ F) @ (((insert @ B) @ A4) @ B2)) = (((insert @ A) @ (F @ A4)) @ ((((image @ B) @ A) @ F) @ B2)))))).
% 3.26/1.70 thf(fact_192_ball__UN, axiom, (! [A:$tType,B:$tType,B2:(B > (set @ A)),A2:(set @ B),P2:(A > $o)]: (((! [X:A]: (((((member @ A) @ X) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ A2))) => (P2 @ X)))) = (! [X:B]: (((((member @ B) @ X) @ A2) => (! [Y:A]: (((((member @ A) @ Y) @ (B2 @ X)) => (P2 @ Y))))))))))).
% 3.26/1.70 thf(fact_193_bex__UN, axiom, (! [A:$tType,B:$tType,B2:(B > (set @ A)),A2:(set @ B),P2:(A > $o)]: (((? [X:A]: (((((member @ A) @ X) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ A2))) & (P2 @ X)))) = (? [X:B]: (((((member @ B) @ X) @ A2) & (? [Y:A]: (((((member @ A) @ Y) @ (B2 @ X)) & (P2 @ Y))))))))))).
% 3.26/1.70 thf(fact_194_UN__ball__bex__simps_I2_J, axiom, (! [C:$tType,B:$tType,B2:(B > (set @ C)),A2:(set @ B),P2:(C > $o)]: (((! [X:C]: (((((member @ C) @ X) @ ((complete_Sup_Sup @ (set @ C)) @ ((((image @ B) @ (set @ C)) @ B2) @ A2))) => (P2 @ X)))) = (! [X:B]: (((((member @ B) @ X) @ A2) => (! [Y:C]: (((((member @ C) @ Y) @ (B2 @ X)) => (P2 @ Y))))))))))).
% 3.26/1.70 thf(fact_195_UN__ball__bex__simps_I4_J, axiom, (! [F3:$tType,E:$tType,B2:(E > (set @ F3)),A2:(set @ E),P2:(F3 > $o)]: (((? [X:F3]: (((((member @ F3) @ X) @ ((complete_Sup_Sup @ (set @ F3)) @ ((((image @ E) @ (set @ F3)) @ B2) @ A2))) & (P2 @ X)))) = (? [X:E]: (((((member @ E) @ X) @ A2) & (? [Y:F3]: (((((member @ F3) @ Y) @ (B2 @ X)) & (P2 @ Y))))))))))).
% 3.26/1.70 thf(fact_196_SUP__identity__eq, axiom, (! [A:$tType]: ((((complete_Sup @ A) @ (type2 @ A)) => (! [A2:(set @ A)]: ((((complete_Sup_Sup @ A) @ ((((image @ A) @ A) @ (^ [X:A]: (X))) @ A2)) = ((complete_Sup_Sup @ A) @ A2)))))))).
% 3.26/1.70 thf(fact_197_SUP__apply, axiom, (! [A:$tType,B:$tType,C:$tType]: ((((complete_Sup @ A) @ (type2 @ A)) => (! [F:(C > (B > A)),A2:(set @ C),X5:B]: (((((complete_Sup_Sup @ (B > A)) @ ((((image @ C) @ (B > A)) @ F) @ A2)) @ X5) = ((complete_Sup_Sup @ A) @ ((((image @ C) @ A) @ (^ [Y:C]: (((F @ Y) @ X5)))) @ A2))))))))).
% 3.26/1.70 thf(fact_198_UN__I, axiom, (! [B:$tType,A:$tType,A4:A,A2:(set @ A),B3:B,B2:(A > (set @ B))]: (((((member @ A) @ A4) @ A2) => ((((member @ B) @ B3) @ (B2 @ A4)) => (((member @ B) @ B3) @ ((complete_Sup_Sup @ (set @ B)) @ ((((image @ A) @ (set @ B)) @ B2) @ A2)))))))).
% 3.26/1.70 thf(fact_199_UN__iff, axiom, (! [A:$tType,B:$tType,B3:A,B2:(B > (set @ A)),A2:(set @ B)]: (((((member @ A) @ B3) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ A2))) = (? [X:B]: (((((member @ B) @ X) @ A2) & (((member @ A) @ B3) @ (B2 @ X))))))))).
% 3.26/1.70 thf(fact_200_SUP__bot, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A2:(set @ B)]: ((((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ (^ [X:B]: ((bot_bot @ A)))) @ A2)) = (bot_bot @ A)))))))).
% 3.26/1.70 thf(fact_201_SUP__bot__conv_I1_J, axiom, (! [A:$tType,B:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [B2:(B > A),A2:(set @ B)]: (((((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ B2) @ A2)) = (bot_bot @ A)) = (! [X:B]: (((((member @ B) @ X) @ A2) => ((B2 @ X) = (bot_bot @ A)))))))))))).
% 3.26/1.70 thf(fact_202_SUP__bot__conv_I2_J, axiom, (! [A:$tType,B:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [B2:(B > A),A2:(set @ B)]: ((((bot_bot @ A) = ((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ B2) @ A2))) = (! [X:B]: (((((member @ B) @ X) @ A2) => ((B2 @ X) = (bot_bot @ A)))))))))))).
% 3.26/1.70 thf(fact_203_cSUP__const, axiom, (! [B:$tType,A:$tType]: ((((condit378418413attice @ A) @ (type2 @ A)) => (! [A2:(set @ B),C3:A]: (((A2 != (bot_bot @ (set @ B))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ (^ [X:B]: (C3))) @ A2)) = C3)))))))).
% 3.26/1.70 thf(fact_204_SUP__const, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A2:(set @ B),F:A]: (((A2 != (bot_bot @ (set @ B))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ (^ [I:B]: (F))) @ A2)) = F)))))))).
% 3.26/1.70 thf(fact_205_UN__constant, axiom, (! [B:$tType,A:$tType,A2:(set @ B),C3:(set @ A)]: ((((A2 = (bot_bot @ (set @ B))) => (((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ (^ [Y:B]: (C3))) @ A2)) = (bot_bot @ (set @ A)))) & ((A2 != (bot_bot @ (set @ B))) => (((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ (^ [Y:B]: (C3))) @ A2)) = C3)))))).
% 3.26/1.70 thf(fact_206_SUP__empty, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [F:(B > A)]: ((((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ F) @ (bot_bot @ (set @ B)))) = (bot_bot @ A)))))))).
% 3.26/1.70 thf(fact_207_UN__simps_I1_J, axiom, (! [A:$tType,B:$tType,C2:(set @ B),A4:A,B2:(B > (set @ A))]: ((((C2 = (bot_bot @ (set @ B))) => (((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ (^ [X:B]: ((((insert @ A) @ A4) @ (B2 @ X))))) @ C2)) = (bot_bot @ (set @ A)))) & ((C2 != (bot_bot @ (set @ B))) => (((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ (^ [X:B]: ((((insert @ A) @ A4) @ (B2 @ X))))) @ C2)) = (((insert @ A) @ A4) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ C2))))))))).
% 3.26/1.70 thf(fact_208_UN__singleton, axiom, (! [A:$tType,A2:(set @ A)]: ((((complete_Sup_Sup @ (set @ A)) @ ((((image @ A) @ (set @ A)) @ (^ [X:A]: ((((insert @ A) @ X) @ (bot_bot @ (set @ A)))))) @ A2)) = A2)))).
% 3.26/1.70 thf(fact_209_SUP__eq__const, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [I2:(set @ B),F:(B > A),X5:A]: (((I2 != (bot_bot @ (set @ B))) => ((! [I3:B]: (((((member @ B) @ I3) @ I2) => ((F @ I3) = X5)))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ F) @ I2)) = X5))))))))).
% 3.26/1.70 thf(fact_210_Sup_OSUP__cong, axiom, (! [A:$tType,B:$tType,A2:(set @ B),B2:(set @ B),C2:(B > A),D3:(B > A),Sup:((set @ A) > A)]: (((A2 = B2) => ((! [X6:B]: (((((member @ B) @ X6) @ B2) => ((C2 @ X6) = (D3 @ X6))))) => ((Sup @ ((((image @ B) @ A) @ C2) @ A2)) = (Sup @ ((((image @ B) @ A) @ D3) @ B2)))))))).
% 3.26/1.70 thf(fact_211_Inf_OINF__cong, axiom, (! [A:$tType,B:$tType,A2:(set @ B),B2:(set @ B),C2:(B > A),D3:(B > A),Inf:((set @ A) > A)]: (((A2 = B2) => ((! [X6:B]: (((((member @ B) @ X6) @ B2) => ((C2 @ X6) = (D3 @ X6))))) => ((Inf @ ((((image @ B) @ A) @ C2) @ A2)) = (Inf @ ((((image @ B) @ A) @ D3) @ B2)))))))).
% 3.26/1.70 thf(fact_212_case__sum__inject, axiom, (! [A:$tType,C:$tType,B:$tType,F1:(A > C),F22:(B > C),G1:(A > C),G22:(B > C)]: ((((((((sum_case_sum @ A) @ C) @ B) @ F1) @ F22) = (((((sum_case_sum @ A) @ C) @ B) @ G1) @ G22)) => (~ (((F1 = G1) => (F22 != G22)))))))).
% 3.26/1.70 thf(fact_213_rev__image__eqI, axiom, (! [B:$tType,A:$tType,X5:A,A2:(set @ A),B3:B,F:(A > B)]: (((((member @ A) @ X5) @ A2) => ((B3 = (F @ X5)) => (((member @ B) @ B3) @ ((((image @ A) @ B) @ F) @ A2))))))).
% 3.26/1.70 thf(fact_214_ball__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:(set @ B),P2:(A > $o)]: (((! [X6:A]: (((((member @ A) @ X6) @ ((((image @ B) @ A) @ F) @ A2)) => (P2 @ X6)))) => (! [X8:B]: (((((member @ B) @ X8) @ A2) => (P2 @ (F @ X8))))))))).
% 3.26/1.70 thf(fact_215_image__cong, axiom, (! [B:$tType,A:$tType,M:(set @ A),N4:(set @ A),F:(A > B),G2:(A > B)]: (((M = N4) => ((! [X6:A]: (((((member @ A) @ X6) @ N4) => ((F @ X6) = (G2 @ X6))))) => (((((image @ A) @ B) @ F) @ M) = ((((image @ A) @ B) @ G2) @ N4))))))).
% 3.26/1.70 thf(fact_216_bex__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:(set @ B),P2:(A > $o)]: (((? [X8:A]: (((((member @ A) @ X8) @ ((((image @ B) @ A) @ F) @ A2)) & (P2 @ X8)))) => (? [X6:B]: (((((member @ B) @ X6) @ A2) & (P2 @ (F @ X6))))))))).
% 3.26/1.70 thf(fact_217_image__iff, axiom, (! [A:$tType,B:$tType,Z3:A,F:(B > A),A2:(set @ B)]: (((((member @ A) @ Z3) @ ((((image @ B) @ A) @ F) @ A2)) = (? [X:B]: (((((member @ B) @ X) @ A2) & (Z3 = (F @ X))))))))).
% 3.26/1.70 thf(fact_218_imageI, axiom, (! [B:$tType,A:$tType,X5:A,A2:(set @ A),F:(A > B)]: (((((member @ A) @ X5) @ A2) => (((member @ B) @ (F @ X5)) @ ((((image @ A) @ B) @ F) @ A2)))))).
% 3.26/1.70 thf(fact_219_SUP__cong, axiom, (! [A:$tType,B:$tType]: ((((complete_Sup @ A) @ (type2 @ A)) => (! [A2:(set @ B),B2:(set @ B),C2:(B > A),D3:(B > A)]: (((A2 = B2) => ((! [X6:B]: (((((member @ B) @ X6) @ B2) => ((C2 @ X6) = (D3 @ X6))))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ C2) @ A2)) = ((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ D3) @ B2))))))))))).
% 3.26/1.70 thf(fact_220_Sup__SUP__eq, axiom, (! [A:$tType]: (((complete_Sup_Sup @ (A > $o)) = (^ [S2:(set @ (A > $o)),X:A]: ((((member @ A) @ X) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ (A > $o)) @ (set @ A)) @ (collect @ A)) @ S2))))))))).
% 3.26/1.70 thf(fact_221_case__sum__step_I1_J, axiom, (! [D:$tType,A:$tType,C:$tType,B:$tType,F4:(B > A),G3:(C > A),G2:(D > A),P4:((sum_sum @ B) @ C)]: ((((((((sum_case_sum @ ((sum_sum @ B) @ C)) @ A) @ D) @ (((((sum_case_sum @ B) @ A) @ C) @ F4) @ G3)) @ G2) @ (((sum_Inl @ ((sum_sum @ B) @ C)) @ D) @ P4)) = ((((((sum_case_sum @ B) @ A) @ C) @ F4) @ G3) @ P4))))).
% 3.26/1.70 thf(fact_222_case__sum__step_I2_J, axiom, (! [E:$tType,A:$tType,C:$tType,B:$tType,F:(E > A),F4:(B > A),G3:(C > A),P4:((sum_sum @ B) @ C)]: ((((((((sum_case_sum @ E) @ A) @ ((sum_sum @ B) @ C)) @ F) @ (((((sum_case_sum @ B) @ A) @ C) @ F4) @ G3)) @ (((sum_Inr @ ((sum_sum @ B) @ C)) @ E) @ P4)) = ((((((sum_case_sum @ B) @ A) @ C) @ F4) @ G3) @ P4))))).
% 3.26/1.70 thf(fact_223_old_Osum_Osimps_I5_J, axiom, (! [B:$tType,C:$tType,A:$tType,F1:(A > C),F22:(B > C),X1:A]: ((((((((sum_case_sum @ A) @ C) @ B) @ F1) @ F22) @ (((sum_Inl @ A) @ B) @ X1)) = (F1 @ X1))))).
% 3.26/1.70 thf(fact_224_old_Osum_Osimps_I6_J, axiom, (! [A:$tType,C:$tType,B:$tType,F1:(A > C),F22:(B > C),X22:B]: ((((((((sum_case_sum @ A) @ C) @ B) @ F1) @ F22) @ (((sum_Inr @ B) @ A) @ X22)) = (F22 @ X22))))).
% 3.26/1.70 thf(fact_225_setcompr__eq__image, axiom, (! [A:$tType,B:$tType,F:(B > A),P2:(B > $o)]: ((((collect @ A) @ (^ [Uu:A]: ((? [X:B]: (((Uu = (F @ X)) & (P2 @ X))))))) = ((((image @ B) @ A) @ F) @ ((collect @ B) @ P2)))))).
% 3.26/1.70 thf(fact_226_Setcompr__eq__image, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:(set @ B)]: ((((collect @ A) @ (^ [Uu:A]: ((? [X:B]: (((Uu = (F @ X)) & (((member @ B) @ X) @ A2))))))) = ((((image @ B) @ A) @ F) @ A2))))).
% 3.26/1.70 thf(fact_227_SUP__commute, axiom, (! [A:$tType,B:$tType,C:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [F:(B > (C > A)),B2:(set @ C),A2:(set @ B)]: ((((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ (^ [I:B]: (((complete_Sup_Sup @ A) @ ((((image @ C) @ A) @ (F @ I)) @ B2))))) @ A2)) = ((complete_Sup_Sup @ A) @ ((((image @ C) @ A) @ (^ [J:C]: (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ (^ [I:B]: (((F @ I) @ J)))) @ A2))))) @ B2))))))))).
% 3.26/1.70 thf(fact_228_UN__extend__simps_I9_J, axiom, (! [S3:$tType,R3:$tType,Q2:$tType,C2:(R3 > (set @ S3)),B2:(Q2 > (set @ R3)),A2:(set @ Q2)]: ((((complete_Sup_Sup @ (set @ S3)) @ ((((image @ Q2) @ (set @ S3)) @ (^ [X:Q2]: (((complete_Sup_Sup @ (set @ S3)) @ ((((image @ R3) @ (set @ S3)) @ C2) @ (B2 @ X)))))) @ A2)) = ((complete_Sup_Sup @ (set @ S3)) @ ((((image @ R3) @ (set @ S3)) @ C2) @ ((complete_Sup_Sup @ (set @ R3)) @ ((((image @ Q2) @ (set @ R3)) @ B2) @ A2)))))))).
% 3.26/1.70 thf(fact_229_UN__E, axiom, (! [A:$tType,B:$tType,B3:A,B2:(B > (set @ A)),A2:(set @ B)]: (((((member @ A) @ B3) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ A2))) => (~ ((! [X6:B]: (((((member @ B) @ X6) @ A2) => (~ ((((member @ A) @ B3) @ (B2 @ X6))))))))))))).
% 3.26/1.70 thf(fact_230_UN__UN__flatten, axiom, (! [A:$tType,B:$tType,C:$tType,C2:(B > (set @ A)),B2:(C > (set @ B)),A2:(set @ C)]: ((((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ C2) @ ((complete_Sup_Sup @ (set @ B)) @ ((((image @ C) @ (set @ B)) @ B2) @ A2)))) = ((complete_Sup_Sup @ (set @ A)) @ ((((image @ C) @ (set @ A)) @ (^ [Y:C]: (((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ C2) @ (B2 @ Y)))))) @ A2)))))).
% 3.26/1.70 thf(fact_231_SUP__UNION, axiom, (! [A:$tType,B:$tType,C:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [F:(B > A),G2:(C > (set @ B)),A2:(set @ C)]: ((((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ F) @ ((complete_Sup_Sup @ (set @ B)) @ ((((image @ C) @ (set @ B)) @ G2) @ A2)))) = ((complete_Sup_Sup @ A) @ ((((image @ C) @ A) @ (^ [Y:C]: (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ F) @ (G2 @ Y)))))) @ A2))))))))).
% 3.26/1.70 thf(fact_232_imageE, axiom, (! [A:$tType,B:$tType,B3:A,F:(B > A),A2:(set @ B)]: (((((member @ A) @ B3) @ ((((image @ B) @ A) @ F) @ A2)) => (~ ((! [X6:B]: (((B3 = (F @ X6)) => (~ ((((member @ B) @ X6) @ A2)))))))))))).
% 3.26/1.70 thf(fact_233_image__image, axiom, (! [A:$tType,B:$tType,C:$tType,F:(B > A),G2:(C > B),A2:(set @ C)]: ((((((image @ B) @ A) @ F) @ ((((image @ C) @ B) @ G2) @ A2)) = ((((image @ C) @ A) @ (^ [X:C]: ((F @ (G2 @ X))))) @ A2))))).
% 3.26/1.70 thf(fact_234_Compr__image__eq, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:(set @ B),P2:(A > $o)]: ((((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((((image @ B) @ A) @ F) @ A2)) & (P2 @ X))))) = ((((image @ B) @ A) @ F) @ ((collect @ B) @ (^ [X:B]: (((((member @ B) @ X) @ A2) & (P2 @ (F @ X))))))))))).
% 3.26/1.70 thf(fact_235_sum_Ocase__distrib, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,H:(C > D),F1:(A > C),F22:(B > C),Sum:((sum_sum @ A) @ B)]: (((H @ ((((((sum_case_sum @ A) @ C) @ B) @ F1) @ F22) @ Sum)) = ((((((sum_case_sum @ A) @ D) @ B) @ (^ [X:A]: ((H @ (F1 @ X))))) @ (^ [X:B]: ((H @ (F22 @ X))))) @ Sum))))).
% 3.26/1.70 thf(fact_236_image__UN, axiom, (! [A:$tType,B:$tType,C:$tType,F:(B > A),B2:(C > (set @ B)),A2:(set @ C)]: ((((((image @ B) @ A) @ F) @ ((complete_Sup_Sup @ (set @ B)) @ ((((image @ C) @ (set @ B)) @ B2) @ A2))) = ((complete_Sup_Sup @ (set @ A)) @ ((((image @ C) @ (set @ A)) @ (^ [X:C]: (((((image @ B) @ A) @ F) @ (B2 @ X))))) @ A2)))))).
% 3.26/1.70 thf(fact_237_UN__extend__simps_I10_J, axiom, (! [V:$tType,U2:$tType,T:$tType,B2:(U2 > (set @ V)),F:(T > U2),A2:(set @ T)]: ((((complete_Sup_Sup @ (set @ V)) @ ((((image @ T) @ (set @ V)) @ (^ [A3:T]: ((B2 @ (F @ A3))))) @ A2)) = ((complete_Sup_Sup @ (set @ V)) @ ((((image @ U2) @ (set @ V)) @ B2) @ ((((image @ T) @ U2) @ F) @ A2))))))).
% 3.26/1.70 thf(fact_238_image__Union, axiom, (! [A:$tType,B:$tType,F:(B > A),S4:(set @ (set @ B))]: ((((((image @ B) @ A) @ F) @ ((complete_Sup_Sup @ (set @ B)) @ S4)) = ((complete_Sup_Sup @ (set @ A)) @ ((((image @ (set @ B)) @ (set @ A)) @ (((image @ B) @ A) @ F)) @ S4)))))).
% 3.26/1.70 thf(fact_239_UN__extend__simps_I8_J, axiom, (! [P5:$tType,O:$tType,B2:(O > (set @ P5)),A2:(set @ (set @ O))]: ((((complete_Sup_Sup @ (set @ P5)) @ ((((image @ (set @ O)) @ (set @ P5)) @ (^ [Y:(set @ O)]: (((complete_Sup_Sup @ (set @ P5)) @ ((((image @ O) @ (set @ P5)) @ B2) @ Y))))) @ A2)) = ((complete_Sup_Sup @ (set @ P5)) @ ((((image @ O) @ (set @ P5)) @ B2) @ ((complete_Sup_Sup @ (set @ O)) @ A2))))))).
% 3.26/1.70 thf(fact_240_Inf_OINF__identity__eq, axiom, (! [A:$tType,Inf:((set @ A) > A),A2:(set @ A)]: (((Inf @ ((((image @ A) @ A) @ (^ [X:A]: (X))) @ A2)) = (Inf @ A2))))).
% 3.26/1.70 thf(fact_241_Sup_OSUP__identity__eq, axiom, (! [A:$tType,Sup:((set @ A) > A),A2:(set @ A)]: (((Sup @ ((((image @ A) @ A) @ (^ [X:A]: (X))) @ A2)) = (Sup @ A2))))).
% 3.26/1.70 thf(fact_242_the__elem__image__unique, axiom, (! [B:$tType,A:$tType,A2:(set @ A),F:(A > B),X5:A]: (((A2 != (bot_bot @ (set @ A))) => ((! [Y4:A]: (((((member @ A) @ Y4) @ A2) => ((F @ Y4) = (F @ X5))))) => (((the_elem @ B) @ ((((image @ A) @ B) @ F) @ A2)) = (F @ X5))))))).
% 3.26/1.70 thf(fact_243_image__constant__conv, axiom, (! [B:$tType,A:$tType,A2:(set @ B),C3:A]: ((((A2 = (bot_bot @ (set @ B))) => (((((image @ B) @ A) @ (^ [X:B]: (C3))) @ A2) = (bot_bot @ (set @ A)))) & ((A2 != (bot_bot @ (set @ B))) => (((((image @ B) @ A) @ (^ [X:B]: (C3))) @ A2) = (((insert @ A) @ C3) @ (bot_bot @ (set @ A))))))))).
% 3.26/1.70 thf(fact_244_image__constant, axiom, (! [A:$tType,B:$tType,X5:A,A2:(set @ A),C3:B]: (((((member @ A) @ X5) @ A2) => (((((image @ A) @ B) @ (^ [X:A]: (C3))) @ A2) = (((insert @ B) @ C3) @ (bot_bot @ (set @ B)))))))).
% 3.26/1.70 thf(fact_245_UN__empty2, axiom, (! [B:$tType,A:$tType,A2:(set @ B)]: ((((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ (^ [X:B]: ((bot_bot @ (set @ A))))) @ A2)) = (bot_bot @ (set @ A)))))).
% 3.26/1.70 thf(fact_246_UN__empty, axiom, (! [B:$tType,A:$tType,B2:(B > (set @ A))]: ((((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ (bot_bot @ (set @ B)))) = (bot_bot @ (set @ A)))))).
% 3.26/1.70 thf(fact_247_UNION__empty__conv_I1_J, axiom, (! [A:$tType,B:$tType,B2:(B > (set @ A)),A2:(set @ B)]: ((((bot_bot @ (set @ A)) = ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ A2))) = (! [X:B]: (((((member @ B) @ X) @ A2) => ((B2 @ X) = (bot_bot @ (set @ A)))))))))).
% 3.26/1.70 thf(fact_248_UNION__empty__conv_I2_J, axiom, (! [A:$tType,B:$tType,B2:(B > (set @ A)),A2:(set @ B)]: (((((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ A2)) = (bot_bot @ (set @ A))) = (! [X:B]: (((((member @ B) @ X) @ A2) => ((B2 @ X) = (bot_bot @ (set @ A)))))))))).
% 3.26/1.70 thf(fact_249_UN__insert__distrib, axiom, (! [B:$tType,A:$tType,U3:A,A2:(set @ A),A4:B,B2:(A > (set @ B))]: (((((member @ A) @ U3) @ A2) => (((complete_Sup_Sup @ (set @ B)) @ ((((image @ A) @ (set @ B)) @ (^ [X:A]: ((((insert @ B) @ A4) @ (B2 @ X))))) @ A2)) = (((insert @ B) @ A4) @ ((complete_Sup_Sup @ (set @ B)) @ ((((image @ A) @ (set @ B)) @ B2) @ A2)))))))).
% 3.26/1.70 thf(fact_250_vimage__UN, axiom, (! [A:$tType,B:$tType,C:$tType,F:(A > B),B2:(C > (set @ B)),A2:(set @ C)]: ((((((vimage @ A) @ B) @ F) @ ((complete_Sup_Sup @ (set @ B)) @ ((((image @ C) @ (set @ B)) @ B2) @ A2))) = ((complete_Sup_Sup @ (set @ A)) @ ((((image @ C) @ (set @ A)) @ (^ [X:C]: (((((vimage @ A) @ B) @ F) @ (B2 @ X))))) @ A2)))))).
% 3.26/1.70 thf(fact_251_vimage__Union, axiom, (! [A:$tType,B:$tType,F:(A > B),A2:(set @ (set @ B))]: ((((((vimage @ A) @ B) @ F) @ ((complete_Sup_Sup @ (set @ B)) @ A2)) = ((complete_Sup_Sup @ (set @ A)) @ ((((image @ (set @ B)) @ (set @ A)) @ (((vimage @ A) @ B) @ F)) @ A2)))))).
% 3.26/1.70 thf(fact_252_case__sum__if, axiom, (! [B:$tType,A:$tType,C:$tType,P4:$o,F:(B > A),G2:(C > A),X5:B,Y3:C]: (((P4 => (((((((sum_case_sum @ B) @ A) @ C) @ F) @ G2) @ ((((if @ ((sum_sum @ B) @ C)) @ P4) @ (((sum_Inl @ B) @ C) @ X5)) @ (((sum_Inr @ C) @ B) @ Y3))) = (F @ X5))) & ((~ (P4)) => (((((((sum_case_sum @ B) @ A) @ C) @ F) @ G2) @ ((((if @ ((sum_sum @ B) @ C)) @ P4) @ (((sum_Inl @ B) @ C) @ X5)) @ (((sum_Inr @ C) @ B) @ Y3))) = (G2 @ Y3))))))).
% 3.26/1.70 thf(fact_253_surjective__sum, axiom, (! [C:$tType,B:$tType,A:$tType,F:(((sum_sum @ A) @ B) > C)]: (((((((sum_case_sum @ A) @ C) @ B) @ (^ [X:A]: ((F @ (((sum_Inl @ A) @ B) @ X))))) @ (^ [Y:B]: ((F @ (((sum_Inr @ B) @ A) @ Y))))) = F)))).
% 3.26/1.70 thf(fact_254_SUP__constant, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A2:(set @ B),C3:A]: ((((A2 = (bot_bot @ (set @ B))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ (^ [Y:B]: (C3))) @ A2)) = (bot_bot @ A))) & ((A2 != (bot_bot @ (set @ B))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ (^ [Y:B]: (C3))) @ A2)) = C3))))))))).
% 3.26/1.70 thf(fact_255_UN__extend__simps_I1_J, axiom, (! [A:$tType,B:$tType,C2:(set @ B),A4:A,B2:(B > (set @ A))]: ((((C2 = (bot_bot @ (set @ B))) => ((((insert @ A) @ A4) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ C2))) = (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))) & ((C2 != (bot_bot @ (set @ B))) => ((((insert @ A) @ A4) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B2) @ C2))) = ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ (^ [X:B]: ((((insert @ A) @ A4) @ (B2 @ X))))) @ C2)))))))).
% 3.26/1.70 thf(tcon_fun___Conditionally__Complete__Lattices_Oconditionally__complete__lattice, axiom, (! [A7:$tType,A10:$tType]: ((((comple187826305attice @ A10) @ (type2 @ A10)) => ((condit378418413attice @ (A7 > A10)) @ (type2 @ (A7 > A10))))))).
% 3.26/1.70 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice, axiom, (! [A7:$tType,A10:$tType]: ((((comple187826305attice @ A10) @ (type2 @ A10)) => ((comple187826305attice @ (A7 > A10)) @ (type2 @ (A7 > A10))))))).
% 3.26/1.70 thf(tcon_fun___Complete__Partial__Order_Occpo, axiom, (! [A7:$tType,A10:$tType]: ((((comple187826305attice @ A10) @ (type2 @ A10)) => ((comple1141879883l_ccpo @ (A7 > A10)) @ (type2 @ (A7 > A10))))))).
% 3.26/1.70 thf(tcon_fun___Complete__Lattices_OSup, axiom, (! [A7:$tType,A10:$tType]: ((((complete_Sup @ A10) @ (type2 @ A10)) => ((complete_Sup @ (A7 > A10)) @ (type2 @ (A7 > A10))))))).
% 3.26/1.70 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A10:$tType]: ((((bot @ A10) @ (type2 @ A10)) => ((bot @ (A7 > A10)) @ (type2 @ (A7 > A10))))))).
% 3.26/1.70 thf(tcon_Set_Oset___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_1, axiom, (! [A7:$tType]: (((condit378418413attice @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.26/1.70 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_2, axiom, (! [A7:$tType]: (((comple187826305attice @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.26/1.70 thf(tcon_Set_Oset___Complete__Partial__Order_Occpo_3, axiom, (! [A7:$tType]: (((comple1141879883l_ccpo @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.26/1.70 thf(tcon_Set_Oset___Complete__Lattices_OSup_4, axiom, (! [A7:$tType]: (((complete_Sup @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.26/1.70 thf(tcon_Set_Oset___Orderings_Obot_5, axiom, (! [A7:$tType]: (((bot @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.26/1.70 thf(tcon_HOL_Obool___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_6, axiom, ((condit378418413attice @ $o) @ (type2 @ $o))).
% 3.26/1.70 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_7, axiom, ((comple187826305attice @ $o) @ (type2 @ $o))).
% 3.26/1.70 thf(tcon_HOL_Obool___Complete__Partial__Order_Occpo_8, axiom, ((comple1141879883l_ccpo @ $o) @ (type2 @ $o))).
% 3.26/1.70 thf(tcon_HOL_Obool___Complete__Lattices_OSup_9, axiom, ((complete_Sup @ $o) @ (type2 @ $o))).
% 3.26/1.70 thf(tcon_HOL_Obool___Orderings_Obot_10, axiom, ((bot @ $o) @ (type2 @ $o))).
% 3.26/1.70 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 3.26/1.70 thf(help_If_2_1_T, axiom, (! [A:$tType,X5:A,Y3:A]: ((((((if @ A) @ $false) @ X5) @ Y3) = Y3)))).
% 3.26/1.70 thf(help_If_1_1_T, axiom, (! [A:$tType,X5:A,Y3:A]: ((((((if @ A) @ $true) @ X5) @ Y3) = X5)))).
% 3.26/1.70 thf(conj_0, conjecture, (((collect @ n) @ ((gram_L830233218_inItr @ ns) @ tr)) = ((collect @ n) @ (^ [Uu:n]: ((? [Tr5:dtree]: (((Uu = (root @ Tr5)) & (((gram_L716654942_subtr @ ns) @ Tr5) @ tr))))))))).
% 3.26/1.70 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.40Ab8elA6V/DTF2DTF21337.p
% 3.26/1.70 ------------------------
% 3.26/1.75 ---- Cleaned THF ---
% 3.26/1.75 thf(ty_t_Sum__Type_Osum,type,
% 3.26/1.75 sum_sum: $tType > $tType > $tType ).
% 3.26/1.75
% 3.26/1.75 thf(ty_t_DTree_Odtree,type,
% 3.26/1.75 dtree: $tType ).
% 3.26/1.75
% 3.26/1.75 thf(ty_t_Set_Oset,type,
% 3.26/1.75 set: $tType > $tType ).
% 3.26/1.75
% 3.26/1.75 thf(ty_t_DTree_OT,type,
% 3.26/1.75 t: $tType ).
% 3.26/1.75
% 3.26/1.75 thf(ty_t_DTree_ON,type,
% 3.26/1.75 n: $tType ).
% 3.26/1.75
% 3.26/1.75 thf(ty_t_itself,type,
% 3.26/1.75 itself: $tType > $tType ).
% 3.26/1.75
% 3.26/1.75 thf(sy_cl_HOL_Otype,type,
% 3.26/1.75 type:
% 3.26/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_cl_Orderings_Obot,type,
% 3.26/1.75 bot:
% 3.26/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_cl_Complete__Lattices_OSup,type,
% 3.26/1.75 complete_Sup:
% 3.26/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_cl_Complete__Partial__Order_Occpo,type,
% 3.26/1.75 comple1141879883l_ccpo:
% 3.26/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 3.26/1.75 comple187826305attice:
% 3.26/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__lattice,type,
% 3.26/1.75 condit378418413attice:
% 3.26/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p,type,
% 3.26/1.75 bNF_Greatest_image2p:
% 3.26/1.75 !>[C: $tType,A: $tType,D: $tType,B: $tType] : ( ( C > A ) > ( D > B ) > ( C > D > $o ) > A > B > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Basic__BNFs_Osetl,type,
% 3.26/1.75 basic_setl:
% 3.26/1.75 !>[A: $tType,B: $tType] : ( ( sum_sum @ A @ B ) > ( set @ A ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Basic__BNFs_Osetr,type,
% 3.26/1.75 basic_setr:
% 3.26/1.75 !>[A: $tType,B: $tType] : ( ( sum_sum @ A @ B ) > ( set @ B ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Complete__Lattices_OSup__class_OSup,type,
% 3.26/1.75 complete_Sup_Sup:
% 3.26/1.75 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_DTree_ONode,type,
% 3.26/1.75 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_DTree_Ocont,type,
% 3.26/1.75 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_DTree_Odtree_Oroot,type,
% 3.26/1.75 root: dtree > n ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFr,type,
% 3.26/1.75 gram_L861583724lle_Fr: ( set @ n ) > dtree > ( set @ t ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OItr,type,
% 3.26/1.75 gram_L1580978439le_Itr: ( set @ n ) > dtree > ( set @ n ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 3.26/1.75 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 3.26/1.75 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 3.26/1.75 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 3.26/1.75 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2,type,
% 3.26/1.75 gram_L1283001940subtr2: ( set @ n ) > dtree > dtree > $o ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_HOL_OThe,type,
% 3.26/1.75 the:
% 3.26/1.75 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_If,type,
% 3.26/1.75 if:
% 3.26/1.75 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Lifting_Orel__pred__comp,type,
% 3.26/1.75 rel_pred_comp:
% 3.26/1.75 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( B > $o ) > A > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.26/1.75 bot_bot:
% 3.26/1.75 !>[A: $tType] : A ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Pure_Otype,type,
% 3.26/1.75 type2:
% 3.26/1.75 !>[A: $tType] : ( itself @ A ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Set_OCollect,type,
% 3.26/1.75 collect:
% 3.26/1.75 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Set_Oimage,type,
% 3.26/1.75 image:
% 3.26/1.75 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Set_Oinsert,type,
% 3.26/1.75 insert:
% 3.26/1.75 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Set_Ois__empty,type,
% 3.26/1.75 is_empty:
% 3.26/1.75 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Set_Ois__singleton,type,
% 3.26/1.75 is_singleton:
% 3.26/1.75 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Set_Othe__elem,type,
% 3.26/1.75 the_elem:
% 3.26/1.75 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Set_Ovimage,type,
% 3.26/1.75 vimage:
% 3.26/1.75 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Sum__Type_OInl,type,
% 3.26/1.75 sum_Inl:
% 3.26/1.75 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Sum__Type_OInr,type,
% 3.26/1.75 sum_Inr:
% 3.26/1.75 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Sum__Type_OSuml,type,
% 3.26/1.75 sum_Suml:
% 3.26/1.75 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( sum_sum @ A @ B ) > C ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Sum__Type_Oold_Osum_Orec__set__sum,type,
% 3.26/1.75 sum_rec_set_sum:
% 3.26/1.75 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 3.26/1.75 sum_rec_sum:
% 3.26/1.75 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_Sum__Type_Osum_Ocase__sum,type,
% 3.26/1.75 sum_case_sum:
% 3.26/1.75 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( B > C ) > ( sum_sum @ A @ B ) > C ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_c_member,type,
% 3.26/1.75 member:
% 3.26/1.75 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(sy_v_ns,type,
% 3.26/1.75 ns: set @ n ).
% 3.26/1.75
% 3.26/1.75 thf(sy_v_tr,type,
% 3.26/1.75 tr: dtree ).
% 3.26/1.75
% 3.26/1.75 thf(fact_0_inItr_OBase,axiom,
% 3.26/1.75 ! [Tr: dtree,Ns: set @ n] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_1_subtr_ORefl,axiom,
% 3.26/1.75 ! [Tr: dtree,Ns: set @ n] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_2_inItr__subtr,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr: dtree,N: n] :
% 3.26/1.75 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 3.26/1.75 => ? [Tr2: dtree] :
% 3.26/1.75 ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr )
% 3.26/1.75 & ( ( root @ Tr2 )
% 3.26/1.75 = N ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_3_subtr__inItr,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr: dtree,N: n,Tr1: dtree] :
% 3.26/1.75 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 3.26/1.75 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 3.26/1.75 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_4_subtr__trans,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 3.26/1.75 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.26/1.75 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 3.26/1.75 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_5_inItr__root__in,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr: dtree,N: n] :
% 3.26/1.75 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 3.26/1.75 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_6_subtr__rootL__in,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.26/1.75 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.26/1.75 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_7_subtr__rootR__in,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.26/1.75 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.26/1.75 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_8_Itr__def,axiom,
% 3.26/1.75 ( gram_L1580978439le_Itr
% 3.26/1.75 = ( ^ [Ns2: set @ n,Tr4: dtree] : ( collect @ n @ ( gram_L830233218_inItr @ Ns2 @ Tr4 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_9_rel__pred__comp__def,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( rel_pred_comp @ A @ B )
% 3.26/1.75 = ( ^ [R: A > B > $o,P: B > $o,X: A] :
% 3.26/1.75 ? [Y: B] :
% 3.26/1.75 ( ( R @ X @ Y )
% 3.26/1.75 & ( P @ Y ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_10_Itr__subtr,axiom,
% 3.26/1.75 ( gram_L1580978439le_Itr
% 3.26/1.75 = ( ^ [Ns2: set @ n,Tr4: dtree] :
% 3.26/1.75 ( complete_Sup_Sup @ ( set @ n )
% 3.26/1.75 @ ( collect @ ( set @ n )
% 3.26/1.75 @ ^ [Uu: set @ n] :
% 3.26/1.75 ? [Tr5: dtree] :
% 3.26/1.75 ( ( Uu
% 3.26/1.75 = ( gram_L1580978439le_Itr @ Ns2 @ Tr5 ) )
% 3.26/1.75 & ( gram_L716654942_subtr @ Ns2 @ Tr5 @ Tr4 ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_11_inFr2__root__in,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 3.26/1.75 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 3.26/1.75 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_12_Fr__subtr,axiom,
% 3.26/1.75 ( gram_L861583724lle_Fr
% 3.26/1.75 = ( ^ [Ns2: set @ n,Tr4: dtree] :
% 3.26/1.75 ( complete_Sup_Sup @ ( set @ t )
% 3.26/1.75 @ ( collect @ ( set @ t )
% 3.26/1.75 @ ^ [Uu: set @ t] :
% 3.26/1.75 ? [Tr5: dtree] :
% 3.26/1.75 ( ( Uu
% 3.26/1.75 = ( gram_L861583724lle_Fr @ Ns2 @ Tr5 ) )
% 3.26/1.75 & ( gram_L716654942_subtr @ Ns2 @ Tr5 @ Tr4 ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_13_subtr__inFr,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr: dtree,T2: t,Tr1: dtree] :
% 3.26/1.75 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 3.26/1.75 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 3.26/1.75 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_14_subtr__subtr2,axiom,
% 3.26/1.75 gram_L716654942_subtr = gram_L1283001940subtr2 ).
% 3.26/1.75
% 3.26/1.75 thf(fact_15_inFr__root__in,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 3.26/1.75 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 3.26/1.75 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_16_not__root__inFr,axiom,
% 3.26/1.75 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 3.26/1.75 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_17_subtr2_ORefl,axiom,
% 3.26/1.75 ! [Tr: dtree,Ns: set @ n] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ( gram_L1283001940subtr2 @ Ns @ Tr @ Tr ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_18_subtr2__rootL__in,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.26/1.75 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 3.26/1.75 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_19_subtr2__rootR__in,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.26/1.75 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 3.26/1.75 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_20_inFr__inFr2,axiom,
% 3.26/1.75 gram_L1333338417e_inFr = gram_L805317441_inFr2 ).
% 3.26/1.75
% 3.26/1.75 thf(fact_21_subtr2__trans,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 3.26/1.75 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 3.26/1.75 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 3.26/1.75 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_22_Fr__def,axiom,
% 3.26/1.75 ( gram_L861583724lle_Fr
% 3.26/1.75 = ( ^ [Ns2: set @ n,Tr4: dtree] : ( collect @ t @ ( gram_L1333338417e_inFr @ Ns2 @ Tr4 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_23_UN__ball__bex__simps_I3_J,axiom,
% 3.26/1.75 ! [D: $tType,A2: set @ ( set @ D ),P2: D > $o] :
% 3.26/1.75 ( ( ? [X: D] :
% 3.26/1.75 ( ( member @ D @ X @ ( complete_Sup_Sup @ ( set @ D ) @ A2 ) )
% 3.26/1.75 & ( P2 @ X ) ) )
% 3.26/1.75 = ( ? [X: set @ D] :
% 3.26/1.75 ( ( member @ ( set @ D ) @ X @ A2 )
% 3.26/1.75 & ? [Y: D] :
% 3.26/1.75 ( ( member @ D @ Y @ X )
% 3.26/1.75 & ( P2 @ Y ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_24_UN__ball__bex__simps_I1_J,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ ( set @ A ),P2: A > $o] :
% 3.26/1.75 ( ( ! [X: A] :
% 3.26/1.75 ( ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ A2 ) )
% 3.26/1.75 => ( P2 @ X ) ) )
% 3.26/1.75 = ( ! [X: set @ A] :
% 3.26/1.75 ( ( member @ ( set @ A ) @ X @ A2 )
% 3.26/1.75 => ! [Y: A] :
% 3.26/1.75 ( ( member @ A @ Y @ X )
% 3.26/1.75 => ( P2 @ Y ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_25_UnionI,axiom,
% 3.26/1.75 ! [A: $tType,X2: set @ A,C2: set @ ( set @ A ),A2: A] :
% 3.26/1.75 ( ( member @ ( set @ A ) @ X2 @ C2 )
% 3.26/1.75 => ( ( member @ A @ A2 @ X2 )
% 3.26/1.75 => ( member @ A @ A2 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_26_Union__iff,axiom,
% 3.26/1.75 ! [A: $tType,A2: A,C2: set @ ( set @ A )] :
% 3.26/1.75 ( ( member @ A @ A2 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) )
% 3.26/1.75 = ( ? [X: set @ A] :
% 3.26/1.75 ( ( member @ ( set @ A ) @ X @ C2 )
% 3.26/1.75 & ( member @ A @ A2 @ X ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_27_Union__SetCompr__eq,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,F: B > ( set @ A ),P2: B > $o] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( collect @ ( set @ A )
% 3.26/1.75 @ ^ [Uu: set @ A] :
% 3.26/1.75 ? [X: B] :
% 3.26/1.75 ( ( Uu
% 3.26/1.75 = ( F @ X ) )
% 3.26/1.75 & ( P2 @ X ) ) ) )
% 3.26/1.75 = ( collect @ A
% 3.26/1.75 @ ^ [A3: A] :
% 3.26/1.75 ? [X: B] :
% 3.26/1.75 ( ( P2 @ X )
% 3.26/1.75 & ( member @ A @ A3 @ ( F @ X ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_28_UnionE,axiom,
% 3.26/1.75 ! [A: $tType,A2: A,C2: set @ ( set @ A )] :
% 3.26/1.75 ( ( member @ A @ A2 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) )
% 3.26/1.75 => ~ ! [X3: set @ A] :
% 3.26/1.75 ( ( member @ A @ A2 @ X3 )
% 3.26/1.75 => ~ ( member @ ( set @ A ) @ X3 @ C2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_29_not__root__Fr,axiom,
% 3.26/1.75 ! [Tr: dtree,Ns: set @ n] :
% 3.26/1.75 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ( ( gram_L861583724lle_Fr @ Ns @ Tr )
% 3.26/1.75 = ( bot_bot @ ( set @ t ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_30_Fr__subtr__cont,axiom,
% 3.26/1.75 ( gram_L861583724lle_Fr
% 3.26/1.75 = ( ^ [Ns2: set @ n,Tr4: dtree] :
% 3.26/1.75 ( complete_Sup_Sup @ ( set @ t )
% 3.26/1.75 @ ( collect @ ( set @ t )
% 3.26/1.75 @ ^ [Uu: set @ t] :
% 3.26/1.75 ? [Tr5: dtree] :
% 3.26/1.75 ( ( Uu
% 3.26/1.75 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr5 ) ) )
% 3.26/1.75 & ( gram_L716654942_subtr @ Ns2 @ Tr5 @ Tr4 ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_31_image2p__def,axiom,
% 3.26/1.75 ! [D: $tType,B: $tType,A: $tType,C: $tType] :
% 3.26/1.75 ( ( bNF_Greatest_image2p @ C @ A @ D @ B )
% 3.26/1.75 = ( ^ [F2: C > A,G: D > B,R: C > D > $o,X: A,Y: B] :
% 3.26/1.75 ? [X4: C,Y2: D] :
% 3.26/1.75 ( ( R @ X4 @ Y2 )
% 3.26/1.75 & ( ( F2 @ X4 )
% 3.26/1.75 = X )
% 3.26/1.75 & ( ( G @ Y2 )
% 3.26/1.75 = Y ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_32_root__Node,axiom,
% 3.26/1.75 ! [N: n,As: set @ ( sum_sum @ t @ dtree )] :
% 3.26/1.75 ( ( root @ ( node @ N @ As ) )
% 3.26/1.75 = N ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_33_Sup__bot__conv_I1_J,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [A2: set @ A] :
% 3.26/1.75 ( ( ( complete_Sup_Sup @ A @ A2 )
% 3.26/1.75 = ( bot_bot @ A ) )
% 3.26/1.75 = ( ! [X: A] :
% 3.26/1.75 ( ( member @ A @ X @ A2 )
% 3.26/1.75 => ( X
% 3.26/1.75 = ( bot_bot @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_34_Sup__bot__conv_I2_J,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [A2: set @ A] :
% 3.26/1.75 ( ( ( bot_bot @ A )
% 3.26/1.75 = ( complete_Sup_Sup @ A @ A2 ) )
% 3.26/1.75 = ( ! [X: A] :
% 3.26/1.75 ( ( member @ A @ X @ A2 )
% 3.26/1.75 => ( X
% 3.26/1.75 = ( bot_bot @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_35_Sup__empty,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ A @ ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 = ( bot_bot @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_36_Node__root__cont,axiom,
% 3.26/1.75 ! [Tr: dtree] :
% 3.26/1.75 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 3.26/1.75 = Tr ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_37_Union__empty,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( set @ A ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_38_image2pI,axiom,
% 3.26/1.75 ! [A: $tType,C: $tType,D: $tType,B: $tType,R2: A > B > $o,X5: A,Y3: B,F: A > C,G2: B > D] :
% 3.26/1.75 ( ( R2 @ X5 @ Y3 )
% 3.26/1.75 => ( bNF_Greatest_image2p @ A @ C @ B @ D @ F @ G2 @ R2 @ ( F @ X5 ) @ ( G2 @ Y3 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_39_image2pE,axiom,
% 3.26/1.75 ! [D: $tType,B: $tType,A: $tType,C: $tType,F: A > B,G2: C > D,R2: A > C > $o,Fx: B,Gy: D] :
% 3.26/1.75 ( ( bNF_Greatest_image2p @ A @ B @ C @ D @ F @ G2 @ R2 @ Fx @ Gy )
% 3.26/1.75 => ~ ! [X6: A] :
% 3.26/1.75 ( ( Fx
% 3.26/1.75 = ( F @ X6 ) )
% 3.26/1.75 => ! [Y4: C] :
% 3.26/1.75 ( ( Gy
% 3.26/1.75 = ( G2 @ Y4 ) )
% 3.26/1.75 => ~ ( R2 @ X6 @ Y4 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_40_empty__Union__conv,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ ( set @ A )] :
% 3.26/1.75 ( ( ( bot_bot @ ( set @ A ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ A ) @ A2 ) )
% 3.26/1.75 = ( ! [X: set @ A] :
% 3.26/1.75 ( ( member @ ( set @ A ) @ X @ A2 )
% 3.26/1.75 => ( X
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_41_Union__empty__conv,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ ( set @ A )] :
% 3.26/1.75 ( ( ( complete_Sup_Sup @ ( set @ A ) @ A2 )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 = ( ! [X: set @ A] :
% 3.26/1.75 ( ( member @ ( set @ A ) @ X @ A2 )
% 3.26/1.75 => ( X
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_42_dtree__cong,axiom,
% 3.26/1.75 ! [Tr: dtree,Tr6: dtree] :
% 3.26/1.75 ( ( ( root @ Tr )
% 3.26/1.75 = ( root @ Tr6 ) )
% 3.26/1.75 => ( ( ( cont @ Tr )
% 3.26/1.75 = ( cont @ Tr6 ) )
% 3.26/1.75 => ( Tr = Tr6 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_43_inFr_OBase,axiom,
% 3.26/1.75 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 3.26/1.75 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_44_inFr2_OBase,axiom,
% 3.26/1.75 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 3.26/1.75 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_45_mem__Collect__eq,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,P2: A > $o] :
% 3.26/1.75 ( ( member @ A @ A4 @ ( collect @ A @ P2 ) )
% 3.26/1.75 = ( P2 @ A4 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_46_Collect__mem__eq,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ A] :
% 3.26/1.75 ( ( collect @ A
% 3.26/1.75 @ ^ [X: A] : ( member @ A @ X @ A2 ) )
% 3.26/1.75 = A2 ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_47_Collect__cong,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 3.26/1.75 ( ! [X6: A] :
% 3.26/1.75 ( ( P2 @ X6 )
% 3.26/1.75 = ( Q @ X6 ) )
% 3.26/1.75 => ( ( collect @ A @ P2 )
% 3.26/1.75 = ( collect @ A @ Q ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_48_ext,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 3.26/1.75 ( ! [X6: A] :
% 3.26/1.75 ( ( F @ X6 )
% 3.26/1.75 = ( G2 @ X6 ) )
% 3.26/1.75 => ( F = G2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_49_inFr__subtr,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 3.26/1.75 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 3.26/1.75 => ? [Tr2: dtree] :
% 3.26/1.75 ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr )
% 3.26/1.75 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_50_vimage__empty,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,F: A > B] :
% 3.26/1.75 ( ( vimage @ A @ B @ F @ ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_51_vimage__Collect__eq,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,F: A > B,P2: B > $o] :
% 3.26/1.75 ( ( vimage @ A @ B @ F @ ( collect @ B @ P2 ) )
% 3.26/1.75 = ( collect @ A
% 3.26/1.75 @ ^ [Y: A] : ( P2 @ ( F @ Y ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_52_vimage__ident,axiom,
% 3.26/1.75 ! [A: $tType,Y5: set @ A] :
% 3.26/1.75 ( ( vimage @ A @ A
% 3.26/1.75 @ ^ [X: A] : X
% 3.26/1.75 @ Y5 )
% 3.26/1.75 = Y5 ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_53_vimage__eq,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,A4: A,F: A > B,B2: set @ B] :
% 3.26/1.75 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ B2 ) )
% 3.26/1.75 = ( member @ B @ ( F @ A4 ) @ B2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_54_vimageI,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,F: B > A,A4: B,B3: A,B2: set @ A] :
% 3.26/1.75 ( ( ( F @ A4 )
% 3.26/1.75 = B3 )
% 3.26/1.75 => ( ( member @ A @ B3 @ B2 )
% 3.26/1.75 => ( member @ B @ A4 @ ( vimage @ B @ A @ F @ B2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_55_old_Osum_Oinject_I1_J,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,A4: A,A5: A] :
% 3.26/1.75 ( ( ( sum_Inl @ A @ B @ A4 )
% 3.26/1.75 = ( sum_Inl @ A @ B @ A5 ) )
% 3.26/1.75 = ( A4 = A5 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_56_sum_Oinject_I1_J,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 3.26/1.75 ( ( ( sum_Inl @ A @ B @ X1 )
% 3.26/1.75 = ( sum_Inl @ A @ B @ Y1 ) )
% 3.26/1.75 = ( X1 = Y1 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_57_empty__Collect__eq,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o] :
% 3.26/1.75 ( ( ( bot_bot @ ( set @ A ) )
% 3.26/1.75 = ( collect @ A @ P2 ) )
% 3.26/1.75 = ( ! [X: A] :
% 3.26/1.75 ~ ( P2 @ X ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_58_Collect__empty__eq,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o] :
% 3.26/1.75 ( ( ( collect @ A @ P2 )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 = ( ! [X: A] :
% 3.26/1.75 ~ ( P2 @ X ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_59_empty__iff,axiom,
% 3.26/1.75 ! [A: $tType,C3: A] :
% 3.26/1.75 ~ ( member @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_60_all__not__in__conv,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ A] :
% 3.26/1.75 ( ( ! [X: A] :
% 3.26/1.75 ~ ( member @ A @ X @ A2 ) )
% 3.26/1.75 = ( A2
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_61_bot__set__def,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( bot_bot @ ( set @ A ) )
% 3.26/1.75 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_62_emptyE,axiom,
% 3.26/1.75 ! [A: $tType,A4: A] :
% 3.26/1.75 ~ ( member @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_63_equals0D,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ A,A4: A] :
% 3.26/1.75 ( ( A2
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 => ~ ( member @ A @ A4 @ A2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_64_equals0I,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ A] :
% 3.26/1.75 ( ! [Y4: A] :
% 3.26/1.75 ~ ( member @ A @ Y4 @ A2 )
% 3.26/1.75 => ( A2
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_65_ex__in__conv,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ A] :
% 3.26/1.75 ( ( ? [X: A] : ( member @ A @ X @ A2 ) )
% 3.26/1.75 = ( A2
% 3.26/1.75 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_66_Inl__inject,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,X5: A,Y3: A] :
% 3.26/1.75 ( ( ( sum_Inl @ A @ B @ X5 )
% 3.26/1.75 = ( sum_Inl @ A @ B @ Y3 ) )
% 3.26/1.75 => ( X5 = Y3 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_67_vimageD,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,A4: A,F: A > B,A2: set @ B] :
% 3.26/1.75 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ A2 ) )
% 3.26/1.75 => ( member @ B @ ( F @ A4 ) @ A2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_68_vimageE,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,A4: A,F: A > B,B2: set @ B] :
% 3.26/1.75 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ B2 ) )
% 3.26/1.75 => ( member @ B @ ( F @ A4 ) @ B2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_69_vimageI2,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,F: B > A,A4: B,A2: set @ A] :
% 3.26/1.75 ( ( member @ A @ ( F @ A4 ) @ A2 )
% 3.26/1.75 => ( member @ B @ A4 @ ( vimage @ B @ A @ F @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_70_vimage__Collect,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,P2: B > $o,F: A > B,Q: A > $o] :
% 3.26/1.75 ( ! [X6: A] :
% 3.26/1.75 ( ( P2 @ ( F @ X6 ) )
% 3.26/1.75 = ( Q @ X6 ) )
% 3.26/1.75 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P2 ) )
% 3.26/1.75 = ( collect @ A @ Q ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_71_empty__def,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( bot_bot @ ( set @ A ) )
% 3.26/1.75 = ( collect @ A
% 3.26/1.75 @ ^ [X: A] : $false ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_72_vimage__def,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( vimage @ A @ B )
% 3.26/1.75 = ( ^ [F2: A > B,B4: set @ B] :
% 3.26/1.75 ( collect @ A
% 3.26/1.75 @ ^ [X: A] : ( member @ B @ ( F2 @ X ) @ B4 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_73_bot__apply,axiom,
% 3.26/1.75 ! [C: $tType,D: $tType] :
% 3.26/1.75 ( ( bot @ C @ ( type2 @ C ) )
% 3.26/1.75 => ( ( bot_bot @ ( D > C ) )
% 3.26/1.75 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_74_old_Osum_Osimps_I7_J,axiom,
% 3.26/1.75 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A4: A] :
% 3.26/1.75 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A4 ) )
% 3.26/1.75 = ( F1 @ A4 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_75_Set_Ois__empty__def,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( is_empty @ A )
% 3.26/1.75 = ( ^ [A6: set @ A] :
% 3.26/1.75 ( A6
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_76_inFr_Ocases,axiom,
% 3.26/1.75 ! [A1: set @ n,A22: dtree,A32: t] :
% 3.26/1.75 ( ( gram_L1333338417e_inFr @ A1 @ A22 @ A32 )
% 3.26/1.75 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.26/1.75 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 3.26/1.75 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.26/1.75 => ! [Tr12: dtree] :
% 3.26/1.75 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 3.26/1.75 => ~ ( gram_L1333338417e_inFr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_77_inFr_Osimps,axiom,
% 3.26/1.75 ( gram_L1333338417e_inFr
% 3.26/1.75 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 3.26/1.75 ( ? [Tr4: dtree,Ns2: set @ n,T3: t] :
% 3.26/1.75 ( ( A12 = Ns2 )
% 3.26/1.75 & ( A23 = Tr4 )
% 3.26/1.75 & ( A33 = T3 )
% 3.26/1.75 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 3.26/1.75 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) ) )
% 3.26/1.75 | ? [Tr4: dtree,Ns2: set @ n,Tr13: dtree,T3: t] :
% 3.26/1.75 ( ( A12 = Ns2 )
% 3.26/1.75 & ( A23 = Tr4 )
% 3.26/1.75 & ( A33 = T3 )
% 3.26/1.75 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 3.26/1.75 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 3.26/1.75 & ( gram_L1333338417e_inFr @ Ns2 @ Tr13 @ T3 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_78_inFr_Oinducts,axiom,
% 3.26/1.75 ! [X1: set @ n,X22: dtree,X32: t,P2: ( set @ n ) > dtree > t > $o] :
% 3.26/1.75 ( ( gram_L1333338417e_inFr @ X1 @ X22 @ X32 )
% 3.26/1.75 => ( ! [Tr7: dtree,Ns3: set @ n,T4: t] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr7 ) )
% 3.26/1.75 => ( P2 @ Ns3 @ Tr7 @ T4 ) ) )
% 3.26/1.75 => ( ! [Tr7: dtree,Ns3: set @ n,Tr12: dtree,T4: t] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 3.26/1.75 => ( ( gram_L1333338417e_inFr @ Ns3 @ Tr12 @ T4 )
% 3.26/1.75 => ( ( P2 @ Ns3 @ Tr12 @ T4 )
% 3.26/1.75 => ( P2 @ Ns3 @ Tr7 @ T4 ) ) ) ) )
% 3.26/1.75 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_79_Suml_Osimps,axiom,
% 3.26/1.75 ! [B: $tType,C: $tType,A: $tType,F: A > C,X5: A] :
% 3.26/1.75 ( ( sum_Suml @ A @ C @ B @ F @ ( sum_Inl @ A @ B @ X5 ) )
% 3.26/1.75 = ( F @ X5 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_80_sum_Oinject_I2_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,X22: B,Y22: B] :
% 3.26/1.75 ( ( ( sum_Inr @ B @ A @ X22 )
% 3.26/1.75 = ( sum_Inr @ B @ A @ Y22 ) )
% 3.26/1.75 = ( X22 = Y22 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_81_old_Osum_Oinject_I2_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,B3: B,B5: B] :
% 3.26/1.75 ( ( ( sum_Inr @ B @ A @ B3 )
% 3.26/1.75 = ( sum_Inr @ B @ A @ B5 ) )
% 3.26/1.75 = ( B3 = B5 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_82_old_Osum_Osimps_I8_J,axiom,
% 3.26/1.75 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F22: B > T,B3: B] :
% 3.26/1.75 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ B3 ) )
% 3.26/1.75 = ( F22 @ B3 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_83_Inr__inject,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,X5: B,Y3: B] :
% 3.26/1.75 ( ( ( sum_Inr @ B @ A @ X5 )
% 3.26/1.75 = ( sum_Inr @ B @ A @ Y3 ) )
% 3.26/1.75 => ( X5 = Y3 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_84_not__arg__cong__Inr,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,X5: A,Y3: A] :
% 3.26/1.75 ( ( X5 != Y3 )
% 3.26/1.75 => ( ( sum_Inr @ A @ B @ X5 )
% 3.26/1.75 != ( sum_Inr @ A @ B @ Y3 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_85_Suml__inject,axiom,
% 3.26/1.75 ! [B: $tType,C: $tType,A: $tType,F: A > C,G2: A > C] :
% 3.26/1.75 ( ( ( sum_Suml @ A @ C @ B @ F )
% 3.26/1.75 = ( sum_Suml @ A @ C @ B @ G2 ) )
% 3.26/1.75 => ( F = G2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_86_obj__sumE,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 3.26/1.75 ( ! [X6: A] :
% 3.26/1.75 ( S
% 3.26/1.75 != ( sum_Inl @ A @ B @ X6 ) )
% 3.26/1.75 => ~ ! [X6: B] :
% 3.26/1.75 ( S
% 3.26/1.75 != ( sum_Inr @ B @ A @ X6 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_87_sum_Odistinct_I1_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,X1: A,X22: B] :
% 3.26/1.75 ( ( sum_Inl @ A @ B @ X1 )
% 3.26/1.75 != ( sum_Inr @ B @ A @ X22 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_88_old_Osum_Odistinct_I2_J,axiom,
% 3.26/1.75 ! [B6: $tType,A7: $tType,B7: B6,A8: A7] :
% 3.26/1.75 ( ( sum_Inr @ B6 @ A7 @ B7 )
% 3.26/1.75 != ( sum_Inl @ A7 @ B6 @ A8 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_89_old_Osum_Odistinct_I1_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,A4: A,B5: B] :
% 3.26/1.75 ( ( sum_Inl @ A @ B @ A4 )
% 3.26/1.75 != ( sum_Inr @ B @ A @ B5 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_90_sumE,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 3.26/1.75 ( ! [X6: A] :
% 3.26/1.75 ( S
% 3.26/1.75 != ( sum_Inl @ A @ B @ X6 ) )
% 3.26/1.75 => ~ ! [Y4: B] :
% 3.26/1.75 ( S
% 3.26/1.75 != ( sum_Inr @ B @ A @ Y4 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_91_Inr__not__Inl,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,B3: B,A4: A] :
% 3.26/1.75 ( ( sum_Inr @ B @ A @ B3 )
% 3.26/1.75 != ( sum_Inl @ A @ B @ A4 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_92_split__sum__ex,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 3.26/1.75 ? [X7: sum_sum @ A @ B] : ( P3 @ X7 ) )
% 3.26/1.75 = ( ^ [P: ( sum_sum @ A @ B ) > $o] :
% 3.26/1.75 ( ? [X: A] : ( P @ ( sum_Inl @ A @ B @ X ) )
% 3.26/1.75 | ? [X: B] : ( P @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_93_split__sum__all,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 3.26/1.75 ! [X7: sum_sum @ A @ B] : ( P3 @ X7 ) )
% 3.26/1.75 = ( ^ [P: ( sum_sum @ A @ B ) > $o] :
% 3.26/1.75 ( ! [X: A] : ( P @ ( sum_Inl @ A @ B @ X ) )
% 3.26/1.75 & ! [X: B] : ( P @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_94_old_Osum_Oexhaust,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,Y3: sum_sum @ A @ B] :
% 3.26/1.75 ( ! [A9: A] :
% 3.26/1.75 ( Y3
% 3.26/1.75 != ( sum_Inl @ A @ B @ A9 ) )
% 3.26/1.75 => ~ ! [B8: B] :
% 3.26/1.75 ( Y3
% 3.26/1.75 != ( sum_Inr @ B @ A @ B8 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_95_old_Osum_Oinducts,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,P2: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 3.26/1.75 ( ! [A9: A] : ( P2 @ ( sum_Inl @ A @ B @ A9 ) )
% 3.26/1.75 => ( ! [B8: B] : ( P2 @ ( sum_Inr @ B @ A @ B8 ) )
% 3.26/1.75 => ( P2 @ Sum ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_96_subtr_OStep,axiom,
% 3.26/1.75 ! [Tr3: dtree,Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 3.26/1.75 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 3.26/1.75 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_97_subtr_Ocases,axiom,
% 3.26/1.75 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 3.26/1.75 ( ( gram_L716654942_subtr @ A1 @ A22 @ A32 )
% 3.26/1.75 => ( ( ( A32 = A22 )
% 3.26/1.75 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 3.26/1.75 => ~ ( ( member @ n @ ( root @ A32 ) @ A1 )
% 3.26/1.75 => ! [Tr23: dtree] :
% 3.26/1.75 ( ( gram_L716654942_subtr @ A1 @ A22 @ Tr23 )
% 3.26/1.75 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ A32 ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_98_subtr_Osimps,axiom,
% 3.26/1.75 ( gram_L716654942_subtr
% 3.26/1.75 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 3.26/1.75 ( ? [Tr4: dtree,Ns2: set @ n] :
% 3.26/1.75 ( ( A12 = Ns2 )
% 3.26/1.75 & ( A23 = Tr4 )
% 3.26/1.75 & ( A33 = Tr4 )
% 3.26/1.75 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 3.26/1.75 | ? [Tr32: dtree,Ns2: set @ n,Tr13: dtree,Tr24: dtree] :
% 3.26/1.75 ( ( A12 = Ns2 )
% 3.26/1.75 & ( A23 = Tr13 )
% 3.26/1.75 & ( A33 = Tr32 )
% 3.26/1.75 & ( member @ n @ ( root @ Tr32 ) @ Ns2 )
% 3.26/1.75 & ( gram_L716654942_subtr @ Ns2 @ Tr13 @ Tr24 )
% 3.26/1.75 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr24 ) @ ( cont @ Tr32 ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_99_subtr__StepL,axiom,
% 3.26/1.75 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 3.26/1.75 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 3.26/1.75 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_100_subtr_Oinducts,axiom,
% 3.26/1.75 ! [X1: set @ n,X22: dtree,X32: dtree,P2: ( set @ n ) > dtree > dtree > $o] :
% 3.26/1.75 ( ( gram_L716654942_subtr @ X1 @ X22 @ X32 )
% 3.26/1.75 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 3.26/1.75 => ( P2 @ Ns3 @ Tr7 @ Tr7 ) )
% 3.26/1.75 => ( ! [Tr33: dtree,Ns3: set @ n,Tr12: dtree,Tr23: dtree] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr33 ) @ Ns3 )
% 3.26/1.75 => ( ( gram_L716654942_subtr @ Ns3 @ Tr12 @ Tr23 )
% 3.26/1.75 => ( ( P2 @ Ns3 @ Tr12 @ Tr23 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr33 ) )
% 3.26/1.75 => ( P2 @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 3.26/1.75 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_101_subtr__inductL,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 3.26/1.75 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.26/1.75 => ( ! [Ns3: set @ n,Tr7: dtree] : ( Phi @ Ns3 @ Tr7 @ Tr7 )
% 3.26/1.75 => ( ! [Ns3: set @ n,Tr12: dtree,Tr23: dtree,Tr33: dtree] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr12 ) @ Ns3 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 3.26/1.75 => ( ( gram_L716654942_subtr @ Ns3 @ Tr23 @ Tr33 )
% 3.26/1.75 => ( ( Phi @ Ns3 @ Tr23 @ Tr33 )
% 3.26/1.75 => ( Phi @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 3.26/1.75 => ( Phi @ Ns @ Tr1 @ Tr22 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_102_bot__fun__def,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( bot @ B @ ( type2 @ B ) )
% 3.26/1.75 => ( ( bot_bot @ ( A > B ) )
% 3.26/1.75 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_103_subtr2_Oinducts,axiom,
% 3.26/1.75 ! [X1: set @ n,X22: dtree,X32: dtree,P2: ( set @ n ) > dtree > dtree > $o] :
% 3.26/1.75 ( ( gram_L1283001940subtr2 @ X1 @ X22 @ X32 )
% 3.26/1.75 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 3.26/1.75 => ( P2 @ Ns3 @ Tr7 @ Tr7 ) )
% 3.26/1.75 => ( ! [Tr12: dtree,Ns3: set @ n,Tr23: dtree,Tr33: dtree] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr12 ) @ Ns3 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 3.26/1.75 => ( ( gram_L1283001940subtr2 @ Ns3 @ Tr23 @ Tr33 )
% 3.26/1.75 => ( ( P2 @ Ns3 @ Tr23 @ Tr33 )
% 3.26/1.75 => ( P2 @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 3.26/1.75 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_104_subtr2__StepR,axiom,
% 3.26/1.75 ! [Tr3: dtree,Ns: set @ n,Tr22: dtree,Tr1: dtree] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 3.26/1.75 => ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 3.26/1.75 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_105_subtr2_Osimps,axiom,
% 3.26/1.75 ( gram_L1283001940subtr2
% 3.26/1.75 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 3.26/1.75 ( ? [Tr4: dtree,Ns2: set @ n] :
% 3.26/1.75 ( ( A12 = Ns2 )
% 3.26/1.75 & ( A23 = Tr4 )
% 3.26/1.75 & ( A33 = Tr4 )
% 3.26/1.75 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 3.26/1.75 | ? [Tr13: dtree,Ns2: set @ n,Tr24: dtree,Tr32: dtree] :
% 3.26/1.75 ( ( A12 = Ns2 )
% 3.26/1.75 & ( A23 = Tr13 )
% 3.26/1.75 & ( A33 = Tr32 )
% 3.26/1.75 & ( member @ n @ ( root @ Tr13 ) @ Ns2 )
% 3.26/1.75 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr24 ) )
% 3.26/1.75 & ( gram_L1283001940subtr2 @ Ns2 @ Tr24 @ Tr32 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_106_subtr2_Ocases,axiom,
% 3.26/1.75 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 3.26/1.75 ( ( gram_L1283001940subtr2 @ A1 @ A22 @ A32 )
% 3.26/1.75 => ( ( ( A32 = A22 )
% 3.26/1.75 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 3.26/1.75 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.26/1.75 => ! [Tr23: dtree] :
% 3.26/1.75 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A22 ) @ ( cont @ Tr23 ) )
% 3.26/1.75 => ~ ( gram_L1283001940subtr2 @ A1 @ Tr23 @ A32 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_107_subtr2_OStep,axiom,
% 3.26/1.75 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 3.26/1.75 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 3.26/1.75 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_108_inFr_OInd,axiom,
% 3.26/1.75 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,T2: t] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.26/1.75 => ( ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 )
% 3.26/1.75 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_109_inItr_OInd,axiom,
% 3.26/1.75 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N: n] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.26/1.75 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N )
% 3.26/1.75 => ( gram_L830233218_inItr @ Ns @ Tr @ N ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_110_inItr_Ocases,axiom,
% 3.26/1.75 ! [A1: set @ n,A22: dtree,A32: n] :
% 3.26/1.75 ( ( gram_L830233218_inItr @ A1 @ A22 @ A32 )
% 3.26/1.75 => ( ( ( A32
% 3.26/1.75 = ( root @ A22 ) )
% 3.26/1.75 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 3.26/1.75 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.26/1.75 => ! [Tr12: dtree] :
% 3.26/1.75 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 3.26/1.75 => ~ ( gram_L830233218_inItr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_111_inItr_Osimps,axiom,
% 3.26/1.75 ( gram_L830233218_inItr
% 3.26/1.75 = ( ^ [A12: set @ n,A23: dtree,A33: n] :
% 3.26/1.75 ( ? [Tr4: dtree,Ns2: set @ n] :
% 3.26/1.75 ( ( A12 = Ns2 )
% 3.26/1.75 & ( A23 = Tr4 )
% 3.26/1.75 & ( A33
% 3.26/1.75 = ( root @ Tr4 ) )
% 3.26/1.75 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 3.26/1.75 | ? [Tr4: dtree,Ns2: set @ n,Tr13: dtree,N2: n] :
% 3.26/1.75 ( ( A12 = Ns2 )
% 3.26/1.75 & ( A23 = Tr4 )
% 3.26/1.75 & ( A33 = N2 )
% 3.26/1.75 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 3.26/1.75 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 3.26/1.75 & ( gram_L830233218_inItr @ Ns2 @ Tr13 @ N2 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_112_inItr_Oinducts,axiom,
% 3.26/1.75 ! [X1: set @ n,X22: dtree,X32: n,P2: ( set @ n ) > dtree > n > $o] :
% 3.26/1.75 ( ( gram_L830233218_inItr @ X1 @ X22 @ X32 )
% 3.26/1.75 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 3.26/1.75 => ( P2 @ Ns3 @ Tr7 @ ( root @ Tr7 ) ) )
% 3.26/1.75 => ( ! [Tr7: dtree,Ns3: set @ n,Tr12: dtree,N3: n] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 3.26/1.75 => ( ( gram_L830233218_inItr @ Ns3 @ Tr12 @ N3 )
% 3.26/1.75 => ( ( P2 @ Ns3 @ Tr12 @ N3 )
% 3.26/1.75 => ( P2 @ Ns3 @ Tr7 @ N3 ) ) ) ) )
% 3.26/1.75 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_113_inFr2__Ind,axiom,
% 3.26/1.75 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 3.26/1.75 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 3.26/1.75 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.26/1.75 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_114_Inl__Inr__False,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,X5: A,Y3: B] :
% 3.26/1.75 ( ( sum_Inl @ A @ B @ X5 )
% 3.26/1.75 != ( sum_Inr @ B @ A @ Y3 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_115_Inr__Inl__False,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,X5: B,Y3: A] :
% 3.26/1.75 ( ( sum_Inr @ B @ A @ X5 )
% 3.26/1.75 != ( sum_Inl @ A @ B @ Y3 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_116_Inl__Inr__image__cong,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,A2: set @ ( sum_sum @ A @ B ),B2: set @ ( sum_sum @ A @ B )] :
% 3.26/1.75 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A2 )
% 3.26/1.75 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B2 ) )
% 3.26/1.75 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A2 )
% 3.26/1.75 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B2 ) )
% 3.26/1.75 => ( A2 = B2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_117_bot__empty__eq,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( bot_bot @ ( A > $o ) )
% 3.26/1.75 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_118_Collect__empty__eq__bot,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o] :
% 3.26/1.75 ( ( ( collect @ A @ P2 )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 = ( P2
% 3.26/1.75 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_119_obj__sumE__f,axiom,
% 3.26/1.75 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P2: $o] :
% 3.26/1.75 ( ! [X6: A] :
% 3.26/1.75 ( ( S
% 3.26/1.75 = ( F @ ( sum_Inl @ A @ C @ X6 ) ) )
% 3.26/1.75 => P2 )
% 3.26/1.75 => ( ! [X6: C] :
% 3.26/1.75 ( ( S
% 3.26/1.75 = ( F @ ( sum_Inr @ C @ A @ X6 ) ) )
% 3.26/1.75 => P2 )
% 3.26/1.75 => ! [X8: sum_sum @ A @ C] :
% 3.26/1.75 ( ( S
% 3.26/1.75 = ( F @ X8 ) )
% 3.26/1.75 => P2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_120_inFr2_Oinducts,axiom,
% 3.26/1.75 ! [X1: set @ n,X22: dtree,X32: t,P2: ( set @ n ) > dtree > t > $o] :
% 3.26/1.75 ( ( gram_L805317441_inFr2 @ X1 @ X22 @ X32 )
% 3.26/1.75 => ( ! [Tr7: dtree,Ns3: set @ n,T4: t] :
% 3.26/1.75 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr7 ) )
% 3.26/1.75 => ( P2 @ Ns3 @ Tr7 @ T4 ) ) )
% 3.26/1.75 => ( ! [Tr12: dtree,Tr7: dtree,Ns1: set @ n,T4: t] :
% 3.26/1.75 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 3.26/1.75 => ( ( gram_L805317441_inFr2 @ Ns1 @ Tr12 @ T4 )
% 3.26/1.75 => ( ( P2 @ Ns1 @ Tr12 @ T4 )
% 3.26/1.75 => ( P2 @ ( insert @ n @ ( root @ Tr7 ) @ Ns1 ) @ Tr7 @ T4 ) ) ) )
% 3.26/1.75 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_121_inFr2_Osimps,axiom,
% 3.26/1.75 ( gram_L805317441_inFr2
% 3.26/1.75 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 3.26/1.75 ( ? [Tr4: dtree,Ns2: set @ n,T3: t] :
% 3.26/1.75 ( ( A12 = Ns2 )
% 3.26/1.75 & ( A23 = Tr4 )
% 3.26/1.75 & ( A33 = T3 )
% 3.26/1.75 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 3.26/1.75 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) ) )
% 3.26/1.75 | ? [Tr13: dtree,Tr4: dtree,Ns12: set @ n,T3: t] :
% 3.26/1.75 ( ( A12
% 3.26/1.75 = ( insert @ n @ ( root @ Tr4 ) @ Ns12 ) )
% 3.26/1.75 & ( A23 = Tr4 )
% 3.26/1.75 & ( A33 = T3 )
% 3.26/1.75 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 3.26/1.75 & ( gram_L805317441_inFr2 @ Ns12 @ Tr13 @ T3 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_122_inFr2_Ocases,axiom,
% 3.26/1.75 ! [A1: set @ n,A22: dtree,A32: t] :
% 3.26/1.75 ( ( gram_L805317441_inFr2 @ A1 @ A22 @ A32 )
% 3.26/1.75 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.26/1.75 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 3.26/1.75 => ~ ! [Tr12: dtree,Tr7: dtree,Ns1: set @ n] :
% 3.26/1.75 ( ( A1
% 3.26/1.75 = ( insert @ n @ ( root @ Tr7 ) @ Ns1 ) )
% 3.26/1.75 => ( ( A22 = Tr7 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 3.26/1.75 => ~ ( gram_L805317441_inFr2 @ Ns1 @ Tr12 @ A32 ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_123_inFr2_OInd,axiom,
% 3.26/1.75 ! [Tr1: dtree,Tr: dtree,Ns13: set @ n,T2: t] :
% 3.26/1.75 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.26/1.75 => ( ( gram_L805317441_inFr2 @ Ns13 @ Tr1 @ T2 )
% 3.26/1.75 => ( gram_L805317441_inFr2 @ ( insert @ n @ ( root @ Tr ) @ Ns13 ) @ Tr @ T2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_124_insertCI,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,B2: set @ A,B3: A] :
% 3.26/1.75 ( ( ~ ( member @ A @ A4 @ B2 )
% 3.26/1.75 => ( A4 = B3 ) )
% 3.26/1.75 => ( member @ A @ A4 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_125_insert__iff,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,B3: A,A2: set @ A] :
% 3.26/1.75 ( ( member @ A @ A4 @ ( insert @ A @ B3 @ A2 ) )
% 3.26/1.75 = ( ( A4 = B3 )
% 3.26/1.75 | ( member @ A @ A4 @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_126_insert__absorb2,axiom,
% 3.26/1.75 ! [A: $tType,X5: A,A2: set @ A] :
% 3.26/1.75 ( ( insert @ A @ X5 @ ( insert @ A @ X5 @ A2 ) )
% 3.26/1.75 = ( insert @ A @ X5 @ A2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_127_singletonI,axiom,
% 3.26/1.75 ! [A: $tType,A4: A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_128_singleton__conv2,axiom,
% 3.26/1.75 ! [A: $tType,A4: A] :
% 3.26/1.75 ( ( collect @ A
% 3.26/1.75 @ ( ^ [Y6: A,Z: A] : ( Y6 = Z )
% 3.26/1.75 @ A4 ) )
% 3.26/1.75 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_129_singleton__conv,axiom,
% 3.26/1.75 ! [A: $tType,A4: A] :
% 3.26/1.75 ( ( collect @ A
% 3.26/1.75 @ ^ [X: A] : ( X = A4 ) )
% 3.26/1.75 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_130_singleton__inject,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,B3: A] :
% 3.26/1.75 ( ( ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 => ( A4 = B3 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_131_insert__not__empty,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,A2: set @ A] :
% 3.26/1.75 ( ( insert @ A @ A4 @ A2 )
% 3.26/1.75 != ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_132_doubleton__eq__iff,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,B3: A,C3: A,D2: A] :
% 3.26/1.75 ( ( ( insert @ A @ A4 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 = ( insert @ A @ C3 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.26/1.75 = ( ( ( A4 = C3 )
% 3.26/1.75 & ( B3 = D2 ) )
% 3.26/1.75 | ( ( A4 = D2 )
% 3.26/1.75 & ( B3 = C3 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_133_singleton__iff,axiom,
% 3.26/1.75 ! [A: $tType,B3: A,A4: A] :
% 3.26/1.75 ( ( member @ A @ B3 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 = ( B3 = A4 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_134_singletonD,axiom,
% 3.26/1.75 ! [A: $tType,B3: A,A4: A] :
% 3.26/1.75 ( ( member @ A @ B3 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 => ( B3 = A4 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_135_insertE,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,B3: A,A2: set @ A] :
% 3.26/1.75 ( ( member @ A @ A4 @ ( insert @ A @ B3 @ A2 ) )
% 3.26/1.75 => ( ( A4 != B3 )
% 3.26/1.75 => ( member @ A @ A4 @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_136_insertI1,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,B2: set @ A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ B2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_137_insertI2,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,B2: set @ A,B3: A] :
% 3.26/1.75 ( ( member @ A @ A4 @ B2 )
% 3.26/1.75 => ( member @ A @ A4 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_138_Set_Oset__insert,axiom,
% 3.26/1.75 ! [A: $tType,X5: A,A2: set @ A] :
% 3.26/1.75 ( ( member @ A @ X5 @ A2 )
% 3.26/1.75 => ~ ! [B9: set @ A] :
% 3.26/1.75 ( ( A2
% 3.26/1.75 = ( insert @ A @ X5 @ B9 ) )
% 3.26/1.75 => ( member @ A @ X5 @ B9 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_139_insert__compr,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( insert @ A )
% 3.26/1.75 = ( ^ [A3: A,B4: set @ A] :
% 3.26/1.75 ( collect @ A
% 3.26/1.75 @ ^ [X: A] :
% 3.26/1.75 ( ( X = A3 )
% 3.26/1.75 | ( member @ A @ X @ B4 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_140_insert__ident,axiom,
% 3.26/1.75 ! [A: $tType,X5: A,A2: set @ A,B2: set @ A] :
% 3.26/1.75 ( ~ ( member @ A @ X5 @ A2 )
% 3.26/1.75 => ( ~ ( member @ A @ X5 @ B2 )
% 3.26/1.75 => ( ( ( insert @ A @ X5 @ A2 )
% 3.26/1.75 = ( insert @ A @ X5 @ B2 ) )
% 3.26/1.75 = ( A2 = B2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_141_insert__absorb,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,A2: set @ A] :
% 3.26/1.75 ( ( member @ A @ A4 @ A2 )
% 3.26/1.75 => ( ( insert @ A @ A4 @ A2 )
% 3.26/1.75 = A2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_142_insert__eq__iff,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,A2: set @ A,B3: A,B2: set @ A] :
% 3.26/1.75 ( ~ ( member @ A @ A4 @ A2 )
% 3.26/1.75 => ( ~ ( member @ A @ B3 @ B2 )
% 3.26/1.75 => ( ( ( insert @ A @ A4 @ A2 )
% 3.26/1.75 = ( insert @ A @ B3 @ B2 ) )
% 3.26/1.75 = ( ( ( A4 = B3 )
% 3.26/1.75 => ( A2 = B2 ) )
% 3.26/1.75 & ( ( A4 != B3 )
% 3.26/1.75 => ? [C4: set @ A] :
% 3.26/1.75 ( ( A2
% 3.26/1.75 = ( insert @ A @ B3 @ C4 ) )
% 3.26/1.75 & ~ ( member @ A @ B3 @ C4 )
% 3.26/1.75 & ( B2
% 3.26/1.75 = ( insert @ A @ A4 @ C4 ) )
% 3.26/1.75 & ~ ( member @ A @ A4 @ C4 ) ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_143_insert__Collect,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,P2: A > $o] :
% 3.26/1.75 ( ( insert @ A @ A4 @ ( collect @ A @ P2 ) )
% 3.26/1.75 = ( collect @ A
% 3.26/1.75 @ ^ [U: A] :
% 3.26/1.75 ( ( U != A4 )
% 3.26/1.75 => ( P2 @ U ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_144_insert__commute,axiom,
% 3.26/1.75 ! [A: $tType,X5: A,Y3: A,A2: set @ A] :
% 3.26/1.75 ( ( insert @ A @ X5 @ ( insert @ A @ Y3 @ A2 ) )
% 3.26/1.75 = ( insert @ A @ Y3 @ ( insert @ A @ X5 @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_145_mk__disjoint__insert,axiom,
% 3.26/1.75 ! [A: $tType,A4: A,A2: set @ A] :
% 3.26/1.75 ( ( member @ A @ A4 @ A2 )
% 3.26/1.75 => ? [B9: set @ A] :
% 3.26/1.75 ( ( A2
% 3.26/1.75 = ( insert @ A @ A4 @ B9 ) )
% 3.26/1.75 & ~ ( member @ A @ A4 @ B9 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_146_Collect__conv__if2,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o,A4: A] :
% 3.26/1.75 ( ( ( P2 @ A4 )
% 3.26/1.75 => ( ( collect @ A
% 3.26/1.75 @ ^ [X: A] :
% 3.26/1.75 ( ( A4 = X )
% 3.26/1.75 & ( P2 @ X ) ) )
% 3.26/1.75 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.26/1.75 & ( ~ ( P2 @ A4 )
% 3.26/1.75 => ( ( collect @ A
% 3.26/1.75 @ ^ [X: A] :
% 3.26/1.75 ( ( A4 = X )
% 3.26/1.75 & ( P2 @ X ) ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_147_Collect__conv__if,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o,A4: A] :
% 3.26/1.75 ( ( ( P2 @ A4 )
% 3.26/1.75 => ( ( collect @ A
% 3.26/1.75 @ ^ [X: A] :
% 3.26/1.75 ( ( X = A4 )
% 3.26/1.75 & ( P2 @ X ) ) )
% 3.26/1.75 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.26/1.75 & ( ~ ( P2 @ A4 )
% 3.26/1.75 => ( ( collect @ A
% 3.26/1.75 @ ^ [X: A] :
% 3.26/1.75 ( ( X = A4 )
% 3.26/1.75 & ( P2 @ X ) ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_148_vimage__singleton__eq,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,A4: A,F: A > B,B3: B] :
% 3.26/1.75 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ ( insert @ B @ B3 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 3.26/1.75 = ( ( F @ A4 )
% 3.26/1.75 = B3 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_149_inFr__Ind__minus,axiom,
% 3.26/1.75 ! [Ns13: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 3.26/1.75 ( ( gram_L1333338417e_inFr @ Ns13 @ Tr1 @ T2 )
% 3.26/1.75 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.26/1.75 => ( gram_L1333338417e_inFr @ ( insert @ n @ ( root @ Tr ) @ Ns13 ) @ Tr @ T2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_150_ccpo__Sup__singleton,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( comple1141879883l_ccpo @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [X5: A] :
% 3.26/1.75 ( ( complete_Sup_Sup @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 = X5 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_151_cSup__singleton,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( condit378418413attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [X5: A] :
% 3.26/1.75 ( ( complete_Sup_Sup @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 = X5 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_152_is__singletonI,axiom,
% 3.26/1.75 ! [A: $tType,X5: A] : ( is_singleton @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_153_the__elem__eq,axiom,
% 3.26/1.75 ! [A: $tType,X5: A] :
% 3.26/1.75 ( ( the_elem @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 = X5 ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_154_is__singleton__the__elem,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( is_singleton @ A )
% 3.26/1.75 = ( ^ [A6: set @ A] :
% 3.26/1.75 ( A6
% 3.26/1.75 = ( insert @ A @ ( the_elem @ A @ A6 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_155_is__singletonI_H,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ A] :
% 3.26/1.75 ( ( A2
% 3.26/1.75 != ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 => ( ! [X6: A,Y4: A] :
% 3.26/1.75 ( ( member @ A @ X6 @ A2 )
% 3.26/1.75 => ( ( member @ A @ Y4 @ A2 )
% 3.26/1.75 => ( X6 = Y4 ) ) )
% 3.26/1.75 => ( is_singleton @ A @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_156_is__singleton__def,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( is_singleton @ A )
% 3.26/1.75 = ( ^ [A6: set @ A] :
% 3.26/1.75 ? [X: A] :
% 3.26/1.75 ( A6
% 3.26/1.75 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_157_is__singletonE,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ A] :
% 3.26/1.75 ( ( is_singleton @ A @ A2 )
% 3.26/1.75 => ~ ! [X6: A] :
% 3.26/1.75 ( A2
% 3.26/1.75 != ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_158_sum__set__simps_I1_J,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,X5: A] :
% 3.26/1.75 ( ( basic_setl @ A @ B @ ( sum_Inl @ A @ B @ X5 ) )
% 3.26/1.75 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_159_sum__set__simps_I4_J,axiom,
% 3.26/1.75 ! [E: $tType,A: $tType,X5: A] :
% 3.26/1.75 ( ( basic_setr @ E @ A @ ( sum_Inr @ A @ E @ X5 ) )
% 3.26/1.75 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_160_the__elem__def,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( the_elem @ A )
% 3.26/1.75 = ( ^ [X9: set @ A] :
% 3.26/1.75 ( the @ A
% 3.26/1.75 @ ^ [X: A] :
% 3.26/1.75 ( X9
% 3.26/1.75 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_161_sum__set__simps_I2_J,axiom,
% 3.26/1.75 ! [A: $tType,C: $tType,X5: A] :
% 3.26/1.75 ( ( basic_setl @ C @ A @ ( sum_Inr @ A @ C @ X5 ) )
% 3.26/1.75 = ( bot_bot @ ( set @ C ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_162_sum__set__simps_I3_J,axiom,
% 3.26/1.75 ! [A: $tType,D: $tType,X5: A] :
% 3.26/1.75 ( ( basic_setr @ A @ D @ ( sum_Inl @ A @ D @ X5 ) )
% 3.26/1.75 = ( bot_bot @ ( set @ D ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_163_old_Orec__sum__def,axiom,
% 3.26/1.75 ! [B: $tType,T: $tType,A: $tType] :
% 3.26/1.75 ( ( sum_rec_sum @ A @ T @ B )
% 3.26/1.75 = ( ^ [F12: A > T,F23: B > T,X: sum_sum @ A @ B] : ( the @ T @ ( sum_rec_set_sum @ A @ T @ B @ F12 @ F23 @ X ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_164_the__sym__eq__trivial,axiom,
% 3.26/1.75 ! [A: $tType,X5: A] :
% 3.26/1.75 ( ( the @ A
% 3.26/1.75 @ ( ^ [Y6: A,Z: A] : ( Y6 = Z )
% 3.26/1.75 @ X5 ) )
% 3.26/1.75 = X5 ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_165_the__eq__trivial,axiom,
% 3.26/1.75 ! [A: $tType,A4: A] :
% 3.26/1.75 ( ( the @ A
% 3.26/1.75 @ ^ [X: A] : ( X = A4 ) )
% 3.26/1.75 = A4 ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_166_the__equality,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o,A4: A] :
% 3.26/1.75 ( ( P2 @ A4 )
% 3.26/1.75 => ( ! [X6: A] :
% 3.26/1.75 ( ( P2 @ X6 )
% 3.26/1.75 => ( X6 = A4 ) )
% 3.26/1.75 => ( ( the @ A @ P2 )
% 3.26/1.75 = A4 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_167_theI,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o,A4: A] :
% 3.26/1.75 ( ( P2 @ A4 )
% 3.26/1.75 => ( ! [X6: A] :
% 3.26/1.75 ( ( P2 @ X6 )
% 3.26/1.75 => ( X6 = A4 ) )
% 3.26/1.75 => ( P2 @ ( the @ A @ P2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_168_theI_H,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o] :
% 3.26/1.75 ( ? [X8: A] :
% 3.26/1.75 ( ( P2 @ X8 )
% 3.26/1.75 & ! [Y4: A] :
% 3.26/1.75 ( ( P2 @ Y4 )
% 3.26/1.75 => ( Y4 = X8 ) ) )
% 3.26/1.75 => ( P2 @ ( the @ A @ P2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_169_theI2,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o,A4: A,Q: A > $o] :
% 3.26/1.75 ( ( P2 @ A4 )
% 3.26/1.75 => ( ! [X6: A] :
% 3.26/1.75 ( ( P2 @ X6 )
% 3.26/1.75 => ( X6 = A4 ) )
% 3.26/1.75 => ( ! [X6: A] :
% 3.26/1.75 ( ( P2 @ X6 )
% 3.26/1.75 => ( Q @ X6 ) )
% 3.26/1.75 => ( Q @ ( the @ A @ P2 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_170_If__def,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( if @ A )
% 3.26/1.75 = ( ^ [P: $o,X: A,Y: A] :
% 3.26/1.75 ( the @ A
% 3.26/1.75 @ ^ [Z2: A] :
% 3.26/1.75 ( ( P
% 3.26/1.75 => ( Z2 = X ) )
% 3.26/1.75 & ( ~ P
% 3.26/1.75 => ( Z2 = Y ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_171_the1I2,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 3.26/1.75 ( ? [X8: A] :
% 3.26/1.75 ( ( P2 @ X8 )
% 3.26/1.75 & ! [Y4: A] :
% 3.26/1.75 ( ( P2 @ Y4 )
% 3.26/1.75 => ( Y4 = X8 ) ) )
% 3.26/1.75 => ( ! [X6: A] :
% 3.26/1.75 ( ( P2 @ X6 )
% 3.26/1.75 => ( Q @ X6 ) )
% 3.26/1.75 => ( Q @ ( the @ A @ P2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_172_the1__equality,axiom,
% 3.26/1.75 ! [A: $tType,P2: A > $o,A4: A] :
% 3.26/1.75 ( ? [X8: A] :
% 3.26/1.75 ( ( P2 @ X8 )
% 3.26/1.75 & ! [Y4: A] :
% 3.26/1.75 ( ( P2 @ Y4 )
% 3.26/1.75 => ( Y4 = X8 ) ) )
% 3.26/1.75 => ( ( P2 @ A4 )
% 3.26/1.75 => ( ( the @ A @ P2 )
% 3.26/1.75 = A4 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_173_setl_Oinducts,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,X5: A,S: sum_sum @ A @ B,P2: A > $o] :
% 3.26/1.75 ( ( member @ A @ X5 @ ( basic_setl @ A @ B @ S ) )
% 3.26/1.75 => ( ! [X6: A] :
% 3.26/1.75 ( ( S
% 3.26/1.75 = ( sum_Inl @ A @ B @ X6 ) )
% 3.26/1.75 => ( P2 @ X6 ) )
% 3.26/1.75 => ( P2 @ X5 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_174_setl_Ointros,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,S: sum_sum @ A @ B,X5: A] :
% 3.26/1.75 ( ( S
% 3.26/1.75 = ( sum_Inl @ A @ B @ X5 ) )
% 3.26/1.75 => ( member @ A @ X5 @ ( basic_setl @ A @ B @ S ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_175_setl_Osimps,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,A4: A,S: sum_sum @ A @ B] :
% 3.26/1.75 ( ( member @ A @ A4 @ ( basic_setl @ A @ B @ S ) )
% 3.26/1.75 = ( ? [X: A] :
% 3.26/1.75 ( ( A4 = X )
% 3.26/1.75 & ( S
% 3.26/1.75 = ( sum_Inl @ A @ B @ X ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_176_setr_Oinducts,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,X5: B,S: sum_sum @ A @ B,P2: B > $o] :
% 3.26/1.75 ( ( member @ B @ X5 @ ( basic_setr @ A @ B @ S ) )
% 3.26/1.75 => ( ! [X6: B] :
% 3.26/1.75 ( ( S
% 3.26/1.75 = ( sum_Inr @ B @ A @ X6 ) )
% 3.26/1.75 => ( P2 @ X6 ) )
% 3.26/1.75 => ( P2 @ X5 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_177_setr_Ointros,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,S: sum_sum @ A @ B,X5: B] :
% 3.26/1.75 ( ( S
% 3.26/1.75 = ( sum_Inr @ B @ A @ X5 ) )
% 3.26/1.75 => ( member @ B @ X5 @ ( basic_setr @ A @ B @ S ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_178_setr_Osimps,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,A4: B,S: sum_sum @ A @ B] :
% 3.26/1.75 ( ( member @ B @ A4 @ ( basic_setr @ A @ B @ S ) )
% 3.26/1.75 = ( ? [X: B] :
% 3.26/1.75 ( ( A4 = X )
% 3.26/1.75 & ( S
% 3.26/1.75 = ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_179_setr_Ocases,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,A4: B,S: sum_sum @ A @ B] :
% 3.26/1.75 ( ( member @ B @ A4 @ ( basic_setr @ A @ B @ S ) )
% 3.26/1.75 => ( S
% 3.26/1.75 = ( sum_Inr @ B @ A @ A4 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_180_setl_Ocases,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,A4: A,S: sum_sum @ A @ B] :
% 3.26/1.75 ( ( member @ A @ A4 @ ( basic_setl @ A @ B @ S ) )
% 3.26/1.75 => ( S
% 3.26/1.75 = ( sum_Inl @ A @ B @ A4 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_181_vimage__eq__UN,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( vimage @ A @ B )
% 3.26/1.75 = ( ^ [F2: A > B,B4: set @ B] :
% 3.26/1.75 ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ B @ ( set @ A )
% 3.26/1.75 @ ^ [Y: B] : ( vimage @ A @ B @ F2 @ ( insert @ B @ Y @ ( bot_bot @ ( set @ B ) ) ) )
% 3.26/1.75 @ B4 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_182_sum__set__defs_I2_J,axiom,
% 3.26/1.75 ! [C: $tType,D: $tType] :
% 3.26/1.75 ( ( basic_setr @ C @ D )
% 3.26/1.75 = ( sum_case_sum @ C @ ( set @ D ) @ D
% 3.26/1.75 @ ^ [A3: C] : ( bot_bot @ ( set @ D ) )
% 3.26/1.75 @ ^ [Z2: D] : ( insert @ D @ Z2 @ ( bot_bot @ ( set @ D ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_183_sum__set__defs_I1_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType] :
% 3.26/1.75 ( ( basic_setl @ A @ B )
% 3.26/1.75 = ( sum_case_sum @ A @ ( set @ A ) @ B
% 3.26/1.75 @ ^ [Z2: A] : ( insert @ A @ Z2 @ ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 @ ^ [B10: B] : ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_184_image__eqI,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,B3: A,F: B > A,X5: B,A2: set @ B] :
% 3.26/1.75 ( ( B3
% 3.26/1.75 = ( F @ X5 ) )
% 3.26/1.75 => ( ( member @ B @ X5 @ A2 )
% 3.26/1.75 => ( member @ A @ B3 @ ( image @ B @ A @ F @ A2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_185_image__ident,axiom,
% 3.26/1.75 ! [A: $tType,Y5: set @ A] :
% 3.26/1.75 ( ( image @ A @ A
% 3.26/1.75 @ ^ [X: A] : X
% 3.26/1.75 @ Y5 )
% 3.26/1.75 = Y5 ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_186_case__sum__KK,axiom,
% 3.26/1.75 ! [C: $tType,B: $tType,A: $tType,A4: C] :
% 3.26/1.75 ( ( sum_case_sum @ A @ C @ B
% 3.26/1.75 @ ^ [X: A] : A4
% 3.26/1.75 @ ^ [X: B] : A4 )
% 3.26/1.75 = ( ^ [X: sum_sum @ A @ B] : A4 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_187_image__is__empty,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: B > A,A2: set @ B] :
% 3.26/1.75 ( ( ( image @ B @ A @ F @ A2 )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 = ( A2
% 3.26/1.75 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_188_empty__is__image,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: B > A,A2: set @ B] :
% 3.26/1.75 ( ( ( bot_bot @ ( set @ A ) )
% 3.26/1.75 = ( image @ B @ A @ F @ A2 ) )
% 3.26/1.75 = ( A2
% 3.26/1.75 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_189_image__empty,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,F: B > A] :
% 3.26/1.75 ( ( image @ B @ A @ F @ ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_190_insert__image,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,X5: A,A2: set @ A,F: A > B] :
% 3.26/1.75 ( ( member @ A @ X5 @ A2 )
% 3.26/1.75 => ( ( insert @ B @ ( F @ X5 ) @ ( image @ A @ B @ F @ A2 ) )
% 3.26/1.75 = ( image @ A @ B @ F @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_191_image__insert,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: B > A,A4: B,B2: set @ B] :
% 3.26/1.75 ( ( image @ B @ A @ F @ ( insert @ B @ A4 @ B2 ) )
% 3.26/1.75 = ( insert @ A @ ( F @ A4 ) @ ( image @ B @ A @ F @ B2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_192_ball__UN,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,B2: B > ( set @ A ),A2: set @ B,P2: A > $o] :
% 3.26/1.75 ( ( ! [X: A] :
% 3.26/1.75 ( ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 3.26/1.75 => ( P2 @ X ) ) )
% 3.26/1.75 = ( ! [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 => ! [Y: A] :
% 3.26/1.75 ( ( member @ A @ Y @ ( B2 @ X ) )
% 3.26/1.75 => ( P2 @ Y ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_193_bex__UN,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,B2: B > ( set @ A ),A2: set @ B,P2: A > $o] :
% 3.26/1.75 ( ( ? [X: A] :
% 3.26/1.75 ( ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 3.26/1.75 & ( P2 @ X ) ) )
% 3.26/1.75 = ( ? [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 & ? [Y: A] :
% 3.26/1.75 ( ( member @ A @ Y @ ( B2 @ X ) )
% 3.26/1.75 & ( P2 @ Y ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_194_UN__ball__bex__simps_I2_J,axiom,
% 3.26/1.75 ! [C: $tType,B: $tType,B2: B > ( set @ C ),A2: set @ B,P2: C > $o] :
% 3.26/1.75 ( ( ! [X: C] :
% 3.26/1.75 ( ( member @ C @ X @ ( complete_Sup_Sup @ ( set @ C ) @ ( image @ B @ ( set @ C ) @ B2 @ A2 ) ) )
% 3.26/1.75 => ( P2 @ X ) ) )
% 3.26/1.75 = ( ! [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 => ! [Y: C] :
% 3.26/1.75 ( ( member @ C @ Y @ ( B2 @ X ) )
% 3.26/1.75 => ( P2 @ Y ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_195_UN__ball__bex__simps_I4_J,axiom,
% 3.26/1.75 ! [F3: $tType,E: $tType,B2: E > ( set @ F3 ),A2: set @ E,P2: F3 > $o] :
% 3.26/1.75 ( ( ? [X: F3] :
% 3.26/1.75 ( ( member @ F3 @ X @ ( complete_Sup_Sup @ ( set @ F3 ) @ ( image @ E @ ( set @ F3 ) @ B2 @ A2 ) ) )
% 3.26/1.75 & ( P2 @ X ) ) )
% 3.26/1.75 = ( ? [X: E] :
% 3.26/1.75 ( ( member @ E @ X @ A2 )
% 3.26/1.75 & ? [Y: F3] :
% 3.26/1.75 ( ( member @ F3 @ Y @ ( B2 @ X ) )
% 3.26/1.75 & ( P2 @ Y ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_196_SUP__identity__eq,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [A2: set @ A] :
% 3.26/1.75 ( ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ A @ A
% 3.26/1.75 @ ^ [X: A] : X
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( complete_Sup_Sup @ A @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_197_SUP__apply,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,C: $tType] :
% 3.26/1.75 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [F: C > B > A,A2: set @ C,X5: B] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( B > A ) @ ( image @ C @ ( B > A ) @ F @ A2 ) @ X5 )
% 3.26/1.75 = ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ C @ A
% 3.26/1.75 @ ^ [Y: C] : ( F @ Y @ X5 )
% 3.26/1.75 @ A2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_198_UN__I,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,A4: A,A2: set @ A,B3: B,B2: A > ( set @ B )] :
% 3.26/1.75 ( ( member @ A @ A4 @ A2 )
% 3.26/1.75 => ( ( member @ B @ B3 @ ( B2 @ A4 ) )
% 3.26/1.75 => ( member @ B @ B3 @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ A @ ( set @ B ) @ B2 @ A2 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_199_UN__iff,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,B3: A,B2: B > ( set @ A ),A2: set @ B] :
% 3.26/1.75 ( ( member @ A @ B3 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 3.26/1.75 = ( ? [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 & ( member @ A @ B3 @ ( B2 @ X ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_200_SUP__bot,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [A2: set @ B] :
% 3.26/1.75 ( ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ B @ A
% 3.26/1.75 @ ^ [X: B] : ( bot_bot @ A )
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( bot_bot @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_201_SUP__bot__conv_I1_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [B2: B > A,A2: set @ B] :
% 3.26/1.75 ( ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ B2 @ A2 ) )
% 3.26/1.75 = ( bot_bot @ A ) )
% 3.26/1.75 = ( ! [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 => ( ( B2 @ X )
% 3.26/1.75 = ( bot_bot @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_202_SUP__bot__conv_I2_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [B2: B > A,A2: set @ B] :
% 3.26/1.75 ( ( ( bot_bot @ A )
% 3.26/1.75 = ( complete_Sup_Sup @ A @ ( image @ B @ A @ B2 @ A2 ) ) )
% 3.26/1.75 = ( ! [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 => ( ( B2 @ X )
% 3.26/1.75 = ( bot_bot @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_203_cSUP__const,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( condit378418413attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [A2: set @ B,C3: A] :
% 3.26/1.75 ( ( A2
% 3.26/1.75 != ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ B @ A
% 3.26/1.75 @ ^ [X: B] : C3
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = C3 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_204_SUP__const,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [A2: set @ B,F: A] :
% 3.26/1.75 ( ( A2
% 3.26/1.75 != ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ B @ A
% 3.26/1.75 @ ^ [I: B] : F
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = F ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_205_UN__constant,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,A2: set @ B,C3: set @ A] :
% 3.26/1.75 ( ( ( A2
% 3.26/1.75 = ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ B @ ( set @ A )
% 3.26/1.75 @ ^ [Y: B] : C3
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 & ( ( A2
% 3.26/1.75 != ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ B @ ( set @ A )
% 3.26/1.75 @ ^ [Y: B] : C3
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = C3 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_206_SUP__empty,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [F: B > A] :
% 3.26/1.75 ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ ( bot_bot @ ( set @ B ) ) ) )
% 3.26/1.75 = ( bot_bot @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_207_UN__simps_I1_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,C2: set @ B,A4: A,B2: B > ( set @ A )] :
% 3.26/1.75 ( ( ( C2
% 3.26/1.75 = ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ B @ ( set @ A )
% 3.26/1.75 @ ^ [X: B] : ( insert @ A @ A4 @ ( B2 @ X ) )
% 3.26/1.75 @ C2 ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 & ( ( C2
% 3.26/1.75 != ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ B @ ( set @ A )
% 3.26/1.75 @ ^ [X: B] : ( insert @ A @ A4 @ ( B2 @ X ) )
% 3.26/1.75 @ C2 ) )
% 3.26/1.75 = ( insert @ A @ A4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ C2 ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_208_UN__singleton,axiom,
% 3.26/1.75 ! [A: $tType,A2: set @ A] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ A @ ( set @ A )
% 3.26/1.75 @ ^ [X: A] : ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = A2 ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_209_SUP__eq__const,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [I2: set @ B,F: B > A,X5: A] :
% 3.26/1.75 ( ( I2
% 3.26/1.75 != ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ! [I3: B] :
% 3.26/1.75 ( ( member @ B @ I3 @ I2 )
% 3.26/1.75 => ( ( F @ I3 )
% 3.26/1.75 = X5 ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ I2 ) )
% 3.26/1.75 = X5 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_210_Sup_OSUP__cong,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,A2: set @ B,B2: set @ B,C2: B > A,D3: B > A,Sup: ( set @ A ) > A] :
% 3.26/1.75 ( ( A2 = B2 )
% 3.26/1.75 => ( ! [X6: B] :
% 3.26/1.75 ( ( member @ B @ X6 @ B2 )
% 3.26/1.75 => ( ( C2 @ X6 )
% 3.26/1.75 = ( D3 @ X6 ) ) )
% 3.26/1.75 => ( ( Sup @ ( image @ B @ A @ C2 @ A2 ) )
% 3.26/1.75 = ( Sup @ ( image @ B @ A @ D3 @ B2 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_211_Inf_OINF__cong,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,A2: set @ B,B2: set @ B,C2: B > A,D3: B > A,Inf: ( set @ A ) > A] :
% 3.26/1.75 ( ( A2 = B2 )
% 3.26/1.75 => ( ! [X6: B] :
% 3.26/1.75 ( ( member @ B @ X6 @ B2 )
% 3.26/1.75 => ( ( C2 @ X6 )
% 3.26/1.75 = ( D3 @ X6 ) ) )
% 3.26/1.75 => ( ( Inf @ ( image @ B @ A @ C2 @ A2 ) )
% 3.26/1.75 = ( Inf @ ( image @ B @ A @ D3 @ B2 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_212_case__sum__inject,axiom,
% 3.26/1.75 ! [A: $tType,C: $tType,B: $tType,F1: A > C,F22: B > C,G1: A > C,G22: B > C] :
% 3.26/1.75 ( ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 )
% 3.26/1.75 = ( sum_case_sum @ A @ C @ B @ G1 @ G22 ) )
% 3.26/1.75 => ~ ( ( F1 = G1 )
% 3.26/1.75 => ( F22 != G22 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_213_rev__image__eqI,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,X5: A,A2: set @ A,B3: B,F: A > B] :
% 3.26/1.75 ( ( member @ A @ X5 @ A2 )
% 3.26/1.75 => ( ( B3
% 3.26/1.75 = ( F @ X5 ) )
% 3.26/1.75 => ( member @ B @ B3 @ ( image @ A @ B @ F @ A2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_214_ball__imageD,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P2: A > $o] :
% 3.26/1.75 ( ! [X6: A] :
% 3.26/1.75 ( ( member @ A @ X6 @ ( image @ B @ A @ F @ A2 ) )
% 3.26/1.75 => ( P2 @ X6 ) )
% 3.26/1.75 => ! [X8: B] :
% 3.26/1.75 ( ( member @ B @ X8 @ A2 )
% 3.26/1.75 => ( P2 @ ( F @ X8 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_215_image__cong,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,M: set @ A,N4: set @ A,F: A > B,G2: A > B] :
% 3.26/1.75 ( ( M = N4 )
% 3.26/1.75 => ( ! [X6: A] :
% 3.26/1.75 ( ( member @ A @ X6 @ N4 )
% 3.26/1.75 => ( ( F @ X6 )
% 3.26/1.75 = ( G2 @ X6 ) ) )
% 3.26/1.75 => ( ( image @ A @ B @ F @ M )
% 3.26/1.75 = ( image @ A @ B @ G2 @ N4 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_216_bex__imageD,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P2: A > $o] :
% 3.26/1.75 ( ? [X8: A] :
% 3.26/1.75 ( ( member @ A @ X8 @ ( image @ B @ A @ F @ A2 ) )
% 3.26/1.75 & ( P2 @ X8 ) )
% 3.26/1.75 => ? [X6: B] :
% 3.26/1.75 ( ( member @ B @ X6 @ A2 )
% 3.26/1.75 & ( P2 @ ( F @ X6 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_217_image__iff,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,Z3: A,F: B > A,A2: set @ B] :
% 3.26/1.75 ( ( member @ A @ Z3 @ ( image @ B @ A @ F @ A2 ) )
% 3.26/1.75 = ( ? [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 & ( Z3
% 3.26/1.75 = ( F @ X ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_218_imageI,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,X5: A,A2: set @ A,F: A > B] :
% 3.26/1.75 ( ( member @ A @ X5 @ A2 )
% 3.26/1.75 => ( member @ B @ ( F @ X5 ) @ ( image @ A @ B @ F @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_219_SUP__cong,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType] :
% 3.26/1.75 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [A2: set @ B,B2: set @ B,C2: B > A,D3: B > A] :
% 3.26/1.75 ( ( A2 = B2 )
% 3.26/1.75 => ( ! [X6: B] :
% 3.26/1.75 ( ( member @ B @ X6 @ B2 )
% 3.26/1.75 => ( ( C2 @ X6 )
% 3.26/1.75 = ( D3 @ X6 ) ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ C2 @ A2 ) )
% 3.26/1.75 = ( complete_Sup_Sup @ A @ ( image @ B @ A @ D3 @ B2 ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_220_Sup__SUP__eq,axiom,
% 3.26/1.75 ! [A: $tType] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( A > $o ) )
% 3.26/1.75 = ( ^ [S2: set @ ( A > $o ),X: A] : ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ ( A > $o ) @ ( set @ A ) @ ( collect @ A ) @ S2 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_221_case__sum__step_I1_J,axiom,
% 3.26/1.75 ! [D: $tType,A: $tType,C: $tType,B: $tType,F4: B > A,G3: C > A,G2: D > A,P4: sum_sum @ B @ C] :
% 3.26/1.75 ( ( sum_case_sum @ ( sum_sum @ B @ C ) @ A @ D @ ( sum_case_sum @ B @ A @ C @ F4 @ G3 ) @ G2 @ ( sum_Inl @ ( sum_sum @ B @ C ) @ D @ P4 ) )
% 3.26/1.75 = ( sum_case_sum @ B @ A @ C @ F4 @ G3 @ P4 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_222_case__sum__step_I2_J,axiom,
% 3.26/1.75 ! [E: $tType,A: $tType,C: $tType,B: $tType,F: E > A,F4: B > A,G3: C > A,P4: sum_sum @ B @ C] :
% 3.26/1.75 ( ( sum_case_sum @ E @ A @ ( sum_sum @ B @ C ) @ F @ ( sum_case_sum @ B @ A @ C @ F4 @ G3 ) @ ( sum_Inr @ ( sum_sum @ B @ C ) @ E @ P4 ) )
% 3.26/1.75 = ( sum_case_sum @ B @ A @ C @ F4 @ G3 @ P4 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_223_old_Osum_Osimps_I5_J,axiom,
% 3.26/1.75 ! [B: $tType,C: $tType,A: $tType,F1: A > C,F22: B > C,X1: A] :
% 3.26/1.75 ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ X1 ) )
% 3.26/1.75 = ( F1 @ X1 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_224_old_Osum_Osimps_I6_J,axiom,
% 3.26/1.75 ! [A: $tType,C: $tType,B: $tType,F1: A > C,F22: B > C,X22: B] :
% 3.26/1.75 ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ X22 ) )
% 3.26/1.75 = ( F22 @ X22 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_225_setcompr__eq__image,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: B > A,P2: B > $o] :
% 3.26/1.75 ( ( collect @ A
% 3.26/1.75 @ ^ [Uu: A] :
% 3.26/1.75 ? [X: B] :
% 3.26/1.75 ( ( Uu
% 3.26/1.75 = ( F @ X ) )
% 3.26/1.75 & ( P2 @ X ) ) )
% 3.26/1.75 = ( image @ B @ A @ F @ ( collect @ B @ P2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_226_Setcompr__eq__image,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: B > A,A2: set @ B] :
% 3.26/1.75 ( ( collect @ A
% 3.26/1.75 @ ^ [Uu: A] :
% 3.26/1.75 ? [X: B] :
% 3.26/1.75 ( ( Uu
% 3.26/1.75 = ( F @ X ) )
% 3.26/1.75 & ( member @ B @ X @ A2 ) ) )
% 3.26/1.75 = ( image @ B @ A @ F @ A2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_227_SUP__commute,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,C: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [F: B > C > A,B2: set @ C,A2: set @ B] :
% 3.26/1.75 ( ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ B @ A
% 3.26/1.75 @ ^ [I: B] : ( complete_Sup_Sup @ A @ ( image @ C @ A @ ( F @ I ) @ B2 ) )
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ C @ A
% 3.26/1.75 @ ^ [J: C] :
% 3.26/1.75 ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ B @ A
% 3.26/1.75 @ ^ [I: B] : ( F @ I @ J )
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 @ B2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_228_UN__extend__simps_I9_J,axiom,
% 3.26/1.75 ! [S3: $tType,R3: $tType,Q2: $tType,C2: R3 > ( set @ S3 ),B2: Q2 > ( set @ R3 ),A2: set @ Q2] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( set @ S3 )
% 3.26/1.75 @ ( image @ Q2 @ ( set @ S3 )
% 3.26/1.75 @ ^ [X: Q2] : ( complete_Sup_Sup @ ( set @ S3 ) @ ( image @ R3 @ ( set @ S3 ) @ C2 @ ( B2 @ X ) ) )
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ S3 ) @ ( image @ R3 @ ( set @ S3 ) @ C2 @ ( complete_Sup_Sup @ ( set @ R3 ) @ ( image @ Q2 @ ( set @ R3 ) @ B2 @ A2 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_229_UN__E,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,B3: A,B2: B > ( set @ A ),A2: set @ B] :
% 3.26/1.75 ( ( member @ A @ B3 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 3.26/1.75 => ~ ! [X6: B] :
% 3.26/1.75 ( ( member @ B @ X6 @ A2 )
% 3.26/1.75 => ~ ( member @ A @ B3 @ ( B2 @ X6 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_230_UN__UN__flatten,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,C: $tType,C2: B > ( set @ A ),B2: C > ( set @ B ),A2: set @ C] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ C2 @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ C @ ( set @ B ) @ B2 @ A2 ) ) ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ C @ ( set @ A )
% 3.26/1.75 @ ^ [Y: C] : ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ C2 @ ( B2 @ Y ) ) )
% 3.26/1.75 @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_231_SUP__UNION,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,C: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [F: B > A,G2: C > ( set @ B ),A2: set @ C] :
% 3.26/1.75 ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ C @ ( set @ B ) @ G2 @ A2 ) ) ) )
% 3.26/1.75 = ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ C @ A
% 3.26/1.75 @ ^ [Y: C] : ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ ( G2 @ Y ) ) )
% 3.26/1.75 @ A2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_232_imageE,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,B3: A,F: B > A,A2: set @ B] :
% 3.26/1.75 ( ( member @ A @ B3 @ ( image @ B @ A @ F @ A2 ) )
% 3.26/1.75 => ~ ! [X6: B] :
% 3.26/1.75 ( ( B3
% 3.26/1.75 = ( F @ X6 ) )
% 3.26/1.75 => ~ ( member @ B @ X6 @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_233_image__image,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,C: $tType,F: B > A,G2: C > B,A2: set @ C] :
% 3.26/1.75 ( ( image @ B @ A @ F @ ( image @ C @ B @ G2 @ A2 ) )
% 3.26/1.75 = ( image @ C @ A
% 3.26/1.75 @ ^ [X: C] : ( F @ ( G2 @ X ) )
% 3.26/1.75 @ A2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_234_Compr__image__eq,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P2: A > $o] :
% 3.26/1.75 ( ( collect @ A
% 3.26/1.75 @ ^ [X: A] :
% 3.26/1.75 ( ( member @ A @ X @ ( image @ B @ A @ F @ A2 ) )
% 3.26/1.75 & ( P2 @ X ) ) )
% 3.26/1.75 = ( image @ B @ A @ F
% 3.26/1.75 @ ( collect @ B
% 3.26/1.75 @ ^ [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_235_sum_Ocase__distrib,axiom,
% 3.26/1.75 ! [D: $tType,C: $tType,B: $tType,A: $tType,H: C > D,F1: A > C,F22: B > C,Sum: sum_sum @ A @ B] :
% 3.26/1.75 ( ( H @ ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ Sum ) )
% 3.26/1.75 = ( sum_case_sum @ A @ D @ B
% 3.26/1.75 @ ^ [X: A] : ( H @ ( F1 @ X ) )
% 3.26/1.75 @ ^ [X: B] : ( H @ ( F22 @ X ) )
% 3.26/1.75 @ Sum ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_236_image__UN,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,C: $tType,F: B > A,B2: C > ( set @ B ),A2: set @ C] :
% 3.26/1.75 ( ( image @ B @ A @ F @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ C @ ( set @ B ) @ B2 @ A2 ) ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ C @ ( set @ A )
% 3.26/1.75 @ ^ [X: C] : ( image @ B @ A @ F @ ( B2 @ X ) )
% 3.26/1.75 @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_237_UN__extend__simps_I10_J,axiom,
% 3.26/1.75 ! [V: $tType,U2: $tType,T: $tType,B2: U2 > ( set @ V ),F: T > U2,A2: set @ T] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( set @ V )
% 3.26/1.75 @ ( image @ T @ ( set @ V )
% 3.26/1.75 @ ^ [A3: T] : ( B2 @ ( F @ A3 ) )
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ V ) @ ( image @ U2 @ ( set @ V ) @ B2 @ ( image @ T @ U2 @ F @ A2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_238_image__Union,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: B > A,S4: set @ ( set @ B )] :
% 3.26/1.75 ( ( image @ B @ A @ F @ ( complete_Sup_Sup @ ( set @ B ) @ S4 ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ A ) @ ( image @ ( set @ B ) @ ( set @ A ) @ ( image @ B @ A @ F ) @ S4 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_239_UN__extend__simps_I8_J,axiom,
% 3.26/1.75 ! [P5: $tType,O: $tType,B2: O > ( set @ P5 ),A2: set @ ( set @ O )] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( set @ P5 )
% 3.26/1.75 @ ( image @ ( set @ O ) @ ( set @ P5 )
% 3.26/1.75 @ ^ [Y: set @ O] : ( complete_Sup_Sup @ ( set @ P5 ) @ ( image @ O @ ( set @ P5 ) @ B2 @ Y ) )
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ P5 ) @ ( image @ O @ ( set @ P5 ) @ B2 @ ( complete_Sup_Sup @ ( set @ O ) @ A2 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_240_Inf_OINF__identity__eq,axiom,
% 3.26/1.75 ! [A: $tType,Inf: ( set @ A ) > A,A2: set @ A] :
% 3.26/1.75 ( ( Inf
% 3.26/1.75 @ ( image @ A @ A
% 3.26/1.75 @ ^ [X: A] : X
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( Inf @ A2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_241_Sup_OSUP__identity__eq,axiom,
% 3.26/1.75 ! [A: $tType,Sup: ( set @ A ) > A,A2: set @ A] :
% 3.26/1.75 ( ( Sup
% 3.26/1.75 @ ( image @ A @ A
% 3.26/1.75 @ ^ [X: A] : X
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( Sup @ A2 ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_242_the__elem__image__unique,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,A2: set @ A,F: A > B,X5: A] :
% 3.26/1.75 ( ( A2
% 3.26/1.75 != ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 => ( ! [Y4: A] :
% 3.26/1.75 ( ( member @ A @ Y4 @ A2 )
% 3.26/1.75 => ( ( F @ Y4 )
% 3.26/1.75 = ( F @ X5 ) ) )
% 3.26/1.75 => ( ( the_elem @ B @ ( image @ A @ B @ F @ A2 ) )
% 3.26/1.75 = ( F @ X5 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_243_image__constant__conv,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,A2: set @ B,C3: A] :
% 3.26/1.75 ( ( ( A2
% 3.26/1.75 = ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( image @ B @ A
% 3.26/1.75 @ ^ [X: B] : C3
% 3.26/1.75 @ A2 )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.75 & ( ( A2
% 3.26/1.75 != ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( image @ B @ A
% 3.26/1.75 @ ^ [X: B] : C3
% 3.26/1.75 @ A2 )
% 3.26/1.75 = ( insert @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_244_image__constant,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,X5: A,A2: set @ A,C3: B] :
% 3.26/1.75 ( ( member @ A @ X5 @ A2 )
% 3.26/1.75 => ( ( image @ A @ B
% 3.26/1.75 @ ^ [X: A] : C3
% 3.26/1.75 @ A2 )
% 3.26/1.75 = ( insert @ B @ C3 @ ( bot_bot @ ( set @ B ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_245_UN__empty2,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,A2: set @ B] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ B @ ( set @ A )
% 3.26/1.75 @ ^ [X: B] : ( bot_bot @ ( set @ A ) )
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_246_UN__empty,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,B2: B > ( set @ A )] :
% 3.26/1.75 ( ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ ( bot_bot @ ( set @ B ) ) ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_247_UNION__empty__conv_I1_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,B2: B > ( set @ A ),A2: set @ B] :
% 3.26/1.75 ( ( ( bot_bot @ ( set @ A ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) ) )
% 3.26/1.75 = ( ! [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 => ( ( B2 @ X )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_248_UNION__empty__conv_I2_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,B2: B > ( set @ A ),A2: set @ B] :
% 3.26/1.75 ( ( ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ A2 ) )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.75 = ( ! [X: B] :
% 3.26/1.75 ( ( member @ B @ X @ A2 )
% 3.26/1.75 => ( ( B2 @ X )
% 3.26/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_249_UN__insert__distrib,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,U3: A,A2: set @ A,A4: B,B2: A > ( set @ B )] :
% 3.26/1.75 ( ( member @ A @ U3 @ A2 )
% 3.26/1.75 => ( ( complete_Sup_Sup @ ( set @ B )
% 3.26/1.75 @ ( image @ A @ ( set @ B )
% 3.26/1.75 @ ^ [X: A] : ( insert @ B @ A4 @ ( B2 @ X ) )
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( insert @ B @ A4 @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ A @ ( set @ B ) @ B2 @ A2 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_250_vimage__UN,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,C: $tType,F: A > B,B2: C > ( set @ B ),A2: set @ C] :
% 3.26/1.75 ( ( vimage @ A @ B @ F @ ( complete_Sup_Sup @ ( set @ B ) @ ( image @ C @ ( set @ B ) @ B2 @ A2 ) ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ C @ ( set @ A )
% 3.26/1.75 @ ^ [X: C] : ( vimage @ A @ B @ F @ ( B2 @ X ) )
% 3.26/1.75 @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_251_vimage__Union,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,F: A > B,A2: set @ ( set @ B )] :
% 3.26/1.75 ( ( vimage @ A @ B @ F @ ( complete_Sup_Sup @ ( set @ B ) @ A2 ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ A ) @ ( image @ ( set @ B ) @ ( set @ A ) @ ( vimage @ A @ B @ F ) @ A2 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_252_case__sum__if,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType,C: $tType,P4: $o,F: B > A,G2: C > A,X5: B,Y3: C] :
% 3.26/1.75 ( ( P4
% 3.26/1.75 => ( ( sum_case_sum @ B @ A @ C @ F @ G2 @ ( if @ ( sum_sum @ B @ C ) @ P4 @ ( sum_Inl @ B @ C @ X5 ) @ ( sum_Inr @ C @ B @ Y3 ) ) )
% 3.26/1.75 = ( F @ X5 ) ) )
% 3.26/1.75 & ( ~ P4
% 3.26/1.75 => ( ( sum_case_sum @ B @ A @ C @ F @ G2 @ ( if @ ( sum_sum @ B @ C ) @ P4 @ ( sum_Inl @ B @ C @ X5 ) @ ( sum_Inr @ C @ B @ Y3 ) ) )
% 3.26/1.75 = ( G2 @ Y3 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_253_surjective__sum,axiom,
% 3.26/1.75 ! [C: $tType,B: $tType,A: $tType,F: ( sum_sum @ A @ B ) > C] :
% 3.26/1.75 ( ( sum_case_sum @ A @ C @ B
% 3.26/1.75 @ ^ [X: A] : ( F @ ( sum_Inl @ A @ B @ X ) )
% 3.26/1.75 @ ^ [Y: B] : ( F @ ( sum_Inr @ B @ A @ Y ) ) )
% 3.26/1.75 = F ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_254_SUP__constant,axiom,
% 3.26/1.75 ! [B: $tType,A: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.26/1.75 => ! [A2: set @ B,C3: A] :
% 3.26/1.75 ( ( ( A2
% 3.26/1.75 = ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ B @ A
% 3.26/1.75 @ ^ [Y: B] : C3
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = ( bot_bot @ A ) ) )
% 3.26/1.75 & ( ( A2
% 3.26/1.75 != ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( complete_Sup_Sup @ A
% 3.26/1.75 @ ( image @ B @ A
% 3.26/1.75 @ ^ [Y: B] : C3
% 3.26/1.75 @ A2 ) )
% 3.26/1.75 = C3 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(fact_255_UN__extend__simps_I1_J,axiom,
% 3.26/1.75 ! [A: $tType,B: $tType,C2: set @ B,A4: A,B2: B > ( set @ A )] :
% 3.26/1.75 ( ( ( C2
% 3.26/1.75 = ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( insert @ A @ A4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ C2 ) ) )
% 3.26/1.75 = ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.26/1.75 & ( ( C2
% 3.26/1.75 != ( bot_bot @ ( set @ B ) ) )
% 3.26/1.75 => ( ( insert @ A @ A4 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B2 @ C2 ) ) )
% 3.26/1.75 = ( complete_Sup_Sup @ ( set @ A )
% 3.26/1.75 @ ( image @ B @ ( set @ A )
% 3.26/1.75 @ ^ [X: B] : ( insert @ A @ A4 @ ( B2 @ X ) )
% 3.26/1.75 @ C2 ) ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_fun___Conditionally__Complete__Lattices_Oconditionally__complete__lattice,axiom,
% 3.26/1.75 ! [A7: $tType,A10: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A10 @ ( type2 @ A10 ) )
% 3.26/1.75 => ( condit378418413attice @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 3.26/1.75 ! [A7: $tType,A10: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A10 @ ( type2 @ A10 ) )
% 3.26/1.75 => ( comple187826305attice @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_fun___Complete__Partial__Order_Occpo,axiom,
% 3.26/1.75 ! [A7: $tType,A10: $tType] :
% 3.26/1.75 ( ( comple187826305attice @ A10 @ ( type2 @ A10 ) )
% 3.26/1.75 => ( comple1141879883l_ccpo @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_fun___Complete__Lattices_OSup,axiom,
% 3.26/1.75 ! [A7: $tType,A10: $tType] :
% 3.26/1.75 ( ( complete_Sup @ A10 @ ( type2 @ A10 ) )
% 3.26/1.75 => ( complete_Sup @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_fun___Orderings_Obot,axiom,
% 3.26/1.75 ! [A7: $tType,A10: $tType] :
% 3.26/1.75 ( ( bot @ A10 @ ( type2 @ A10 ) )
% 3.26/1.75 => ( bot @ ( A7 > A10 ) @ ( type2 @ ( A7 > A10 ) ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_Set_Oset___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_1,axiom,
% 3.26/1.75 ! [A7: $tType] : ( condit378418413attice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_2,axiom,
% 3.26/1.75 ! [A7: $tType] : ( comple187826305attice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_Set_Oset___Complete__Partial__Order_Occpo_3,axiom,
% 3.26/1.75 ! [A7: $tType] : ( comple1141879883l_ccpo @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_Set_Oset___Complete__Lattices_OSup_4,axiom,
% 3.26/1.75 ! [A7: $tType] : ( complete_Sup @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_Set_Oset___Orderings_Obot_5,axiom,
% 3.26/1.75 ! [A7: $tType] : ( bot @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_HOL_Obool___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_6,axiom,
% 3.26/1.75 condit378418413attice @ $o @ ( type2 @ $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_7,axiom,
% 3.26/1.75 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_HOL_Obool___Complete__Partial__Order_Occpo_8,axiom,
% 3.26/1.75 comple1141879883l_ccpo @ $o @ ( type2 @ $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_HOL_Obool___Complete__Lattices_OSup_9,axiom,
% 3.26/1.75 complete_Sup @ $o @ ( type2 @ $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(tcon_HOL_Obool___Orderings_Obot_10,axiom,
% 3.26/1.75 bot @ $o @ ( type2 @ $o ) ).
% 3.26/1.75
% 3.26/1.75 thf(help_If_3_1_T,axiom,
% 3.26/1.75 ! [P2: $o] :
% 3.26/1.75 ( ( P2 = $true )
% 3.26/1.75 | ( P2 = $false ) ) ).
% 3.26/1.75
% 3.26/1.75 thf(help_If_2_1_T,axiom,
% 3.26/1.75 ! [A: $tType,X5: A,Y3: A] :
% 3.26/1.75 ( ( if @ A @ $false @ X5 @ Y3 )
% 3.26/1.75 = Y3 ) ).
% 3.26/1.75
% 3.26/1.75 thf(help_If_1_1_T,axiom,
% 3.26/1.75 ! [A: $tType,X5: A,Y3: A] :
% 3.26/1.75 ( ( if @ A @ $true @ X5 @ Y3 )
% 3.26/1.75 = X5 ) ).
% 3.26/1.75
% 3.26/1.75 thf(conj_0,conjecture,
% 3.26/1.75 ( ( collect @ n @ ( gram_L830233218_inItr @ ns @ tr ) )
% 3.26/1.75 = ( collect @ n
% 3.26/1.75 @ ^ [Uu: n] :
% 3.26/1.75 ? [Tr5: dtree] :
% 3.26/1.75 ( ( Uu
% 3.26/1.75 = ( root @ Tr5 ) )
% 3.26/1.75 & ( gram_L716654942_subtr @ ns @ Tr5 @ tr ) ) ) ) ).
% 3.26/1.75 ------------------------
% 3.26/1.79 % (21438)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_21337 for (2999ds/27Mi)
% 3.26/1.79 % (21440)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_21337 for (2999ds/2Mi)
% 3.26/1.79 % (21439)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/2Mi)
% 3.26/1.79 % (21442)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/18Mi)
% 3.26/1.79 % (21437)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_21337 for (2999ds/4Mi)
% 3.26/1.79 % (21441)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_21337 for (2999ds/275Mi)
% 3.26/1.79 % (21436)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/183Mi)
% 3.26/1.79 % (21440)Instruction limit reached!
% 3.26/1.79 % (21440)------------------------------
% 3.26/1.79 % (21440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.79 % (21440)Termination reason: Unknown
% 3.26/1.79 % (21440)Termination phase: shuffling
% 3.26/1.79
% 3.26/1.79 % (21440)Memory used [KB]: 1407
% 3.26/1.79 % (21440)Time elapsed: 0.003 s
% 3.26/1.79 % (21440)Instructions burned: 2 (million)
% 3.26/1.79 % (21440)------------------------------
% 3.26/1.79 % (21440)------------------------------
% 3.26/1.79 % (21439)Instruction limit reached!
% 3.26/1.79 % (21439)------------------------------
% 3.26/1.79 % (21439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.79 % (21439)Termination reason: Unknown
% 3.26/1.79 % (21439)Termination phase: shuffling
% 3.26/1.79
% 3.26/1.79 % (21439)Memory used [KB]: 1407
% 3.26/1.79 % (21439)Time elapsed: 0.004 s
% 3.26/1.79 % (21439)Instructions burned: 3 (million)
% 3.26/1.79 % (21439)------------------------------
% 3.26/1.79 % (21439)------------------------------
% 3.26/1.79 % (21437)Instruction limit reached!
% 3.26/1.79 % (21437)------------------------------
% 3.26/1.79 % (21437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.79 % (21437)Termination reason: Unknown
% 3.26/1.79 % (21437)Termination phase: shuffling
% 3.26/1.79
% 3.26/1.79 % (21437)Memory used [KB]: 1535
% 3.26/1.79 % (21437)Time elapsed: 0.004 s
% 3.26/1.79 % (21437)Instructions burned: 5 (million)
% 3.26/1.79 % (21437)------------------------------
% 3.26/1.79 % (21437)------------------------------
% 3.31/1.80 % (21442)Instruction limit reached!
% 3.31/1.80 % (21442)------------------------------
% 3.31/1.80 % (21442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.80 % (21442)Termination reason: Unknown
% 3.31/1.80 % (21442)Termination phase: shuffling
% 3.31/1.80
% 3.31/1.80 % (21442)Memory used [KB]: 1791
% 3.31/1.80 % (21442)Time elapsed: 0.012 s
% 3.31/1.80 % (21442)Instructions burned: 19 (million)
% 3.31/1.80 % (21442)------------------------------
% 3.31/1.80 % (21442)------------------------------
% 3.31/1.81 % (21438)Instruction limit reached!
% 3.31/1.81 % (21438)------------------------------
% 3.31/1.81 % (21438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.81 % (21438)Termination reason: Unknown
% 3.31/1.81 % (21438)Termination phase: shuffling
% 3.31/1.81
% 3.31/1.81 % (21438)Memory used [KB]: 2046
% 3.31/1.81 % (21438)Time elapsed: 0.017 s
% 3.31/1.81 % (21438)Instructions burned: 28 (million)
% 3.31/1.81 % (21438)------------------------------
% 3.31/1.81 % (21438)------------------------------
% 3.31/1.81 % (21443)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/3Mi)
% 3.31/1.81 % (21444)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_21337 for (2999ds/37Mi)
% 3.31/1.81 % (21445)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_21337 for (2999ds/15Mi)
% 3.31/1.81 % (21443)Instruction limit reached!
% 3.31/1.81 % (21443)------------------------------
% 3.31/1.81 % (21443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.81 % (21443)Termination reason: Unknown
% 3.31/1.81 % (21443)Termination phase: shuffling
% 3.31/1.81
% 3.31/1.81 % (21443)Memory used [KB]: 1535
% 3.31/1.81 % (21443)Time elapsed: 0.004 s
% 3.31/1.81 % (21443)Instructions burned: 4 (million)
% 3.31/1.81 % (21443)------------------------------
% 3.31/1.81 % (21443)------------------------------
% 3.31/1.82 % (21446)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_21337 for (2999ds/3Mi)
% 3.31/1.82 % (21445)Instruction limit reached!
% 3.31/1.82 % (21445)------------------------------
% 3.31/1.82 % (21445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.82 % (21445)Termination reason: Unknown
% 3.31/1.82 % (21445)Termination phase: shuffling
% 3.31/1.82
% 3.31/1.82 % (21445)Memory used [KB]: 1791
% 3.31/1.82 % (21445)Time elapsed: 0.010 s
% 3.31/1.82 % (21445)Instructions burned: 16 (million)
% 3.31/1.82 % (21445)------------------------------
% 3.31/1.82 % (21445)------------------------------
% 3.31/1.82 % (21446)Instruction limit reached!
% 3.31/1.82 % (21446)------------------------------
% 3.31/1.82 % (21446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.82 % (21446)Termination reason: Unknown
% 3.31/1.82 % (21446)Termination phase: shuffling
% 3.31/1.82
% 3.31/1.82 % (21446)Memory used [KB]: 1535
% 3.31/1.82 % (21446)Time elapsed: 0.004 s
% 3.31/1.82 % (21446)Instructions burned: 5 (million)
% 3.31/1.82 % (21446)------------------------------
% 3.31/1.82 % (21446)------------------------------
% 3.31/1.82 % (21447)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_21337 for (2999ds/1041Mi)
% 3.31/1.83 % (21444)Instruction limit reached!
% 3.31/1.83 % (21444)------------------------------
% 3.31/1.83 % (21444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.83 % (21444)Termination reason: Unknown
% 3.31/1.83 % (21444)Termination phase: shuffling
% 3.31/1.83
% 3.31/1.83 % (21444)Memory used [KB]: 2174
% 3.31/1.83 % (21444)Time elapsed: 0.019 s
% 3.31/1.83 % (21444)Instructions burned: 37 (million)
% 3.31/1.83 % (21444)------------------------------
% 3.31/1.83 % (21444)------------------------------
% 3.31/1.83 % (21448)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/7Mi)
% 3.31/1.83 % (21448)Instruction limit reached!
% 3.31/1.83 % (21448)------------------------------
% 3.31/1.83 % (21448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.83 % (21448)Termination reason: Unknown
% 3.31/1.83 % (21448)Termination phase: shuffling
% 3.31/1.83
% 3.31/1.83 % (21448)Memory used [KB]: 1535
% 3.31/1.83 % (21448)Time elapsed: 0.005 s
% 3.31/1.83 % (21448)Instructions burned: 7 (million)
% 3.31/1.83 % (21448)------------------------------
% 3.31/1.83 % (21448)------------------------------
% 3.31/1.83 % (21449)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/16Mi)
% 3.31/1.83 % (21450)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_21337 for (2999ds/3Mi)
% 3.31/1.84 % (21450)Instruction limit reached!
% 3.31/1.84 % (21450)------------------------------
% 3.31/1.84 % (21450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.84 % (21450)Termination reason: Unknown
% 3.31/1.84 % (21450)Termination phase: shuffling
% 3.31/1.84
% 3.31/1.84 % (21450)Memory used [KB]: 1407
% 3.31/1.84 % (21450)Time elapsed: 0.003 s
% 3.31/1.84 % (21450)Instructions burned: 3 (million)
% 3.31/1.84 % (21450)------------------------------
% 3.31/1.84 % (21450)------------------------------
% 3.31/1.84 % (21451)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_21337 for (2999ds/3Mi)
% 3.31/1.84 % (21449)Instruction limit reached!
% 3.31/1.84 % (21449)------------------------------
% 3.31/1.84 % (21449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.84 % (21449)Termination reason: Unknown
% 3.31/1.84 % (21449)Termination phase: shuffling
% 3.31/1.84
% 3.31/1.84 % (21449)Memory used [KB]: 1791
% 3.31/1.84 % (21449)Time elapsed: 0.010 s
% 3.31/1.84 % (21449)Instructions burned: 17 (million)
% 3.31/1.84 % (21449)------------------------------
% 3.31/1.84 % (21449)------------------------------
% 3.31/1.84 % (21451)Instruction limit reached!
% 3.31/1.84 % (21451)------------------------------
% 3.31/1.84 % (21451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.84 % (21451)Termination reason: Unknown
% 3.31/1.84 % (21451)Termination phase: shuffling
% 3.31/1.84
% 3.31/1.84 % (21451)Memory used [KB]: 1407
% 3.31/1.84 % (21451)Time elapsed: 0.003 s
% 3.31/1.84 % (21451)Instructions burned: 3 (million)
% 3.31/1.84 % (21451)------------------------------
% 3.31/1.84 % (21451)------------------------------
% 3.31/1.85 % (21452)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/7Mi)
% 3.31/1.85 % (21452)Instruction limit reached!
% 3.31/1.85 % (21452)------------------------------
% 3.31/1.85 % (21452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.85 % (21452)Termination reason: Unknown
% 3.31/1.85 % (21452)Termination phase: shuffling
% 3.31/1.85
% 3.31/1.85 % (21452)Memory used [KB]: 1535
% 3.31/1.85 % (21452)Time elapsed: 0.005 s
% 3.31/1.85 % (21452)Instructions burned: 7 (million)
% 3.31/1.85 % (21452)------------------------------
% 3.31/1.85 % (21452)------------------------------
% 3.31/1.85 % (21453)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/3Mi)
% 3.31/1.85 % (21453)Instruction limit reached!
% 3.31/1.85 % (21453)------------------------------
% 3.31/1.85 % (21453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.85 % (21453)Termination reason: Unknown
% 3.31/1.85 % (21453)Termination phase: shuffling
% 3.31/1.85
% 3.31/1.85 % (21453)Memory used [KB]: 1407
% 3.31/1.85 % (21453)Time elapsed: 0.003 s
% 3.31/1.85 % (21453)Instructions burned: 3 (million)
% 3.31/1.85 % (21453)------------------------------
% 3.31/1.85 % (21453)------------------------------
% 3.31/1.86 % (21454)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/4Mi)
% 3.31/1.86 % (21455)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/18Mi)
% 3.31/1.86 % (21454)Instruction limit reached!
% 3.31/1.86 % (21454)------------------------------
% 3.31/1.86 % (21454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.86 % (21454)Termination reason: Unknown
% 3.31/1.86 % (21454)Termination phase: shuffling
% 3.31/1.86
% 3.31/1.86 % (21454)Memory used [KB]: 1535
% 3.31/1.86 % (21454)Time elapsed: 0.004 s
% 3.31/1.86 % (21454)Instructions burned: 5 (million)
% 3.31/1.86 % (21454)------------------------------
% 3.31/1.86 % (21454)------------------------------
% 3.31/1.87 % (21456)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/710Mi)
% 3.31/1.87 % (21455)Instruction limit reached!
% 3.31/1.87 % (21455)------------------------------
% 3.31/1.87 % (21455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.87 % (21455)Termination reason: Unknown
% 3.31/1.87 % (21455)Termination phase: shuffling
% 3.31/1.87
% 3.31/1.87 % (21455)Memory used [KB]: 1791
% 3.31/1.87 % (21455)Time elapsed: 0.011 s
% 3.31/1.87 % (21455)Instructions burned: 19 (million)
% 3.31/1.87 % (21455)------------------------------
% 3.31/1.87 % (21455)------------------------------
% 3.31/1.87 % (21457)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21337 for (2999ds/6Mi)
% 3.31/1.87 % (21457)Instruction limit reached!
% 3.31/1.87 % (21457)------------------------------
% 3.31/1.87 % (21457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.87 % (21457)Termination reason: Unknown
% 3.31/1.87 % (21457)Termination phase: shuffling
% 3.31/1.87
% 3.31/1.87 % (21457)Memory used [KB]: 1535
% 3.31/1.87 % (21457)Time elapsed: 0.005 s
% 3.31/1.87 % (21457)Instructions burned: 7 (million)
% 3.31/1.87 % (21457)------------------------------
% 3.31/1.87 % (21457)------------------------------
% 3.31/1.88 % (21458)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_21337 for (2999ds/902Mi)
% 3.31/1.88 % (21436)Instruction limit reached!
% 3.31/1.88 % (21436)------------------------------
% 3.31/1.88 % (21436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.88 % (21436)Termination reason: Unknown
% 3.31/1.88 % (21436)Termination phase: Saturation
% 3.31/1.88
% 3.31/1.88 % (21436)Memory used [KB]: 7419
% 3.31/1.88 % (21436)Time elapsed: 0.091 s
% 3.31/1.88 % (21436)Instructions burned: 184 (million)
% 3.31/1.88 % (21436)------------------------------
% 3.31/1.88 % (21436)------------------------------
% 3.31/1.89 % (21459)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_21337 for (2998ds/21Mi)
% 3.31/1.89 % (21460)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21337 for (2998ds/5Mi)
% 3.31/1.89 % (21460)Instruction limit reached!
% 3.31/1.89 % (21460)------------------------------
% 3.31/1.89 % (21460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.89 % (21460)Termination reason: Unknown
% 3.31/1.89 % (21460)Termination phase: shuffling
% 3.31/1.89
% 3.31/1.89 % (21460)Memory used [KB]: 1535
% 3.31/1.89 % (21460)Time elapsed: 0.004 s
% 3.31/1.89 % (21460)Instructions burned: 5 (million)
% 3.31/1.89 % (21460)------------------------------
% 3.31/1.89 % (21460)------------------------------
% 3.31/1.90 % (21459)Instruction limit reached!
% 3.31/1.90 % (21459)------------------------------
% 3.31/1.90 % (21459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.90 % (21459)Termination reason: Unknown
% 3.31/1.90 % (21459)Termination phase: shuffling
% 3.31/1.90
% 3.31/1.90 % (21459)Memory used [KB]: 1918
% 3.31/1.90 % (21459)Time elapsed: 0.012 s
% 3.31/1.90 % (21459)Instructions burned: 21 (million)
% 3.31/1.90 % (21459)------------------------------
% 3.31/1.90 % (21459)------------------------------
% 3.31/1.90 % (21461)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_21337 for (2998ds/6Mi)
% 3.31/1.90 % (21461)Instruction limit reached!
% 3.31/1.90 % (21461)------------------------------
% 3.31/1.90 % (21461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.90 % (21461)Termination reason: Unknown
% 3.31/1.90 % (21461)Termination phase: shuffling
% 3.31/1.90
% 3.31/1.90 % (21461)Memory used [KB]: 1535
% 3.31/1.90 % (21461)Time elapsed: 0.005 s
% 3.31/1.90 % (21461)Instructions burned: 7 (million)
% 3.31/1.90 % (21461)------------------------------
% 3.31/1.90 % (21461)------------------------------
% 3.31/1.91 % (21462)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21337 for (2998ds/377Mi)
% 3.31/1.91 % (21463)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_21337 for (2998ds/779Mi)
% 3.31/1.92 % (21464)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_21337 for (2998ds/19Mi)
% 3.31/1.93 % (21441)Instruction limit reached!
% 3.31/1.93 % (21441)------------------------------
% 3.31/1.93 % (21441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.93 % (21441)Termination reason: Unknown
% 3.31/1.93 % (21464)Instruction limit reached!
% 3.31/1.93 % (21464)------------------------------
% 3.31/1.93 % (21464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.93 % (21441)Termination phase: Saturation
% 3.31/1.93
% 3.31/1.93 % (21441)Memory used [KB]: 7547
% 3.31/1.93 % (21441)Time elapsed: 0.137 s
% 3.31/1.93 % (21441)Instructions burned: 276 (million)
% 3.31/1.93 % (21441)------------------------------
% 3.31/1.93 % (21441)------------------------------
% 3.31/1.93 % (21464)Termination reason: Unknown
% 3.31/1.93 % (21464)Termination phase: shuffling
% 3.31/1.93
% 3.31/1.93 % (21464)Memory used [KB]: 1791
% 3.31/1.93 % (21464)Time elapsed: 0.011 s
% 3.31/1.93 % (21464)Instructions burned: 20 (million)
% 3.31/1.93 % (21464)------------------------------
% 3.31/1.93 % (21464)------------------------------
% 3.31/1.94 % (21466)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21337 for (2998ds/17Mi)
% 3.31/1.94 % (21465)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21337 for (2998ds/879Mi)
% 3.31/1.95 % (21466)Instruction limit reached!
% 3.31/1.95 % (21466)------------------------------
% 3.31/1.95 % (21466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.95 % (21466)Termination reason: Unknown
% 3.31/1.95 % (21466)Termination phase: shuffling
% 3.31/1.95
% 3.31/1.95 % (21466)Memory used [KB]: 1791
% 3.31/1.95 % (21466)Time elapsed: 0.011 s
% 3.31/1.95 % (21466)Instructions burned: 17 (million)
% 3.31/1.95 % (21466)------------------------------
% 3.31/1.95 % (21466)------------------------------
% 3.31/1.97 % (21467)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21337 for (2998ds/3Mi)
% 3.31/1.97 % (21467)Instruction limit reached!
% 3.31/1.97 % (21467)------------------------------
% 3.31/1.97 % (21467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/1.97 % (21467)Termination reason: Unknown
% 3.31/1.97 % (21467)Termination phase: shuffling
% 3.31/1.97
% 3.31/1.97 % (21467)Memory used [KB]: 1407
% 3.31/1.97 % (21467)Time elapsed: 0.004 s
% 3.31/1.97 % (21467)Instructions burned: 3 (million)
% 3.31/1.97 % (21467)------------------------------
% 3.31/1.97 % (21467)------------------------------
% 3.31/1.99 % (21468)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21337 for (2997ds/30Mi)
% 3.31/2.00 % (21468)Instruction limit reached!
% 3.31/2.00 % (21468)------------------------------
% 3.31/2.00 % (21468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.31/2.00 % (21468)Termination reason: Unknown
% 3.31/2.00 % (21468)Termination phase: shuffling
% 3.31/2.00
% 3.31/2.00 % (21468)Memory used [KB]: 2046
% 3.31/2.00 % (21468)Time elapsed: 0.018 s
% 3.31/2.00 % (21468)Instructions burned: 31 (million)
% 3.31/2.00 % (21468)------------------------------
% 3.31/2.00 % (21468)------------------------------
% 3.31/2.02 % (21469)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21337 for (2997ds/127Mi)
% 4.99/2.08 % (21469)Instruction limit reached!
% 4.99/2.08 % (21469)------------------------------
% 4.99/2.08 % (21469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.99/2.08 % (21469)Termination reason: Unknown
% 4.99/2.08 % (21469)Termination phase: Saturation
% 4.99/2.08
% 4.99/2.08 % (21469)Memory used [KB]: 7164
% 4.99/2.08 % (21469)Time elapsed: 0.066 s
% 4.99/2.08 % (21469)Instructions burned: 128 (million)
% 4.99/2.08 % (21469)------------------------------
% 4.99/2.08 % (21469)------------------------------
% 4.99/2.10 % (21462)Instruction limit reached!
% 4.99/2.10 % (21462)------------------------------
% 4.99/2.10 % (21462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.99/2.10 % (21462)Termination reason: Unknown
% 4.99/2.10 % (21462)Termination phase: Saturation
% 4.99/2.10
% 4.99/2.10 % (21462)Memory used [KB]: 8443
% 4.99/2.10 % (21462)Time elapsed: 0.190 s
% 4.99/2.10 % (21462)Instructions burned: 378 (million)
% 4.99/2.10 % (21462)------------------------------
% 4.99/2.10 % (21462)------------------------------
% 4.99/2.10 % (21470)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_21337 for (2996ds/100Mi)
% 4.99/2.11 % (21472)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_21337 for (2996ds/3Mi)
% 4.99/2.12 % (21472)Instruction limit reached!
% 4.99/2.12 % (21472)------------------------------
% 4.99/2.12 % (21472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.99/2.12 % (21472)Termination reason: Unknown
% 4.99/2.12 % (21472)Termination phase: shuffling
% 4.99/2.12
% 4.99/2.12 % (21472)Memory used [KB]: 1407
% 4.99/2.12 % (21472)Time elapsed: 0.004 s
% 4.99/2.12 % (21472)Instructions burned: 3 (million)
% 4.99/2.12 % (21472)------------------------------
% 4.99/2.12 % (21472)------------------------------
% 5.68/2.13 % (21473)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_21337 for (2996ds/20Mi)
% 5.68/2.14 % (21473)Instruction limit reached!
% 5.68/2.14 % (21473)------------------------------
% 5.68/2.14 % (21473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.14 % (21473)Termination reason: Unknown
% 5.68/2.14 % (21473)Termination phase: shuffling
% 5.68/2.14
% 5.68/2.14 % (21473)Memory used [KB]: 1918
% 5.68/2.14 % (21473)Time elapsed: 0.013 s
% 5.68/2.14 % (21473)Instructions burned: 21 (million)
% 5.68/2.14 % (21473)------------------------------
% 5.68/2.14 % (21473)------------------------------
% 5.68/2.15 % (21470)Instruction limit reached!
% 5.68/2.15 % (21470)------------------------------
% 5.68/2.15 % (21470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.15 % (21470)Termination reason: Unknown
% 5.68/2.15 % (21470)Termination phase: Property scanning
% 5.68/2.15
% 5.68/2.15 % (21470)Memory used [KB]: 2814
% 5.68/2.15 % (21470)Time elapsed: 0.051 s
% 5.68/2.15 % (21470)Instructions burned: 101 (million)
% 5.68/2.15 % (21470)------------------------------
% 5.68/2.15 % (21470)------------------------------
% 5.68/2.16 % (21474)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_21337 for (2996ds/86Mi)
% 5.68/2.17 % (21475)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_21337 for (2996ds/107Mi)
% 6.13/2.20 % (21474)Instruction limit reached!
% 6.13/2.20 % (21474)------------------------------
% 6.13/2.20 % (21474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.20 % (21474)Termination reason: Unknown
% 6.13/2.20 % (21474)Termination phase: Property scanning
% 6.13/2.20
% 6.13/2.20 % (21474)Memory used [KB]: 2558
% 6.13/2.20 % (21474)Time elapsed: 0.046 s
% 6.13/2.20 % (21474)Instructions burned: 87 (million)
% 6.13/2.20 % (21474)------------------------------
% 6.13/2.20 % (21474)------------------------------
% 6.13/2.22 % (21475)Instruction limit reached!
% 6.13/2.22 % (21475)------------------------------
% 6.13/2.22 % (21475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.22 % (21475)Termination reason: Unknown
% 6.13/2.22 % (21475)Termination phase: Property scanning
% 6.13/2.22
% 6.13/2.22 % (21475)Memory used [KB]: 2558
% 6.13/2.22 % (21475)Time elapsed: 0.054 s
% 6.13/2.22 % (21475)Instructions burned: 107 (million)
% 6.13/2.22 % (21475)------------------------------
% 6.13/2.22 % (21475)------------------------------
% 6.13/2.22 % (21476)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_21337 for (2995ds/39Mi)
% 6.13/2.22 % (21456)Instruction limit reached!
% 6.13/2.22 % (21456)------------------------------
% 6.13/2.22 % (21456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.22 % (21456)Termination reason: Unknown
% 6.13/2.22 % (21456)Termination phase: Saturation
% 6.13/2.22
% 6.13/2.22 % (21456)Memory used [KB]: 8443
% 6.13/2.22 % (21456)Time elapsed: 0.361 s
% 6.13/2.22 % (21456)Instructions burned: 710 (million)
% 6.13/2.22 % (21456)------------------------------
% 6.13/2.22 % (21456)------------------------------
% 6.13/2.24 % (21477)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_21337 for (2995ds/448Mi)
% 6.13/2.24 % (21476)Instruction limit reached!
% 6.13/2.24 % (21476)------------------------------
% 6.13/2.24 % (21476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.24 % (21476)Termination reason: Unknown
% 6.13/2.24 % (21476)Termination phase: shuffling
% 6.13/2.24
% 6.13/2.24 % (21476)Memory used [KB]: 2302
% 6.13/2.24 % (21476)Time elapsed: 0.020 s
% 6.13/2.24 % (21476)Instructions burned: 39 (million)
% 6.13/2.24 % (21476)------------------------------
% 6.13/2.24 % (21476)------------------------------
% 6.13/2.24 % (21478)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_21337 for (2995ds/46Mi)
% 6.13/2.26 % (21479)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_21337 for (2995ds/98Mi)
% 6.13/2.26 % (21478)Instruction limit reached!
% 6.13/2.26 % (21478)------------------------------
% 6.13/2.26 % (21478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.26 % (21478)Termination reason: Unknown
% 6.13/2.26 % (21478)Termination phase: SInE selection
% 6.13/2.26
% 6.13/2.26 % (21478)Memory used [KB]: 2046
% 6.13/2.26 % (21478)Time elapsed: 0.025 s
% 6.13/2.26 % (21478)Instructions burned: 47 (million)
% 6.13/2.26 % (21478)------------------------------
% 6.13/2.26 % (21478)------------------------------
% 6.13/2.28 % (21480)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_21337 for (2994ds/507Mi)
% 6.13/2.29 % (21463)Instruction limit reached!
% 6.13/2.29 % (21463)------------------------------
% 6.13/2.29 % (21463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.29 % (21463)Termination reason: Unknown
% 6.13/2.29 % (21463)Termination phase: Saturation
% 6.13/2.29
% 6.13/2.29 % (21463)Memory used [KB]: 9210
% 6.13/2.29 % (21463)Time elapsed: 0.406 s
% 6.13/2.29 % (21463)Instructions burned: 780 (million)
% 6.13/2.29 % (21463)------------------------------
% 6.13/2.29 % (21463)------------------------------
% 6.76/2.30 % (21479)Instruction limit reached!
% 6.76/2.30 % (21479)------------------------------
% 6.76/2.30 % (21479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.30 % (21479)Termination reason: Unknown
% 6.76/2.30 % (21479)Termination phase: Property scanning
% 6.76/2.30
% 6.76/2.30 % (21479)Memory used [KB]: 2814
% 6.76/2.30 % (21479)Time elapsed: 0.049 s
% 6.76/2.30 % (21479)Instructions burned: 99 (million)
% 6.76/2.30 % (21479)------------------------------
% 6.76/2.30 % (21479)------------------------------
% 6.76/2.31 % (21481)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_21337 for (2994ds/149Mi)
% 6.76/2.31 % (21458)Instruction limit reached!
% 6.76/2.31 % (21458)------------------------------
% 6.76/2.31 % (21458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.31 % (21458)Termination reason: Unknown
% 6.76/2.31 % (21458)Termination phase: Saturation
% 6.76/2.31
% 6.76/2.31 % (21458)Memory used [KB]: 8699
% 6.76/2.31 % (21458)Time elapsed: 0.457 s
% 6.76/2.31 % (21458)Instructions burned: 902 (million)
% 6.76/2.31 % (21458)------------------------------
% 6.76/2.31 % (21458)------------------------------
% 6.76/2.32 % (21482)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_21337 for (2994ds/39Mi)
% 6.76/2.33 % (21483)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_21337 for (2994ds/6Mi)
% 6.76/2.33 % (21483)Instruction limit reached!
% 6.76/2.33 % (21483)------------------------------
% 6.76/2.33 % (21483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.33 % (21483)Termination reason: Unknown
% 6.76/2.33 % (21483)Termination phase: shuffling
% 6.76/2.33
% 6.76/2.33 % (21483)Memory used [KB]: 1535
% 6.76/2.33 % (21483)Time elapsed: 0.005 s
% 6.76/2.33 % (21483)Instructions burned: 6 (million)
% 6.76/2.33 % (21483)------------------------------
% 6.76/2.33 % (21483)------------------------------
% 6.76/2.34 % (21447)Instruction limit reached!
% 6.76/2.34 % (21447)------------------------------
% 6.76/2.34 % (21447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.34 % (21447)Termination reason: Unknown
% 6.76/2.34 % (21447)Termination phase: Saturation
% 6.76/2.34
% 6.76/2.34 % (21447)Memory used [KB]: 9978
% 6.76/2.34 % (21447)Time elapsed: 0.518 s
% 6.76/2.34 % (21447)Instructions burned: 1042 (million)
% 6.76/2.34 % (21447)------------------------------
% 6.76/2.34 % (21447)------------------------------
% 6.76/2.34 % (21482)Instruction limit reached!
% 6.76/2.34 % (21482)------------------------------
% 6.76/2.34 % (21482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.34 % (21482)Termination reason: Unknown
% 6.76/2.34 % (21482)Termination phase: Property scanning
% 6.76/2.34
% 6.76/2.34 % (21482)Memory used [KB]: 2046
% 6.76/2.34 % (21482)Time elapsed: 0.022 s
% 6.76/2.34 % (21482)Instructions burned: 40 (million)
% 6.76/2.34 % (21482)------------------------------
% 6.76/2.34 % (21482)------------------------------
% 6.76/2.35 % (21484)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_21337 for (2994ds/1087Mi)
% 6.76/2.36 % (21485)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_21337 for (2994ds/47Mi)
% 6.76/2.36 % (21486)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_21337 for (2994ds/44Mi)
% 6.76/2.38 % (21486)Instruction limit reached!
% 6.76/2.38 % (21486)------------------------------
% 6.76/2.38 % (21486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.38 % (21486)Termination reason: Unknown
% 6.76/2.38 % (21486)Termination phase: shuffling
% 6.76/2.38
% 6.76/2.38 % (21486)Memory used [KB]: 2302
% 6.76/2.38 % (21486)Time elapsed: 0.022 s
% 6.76/2.38 % (21486)Instructions burned: 44 (million)
% 6.76/2.38 % (21486)------------------------------
% 6.76/2.38 % (21486)------------------------------
% 6.76/2.38 % (21485)Instruction limit reached!
% 6.76/2.38 % (21485)------------------------------
% 6.76/2.38 % (21485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.38 % (21485)Termination reason: Unknown
% 6.76/2.38 % (21485)Termination phase: Preprocessing 2
% 6.76/2.38
% 6.76/2.38 % (21485)Memory used [KB]: 2174
% 6.76/2.38 % (21485)Time elapsed: 0.026 s
% 6.76/2.38 % (21485)Instructions burned: 48 (million)
% 6.76/2.38 % (21485)------------------------------
% 6.76/2.38 % (21485)------------------------------
% 6.76/2.38 % (21481)Instruction limit reached!
% 6.76/2.38 % (21481)------------------------------
% 6.76/2.38 % (21481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.38 % (21481)Termination reason: Unknown
% 6.76/2.38 % (21481)Termination phase: Saturation
% 6.76/2.38
% 6.76/2.38 % (21481)Memory used [KB]: 7164
% 6.76/2.38 % (21481)Time elapsed: 0.074 s
% 6.76/2.38 % (21481)Instructions burned: 150 (million)
% 6.76/2.38 % (21481)------------------------------
% 6.76/2.38 % (21481)------------------------------
% 6.76/2.39 % (21487)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_21337 for (2993ds/432Mi)
% 6.76/2.40 % (21488)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_21337 for (2993ds/62Mi)
% 7.23/2.40 % (21489)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_21337 for (2993ds/31Mi)
% 7.23/2.40 % (21465)Instruction limit reached!
% 7.23/2.40 % (21465)------------------------------
% 7.23/2.40 % (21465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.40 % (21465)Termination reason: Unknown
% 7.23/2.40 % (21465)Termination phase: Saturation
% 7.23/2.40
% 7.23/2.40 % (21465)Memory used [KB]: 8187
% 7.23/2.40 % (21465)Time elapsed: 0.486 s
% 7.23/2.40 % (21465)Instructions burned: 880 (million)
% 7.23/2.40 % (21465)------------------------------
% 7.23/2.40 % (21465)------------------------------
% 7.23/2.42 % (21489)Instruction limit reached!
% 7.23/2.42 % (21489)------------------------------
% 7.23/2.42 % (21489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.42 % (21489)Termination reason: Unknown
% 7.23/2.42 % (21489)Termination phase: Property scanning
% 7.23/2.42
% 7.23/2.42 % (21489)Memory used [KB]: 2046
% 7.23/2.42 % (21489)Time elapsed: 0.018 s
% 7.23/2.42 % (21489)Instructions burned: 32 (million)
% 7.23/2.42 % (21489)------------------------------
% 7.23/2.42 % (21489)------------------------------
% 7.23/2.42 % (21490)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_21337 for (2993ds/96Mi)
% 7.23/2.43 % (21488)Instruction limit reached!
% 7.23/2.43 % (21488)------------------------------
% 7.23/2.43 % (21488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.43 % (21488)Termination reason: Unknown
% 7.23/2.43 % (21488)Termination phase: Property scanning
% 7.23/2.43
% 7.23/2.43 % (21488)Memory used [KB]: 2302
% 7.23/2.43 % (21488)Time elapsed: 0.033 s
% 7.23/2.43 % (21488)Instructions burned: 63 (million)
% 7.23/2.43 % (21488)------------------------------
% 7.23/2.43 % (21488)------------------------------
% 7.23/2.43 % (21491)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_21337 for (2993ds/453Mi)
% 7.23/2.44 % (21492)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_21337 for (2993ds/71Mi)
% 7.23/2.46 % (21477)Instruction limit reached!
% 7.23/2.46 % (21477)------------------------------
% 7.23/2.46 % (21477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.46 % (21477)Termination reason: Unknown
% 7.23/2.46 % (21477)Termination phase: Saturation
% 7.23/2.46
% 7.23/2.46 % (21477)Memory used [KB]: 8827
% 7.23/2.46 % (21477)Time elapsed: 0.227 s
% 7.23/2.46 % (21477)Instructions burned: 449 (million)
% 7.23/2.46 % (21477)------------------------------
% 7.23/2.46 % (21477)------------------------------
% 7.23/2.47 % (21490)Instruction limit reached!
% 7.23/2.47 % (21490)------------------------------
% 7.23/2.47 % (21490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.47 % (21490)Termination reason: Unknown
% 7.23/2.47 % (21490)Termination phase: Property scanning
% 7.23/2.47
% 7.23/2.47 % (21490)Memory used [KB]: 2558
% 7.23/2.47 % (21490)Time elapsed: 0.052 s
% 7.23/2.47 % (21490)Instructions burned: 97 (million)
% 7.23/2.47 % (21490)------------------------------
% 7.23/2.47 % (21490)------------------------------
% 7.23/2.48 % (21493)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_21337 for (2993ds/83Mi)
% 7.23/2.48 % (21492)Instruction limit reached!
% 7.23/2.48 % (21492)------------------------------
% 7.23/2.48 % (21492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.48 % (21492)Termination reason: Unknown
% 7.23/2.48 % (21492)Termination phase: Property scanning
% 7.23/2.48
% 7.23/2.48 % (21492)Memory used [KB]: 2430
% 7.23/2.48 % (21492)Time elapsed: 0.038 s
% 7.23/2.48 % (21492)Instructions burned: 72 (million)
% 7.23/2.48 % (21492)------------------------------
% 7.23/2.48 % (21492)------------------------------
% 7.23/2.49 % (21494)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_21337 for (2992ds/11Mi)
% 7.23/2.49 % (21494)Instruction limit reached!
% 7.23/2.49 % (21494)------------------------------
% 7.23/2.49 % (21494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.49 % (21494)Termination reason: Unknown
% 7.23/2.49 % (21494)Termination phase: shuffling
% 7.23/2.49
% 7.23/2.49 % (21494)Memory used [KB]: 1663
% 7.23/2.49 % (21494)Time elapsed: 0.007 s
% 7.23/2.49 % (21494)Instructions burned: 11 (million)
% 7.23/2.49 % (21494)------------------------------
% 7.23/2.49 % (21494)------------------------------
% 7.23/2.50 % (21495)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_21337 for (2992ds/41Mi)
% 7.72/2.51 % (21496)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21337 for (2992ds/6Mi)
% 7.72/2.51 % (21496)Instruction limit reached!
% 7.72/2.51 % (21496)------------------------------
% 7.72/2.51 % (21496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.51 % (21496)Termination reason: Unknown
% 7.72/2.51 % (21496)Termination phase: shuffling
% 7.72/2.51
% 7.72/2.51 % (21496)Memory used [KB]: 1535
% 7.72/2.51 % (21496)Time elapsed: 0.005 s
% 7.72/2.51 % (21496)Instructions burned: 6 (million)
% 7.72/2.51 % (21496)------------------------------
% 7.72/2.51 % (21496)------------------------------
% 7.72/2.52 % (21495)Instruction limit reached!
% 7.72/2.52 % (21495)------------------------------
% 7.72/2.52 % (21495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.52 % (21495)Termination reason: Unknown
% 7.72/2.52 % (21495)Termination phase: shuffling
% 7.72/2.52
% 7.72/2.52 % (21495)Memory used [KB]: 2302
% 7.72/2.52 % (21495)Time elapsed: 0.021 s
% 7.72/2.52 % (21495)Instructions burned: 41 (million)
% 7.72/2.52 % (21495)------------------------------
% 7.72/2.52 % (21495)------------------------------
% 7.72/2.52 % (21493)Instruction limit reached!
% 7.72/2.52 % (21493)------------------------------
% 7.72/2.52 % (21493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.52 % (21493)Termination reason: Unknown
% 7.72/2.52 % (21493)Termination phase: Saturation
% 7.72/2.52
% 7.72/2.52 % (21493)Memory used [KB]: 6652
% 7.72/2.52 % (21493)Time elapsed: 0.044 s
% 7.72/2.52 % (21493)Instructions burned: 84 (million)
% 7.72/2.52 % (21493)------------------------------
% 7.72/2.52 % (21493)------------------------------
% 7.72/2.53 % (21497)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_21337 for (2992ds/150Mi)
% 7.72/2.53 % (21480)Instruction limit reached!
% 7.72/2.53 % (21480)------------------------------
% 7.72/2.53 % (21480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.53 % (21480)Termination reason: Unknown
% 7.72/2.53 % (21480)Termination phase: Saturation
% 7.72/2.53
% 7.72/2.53 % (21480)Memory used [KB]: 8443
% 7.72/2.53 % (21480)Time elapsed: 0.248 s
% 7.72/2.53 % (21480)Instructions burned: 507 (million)
% 7.72/2.53 % (21480)------------------------------
% 7.72/2.53 % (21480)------------------------------
% 7.72/2.53 % (21498)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_21337 for (2992ds/343Mi)
% 7.72/2.54 % (21499)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_21337 for (2992ds/109Mi)
% 7.72/2.55 % (21500)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_21337 for (2992ds/253Mi)
% 7.72/2.59 % (21499)Instruction limit reached!
% 7.72/2.59 % (21499)------------------------------
% 7.72/2.59 % (21499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.59 % (21499)Termination reason: Unknown
% 7.72/2.59 % (21499)Termination phase: Property scanning
% 7.72/2.60
% 7.72/2.60 % (21499)Memory used [KB]: 2558
% 7.72/2.60 % (21499)Time elapsed: 0.060 s
% 7.72/2.60 % (21499)Instructions burned: 109 (million)
% 7.72/2.60 % (21499)------------------------------
% 7.72/2.60 % (21499)------------------------------
% 8.17/2.60 % (21497)Instruction limit reached!
% 8.17/2.60 % (21497)------------------------------
% 8.17/2.60 % (21497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.17/2.60 % (21497)Termination reason: Unknown
% 8.17/2.60 % (21497)Termination phase: Saturation
% 8.17/2.60
% 8.17/2.60 % (21497)Memory used [KB]: 7291
% 8.17/2.60 % (21497)Time elapsed: 0.075 s
% 8.17/2.60 % (21497)Instructions burned: 151 (million)
% 8.17/2.60 % (21497)------------------------------
% 8.17/2.60 % (21497)------------------------------
% 8.17/2.61 % (21487)Instruction limit reached!
% 8.17/2.61 % (21487)------------------------------
% 8.17/2.61 % (21487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.17/2.61 % (21487)Termination reason: Unknown
% 8.17/2.61 % (21487)Termination phase: Saturation
% 8.17/2.61
% 8.17/2.61 % (21487)Memory used [KB]: 3709
% 8.17/2.61 % (21487)Time elapsed: 0.218 s
% 8.17/2.61 % (21487)Instructions burned: 433 (million)
% 8.17/2.61 % (21487)------------------------------
% 8.17/2.61 % (21487)------------------------------
% 8.17/2.61 % (21501)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_21337 for (2991ds/140Mi)
% 8.17/2.62 % (21502)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_21337 for (2991ds/614Mi)
% 8.17/2.63 % (21503)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_21337 for (2991ds/202Mi)
% 8.17/2.65 % (21491)Instruction limit reached!
% 8.17/2.65 % (21491)------------------------------
% 8.17/2.65 % (21491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.17/2.65 % (21491)Termination reason: Unknown
% 8.17/2.65 % (21491)Termination phase: Saturation
% 8.17/2.65
% 8.17/2.65 % (21491)Memory used [KB]: 8187
% 8.17/2.65 % (21491)Time elapsed: 0.240 s
% 8.17/2.65 % (21491)Instructions burned: 454 (million)
% 8.17/2.65 % (21491)------------------------------
% 8.17/2.65 % (21491)------------------------------
% 8.17/2.67 % (21504)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_21337 for (2991ds/339Mi)
% 8.17/2.67 % (21500)Instruction limit reached!
% 8.17/2.67 % (21500)------------------------------
% 8.17/2.67 % (21500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.17/2.67 % (21500)Termination reason: Unknown
% 8.17/2.67 % (21500)Termination phase: Saturation
% 8.17/2.67
% 8.17/2.67 % (21500)Memory used [KB]: 7803
% 8.17/2.67 % (21500)Time elapsed: 0.130 s
% 8.17/2.67 % (21500)Instructions burned: 254 (million)
% 8.17/2.67 % (21500)------------------------------
% 8.17/2.67 % (21500)------------------------------
% 8.17/2.68 % (21501)Instruction limit reached!
% 8.17/2.68 % (21501)------------------------------
% 8.17/2.68 % (21501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.17/2.68 % (21501)Termination reason: Unknown
% 8.17/2.68 % (21501)Termination phase: Saturation
% 8.17/2.68
% 8.17/2.68 % (21501)Memory used [KB]: 7164
% 8.17/2.68 % (21501)Time elapsed: 0.072 s
% 8.17/2.68 % (21501)Instructions burned: 140 (million)
% 8.17/2.68 % (21501)------------------------------
% 8.17/2.68 % (21501)------------------------------
% 8.17/2.69 % (21505)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_21337 for (2990ds/283Mi)
% 8.96/2.70 % (21506)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_21337 for (2990ds/134Mi)
% 8.96/2.71 % (21498)Instruction limit reached!
% 8.96/2.71 % (21498)------------------------------
% 8.96/2.71 % (21498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.71 % (21498)Termination reason: Unknown
% 8.96/2.71 % (21498)Termination phase: Saturation
% 8.96/2.71
% 8.96/2.71 % (21498)Memory used [KB]: 7675
% 8.96/2.71 % (21498)Time elapsed: 0.176 s
% 8.96/2.71 % (21498)Instructions burned: 343 (million)
% 8.96/2.71 % (21498)------------------------------
% 8.96/2.71 % (21498)------------------------------
% 8.96/2.72 % (21507)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_21337 for (2990ds/298Mi)
% 8.96/2.73 % (21503)Instruction limit reached!
% 8.96/2.73 % (21503)------------------------------
% 8.96/2.73 % (21503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.73 % (21503)Termination reason: Unknown
% 8.96/2.73 % (21503)Termination phase: Saturation
% 8.96/2.73
% 8.96/2.73 % (21503)Memory used [KB]: 7291
% 8.96/2.73 % (21503)Time elapsed: 0.101 s
% 8.96/2.73 % (21503)Instructions burned: 202 (million)
% 8.96/2.73 % (21503)------------------------------
% 8.96/2.73 % (21503)------------------------------
% 8.96/2.74 % (21508)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_21337 for (2990ds/192Mi)
% 8.96/2.76 % (21506)Instruction limit reached!
% 8.96/2.76 % (21506)------------------------------
% 8.96/2.76 % (21506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.76 % (21506)Termination reason: Unknown
% 8.96/2.76 % (21506)Termination phase: Saturation
% 8.96/2.76
% 8.96/2.76 % (21506)Memory used [KB]: 7164
% 8.96/2.76 % (21506)Time elapsed: 0.066 s
% 8.96/2.76 % (21506)Instructions burned: 135 (million)
% 8.96/2.76 % (21506)------------------------------
% 8.96/2.76 % (21506)------------------------------
% 8.96/2.78 % (21509)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_21337 for (2989ds/258Mi)
% 9.35/2.82 % (21484)Instruction limit reached!
% 9.35/2.82 % (21484)------------------------------
% 9.35/2.82 % (21484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.82 % (21484)Termination reason: Unknown
% 9.35/2.82 % (21484)Termination phase: Saturation
% 9.35/2.82
% 9.35/2.82 % (21484)Memory used [KB]: 8187
% 9.35/2.82 % (21484)Time elapsed: 0.471 s
% 9.35/2.82 % (21484)Instructions burned: 1089 (million)
% 9.35/2.82 % (21484)------------------------------
% 9.35/2.82 % (21484)------------------------------
% 9.35/2.82 % (21504)Instruction limit reached!
% 9.35/2.82 % (21504)------------------------------
% 9.35/2.82 % (21504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.82 % (21504)Termination reason: Unknown
% 9.35/2.82 % (21504)Termination phase: Saturation
% 9.35/2.82
% 9.35/2.82 % (21504)Memory used [KB]: 7419
% 9.35/2.82 % (21504)Time elapsed: 0.158 s
% 9.35/2.82 % (21504)Instructions burned: 340 (million)
% 9.35/2.82 % (21504)------------------------------
% 9.35/2.82 % (21504)------------------------------
% 9.35/2.83 % (21505)Instruction limit reached!
% 9.35/2.83 % (21505)------------------------------
% 9.35/2.83 % (21505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.83 % (21505)Termination reason: Unknown
% 9.35/2.83 % (21505)Termination phase: Saturation
% 9.35/2.83
% 9.35/2.83 % (21505)Memory used [KB]: 7803
% 9.35/2.83 % (21505)Time elapsed: 0.143 s
% 9.35/2.83 % (21505)Instructions burned: 283 (million)
% 9.35/2.83 % (21505)------------------------------
% 9.35/2.83 % (21505)------------------------------
% 9.35/2.84 % (21510)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_21337 for (2989ds/90Mi)
% 9.35/2.84 % (21511)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_21337 for (2989ds/231Mi)
% 9.35/2.84 % (21508)Instruction limit reached!
% 9.35/2.84 % (21508)------------------------------
% 9.35/2.84 % (21508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.84 % (21508)Termination reason: Unknown
% 9.35/2.84 % (21508)Termination phase: Saturation
% 9.35/2.84
% 9.35/2.84 % (21508)Memory used [KB]: 3709
% 9.35/2.84 % (21508)Time elapsed: 0.099 s
% 9.35/2.84 % (21508)Instructions burned: 192 (million)
% 9.35/2.84 % (21508)------------------------------
% 9.35/2.84 % (21508)------------------------------
% 9.35/2.85 % (21512)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_21337 for (2989ds/458Mi)
% 9.35/2.86 % (21513)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_21337 for (2989ds/31Mi)
% 9.35/2.86 % (21507)Instruction limit reached!
% 9.35/2.86 % (21507)------------------------------
% 9.35/2.86 % (21507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.86 % (21507)Termination reason: Unknown
% 9.35/2.86 % (21507)Termination phase: Saturation
% 9.35/2.86
% 9.35/2.86 % (21507)Memory used [KB]: 8571
% 9.35/2.86 % (21507)Time elapsed: 0.142 s
% 9.35/2.86 % (21507)Instructions burned: 298 (million)
% 9.35/2.86 % (21507)------------------------------
% 9.35/2.86 % (21507)------------------------------
% 9.35/2.87 % (21513)Instruction limit reached!
% 9.35/2.87 % (21513)------------------------------
% 9.35/2.87 % (21513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.87 % (21513)Termination reason: Unknown
% 9.35/2.87 % (21513)Termination phase: Property scanning
% 9.35/2.87
% 9.35/2.87 % (21513)Memory used [KB]: 2046
% 9.35/2.87 % (21513)Time elapsed: 0.018 s
% 9.35/2.87 % (21513)Instructions burned: 32 (million)
% 9.35/2.87 % (21513)------------------------------
% 9.35/2.87 % (21513)------------------------------
% 9.35/2.88 % (21510)Instruction limit reached!
% 9.35/2.88 % (21510)------------------------------
% 9.35/2.88 % (21510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.88 % (21510)Termination reason: Unknown
% 9.35/2.88 % (21510)Termination phase: Property scanning
% 9.35/2.88
% 9.35/2.88 % (21510)Memory used [KB]: 2558
% 9.35/2.88 % (21510)Time elapsed: 0.046 s
% 9.35/2.88 % (21510)Instructions burned: 90 (million)
% 9.35/2.88 % (21510)------------------------------
% 9.35/2.88 % (21510)------------------------------
% 9.35/2.88 % (21514)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_21337 for (2988ds/297Mi)
% 9.35/2.89 % (21515)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_21337 for (2988ds/987Mi)
% 9.35/2.90 % (21516)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_21337 for (2988ds/182Mi)
% 10.53/2.90 % (21502)Instruction limit reached!
% 10.53/2.90 % (21502)------------------------------
% 10.53/2.90 % (21502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.90 % (21502)Termination reason: Unknown
% 10.53/2.90 % (21502)Termination phase: Saturation
% 10.53/2.90
% 10.53/2.90 % (21502)Memory used [KB]: 8955
% 10.53/2.90 % (21502)Time elapsed: 0.282 s
% 10.53/2.90 % (21502)Instructions burned: 615 (million)
% 10.53/2.90 % (21502)------------------------------
% 10.53/2.90 % (21502)------------------------------
% 10.53/2.91 % (21509)Instruction limit reached!
% 10.53/2.91 % (21509)------------------------------
% 10.53/2.91 % (21509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.91 % (21509)Termination reason: Unknown
% 10.53/2.91 % (21509)Termination phase: Saturation
% 10.53/2.91
% 10.53/2.91 % (21509)Memory used [KB]: 8059
% 10.53/2.91 % (21509)Time elapsed: 0.129 s
% 10.53/2.91 % (21509)Instructions burned: 259 (million)
% 10.53/2.91 % (21509)------------------------------
% 10.53/2.91 % (21509)------------------------------
% 10.53/2.91 % (21517)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_21337 for (2988ds/182Mi)
% 10.53/2.92 % (21518)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_21337 for (2988ds/154Mi)
% 10.53/2.95 % (21511)Instruction limit reached!
% 10.53/2.95 % (21511)------------------------------
% 10.53/2.95 % (21511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.95 % (21511)Termination reason: Unknown
% 10.53/2.95 % (21511)Termination phase: Saturation
% 10.53/2.95
% 10.53/2.95 % (21511)Memory used [KB]: 7547
% 10.53/2.95 % (21511)Time elapsed: 0.113 s
% 10.53/2.95 % (21511)Instructions burned: 232 (million)
% 10.53/2.95 % (21511)------------------------------
% 10.53/2.95 % (21511)------------------------------
% 10.53/2.97 % (21519)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_21337 for (2988ds/79Mi)
% 10.53/2.98 % (21516)Instruction limit reached!
% 10.53/2.98 % (21516)------------------------------
% 10.53/2.98 % (21516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.98 % (21516)Termination reason: Unknown
% 10.53/2.98 % (21516)Termination phase: Saturation
% 10.53/2.98
% 10.53/2.98 % (21516)Memory used [KB]: 7419
% 10.53/2.98 % (21516)Time elapsed: 0.089 s
% 10.53/2.98 % (21516)Instructions burned: 182 (million)
% 10.53/2.98 % (21516)------------------------------
% 10.53/2.98 % (21516)------------------------------
% 10.53/2.99 % (21518)Instruction limit reached!
% 10.53/2.99 % (21518)------------------------------
% 10.53/2.99 % (21518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.99 % (21518)Termination reason: Unknown
% 10.53/2.99 % (21518)Termination phase: Property scanning
% 10.53/2.99
% 10.53/2.99 % (21518)Memory used [KB]: 2814
% 10.53/2.99 % (21518)Time elapsed: 0.072 s
% 10.53/2.99 % (21518)Instructions burned: 155 (million)
% 10.53/2.99 % (21518)------------------------------
% 10.53/2.99 % (21518)------------------------------
% 10.53/3.00 % (21520)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_21337 for (2987ds/216Mi)
% 10.53/3.01 % (21519)Instruction limit reached!
% 10.53/3.01 % (21519)------------------------------
% 10.53/3.01 % (21519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/3.01 % (21519)Termination reason: Unknown
% 10.53/3.01 % (21519)Termination phase: Function definition elimination
% 10.53/3.01
% 10.53/3.01 % (21519)Memory used [KB]: 2302
% 10.53/3.01 % (21519)Time elapsed: 0.041 s
% 10.53/3.01 % (21519)Instructions burned: 79 (million)
% 10.53/3.01 % (21519)------------------------------
% 10.53/3.01 % (21519)------------------------------
% 10.53/3.01 % (21517)Instruction limit reached!
% 10.53/3.01 % (21517)------------------------------
% 10.53/3.01 % (21517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/3.01 % (21517)Termination reason: Unknown
% 10.53/3.01 % (21517)Termination phase: Saturation
% 10.53/3.01
% 10.53/3.01 % (21517)Memory used [KB]: 7419
% 10.53/3.01 % (21517)Time elapsed: 0.095 s
% 10.53/3.01 % (21517)Instructions burned: 182 (million)
% 10.53/3.01 % (21517)------------------------------
% 10.53/3.01 % (21517)------------------------------
% 10.53/3.01 % (21521)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_21337 for (2987ds/114Mi)
% 10.53/3.02 % (21522)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_21337 for (2987ds/922Mi)
% 10.53/3.02 % (21523)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_21337 for (2987ds/182Mi)
% 11.97/3.03 % (21514)Instruction limit reached!
% 11.97/3.03 % (21514)------------------------------
% 11.97/3.03 % (21514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.03 % (21514)Termination reason: Unknown
% 11.97/3.03 % (21514)Termination phase: Saturation
% 11.97/3.03
% 11.97/3.03 % (21514)Memory used [KB]: 7803
% 11.97/3.03 % (21514)Time elapsed: 0.149 s
% 11.97/3.03 % (21514)Instructions burned: 297 (million)
% 11.97/3.03 % (21514)------------------------------
% 11.97/3.03 % (21514)------------------------------
% 11.97/3.04 % (21524)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_21337 for (2987ds/164Mi)
% 11.97/3.07 % (21521)Instruction limit reached!
% 11.97/3.07 % (21521)------------------------------
% 11.97/3.07 % (21521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.07 % (21521)Termination reason: Unknown
% 11.97/3.07 % (21521)Termination phase: Saturation
% 11.97/3.07
% 11.97/3.07 % (21521)Memory used [KB]: 7036
% 11.97/3.07 % (21521)Time elapsed: 0.057 s
% 11.97/3.07 % (21521)Instructions burned: 115 (million)
% 11.97/3.07 % (21521)------------------------------
% 11.97/3.07 % (21521)------------------------------
% 11.97/3.08 % (21512)Instruction limit reached!
% 11.97/3.08 % (21512)------------------------------
% 11.97/3.08 % (21512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.08 % (21512)Termination reason: Unknown
% 11.97/3.08 % (21512)Termination phase: Saturation
% 11.97/3.08
% 11.97/3.08 % (21512)Memory used [KB]: 8315
% 11.97/3.08 % (21512)Time elapsed: 0.230 s
% 11.97/3.08 % (21512)Instructions burned: 458 (million)
% 11.97/3.08 % (21512)------------------------------
% 11.97/3.08 % (21512)------------------------------
% 11.97/3.08 % (21525)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_21337 for (2986ds/50Mi)
% 11.97/3.09 % (21526)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_21337 for (2986ds/368Mi)
% 11.97/3.10 % (21520)Instruction limit reached!
% 11.97/3.10 % (21520)------------------------------
% 11.97/3.10 % (21520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.10 % (21520)Termination reason: Unknown
% 11.97/3.10 % (21520)Termination phase: Saturation
% 11.97/3.10
% 11.97/3.10 % (21520)Memory used [KB]: 7419
% 11.97/3.10 % (21520)Time elapsed: 0.102 s
% 11.97/3.10 % (21520)Instructions burned: 216 (million)
% 11.97/3.10 % (21520)------------------------------
% 11.97/3.10 % (21520)------------------------------
% 11.97/3.11 % (21525)Instruction limit reached!
% 11.97/3.11 % (21525)------------------------------
% 11.97/3.11 % (21525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.11 % (21525)Termination reason: Unknown
% 11.97/3.11 % (21525)Termination phase: Property scanning
% 11.97/3.11
% 11.97/3.11 % (21525)Memory used [KB]: 2302
% 11.97/3.11 % (21525)Time elapsed: 0.025 s
% 11.97/3.11 % (21525)Instructions burned: 50 (million)
% 11.97/3.11 % (21525)------------------------------
% 11.97/3.11 % (21525)------------------------------
% 11.97/3.11 % (21523)Instruction limit reached!
% 11.97/3.11 % (21523)------------------------------
% 11.97/3.11 % (21523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.11 % (21523)Termination reason: Unknown
% 11.97/3.11 % (21523)Termination phase: Saturation
% 11.97/3.11
% 11.97/3.11 % (21523)Memory used [KB]: 7291
% 11.97/3.11 % (21523)Time elapsed: 0.089 s
% 11.97/3.11 % (21523)Instructions burned: 182 (million)
% 11.97/3.11 % (21523)------------------------------
% 11.97/3.11 % (21523)------------------------------
% 11.97/3.12 % (21527)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_21337 for (2986ds/1021Mi)
% 11.97/3.12 % (21524)Instruction limit reached!
% 11.97/3.12 % (21524)------------------------------
% 11.97/3.12 % (21524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.12 % (21524)Termination reason: Unknown
% 11.97/3.12 % (21524)Termination phase: Saturation
% 11.97/3.12
% 11.97/3.12 % (21524)Memory used [KB]: 2814
% 11.97/3.12 % (21524)Time elapsed: 0.079 s
% 11.97/3.12 % (21524)Instructions burned: 165 (million)
% 11.97/3.12 % (21524)------------------------------
% 11.97/3.12 % (21524)------------------------------
% 11.97/3.12 % (21528)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_21337 for (2986ds/267Mi)
% 12.52/3.13 % (21529)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_21337 for (2986ds/204Mi)
% 12.52/3.14 % (21530)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_21337 for (2986ds/26Mi)
% 12.52/3.15 % (21530)Instruction limit reached!
% 12.52/3.15 % (21530)------------------------------
% 12.52/3.15 % (21530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.52/3.15 % (21530)Termination reason: Unknown
% 12.52/3.15 % (21530)Termination phase: shuffling
% 12.52/3.15
% 12.52/3.15 % (21530)Memory used [KB]: 2046
% 12.52/3.15 % (21530)Time elapsed: 0.015 s
% 12.52/3.15 % (21530)Instructions burned: 27 (million)
% 12.52/3.15 % (21530)------------------------------
% 12.52/3.15 % (21530)------------------------------
% 12.52/3.17 % (21531)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_21337 for (2986ds/53Mi)
% 12.52/3.19 % (21531)Instruction limit reached!
% 12.52/3.19 % (21531)------------------------------
% 12.52/3.19 % (21531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.52/3.19 % (21531)Termination reason: Unknown
% 12.52/3.19 % (21531)Termination phase: Property scanning
% 12.52/3.19
% 12.52/3.19 % (21531)Memory used [KB]: 2302
% 12.52/3.19 % (21531)Time elapsed: 0.028 s
% 12.52/3.19 % (21531)Instructions burned: 54 (million)
% 12.52/3.19 % (21531)------------------------------
% 12.52/3.19 % (21531)------------------------------
% 12.68/3.21 % (21532)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_21337 for (2985ds/4436Mi)
% 12.68/3.23 % (21529)Instruction limit reached!
% 12.68/3.23 % (21529)------------------------------
% 12.68/3.23 % (21529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.68/3.23 % (21529)Termination reason: Unknown
% 12.68/3.23 % (21529)Termination phase: Saturation
% 12.68/3.23
% 12.68/3.23 % (21529)Memory used [KB]: 7419
% 12.68/3.23 % (21529)Time elapsed: 0.104 s
% 12.68/3.23 % (21529)Instructions burned: 204 (million)
% 12.68/3.23 % (21529)------------------------------
% 12.68/3.23 % (21529)------------------------------
% 12.68/3.25 % (21533)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_21337 for (2985ds/1539Mi)
% 12.68/3.25 % (21528)Instruction limit reached!
% 12.68/3.25 % (21528)------------------------------
% 12.68/3.25 % (21528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.68/3.25 % (21528)Termination reason: Unknown
% 12.68/3.25 % (21528)Termination phase: Saturation
% 12.68/3.25
% 12.68/3.25 % (21528)Memory used [KB]: 7803
% 12.68/3.25 % (21528)Time elapsed: 0.132 s
% 12.68/3.25 % (21528)Instructions burned: 268 (million)
% 12.68/3.25 % (21528)------------------------------
% 12.68/3.25 % (21528)------------------------------
% 12.68/3.27 % (21534)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_21337 for (2985ds/408Mi)
% 12.68/3.28 % (21526)Instruction limit reached!
% 12.68/3.28 % (21526)------------------------------
% 12.68/3.28 % (21526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.68/3.28 % (21526)Termination reason: Unknown
% 12.68/3.28 % (21526)Termination phase: Saturation
% 12.68/3.28
% 12.68/3.28 % (21526)Memory used [KB]: 8827
% 12.68/3.28 % (21526)Time elapsed: 0.184 s
% 12.68/3.28 % (21526)Instructions burned: 369 (million)
% 12.68/3.28 % (21526)------------------------------
% 12.68/3.28 % (21526)------------------------------
% 12.68/3.29 % (21535)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_21337 for (2984ds/5205Mi)
% 13.24/3.38 % (21515)Instruction limit reached!
% 13.24/3.38 % (21515)------------------------------
% 13.24/3.38 % (21515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.24/3.38 % (21515)Termination reason: Unknown
% 13.24/3.38 % (21515)Termination phase: Saturation
% 13.24/3.38
% 13.24/3.38 % (21515)Memory used [KB]: 8699
% 13.24/3.38 % (21515)Time elapsed: 0.492 s
% 13.24/3.38 % (21515)Instructions burned: 988 (million)
% 13.24/3.38 % (21515)------------------------------
% 13.24/3.38 % (21515)------------------------------
% 13.34/3.40 % (21536)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_21337 for (2983ds/1913Mi)
% 13.34/3.47 % (21534)Instruction limit reached!
% 13.34/3.47 % (21534)------------------------------
% 13.34/3.47 % (21534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.47 % (21534)Termination reason: Unknown
% 13.34/3.47 % (21534)Termination phase: Saturation
% 13.34/3.47
% 13.34/3.47 % (21534)Memory used [KB]: 8571
% 13.34/3.47 % (21534)Time elapsed: 0.203 s
% 13.34/3.47 % (21534)Instructions burned: 408 (million)
% 13.34/3.47 % (21534)------------------------------
% 13.34/3.47 % (21534)------------------------------
% 13.34/3.49 % (21537)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_21337 for (2982ds/4350Mi)
% 13.34/3.49 % (21522)Instruction limit reached!
% 13.34/3.49 % (21522)------------------------------
% 13.34/3.49 % (21522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.49 % (21522)Termination reason: Unknown
% 13.34/3.49 % (21522)Termination phase: Saturation
% 13.34/3.49
% 13.34/3.49 % (21522)Memory used [KB]: 8699
% 13.34/3.49 % (21522)Time elapsed: 0.498 s
% 13.34/3.49 % (21522)Instructions burned: 923 (million)
% 13.34/3.49 % (21522)------------------------------
% 13.34/3.49 % (21522)------------------------------
% 14.05/3.51 % (21538)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_21337 for (2982ds/68Mi)
% 14.05/3.54 % (21538)Instruction limit reached!
% 14.05/3.54 % (21538)------------------------------
% 14.05/3.54 % (21538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.05/3.54 % (21538)Termination reason: Unknown
% 14.05/3.54 % (21538)Termination phase: Preprocessing 3
% 14.05/3.54
% 14.05/3.54 % (21538)Memory used [KB]: 2302
% 14.05/3.54 % (21538)Time elapsed: 0.036 s
% 14.05/3.54 % (21538)Instructions burned: 68 (million)
% 14.05/3.54 % (21538)------------------------------
% 14.05/3.54 % (21538)------------------------------
% 14.05/3.56 % (21539)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_21337 for (2982ds/358Mi)
% 14.11/3.63 % (21527)Instruction limit reached!
% 14.11/3.63 % (21527)------------------------------
% 14.11/3.63 % (21527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.11/3.63 % (21527)Termination reason: Unknown
% 14.11/3.63 % (21527)Termination phase: Saturation
% 14.11/3.63
% 14.11/3.63 % (21527)Memory used [KB]: 9722
% 14.11/3.63 % (21527)Time elapsed: 0.519 s
% 14.11/3.63 % (21527)Instructions burned: 1022 (million)
% 14.11/3.63 % (21527)------------------------------
% 14.11/3.63 % (21527)------------------------------
% 14.11/3.65 % (21540)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_21337 for (2981ds/31Mi)
% 14.11/3.67 % (21540)Instruction limit reached!
% 14.11/3.67 % (21540)------------------------------
% 14.11/3.67 % (21540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.11/3.67 % (21540)Termination reason: Unknown
% 14.11/3.67 % (21540)Termination phase: Property scanning
% 14.11/3.67
% 14.11/3.67 % (21540)Memory used [KB]: 2046
% 14.11/3.67 % (21540)Time elapsed: 0.019 s
% 14.11/3.67 % (21540)Instructions burned: 32 (million)
% 14.11/3.67 % (21540)------------------------------
% 14.11/3.67 % (21540)------------------------------
% 14.11/3.68 % (21541)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_21337 for (2980ds/279Mi)
% 14.67/3.74 % (21539)Instruction limit reached!
% 14.67/3.74 % (21539)------------------------------
% 14.67/3.74 % (21539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.67/3.74 % (21539)Termination reason: Unknown
% 14.67/3.74 % (21539)Termination phase: Saturation
% 14.67/3.74
% 14.67/3.74 % (21539)Memory used [KB]: 7675
% 14.67/3.74 % (21539)Time elapsed: 0.179 s
% 14.67/3.74 % (21539)Instructions burned: 359 (million)
% 14.67/3.74 % (21539)------------------------------
% 14.67/3.74 % (21539)------------------------------
% 14.67/3.75 % (21541)Refutation not found, incomplete strategy
% 14.67/3.75 % (21541)------------------------------
% 14.67/3.75 % (21541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.67/3.75 % (21541)Termination reason: Refutation not found, incomplete strategy
% 14.67/3.75
% 14.67/3.75
% 14.67/3.75 % (21541)Memory used [KB]: 7291
% 14.67/3.75 % (21541)Time elapsed: 0.067 s
% 14.67/3.75 % (21541)Instructions burned: 137 (million)
% 14.67/3.75 % (21541)------------------------------
% 14.67/3.75 % (21541)------------------------------
% 14.67/3.75 % (21542)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_21337 for (2980ds/258Mi)
% 14.67/3.77 % (21543)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_21337 for (2980ds/26Mi)
% 14.67/3.78 % (21543)Instruction limit reached!
% 14.67/3.78 % (21543)------------------------------
% 14.67/3.78 % (21543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.67/3.78 % (21543)Termination reason: Unknown
% 14.67/3.78 % (21543)Termination phase: shuffling
% 14.67/3.78
% 14.67/3.78 % (21543)Memory used [KB]: 2046
% 14.67/3.78 % (21543)Time elapsed: 0.017 s
% 14.67/3.78 % (21543)Instructions burned: 26 (million)
% 14.67/3.78 % (21543)------------------------------
% 14.67/3.78 % (21543)------------------------------
% 14.98/3.81 % (21544)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_21337 for (2979ds/995Mi)
% 14.98/3.88 % (21542)Instruction limit reached!
% 14.98/3.88 % (21542)------------------------------
% 14.98/3.88 % (21542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.98/3.88 % (21542)Termination reason: Unknown
% 14.98/3.88 % (21542)Termination phase: Saturation
% 14.98/3.88
% 14.98/3.88 % (21542)Memory used [KB]: 7675
% 14.98/3.88 % (21542)Time elapsed: 0.131 s
% 14.98/3.88 % (21542)Instructions burned: 258 (million)
% 14.98/3.88 % (21542)------------------------------
% 14.98/3.88 % (21542)------------------------------
% 15.13/3.90 % (21545)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_21337 for (2978ds/373Mi)
% 19.01/4.03 % (21533)Instruction limit reached!
% 19.01/4.03 % (21533)------------------------------
% 19.01/4.03 % (21533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.01/4.03 % (21533)Termination reason: Unknown
% 19.01/4.03 % (21533)Termination phase: Saturation
% 19.01/4.03
% 19.01/4.03 % (21533)Memory used [KB]: 10490
% 19.01/4.03 % (21533)Time elapsed: 0.789 s
% 19.01/4.03 % (21533)Instructions burned: 1539 (million)
% 19.01/4.03 % (21533)------------------------------
% 19.01/4.03 % (21533)------------------------------
% 19.01/4.05 % (21546)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_21337 for (2977ds/253Mi)
% 19.01/4.09 % (21545)Instruction limit reached!
% 19.01/4.09 % (21545)------------------------------
% 19.01/4.09 % (21545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.01/4.09 % (21545)Termination reason: Unknown
% 19.01/4.09 % (21545)Termination phase: Saturation
% 19.01/4.09
% 19.01/4.09 % (21545)Memory used [KB]: 8443
% 19.01/4.09 % (21545)Time elapsed: 0.186 s
% 19.01/4.09 % (21545)Instructions burned: 374 (million)
% 19.01/4.09 % (21545)------------------------------
% 19.01/4.09 % (21545)------------------------------
% 19.01/4.10 % (21547)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_21337 for (2976ds/832Mi)
% 19.60/4.17 % (21546)Instruction limit reached!
% 19.60/4.17 % (21546)------------------------------
% 19.60/4.17 % (21546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.60/4.17 % (21546)Termination reason: Unknown
% 19.60/4.17 % (21546)Termination phase: Saturation
% 19.60/4.17
% 19.60/4.17 % (21546)Memory used [KB]: 7931
% 19.60/4.17 % (21546)Time elapsed: 0.125 s
% 19.60/4.17 % (21546)Instructions burned: 254 (million)
% 19.60/4.17 % (21546)------------------------------
% 19.60/4.17 % (21546)------------------------------
% 19.60/4.19 % (21548)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_21337 for (2975ds/668Mi)
% 20.59/4.30 % (21544)Instruction limit reached!
% 20.59/4.30 % (21544)------------------------------
% 20.59/4.30 % (21544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.59/4.30 % (21544)Termination reason: Unknown
% 20.59/4.30 % (21544)Termination phase: Saturation
% 20.59/4.30
% 20.59/4.30 % (21544)Memory used [KB]: 9850
% 20.59/4.30 % (21544)Time elapsed: 0.494 s
% 20.59/4.30 % (21544)Instructions burned: 995 (million)
% 20.59/4.30 % (21544)------------------------------
% 20.59/4.30 % (21544)------------------------------
% 20.59/4.32 % (21549)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_21337 for (2974ds/40Mi)
% 20.59/4.33 % (21549)Instruction limit reached!
% 20.59/4.33 % (21549)------------------------------
% 20.59/4.33 % (21549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.59/4.33 % (21549)Termination reason: Unknown
% 20.59/4.33 % (21549)Termination phase: shuffling
% 20.59/4.33
% 20.59/4.33 % (21549)Memory used [KB]: 2302
% 20.59/4.33 % (21549)Time elapsed: 0.021 s
% 20.59/4.33 % (21549)Instructions burned: 40 (million)
% 20.59/4.33 % (21549)------------------------------
% 20.59/4.33 % (21549)------------------------------
% 20.59/4.35 % (21550)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_21337 for (2974ds/294Mi)
% 20.59/4.36 % (21536)Instruction limit reached!
% 20.59/4.36 % (21536)------------------------------
% 20.59/4.36 % (21536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.59/4.36 % (21536)Termination reason: Unknown
% 20.59/4.36 % (21536)Termination phase: Saturation
% 20.59/4.36
% 20.59/4.36 % (21536)Memory used [KB]: 5500
% 20.59/4.36 % (21536)Time elapsed: 0.960 s
% 20.59/4.36 % (21536)Instructions burned: 1914 (million)
% 20.59/4.36 % (21536)------------------------------
% 20.59/4.36 % (21536)------------------------------
% 20.59/4.37 % (21551)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_21337 for (2974ds/187Mi)
% 21.00/4.41 % (21550)Refutation not found, incomplete strategy
% 21.00/4.41 % (21550)------------------------------
% 21.00/4.41 % (21550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.00/4.41 % (21550)Termination reason: Refutation not found, incomplete strategy
% 21.00/4.41
% 21.00/4.41
% 21.00/4.41 % (21550)Memory used [KB]: 7036
% 21.00/4.41 % (21550)Time elapsed: 0.062 s
% 21.00/4.41 % (21550)Instructions burned: 124 (million)
% 21.00/4.41 % (21550)------------------------------
% 21.00/4.41 % (21550)------------------------------
% 21.00/4.43 % (21552)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_21337 for (2973ds/371Mi)
% 21.00/4.47 % (21551)Instruction limit reached!
% 21.00/4.47 % (21551)------------------------------
% 21.00/4.47 % (21551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.00/4.47 % (21551)Termination reason: Unknown
% 21.00/4.47 % (21551)Termination phase: Saturation
% 21.00/4.47
% 21.00/4.47 % (21551)Memory used [KB]: 7547
% 21.00/4.47 % (21551)Time elapsed: 0.096 s
% 21.00/4.47 % (21551)Instructions burned: 187 (million)
% 21.00/4.47 % (21551)------------------------------
% 21.00/4.47 % (21551)------------------------------
% 21.00/4.48 % (21553)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_21337 for (2973ds/1827Mi)
% 21.50/4.52 % (21547)Instruction limit reached!
% 21.50/4.52 % (21547)------------------------------
% 21.50/4.52 % (21547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.50/4.52 % (21547)Termination reason: Unknown
% 21.50/4.52 % (21547)Termination phase: Saturation
% 21.50/4.52
% 21.50/4.52 % (21547)Memory used [KB]: 8571
% 21.50/4.52 % (21547)Time elapsed: 0.416 s
% 21.50/4.52 % (21547)Instructions burned: 832 (million)
% 21.50/4.52 % (21547)------------------------------
% 21.50/4.52 % (21547)------------------------------
% 21.50/4.53 % (21548)Instruction limit reached!
% 21.50/4.53 % (21548)------------------------------
% 21.50/4.53 % (21548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.50/4.53 % (21548)Termination reason: Unknown
% 21.50/4.53 % (21548)Termination phase: Saturation
% 21.50/4.53
% 21.50/4.53 % (21548)Memory used [KB]: 13944
% 21.50/4.53 % (21548)Time elapsed: 0.337 s
% 21.50/4.53 % (21548)Instructions burned: 669 (million)
% 21.50/4.53 % (21548)------------------------------
% 21.50/4.53 % (21548)------------------------------
% 21.50/4.54 % (21554)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_21337 for (2972ds/70Mi)
% 21.50/4.55 % (21555)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_21337 for (2972ds/316Mi)
% 21.50/4.57 % (21554)Instruction limit reached!
% 21.50/4.57 % (21554)------------------------------
% 21.50/4.57 % (21554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.50/4.57 % (21554)Termination reason: Unknown
% 21.50/4.57 % (21554)Termination phase: Property scanning
% 21.50/4.57
% 21.50/4.57 % (21554)Memory used [KB]: 2302
% 21.50/4.57 % (21554)Time elapsed: 0.035 s
% 21.50/4.57 % (21554)Instructions burned: 70 (million)
% 21.50/4.57 % (21554)------------------------------
% 21.50/4.57 % (21554)------------------------------
% 21.50/4.59 % (21556)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_21337 for (2971ds/932Mi)
% 22.63/4.62 % (21552)Instruction limit reached!
% 22.63/4.62 % (21552)------------------------------
% 22.63/4.62 % (21552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.63/4.62 % (21552)Termination reason: Unknown
% 22.63/4.62 % (21552)Termination phase: Saturation
% 22.63/4.62
% 22.63/4.62 % (21552)Memory used [KB]: 7675
% 22.63/4.62 % (21552)Time elapsed: 0.195 s
% 22.63/4.62 % (21552)Instructions burned: 371 (million)
% 22.63/4.62 % (21552)------------------------------
% 22.63/4.62 % (21552)------------------------------
% 22.63/4.64 % (21557)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_21337 for (2971ds/4714Mi)
% 22.63/4.66 % (21555)Refutation not found, incomplete strategy
% 22.63/4.66 % (21555)------------------------------
% 22.63/4.66 % (21555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.63/4.66 % (21555)Termination reason: Refutation not found, incomplete strategy
% 22.63/4.66
% 22.63/4.66
% 22.63/4.66 % (21555)Memory used [KB]: 7803
% 22.63/4.66 % (21555)Time elapsed: 0.113 s
% 22.63/4.66 % (21555)Instructions burned: 224 (million)
% 22.63/4.66 % (21555)------------------------------
% 22.63/4.66 % (21555)------------------------------
% 22.63/4.68 % (21558)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_21337 for (2971ds/8250Mi)
% 23.28/4.76 % (21557)Refutation not found, incomplete strategy
% 23.28/4.76 % (21557)------------------------------
% 23.28/4.76 % (21557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.28/4.76 % (21557)Termination reason: Refutation not found, incomplete strategy
% 23.28/4.76
% 23.28/4.76
% 23.28/4.76 % (21557)Memory used [KB]: 7931
% 23.28/4.76 % (21557)Time elapsed: 0.122 s
% 23.28/4.76 % (21557)Instructions burned: 247 (million)
% 23.28/4.76 % (21557)------------------------------
% 23.28/4.76 % (21557)------------------------------
% 23.28/4.78 % (21559)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_21337 for (2970ds/770Mi)
% 26.00/5.05 % (21556)Instruction limit reached!
% 26.00/5.05 % (21556)------------------------------
% 26.00/5.05 % (21556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.00/5.05 % (21556)Termination reason: Unknown
% 26.00/5.05 % (21556)Termination phase: Saturation
% 26.00/5.05
% 26.00/5.05 % (21556)Memory used [KB]: 10234
% 26.00/5.05 % (21556)Time elapsed: 0.485 s
% 26.00/5.05 % (21556)Instructions burned: 932 (million)
% 26.00/5.05 % (21556)------------------------------
% 26.00/5.05 % (21556)------------------------------
% 26.00/5.05 % (21532)Instruction limit reached!
% 26.00/5.05 % (21532)------------------------------
% 26.00/5.05 % (21532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.00/5.05 % (21532)Termination reason: Unknown
% 26.00/5.05 % (21532)Termination phase: Saturation
% 26.00/5.05
% 26.00/5.05 % (21532)Memory used [KB]: 10618
% 26.00/5.05 % (21532)Time elapsed: 1.841 s
% 26.00/5.05 % (21532)Instructions burned: 4438 (million)
% 26.00/5.05 % (21532)------------------------------
% 26.00/5.05 % (21532)------------------------------
% 26.00/5.07 % (21560)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_21337 for (2967ds/794Mi)
% 26.00/5.07 % (21561)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_21337 for (2967ds/464Mi)
% 26.59/5.18 % (21559)Instruction limit reached!
% 26.59/5.18 % (21559)------------------------------
% 26.59/5.18 % (21559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.59/5.18 % (21559)Termination reason: Unknown
% 26.59/5.18 % (21559)Termination phase: Saturation
% 26.59/5.18
% 26.59/5.18 % (21559)Memory used [KB]: 8827
% 26.59/5.18 % (21559)Time elapsed: 0.419 s
% 26.59/5.18 % (21559)Instructions burned: 770 (million)
% 26.59/5.18 % (21559)------------------------------
% 26.59/5.18 % (21559)------------------------------
% 26.59/5.19 % (21562)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_21337 for (2965ds/1376Mi)
% 27.34/5.31 % (21561)Instruction limit reached!
% 27.34/5.31 % (21561)------------------------------
% 27.34/5.31 % (21561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.34/5.31 % (21561)Termination reason: Unknown
% 27.34/5.31 % (21561)Termination phase: Saturation
% 27.34/5.31
% 27.34/5.31 % (21561)Memory used [KB]: 8059
% 27.34/5.31 % (21561)Time elapsed: 0.266 s
% 27.34/5.31 % (21561)Instructions burned: 464 (million)
% 27.34/5.31 % (21561)------------------------------
% 27.34/5.31 % (21561)------------------------------
% 27.34/5.33 % (21563)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_21337 for (2964ds/906Mi)
% 27.99/5.42 % (21553)Instruction limit reached!
% 27.99/5.42 % (21553)------------------------------
% 27.99/5.42 % (21553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.99/5.42 % (21553)Termination reason: Unknown
% 27.99/5.42 % (21553)Termination phase: Saturation
% 27.99/5.42
% 27.99/5.42 % (21553)Memory used [KB]: 10746
% 27.99/5.42 % (21553)Time elapsed: 0.941 s
% 27.99/5.42 % (21553)Instructions burned: 1828 (million)
% 27.99/5.42 % (21553)------------------------------
% 27.99/5.42 % (21553)------------------------------
% 27.99/5.44 % (21564)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_21337 for (2963ds/434Mi)
% 27.99/5.47 % (21560)Instruction limit reached!
% 27.99/5.47 % (21560)------------------------------
% 27.99/5.47 % (21560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.99/5.47 % (21560)Termination reason: Unknown
% 27.99/5.47 % (21560)Termination phase: Saturation
% 27.99/5.47
% 27.99/5.47 % (21560)Memory used [KB]: 5884
% 27.99/5.47 % (21560)Time elapsed: 0.429 s
% 27.99/5.47 % (21560)Instructions burned: 794 (million)
% 27.99/5.47 % (21560)------------------------------
% 27.99/5.47 % (21560)------------------------------
% 27.99/5.49 % (21565)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_21337 for (2962ds/865Mi)
% 28.74/5.52 % (21537)Instruction limit reached!
% 28.74/5.52 % (21537)------------------------------
% 28.74/5.52 % (21537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.74/5.52 % (21537)Termination reason: Unknown
% 28.74/5.52 % (21537)Termination phase: Saturation
% 28.74/5.52
% 28.74/5.52 % (21537)Memory used [KB]: 12665
% 28.74/5.52 % (21537)Time elapsed: 2.031 s
% 28.74/5.52 % (21537)Instructions burned: 4351 (million)
% 28.74/5.52 % (21537)------------------------------
% 28.74/5.52 % (21537)------------------------------
% 28.74/5.53 % (21566)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_21337 for (2962ds/593Mi)
% 28.97/5.66 % (21564)Instruction limit reached!
% 28.97/5.66 % (21564)------------------------------
% 28.97/5.66 % (21564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.97/5.66 % (21564)Termination reason: Unknown
% 28.97/5.66 % (21564)Termination phase: Saturation
% 28.97/5.66
% 28.97/5.66 % (21564)Memory used [KB]: 8059
% 28.97/5.66 % (21564)Time elapsed: 0.217 s
% 28.97/5.66 % (21564)Instructions burned: 434 (million)
% 28.97/5.66 % (21564)------------------------------
% 28.97/5.66 % (21564)------------------------------
% 28.97/5.67 % (21567)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_21337 for (2960ds/443Mi)
% 29.60/5.82 % (21563)Instruction limit reached!
% 29.60/5.82 % (21563)------------------------------
% 29.60/5.82 % (21563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.60/5.82 % (21563)Termination reason: Unknown
% 29.60/5.82 % (21563)Termination phase: Saturation
% 29.60/5.82
% 29.60/5.82 % (21563)Memory used [KB]: 12665
% 29.60/5.82 % (21563)Time elapsed: 0.492 s
% 29.60/5.82 % (21563)Instructions burned: 906 (million)
% 29.60/5.82 % (21563)------------------------------
% 29.60/5.82 % (21563)------------------------------
% 29.60/5.83 % (21566)Instruction limit reached!
% 29.60/5.83 % (21566)------------------------------
% 29.60/5.83 % (21566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.60/5.83 % (21566)Termination reason: Unknown
% 29.60/5.83 % (21566)Termination phase: Saturation
% 29.60/5.83
% 29.60/5.83 % (21566)Memory used [KB]: 9466
% 29.60/5.83 % (21566)Time elapsed: 0.298 s
% 29.60/5.83 % (21566)Instructions burned: 593 (million)
% 29.60/5.83 % (21566)------------------------------
% 29.60/5.83 % (21566)------------------------------
% 29.60/5.84 % (21568)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_21337 for (2959ds/594Mi)
% 29.60/5.85 % (21569)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_21337 for (2959ds/327Mi)
% 29.60/5.90 % (21562)Instruction limit reached!
% 29.60/5.90 % (21562)------------------------------
% 29.60/5.90 % (21562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.60/5.90 % (21562)Termination reason: Unknown
% 29.60/5.90 % (21562)Termination phase: Saturation
% 29.60/5.90
% 29.60/5.90 % (21562)Memory used [KB]: 13560
% 29.60/5.90 % (21562)Time elapsed: 0.729 s
% 29.60/5.90 % (21562)Instructions burned: 1377 (million)
% 29.60/5.90 % (21562)------------------------------
% 29.60/5.90 % (21562)------------------------------
% 30.63/5.90 % (21567)Instruction limit reached!
% 30.63/5.90 % (21567)------------------------------
% 30.63/5.90 % (21567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.63/5.90 % (21567)Termination reason: Unknown
% 30.63/5.90 % (21567)Termination phase: Saturation
% 30.63/5.90
% 30.63/5.90 % (21567)Memory used [KB]: 8187
% 30.63/5.90 % (21567)Time elapsed: 0.227 s
% 30.63/5.90 % (21567)Instructions burned: 443 (million)
% 30.63/5.90 % (21567)------------------------------
% 30.63/5.90 % (21567)------------------------------
% 30.63/5.91 % (21571)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_21337 for (2958ds/1762Mi)
% 30.63/5.91 % (21570)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_21337 for (2958ds/5411Mi)
% 30.63/5.92 % (21565)Instruction limit reached!
% 30.63/5.92 % (21565)------------------------------
% 30.63/5.92 % (21565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.63/5.92 % (21565)Termination reason: Unknown
% 30.63/5.92 % (21565)Termination phase: Saturation
% 30.63/5.92
% 30.63/5.92 % (21565)Memory used [KB]: 9210
% 30.63/5.92 % (21565)Time elapsed: 0.432 s
% 30.63/5.92 % (21565)Instructions burned: 865 (million)
% 30.63/5.92 % (21565)------------------------------
% 30.63/5.92 % (21565)------------------------------
% 30.63/5.93 % (21535)Instruction limit reached!
% 30.63/5.93 % (21535)------------------------------
% 30.63/5.93 % (21535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.63/5.93 % (21535)Termination reason: Unknown
% 30.63/5.93 % (21535)Termination phase: Saturation
% 30.63/5.93
% 30.63/5.93 % (21535)Memory used [KB]: 14200
% 30.63/5.93 % (21535)Time elapsed: 2.641 s
% 30.63/5.93 % (21535)Instructions burned: 5205 (million)
% 30.63/5.93 % (21535)------------------------------
% 30.63/5.93 % (21535)------------------------------
% 30.63/5.94 % (21572)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_21337 for (2958ds/96Mi)
% 30.63/5.95 % (21573)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_21337 for (2958ds/503Mi)
% 30.63/5.98 % (21572)Instruction limit reached!
% 30.63/5.98 % (21572)------------------------------
% 30.63/5.98 % (21572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.63/5.98 % (21572)Termination reason: Unknown
% 30.63/5.98 % (21572)Termination phase: Property scanning
% 30.63/5.98
% 30.63/5.98 % (21572)Memory used [KB]: 2814
% 30.63/5.98 % (21572)Time elapsed: 0.048 s
% 30.63/5.98 % (21572)Instructions burned: 97 (million)
% 30.63/5.98 % (21572)------------------------------
% 30.63/5.98 % (21572)------------------------------
% 30.63/6.00 % (21574)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_21337 for (2957ds/90Mi)
% 30.63/6.02 % (21569)Instruction limit reached!
% 30.63/6.02 % (21569)------------------------------
% 30.63/6.02 % (21569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.63/6.02 % (21569)Termination reason: Unknown
% 30.63/6.02 % (21569)Termination phase: Saturation
% 30.63/6.02
% 30.63/6.02 % (21569)Memory used [KB]: 8059
% 30.63/6.02 % (21569)Time elapsed: 0.173 s
% 30.63/6.02 % (21569)Instructions burned: 328 (million)
% 30.63/6.02 % (21569)------------------------------
% 30.63/6.02 % (21569)------------------------------
% 33.03/6.04 % (21575)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_21337 for (2957ds/593Mi)
% 33.03/6.05 % (21574)Instruction limit reached!
% 33.03/6.05 % (21574)------------------------------
% 33.03/6.05 % (21574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.03/6.05 % (21574)Termination reason: Unknown
% 33.03/6.05 % (21574)Termination phase: Property scanning
% 33.03/6.05
% 33.03/6.05 % (21574)Memory used [KB]: 2558
% 33.03/6.05 % (21574)Time elapsed: 0.047 s
% 33.03/6.05 % (21574)Instructions burned: 92 (million)
% 33.03/6.05 % (21574)------------------------------
% 33.03/6.05 % (21574)------------------------------
% 33.03/6.06 % (21576)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_21337 for (2957ds/1512Mi)
% 33.56/6.14 % (21568)Instruction limit reached!
% 33.56/6.14 % (21568)------------------------------
% 33.56/6.14 % (21568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.56/6.14 % (21568)Termination reason: Unknown
% 33.56/6.14 % (21568)Termination phase: Saturation
% 33.56/6.14
% 33.56/6.14 % (21568)Memory used [KB]: 8443
% 33.56/6.14 % (21568)Time elapsed: 0.301 s
% 33.56/6.14 % (21568)Instructions burned: 594 (million)
% 33.56/6.14 % (21568)------------------------------
% 33.56/6.14 % (21568)------------------------------
% 33.56/6.15 % (21577)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_21337 for (2956ds/569Mi)
% 33.86/6.20 % (21573)Instruction limit reached!
% 33.86/6.20 % (21573)------------------------------
% 33.86/6.20 % (21573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.86/6.20 % (21573)Termination reason: Unknown
% 33.86/6.20 % (21573)Termination phase: Saturation
% 33.86/6.20
% 33.86/6.20 % (21573)Memory used [KB]: 8059
% 33.86/6.20 % (21573)Time elapsed: 0.251 s
% 33.86/6.20 % (21573)Instructions burned: 504 (million)
% 33.86/6.20 % (21573)------------------------------
% 33.86/6.20 % (21573)------------------------------
% 33.86/6.21 % (21578)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_21337 for (2955ds/501Mi)
% 34.17/6.33 % (21575)Instruction limit reached!
% 34.17/6.33 % (21575)------------------------------
% 34.17/6.33 % (21575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.17/6.33 % (21575)Termination reason: Unknown
% 34.17/6.33 % (21575)Termination phase: Saturation
% 34.17/6.33
% 34.17/6.33 % (21575)Memory used [KB]: 8571
% 34.17/6.33 % (21575)Time elapsed: 0.295 s
% 34.17/6.33 % (21575)Instructions burned: 594 (million)
% 34.17/6.33 % (21575)------------------------------
% 34.17/6.33 % (21575)------------------------------
% 34.17/6.35 % (21579)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_21337 for (2954ds/562Mi)
% 34.78/6.43 % (21577)Instruction limit reached!
% 34.78/6.43 % (21577)------------------------------
% 34.78/6.43 % (21577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.78/6.43 % (21577)Termination reason: Unknown
% 34.78/6.43 % (21577)Termination phase: Saturation
% 34.78/6.43
% 34.78/6.43 % (21577)Memory used [KB]: 8827
% 34.78/6.43 % (21577)Time elapsed: 0.281 s
% 34.78/6.43 % (21577)Instructions burned: 570 (million)
% 34.78/6.43 % (21577)------------------------------
% 34.78/6.43 % (21577)------------------------------
% 34.78/6.44 % (21578)Instruction limit reached!
% 34.78/6.44 % (21578)------------------------------
% 34.78/6.44 % (21578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.78/6.44 % (21578)Termination reason: Unknown
% 34.78/6.44 % (21578)Termination phase: Saturation
% 34.78/6.44
% 34.78/6.44 % (21578)Memory used [KB]: 9594
% 34.78/6.44 % (21578)Time elapsed: 0.229 s
% 34.78/6.44 % (21578)Instructions burned: 502 (million)
% 34.78/6.44 % (21578)------------------------------
% 34.78/6.44 % (21578)------------------------------
% 34.78/6.45 % (21580)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_21337 for (2953ds/406Mi)
% 34.78/6.45 % (21581)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_21337 for (2953ds/582Mi)
% 35.62/6.58 % (21579)Instruction limit reached!
% 35.62/6.58 % (21579)------------------------------
% 35.62/6.58 % (21579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.62/6.58 % (21579)Termination reason: Unknown
% 35.62/6.58 % (21579)Termination phase: Saturation
% 35.62/6.58
% 35.62/6.58 % (21579)Memory used [KB]: 8827
% 35.62/6.58 % (21579)Time elapsed: 0.229 s
% 35.62/6.58 % (21579)Instructions burned: 562 (million)
% 35.62/6.58 % (21579)------------------------------
% 35.62/6.58 % (21579)------------------------------
% 35.62/6.59 % (21582)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_21337 for (2951ds/456Mi)
% 36.16/6.60 % (21580)Instruction limit reached!
% 36.16/6.60 % (21580)------------------------------
% 36.16/6.60 % (21580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.16/6.60 % (21580)Termination reason: Unknown
% 36.16/6.60 % (21580)Termination phase: Saturation
% 36.16/6.60
% 36.16/6.60 % (21580)Memory used [KB]: 8187
% 36.16/6.60 % (21580)Time elapsed: 0.153 s
% 36.16/6.60 % (21580)Instructions burned: 408 (million)
% 36.16/6.60 % (21580)------------------------------
% 36.16/6.60 % (21580)------------------------------
% 36.16/6.61 % (21583)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_21337 for (2951ds/393Mi)
% 36.16/6.64 % (21581)Instruction limit reached!
% 36.16/6.64 % (21581)------------------------------
% 36.16/6.64 % (21581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.16/6.64 % (21581)Termination reason: Unknown
% 36.16/6.64 % (21581)Termination phase: Saturation
% 36.16/6.64
% 36.16/6.64 % (21581)Memory used [KB]: 8315
% 36.16/6.64 % (21581)Time elapsed: 0.191 s
% 36.16/6.64 % (21581)Instructions burned: 584 (million)
% 36.16/6.64 % (21581)------------------------------
% 36.16/6.64 % (21581)------------------------------
% 36.16/6.65 % (21584)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_21337 for (2951ds/1335Mi)
% 36.16/6.69 % (21571)Instruction limit reached!
% 36.16/6.69 % (21571)------------------------------
% 36.16/6.69 % (21571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.16/6.69 % (21571)Termination reason: Unknown
% 36.16/6.69 % (21571)Termination phase: Saturation
% 36.16/6.69
% 36.16/6.69 % (21571)Memory used [KB]: 10362
% 36.16/6.69 % (21571)Time elapsed: 0.780 s
% 36.16/6.69 % (21571)Instructions burned: 1765 (million)
% 36.16/6.69 % (21571)------------------------------
% 36.16/6.69 % (21571)------------------------------
% 36.83/6.70 % (21576)Instruction limit reached!
% 36.83/6.70 % (21576)------------------------------
% 36.83/6.70 % (21576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.83/6.70 % (21576)Termination reason: Unknown
% 36.83/6.70 % (21576)Termination phase: Saturation
% 36.83/6.70
% 36.83/6.70 % (21576)Memory used [KB]: 8827
% 36.83/6.70 % (21576)Time elapsed: 0.637 s
% 36.83/6.70 % (21576)Instructions burned: 1512 (million)
% 36.83/6.70 % (21576)------------------------------
% 36.83/6.70 % (21576)------------------------------
% 36.83/6.70 % (21585)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_21337 for (2950ds/3373Mi)
% 36.83/6.71 % (21586)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_21337 for (2950ds/474Mi)
% 36.83/6.72 % (21582)Instruction limit reached!
% 36.83/6.72 % (21582)------------------------------
% 36.83/6.72 % (21582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.83/6.72 % (21582)Termination reason: Unknown
% 36.83/6.72 % (21582)Termination phase: Saturation
% 36.83/6.72
% 36.83/6.73 % (21582)Memory used [KB]: 8443
% 36.83/6.73 % (21582)Time elapsed: 0.141 s
% 36.83/6.73 % (21582)Instructions burned: 458 (million)
% 36.83/6.73 % (21582)------------------------------
% 36.83/6.73 % (21582)------------------------------
% 36.83/6.73 % (21583)Instruction limit reached!
% 36.83/6.73 % (21583)------------------------------
% 36.83/6.73 % (21583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.83/6.73 % (21583)Termination reason: Unknown
% 36.83/6.73 % (21583)Termination phase: Saturation
% 36.83/6.73
% 36.83/6.73 % (21583)Memory used [KB]: 7931
% 36.83/6.73 % (21583)Time elapsed: 0.115 s
% 36.83/6.73 % (21583)Instructions burned: 393 (million)
% 36.83/6.73 % (21583)------------------------------
% 36.83/6.73 % (21583)------------------------------
% 36.83/6.73 % (21587)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_21337 for (2950ds/157Mi)
% 36.83/6.73 % (21588)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_21337 for (2950ds/590Mi)
% 36.83/6.78 % (21587)Instruction limit reached!
% 36.83/6.78 % (21587)------------------------------
% 36.83/6.78 % (21587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.83/6.78 % (21587)Termination reason: Unknown
% 36.83/6.78 % (21587)Termination phase: Property scanning
% 36.83/6.78
% 36.83/6.78 % (21587)Memory used [KB]: 2814
% 36.83/6.78 % (21587)Time elapsed: 0.044 s
% 36.83/6.78 % (21587)Instructions burned: 157 (million)
% 36.83/6.78 % (21587)------------------------------
% 36.83/6.78 % (21587)------------------------------
% 36.83/6.79 % (21589)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_21337 for (2949ds/104Mi)
% 38.01/6.82 % (21589)Instruction limit reached!
% 38.01/6.82 % (21589)------------------------------
% 38.01/6.82 % (21589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.01/6.82 % (21589)Termination reason: Unknown
% 38.01/6.82 % (21589)Termination phase: Property scanning
% 38.01/6.82
% 38.01/6.82 % (21589)Memory used [KB]: 2558
% 38.01/6.82 % (21589)Time elapsed: 0.034 s
% 38.01/6.82 % (21589)Instructions burned: 107 (million)
% 38.01/6.82 % (21589)------------------------------
% 38.01/6.82 % (21589)------------------------------
% 38.01/6.83 % (21593)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_21337 for (2949ds/414Mi)
% 38.01/6.85 % (21586)Instruction limit reached!
% 38.01/6.85 % (21586)------------------------------
% 38.01/6.85 % (21586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.01/6.85 % (21586)Termination reason: Unknown
% 38.01/6.85 % (21586)Termination phase: Saturation
% 38.01/6.85
% 38.01/6.85 % (21586)Memory used [KB]: 8059
% 38.01/6.85 % (21586)Time elapsed: 0.168 s
% 38.01/6.85 % (21586)Instructions burned: 476 (million)
% 38.01/6.85 % (21586)------------------------------
% 38.01/6.85 % (21586)------------------------------
% 38.01/6.86 % (21610)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_21337 for (2948ds/715Mi)
% 38.42/6.90 % (21588)Instruction limit reached!
% 38.42/6.90 % (21588)------------------------------
% 38.42/6.90 % (21588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.42/6.90 % (21588)Termination reason: Unknown
% 38.42/6.90 % (21588)Termination phase: Saturation
% 38.42/6.90
% 38.42/6.90 % (21588)Memory used [KB]: 7675
% 38.42/6.90 % (21588)Time elapsed: 0.168 s
% 38.42/6.90 % (21588)Instructions burned: 592 (million)
% 38.42/6.90 % (21588)------------------------------
% 38.42/6.90 % (21588)------------------------------
% 38.42/6.91 % (21633)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_21337 for (2948ds/961Mi)
% 38.42/6.95 % (21593)Instruction limit reached!
% 38.42/6.95 % (21593)------------------------------
% 38.42/6.95 % (21593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.42/6.95 % (21593)Termination reason: Unknown
% 38.42/6.95 % (21593)Termination phase: Saturation
% 38.42/6.95
% 38.42/6.95 % (21593)Memory used [KB]: 8571
% 38.42/6.95 % (21593)Time elapsed: 0.126 s
% 38.42/6.95 % (21593)Instructions burned: 415 (million)
% 38.42/6.95 % (21593)------------------------------
% 38.42/6.95 % (21593)------------------------------
% 38.42/6.96 % (21652)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_21337 for (2947ds/1213Mi)
% 39.92/7.09 % (21610)Instruction limit reached!
% 39.92/7.09 % (21610)------------------------------
% 39.92/7.09 % (21610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.92/7.09 % (21610)Termination reason: Unknown
% 39.92/7.09 % (21610)Termination phase: Saturation
% 39.92/7.09
% 39.92/7.09 % (21610)Memory used [KB]: 4861
% 39.92/7.09 % (21610)Time elapsed: 0.228 s
% 39.92/7.09 % (21610)Instructions burned: 715 (million)
% 39.92/7.09 % (21610)------------------------------
% 39.92/7.09 % (21610)------------------------------
% 39.92/7.10 % (21584)Instruction limit reached!
% 39.92/7.10 % (21584)------------------------------
% 39.92/7.10 % (21584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.92/7.10 % (21584)Termination reason: Unknown
% 39.92/7.10 % (21584)Termination phase: Saturation
% 39.92/7.10
% 39.92/7.10 % (21584)Memory used [KB]: 9850
% 39.92/7.10 % (21584)Time elapsed: 0.461 s
% 39.92/7.10 % (21584)Instructions burned: 1336 (million)
% 39.92/7.10 % (21584)------------------------------
% 39.92/7.10 % (21584)------------------------------
% 39.92/7.10 % (21720)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_21337 for (2946ds/1979Mi)
% 39.92/7.11 % (21724)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_21337 for (2946ds/481Mi)
% 41.00/7.22 % (21633)Instruction limit reached!
% 41.00/7.22 % (21633)------------------------------
% 41.00/7.22 % (21633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.00/7.22 % (21633)Termination reason: Unknown
% 41.00/7.22 % (21633)Termination phase: Saturation
% 41.00/7.22
% 41.00/7.22 % (21633)Memory used [KB]: 8955
% 41.00/7.22 % (21633)Time elapsed: 0.311 s
% 41.00/7.22 % (21633)Instructions burned: 961 (million)
% 41.00/7.22 % (21633)------------------------------
% 41.00/7.22 % (21633)------------------------------
% 41.00/7.23 % (21773)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_21337 for (2945ds/783Mi)
% 41.00/7.26 % (21724)Instruction limit reached!
% 41.00/7.26 % (21724)------------------------------
% 41.00/7.26 % (21724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.00/7.26 % (21724)Termination reason: Unknown
% 41.00/7.26 % (21724)Termination phase: Saturation
% 41.00/7.26
% 41.00/7.26 % (21724)Memory used [KB]: 7931
% 41.00/7.26 % (21724)Time elapsed: 0.149 s
% 41.00/7.26 % (21724)Instructions burned: 482 (million)
% 41.00/7.26 % (21724)------------------------------
% 41.00/7.26 % (21724)------------------------------
% 41.00/7.27 % (21785)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_21337 for (2944ds/432Mi)
% 41.60/7.35 % (21652)Instruction limit reached!
% 41.60/7.35 % (21652)------------------------------
% 41.60/7.35 % (21652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.60/7.35 % (21652)Termination reason: Unknown
% 41.60/7.35 % (21652)Termination phase: Saturation
% 41.60/7.35
% 41.60/7.35 % (21652)Memory used [KB]: 9722
% 41.60/7.35 % (21652)Time elapsed: 0.387 s
% 41.60/7.35 % (21652)Instructions burned: 1213 (million)
% 41.60/7.35 % (21652)------------------------------
% 41.60/7.35 % (21652)------------------------------
% 41.60/7.36 % (21828)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_21337 for (2944ds/1670Mi)
% 41.96/7.41 % (21785)Instruction limit reached!
% 41.96/7.41 % (21785)------------------------------
% 41.96/7.41 % (21785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.96/7.41 % (21785)Termination reason: Unknown
% 41.96/7.41 % (21785)Termination phase: Saturation
% 41.96/7.41
% 41.96/7.41 % (21785)Memory used [KB]: 8699
% 41.96/7.41 % (21785)Time elapsed: 0.148 s
% 41.96/7.41 % (21785)Instructions burned: 432 (million)
% 41.96/7.41 % (21785)------------------------------
% 41.96/7.41 % (21785)------------------------------
% 41.96/7.42 % (21829)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_21337 for (2943ds/90Mi)
% 41.96/7.45 % (21829)Instruction limit reached!
% 41.96/7.45 % (21829)------------------------------
% 41.96/7.45 % (21829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.96/7.45 % (21829)Termination reason: Unknown
% 41.96/7.45 % (21829)Termination phase: Property scanning
% 41.96/7.45
% 41.96/7.45 % (21829)Memory used [KB]: 2558
% 41.96/7.45 % (21829)Time elapsed: 0.030 s
% 41.96/7.45 % (21829)Instructions burned: 93 (million)
% 41.96/7.45 % (21829)------------------------------
% 41.96/7.45 % (21829)------------------------------
% 41.96/7.46 % (21830)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_21337 for (2943ds/346Mi)
% 41.96/7.48 % (21773)Instruction limit reached!
% 41.96/7.48 % (21773)------------------------------
% 41.96/7.48 % (21773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.96/7.48 % (21773)Termination reason: Unknown
% 41.96/7.48 % (21773)Termination phase: Saturation
% 41.96/7.48
% 41.96/7.48 % (21773)Memory used [KB]: 9210
% 41.96/7.48 % (21773)Time elapsed: 0.247 s
% 41.96/7.48 % (21773)Instructions burned: 784 (million)
% 41.96/7.48 % (21773)------------------------------
% 41.96/7.48 % (21773)------------------------------
% 41.96/7.49 % (21831)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_21337 for (2942ds/401Mi)
% 42.72/7.57 % (21830)Instruction limit reached!
% 42.72/7.57 % (21830)------------------------------
% 42.72/7.57 % (21830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.72/7.57 % (21830)Termination reason: Unknown
% 42.72/7.57 % (21830)Termination phase: Saturation
% 42.72/7.57
% 42.72/7.57 % (21830)Memory used [KB]: 7803
% 42.72/7.57 % (21830)Time elapsed: 0.106 s
% 42.72/7.57 % (21830)Instructions burned: 348 (million)
% 42.72/7.57 % (21830)------------------------------
% 42.72/7.57 % (21830)------------------------------
% 42.72/7.58 % (21832)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_21337 for (2941ds/6454Mi)
% 43.14/7.60 % (21831)Instruction limit reached!
% 43.14/7.60 % (21831)------------------------------
% 43.14/7.60 % (21831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.14/7.60 % (21831)Termination reason: Unknown
% 43.14/7.60 % (21831)Termination phase: Saturation
% 43.14/7.60
% 43.14/7.60 % (21831)Memory used [KB]: 9083
% 43.14/7.60 % (21831)Time elapsed: 0.117 s
% 43.14/7.60 % (21831)Instructions burned: 401 (million)
% 43.14/7.60 % (21831)------------------------------
% 43.14/7.60 % (21831)------------------------------
% 43.14/7.61 % (21833)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_21337 for (2941ds/283Mi)
% 43.14/7.64 % (21585)Instruction limit reached!
% 43.14/7.64 % (21585)------------------------------
% 43.14/7.64 % (21585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.14/7.64 % (21585)Termination reason: Unknown
% 43.14/7.64 % (21585)Termination phase: Saturation
% 43.14/7.64
% 43.14/7.64 % (21585)Memory used [KB]: 11513
% 43.14/7.64 % (21585)Time elapsed: 0.957 s
% 43.14/7.64 % (21585)Instructions burned: 3375 (million)
% 43.14/7.64 % (21585)------------------------------
% 43.14/7.64 % (21585)------------------------------
% 43.14/7.65 % (21834)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_21337 for (2941ds/865Mi)
% 43.52/7.70 % (21833)Instruction limit reached!
% 43.52/7.70 % (21833)------------------------------
% 43.52/7.70 % (21833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.52/7.70 % (21833)Termination reason: Unknown
% 43.52/7.70 % (21833)Termination phase: Saturation
% 43.52/7.70
% 43.52/7.70 % (21833)Memory used [KB]: 8059
% 43.52/7.70 % (21833)Time elapsed: 0.089 s
% 43.52/7.70 % (21833)Instructions burned: 283 (million)
% 43.52/7.70 % (21833)------------------------------
% 43.52/7.70 % (21833)------------------------------
% 43.52/7.71 % (21835)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_21337 for (2940ds/4528Mi)
% 43.52/7.73 % (21720)Instruction limit reached!
% 43.52/7.73 % (21720)------------------------------
% 43.52/7.73 % (21720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.52/7.73 % (21720)Termination reason: Unknown
% 43.52/7.73 % (21720)Termination phase: Saturation
% 43.52/7.73
% 43.52/7.73 % (21720)Memory used [KB]: 9850
% 43.52/7.73 % (21720)Time elapsed: 0.626 s
% 43.52/7.73 % (21720)Instructions burned: 1980 (million)
% 43.52/7.73 % (21720)------------------------------
% 43.52/7.73 % (21720)------------------------------
% 43.52/7.74 % (21836)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_21337 for (2940ds/1001Mi)
% 44.46/7.84 % (21570)Instruction limit reached!
% 44.46/7.84 % (21570)------------------------------
% 44.46/7.84 % (21570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.46/7.84 % (21570)Termination reason: Unknown
% 44.46/7.84 % (21570)Termination phase: Saturation
% 44.46/7.84
% 44.46/7.84 % (21570)Memory used [KB]: 11257
% 44.46/7.84 % (21570)Time elapsed: 1.924 s
% 44.46/7.84 % (21570)Instructions burned: 5413 (million)
% 44.46/7.84 % (21570)------------------------------
% 44.46/7.84 % (21570)------------------------------
% 44.46/7.85 % (21837)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_21337 for (2939ds/102Mi)
% 44.46/7.87 % (21828)Instruction limit reached!
% 44.46/7.87 % (21828)------------------------------
% 44.46/7.87 % (21828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.46/7.87 % (21828)Termination reason: Unknown
% 44.46/7.87 % (21828)Termination phase: Saturation
% 44.46/7.87
% 44.46/7.87 % (21828)Memory used [KB]: 10362
% 44.46/7.87 % (21828)Time elapsed: 0.509 s
% 44.46/7.87 % (21828)Instructions burned: 1670 (million)
% 44.46/7.87 % (21828)------------------------------
% 44.46/7.87 % (21828)------------------------------
% 44.46/7.88 % (21837)Instruction limit reached!
% 44.46/7.88 % (21837)------------------------------
% 44.46/7.88 % (21837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.46/7.88 % (21837)Termination reason: Unknown
% 44.46/7.88 % (21837)Termination phase: Property scanning
% 44.46/7.88
% 44.46/7.88 % (21837)Memory used [KB]: 2814
% 44.46/7.88 % (21837)Time elapsed: 0.031 s
% 44.46/7.88 % (21837)Instructions burned: 105 (million)
% 44.46/7.88 % (21837)------------------------------
% 44.46/7.88 % (21837)------------------------------
% 44.46/7.88 % (21838)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_21337 for (2938ds/952Mi)
% 44.46/7.88 % (21558)Instruction limit reached!
% 44.46/7.88 % (21558)------------------------------
% 44.46/7.88 % (21558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.46/7.88 % (21558)Termination reason: Unknown
% 44.46/7.88 % (21558)Termination phase: Saturation
% 44.46/7.88
% 44.46/7.88 % (21558)Memory used [KB]: 14583
% 44.46/7.88 % (21558)Time elapsed: 3.230 s
% 44.46/7.88 % (21558)Instructions burned: 8250 (million)
% 44.46/7.88 % (21558)------------------------------
% 44.46/7.88 % (21558)------------------------------
% 44.46/7.89 % (21839)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_21337 for (2938ds/578Mi)
% 44.46/7.89 % (21840)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_21337 for (2938ds/643Mi)
% 45.16/7.92 % (21834)Instruction limit reached!
% 45.16/7.92 % (21834)------------------------------
% 45.16/7.92 % (21834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.16/7.92 % (21834)Termination reason: Unknown
% 45.16/7.92 % (21834)Termination phase: Saturation
% 45.16/7.92
% 45.16/7.92 % (21834)Memory used [KB]: 9338
% 45.16/7.92 % (21834)Time elapsed: 0.273 s
% 45.16/7.92 % (21834)Instructions burned: 868 (million)
% 45.16/7.92 % (21834)------------------------------
% 45.16/7.92 % (21834)------------------------------
% 45.16/7.93 % (21841)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_21337 for (2938ds/865Mi)
% 46.91/8.05 % (21836)Instruction limit reached!
% 46.91/8.05 % (21836)------------------------------
% 46.91/8.05 % (21836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.91/8.05 % (21836)Termination reason: Unknown
% 46.91/8.05 % (21836)Termination phase: Saturation
% 46.91/8.05
% 46.91/8.05 % (21836)Memory used [KB]: 11641
% 46.91/8.05 % (21836)Time elapsed: 0.320 s
% 46.91/8.05 % (21836)Instructions burned: 1001 (million)
% 46.91/8.05 % (21836)------------------------------
% 46.91/8.05 % (21836)------------------------------
% 46.91/8.06 % (21839)Instruction limit reached!
% 46.91/8.06 % (21839)------------------------------
% 46.91/8.06 % (21839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.91/8.06 % (21839)Termination reason: Unknown
% 46.91/8.06 % (21839)Termination phase: Saturation
% 46.91/8.06
% 46.91/8.06 % (21839)Memory used [KB]: 9210
% 46.91/8.06 % (21839)Time elapsed: 0.179 s
% 46.91/8.06 % (21839)Instructions burned: 578 (million)
% 46.91/8.06 % (21839)------------------------------
% 46.91/8.06 % (21839)------------------------------
% 46.91/8.06 % (21842)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_21337 for (2937ds/1174Mi)
% 46.91/8.07 % (21843)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_21337 for (2937ds/644Mi)
% 46.91/8.09 % (21840)Instruction limit reached!
% 46.91/8.09 % (21840)------------------------------
% 46.91/8.09 % (21840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.91/8.09 % (21840)Termination reason: Unknown
% 46.91/8.09 % (21840)Termination phase: Saturation
% 46.91/8.09
% 46.91/8.09 % (21840)Memory used [KB]: 9466
% 46.91/8.09 % (21840)Time elapsed: 0.201 s
% 46.91/8.09 % (21840)Instructions burned: 645 (million)
% 46.91/8.09 % (21840)------------------------------
% 46.91/8.09 % (21840)------------------------------
% 46.91/8.10 % (21844)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_21337 for (2936ds/1201Mi)
% 47.53/8.18 % (21838)Instruction limit reached!
% 47.53/8.18 % (21838)------------------------------
% 47.53/8.18 % (21838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.53/8.18 % (21838)Termination reason: Unknown
% 47.53/8.18 % (21838)Termination phase: Saturation
% 47.53/8.18
% 47.53/8.18 % (21838)Memory used [KB]: 8955
% 47.53/8.18 % (21838)Time elapsed: 0.305 s
% 47.53/8.18 % (21838)Instructions burned: 954 (million)
% 47.53/8.18 % (21838)------------------------------
% 47.53/8.18 % (21838)------------------------------
% 47.53/8.19 % (21845)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_21337 for (2935ds/1046Mi)
% 47.86/8.20 % (21841)Instruction limit reached!
% 47.86/8.20 % (21841)------------------------------
% 47.86/8.20 % (21841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.86/8.20 % (21841)Termination reason: Unknown
% 47.86/8.20 % (21841)Termination phase: Saturation
% 47.86/8.20
% 47.86/8.20 % (21841)Memory used [KB]: 9850
% 47.86/8.20 % (21841)Time elapsed: 0.277 s
% 47.86/8.20 % (21841)Instructions burned: 867 (million)
% 47.86/8.20 % (21841)------------------------------
% 47.86/8.20 % (21841)------------------------------
% 47.86/8.21 % (21846)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_21337 for (2935ds/222Mi)
% 47.86/8.27 % (21843)Instruction limit reached!
% 47.86/8.27 % (21843)------------------------------
% 47.86/8.27 % (21843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.86/8.27 % (21843)Termination reason: Unknown
% 47.86/8.27 % (21843)Termination phase: Saturation
% 47.86/8.27
% 47.86/8.27 % (21843)Memory used [KB]: 9210
% 47.86/8.27 % (21843)Time elapsed: 0.224 s
% 47.86/8.27 % (21843)Instructions burned: 645 (million)
% 47.86/8.27 % (21843)------------------------------
% 47.86/8.27 % (21843)------------------------------
% 47.86/8.28 % (21846)Instruction limit reached!
% 47.86/8.28 % (21846)------------------------------
% 47.86/8.28 % (21846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.86/8.28 % (21846)Termination reason: Unknown
% 47.86/8.28 % (21846)Termination phase: Saturation
% 47.86/8.28
% 47.86/8.28 % (21846)Memory used [KB]: 7547
% 47.86/8.28 % (21846)Time elapsed: 0.063 s
% 47.86/8.28 % (21846)Instructions burned: 224 (million)
% 47.86/8.28 % (21846)------------------------------
% 47.86/8.28 % (21846)------------------------------
% 47.86/8.28 % (21847)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_21337 for (2934ds/68Mi)
% 47.86/8.29 % (21848)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_21337 for (2934ds/454Mi)
% 48.36/8.31 % (21847)Instruction limit reached!
% 48.36/8.31 % (21847)------------------------------
% 48.36/8.31 % (21847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.36/8.31 % (21847)Termination reason: Unknown
% 48.36/8.31 % (21847)Termination phase: Property scanning
% 48.36/8.31
% 48.36/8.31 % (21847)Memory used [KB]: 2302
% 48.36/8.31 % (21847)Time elapsed: 0.023 s
% 48.36/8.31 % (21847)Instructions burned: 71 (million)
% 48.36/8.31 % (21847)------------------------------
% 48.36/8.31 % (21847)------------------------------
% 48.36/8.32 % (21849)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_21337 for (2934ds/360Mi)
% 48.59/8.42 % (21849)Instruction limit reached!
% 48.59/8.42 % (21849)------------------------------
% 48.59/8.42 % (21849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.59/8.42 % (21849)Termination reason: Unknown
% 48.59/8.42 % (21849)Termination phase: Saturation
% 48.59/8.42
% 48.59/8.42 % (21849)Memory used [KB]: 8827
% 48.59/8.42 % (21849)Time elapsed: 0.103 s
% 48.59/8.42 % (21849)Instructions burned: 360 (million)
% 48.59/8.42 % (21849)------------------------------
% 48.59/8.42 % (21849)------------------------------
% 48.59/8.42 % (21848)Instruction limit reached!
% 48.59/8.42 % (21848)------------------------------
% 48.59/8.42 % (21848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.59/8.42 % (21848)Termination reason: Unknown
% 48.59/8.42 % (21848)Termination phase: Saturation
% 48.59/8.42
% 48.59/8.42 % (21848)Memory used [KB]: 13560
% 48.59/8.42 % (21848)Time elapsed: 0.135 s
% 48.59/8.42 % (21848)Instructions burned: 456 (million)
% 48.59/8.42 % (21848)------------------------------
% 48.59/8.42 % (21848)------------------------------
% 48.59/8.43 % (21842)Instruction limit reached!
% 48.59/8.43 % (21842)------------------------------
% 48.59/8.43 % (21842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.59/8.43 % (21842)Termination reason: Unknown
% 48.59/8.43 % (21842)Termination phase: Saturation
% 48.59/8.43
% 48.59/8.43 % (21842)Memory used [KB]: 9722
% 48.59/8.43 % (21842)Time elapsed: 0.384 s
% 48.59/8.43 % (21842)Instructions burned: 1175 (million)
% 48.59/8.43 % (21842)------------------------------
% 48.59/8.43 % (21842)------------------------------
% 48.59/8.43 % (21850)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_21337 for (2933ds/157Mi)
% 48.59/8.43 % (21851)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_21337 for (2933ds/5061Mi)
% 48.59/8.43 % (21844)Instruction limit reached!
% 48.59/8.43 % (21844)------------------------------
% 48.59/8.43 % (21844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.59/8.43 % (21844)Termination reason: Unknown
% 48.59/8.43 % (21844)Termination phase: Saturation
% 48.59/8.43
% 48.59/8.43 % (21844)Memory used [KB]: 8059
% 48.59/8.43 % (21844)Time elapsed: 0.330 s
% 48.59/8.43 % (21844)Instructions burned: 1202 (million)
% 48.59/8.43 % (21844)------------------------------
% 48.59/8.43 % (21844)------------------------------
% 48.59/8.43 % (21852)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_21337 for (2933ds/2401Mi)
% 48.59/8.44 % (21853)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_21337 for (2933ds/5798Mi)
% 48.59/8.47 % (21850)Instruction limit reached!
% 48.59/8.47 % (21850)------------------------------
% 48.59/8.47 % (21850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.59/8.47 % (21850)Termination reason: Unknown
% 48.59/8.47 % (21850)Termination phase: Property scanning
% 48.59/8.47
% 48.59/8.47 % (21850)Memory used [KB]: 2814
% 48.59/8.47 % (21850)Time elapsed: 0.045 s
% 48.59/8.47 % (21850)Instructions burned: 158 (million)
% 48.59/8.47 % (21850)------------------------------
% 48.59/8.47 % (21850)------------------------------
% 48.59/8.48 % (21854)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_21337 for (2932ds/346Mi)
% 49.81/8.51 % (21845)Instruction limit reached!
% 49.81/8.51 % (21845)------------------------------
% 49.81/8.51 % (21845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.81/8.51 % (21845)Termination reason: Unknown
% 49.81/8.51 % (21845)Termination phase: Saturation
% 49.81/8.51
% 49.81/8.51 % (21845)Memory used [KB]: 9594
% 49.81/8.51 % (21845)Time elapsed: 0.317 s
% 49.81/8.51 % (21845)Instructions burned: 1046 (million)
% 49.81/8.51 % (21845)------------------------------
% 49.81/8.51 % (21845)------------------------------
% 49.81/8.52 % (21855)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_21337 for (2932ds/1321Mi)
% 49.81/8.59 % (21854)Instruction limit reached!
% 49.81/8.59 % (21854)------------------------------
% 49.81/8.59 % (21854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.81/8.59 % (21854)Termination reason: Unknown
% 49.81/8.59 % (21854)Termination phase: Saturation
% 49.81/8.59
% 49.81/8.59 % (21854)Memory used [KB]: 7803
% 49.81/8.59 % (21854)Time elapsed: 0.106 s
% 49.81/8.59 % (21854)Instructions burned: 348 (million)
% 49.81/8.59 % (21854)------------------------------
% 49.81/8.59 % (21854)------------------------------
% 49.81/8.60 % (21856)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_21337 for (2931ds/1312Mi)
% 50.86/8.83 % (21835)Refutation not found, non-redundant clauses discarded% (21835)------------------------------
% 50.86/8.83 % (21835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.86/8.83 % (21835)Termination reason: Refutation not found, non-redundant clauses discarded
% 50.86/8.83
% 50.86/8.83 % (21835)Memory used [KB]: 5117
% 50.86/8.83 % (21835)Time elapsed: 1.119 s
% 50.86/8.83 % (21835)Instructions burned: 4451 (million)
% 50.86/8.83 % (21835)------------------------------
% 50.86/8.83 % (21835)------------------------------
% 50.86/8.84 % (21857)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_21337 for (2929ds/672Mi)
% 51.00/8.91 % (21855)Instruction limit reached!
% 51.00/8.91 % (21855)------------------------------
% 51.00/8.91 % (21855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.00/8.91 % (21855)Termination reason: Unknown
% 51.00/8.91 % (21855)Termination phase: Saturation
% 51.00/8.91
% 51.00/8.91 % (21855)Memory used [KB]: 5756
% 51.00/8.91 % (21855)Time elapsed: 0.391 s
% 51.00/8.91 % (21855)Instructions burned: 1324 (million)
% 51.00/8.91 % (21855)------------------------------
% 51.00/8.91 % (21855)------------------------------
% 51.00/8.92 % (21858)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_21337 for (2928ds/1897Mi)
% 51.00/9.00 % (21856)Instruction limit reached!
% 51.00/9.00 % (21856)------------------------------
% 51.00/9.00 % (21856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.00/9.00 % (21856)Termination reason: Unknown
% 51.00/9.00 % (21856)Termination phase: Saturation
% 51.00/9.00
% 51.00/9.00 % (21856)Memory used [KB]: 10106
% 51.00/9.00 % (21856)Time elapsed: 0.404 s
% 51.00/9.00 % (21856)Instructions burned: 1313 (million)
% 51.00/9.00 % (21856)------------------------------
% 51.00/9.00 % (21856)------------------------------
% 51.00/9.01 % (21859)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_21337 for (2927ds/1202Mi)
% 53.97/9.04 % (21857)Instruction limit reached!
% 53.97/9.04 % (21857)------------------------------
% 53.97/9.04 % (21857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.97/9.04 % (21857)Termination reason: Unknown
% 53.97/9.04 % (21857)Termination phase: Saturation
% 53.97/9.04
% 53.97/9.04 % (21857)Memory used [KB]: 9338
% 53.97/9.04 % (21857)Time elapsed: 0.203 s
% 53.97/9.04 % (21857)Instructions burned: 674 (million)
% 53.97/9.04 % (21857)------------------------------
% 53.97/9.04 % (21857)------------------------------
% 53.97/9.05 % (21860)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_21337 for (2927ds/1493Mi)
% 53.97/9.09 % (21860)Refutation not found, incomplete strategy
% 53.97/9.09 % (21860)------------------------------
% 53.97/9.09 % (21860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.97/9.09 % (21860)Termination reason: Refutation not found, incomplete strategy
% 53.97/9.09
% 53.97/9.09
% 53.97/9.09 % (21860)Memory used [KB]: 7291
% 53.97/9.09 % (21860)Time elapsed: 0.039 s
% 53.97/9.09 % (21860)Instructions burned: 135 (million)
% 53.97/9.09 % (21860)------------------------------
% 53.97/9.09 % (21860)------------------------------
% 53.97/9.10 % (21861)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_21337 for (2926ds/7679Mi)
% 54.57/9.18 % (21852)Instruction limit reached!
% 54.57/9.18 % (21852)------------------------------
% 54.57/9.18 % (21852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.57/9.18 % (21852)Termination reason: Unknown
% 54.57/9.18 % (21852)Termination phase: Saturation
% 54.57/9.18
% 54.57/9.18 % (21852)Memory used [KB]: 12409
% 54.57/9.18 % (21852)Time elapsed: 0.747 s
% 54.57/9.18 % (21852)Instructions burned: 2401 (million)
% 54.57/9.18 % (21852)------------------------------
% 54.57/9.18 % (21852)------------------------------
% 54.57/9.19 % (21862)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_21337 for (2925ds/340Mi)
% 55.35/9.30 % (21862)Instruction limit reached!
% 55.35/9.30 % (21862)------------------------------
% 55.35/9.30 % (21862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.35/9.30 % (21862)Termination reason: Unknown
% 55.35/9.30 % (21862)Termination phase: Saturation
% 55.35/9.30
% 55.35/9.30 % (21862)Memory used [KB]: 9083
% 55.35/9.30 % (21862)Time elapsed: 0.109 s
% 55.35/9.30 % (21862)Instructions burned: 343 (million)
% 55.35/9.30 % (21862)------------------------------
% 55.35/9.30 % (21862)------------------------------
% 55.35/9.31 % (21863)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_21337 for (2924ds/3672Mi)
% 55.35/9.39 % (21859)Instruction limit reached!
% 55.35/9.39 % (21859)------------------------------
% 55.35/9.39 % (21859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.35/9.39 % (21859)Termination reason: Unknown
% 55.35/9.39 % (21859)Termination phase: Saturation
% 55.35/9.39
% 55.35/9.39 % (21859)Memory used [KB]: 5884
% 55.35/9.39 % (21859)Time elapsed: 0.382 s
% 55.35/9.39 % (21859)Instructions burned: 1203 (million)
% 55.35/9.39 % (21859)------------------------------
% 55.35/9.39 % (21859)------------------------------
% 56.27/9.40 % (21864)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_21337 for (2923ds/1535Mi)
% 56.66/9.52 % (21858)Instruction limit reached!
% 56.66/9.52 % (21858)------------------------------
% 56.66/9.52 % (21858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.66/9.52 % (21858)Termination reason: Unknown
% 56.66/9.52 % (21858)Termination phase: Saturation
% 56.66/9.52
% 56.66/9.52 % (21858)Memory used [KB]: 10234
% 56.66/9.52 % (21858)Time elapsed: 0.599 s
% 56.66/9.52 % (21858)Instructions burned: 1897 (million)
% 56.66/9.52 % (21858)------------------------------
% 56.66/9.52 % (21858)------------------------------
% 56.66/9.53 % (21865)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_21337 for (2922ds/4637Mi)
% 57.28/9.71 % (21832)Instruction limit reached!
% 57.28/9.71 % (21832)------------------------------
% 57.28/9.71 % (21832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.28/9.71 % (21832)Termination reason: Unknown
% 57.28/9.71 % (21832)Termination phase: Saturation
% 57.28/9.71
% 57.28/9.71 % (21832)Memory used [KB]: 12665
% 57.28/9.71 % (21832)Time elapsed: 2.123 s
% 57.28/9.71 % (21832)Instructions burned: 6454 (million)
% 57.28/9.71 % (21832)------------------------------
% 57.28/9.71 % (21832)------------------------------
% 57.28/9.72 % (21866)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_21337 for (2920ds/3174Mi)
% 57.51/9.85 % (21864)Instruction limit reached!
% 57.51/9.85 % (21864)------------------------------
% 57.51/9.85 % (21864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.51/9.85 % (21864)Termination reason: Unknown
% 57.51/9.85 % (21864)Termination phase: Saturation
% 57.51/9.85
% 57.51/9.85 % (21864)Memory used [KB]: 13560
% 57.51/9.85 % (21864)Time elapsed: 0.456 s
% 57.51/9.85 % (21864)Instructions burned: 1536 (million)
% 57.51/9.85 % (21864)------------------------------
% 57.51/9.85 % (21864)------------------------------
% 57.51/9.87 % (21867)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_21337 for (2919ds/307Mi)
% 58.17/9.95 % (21867)Instruction limit reached!
% 58.17/9.95 % (21867)------------------------------
% 58.17/9.95 % (21867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.17/9.95 % (21867)Termination reason: Unknown
% 58.17/9.95 % (21867)Termination phase: Saturation
% 58.17/9.95
% 58.17/9.95 % (21867)Memory used [KB]: 7803
% 58.17/9.95 % (21867)Time elapsed: 0.087 s
% 58.17/9.95 % (21867)Instructions burned: 310 (million)
% 58.17/9.95 % (21867)------------------------------
% 58.17/9.95 % (21867)------------------------------
% 58.17/9.96 % (21868)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_21337 for (2918ds/3619Mi)
% 58.17/9.99 % (21851)Instruction limit reached!
% 58.17/9.99 % (21851)------------------------------
% 58.17/9.99 % (21851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.17/9.99 % (21851)Termination reason: Unknown
% 58.17/9.99 % (21851)Termination phase: Saturation
% 58.17/9.99
% 58.17/9.99 % (21851)Memory used [KB]: 13944
% 58.17/9.99 % (21851)Time elapsed: 1.557 s
% 58.17/9.99 % (21851)Instructions burned: 5063 (million)
% 58.17/9.99 % (21851)------------------------------
% 58.17/9.99 % (21851)------------------------------
% 58.17/10.00 % (21869)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_21337 for (2917ds/2325Mi)
% 62.25/10.21 % (21853)Instruction limit reached!
% 62.25/10.21 % (21853)------------------------------
% 62.25/10.21 % (21853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.25/10.21 % (21853)Termination reason: Unknown
% 62.25/10.21 % (21853)Termination phase: Saturation
% 62.25/10.21
% 62.25/10.21 % (21853)Memory used [KB]: 10362
% 62.25/10.21 % (21853)Time elapsed: 1.775 s
% 62.25/10.21 % (21853)Instructions burned: 5799 (million)
% 62.25/10.21 % (21853)------------------------------
% 62.25/10.21 % (21853)------------------------------
% 62.25/10.23 % (21870)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_21337 for (2915ds/2341Mi)
% 62.89/10.35 % (21863)Instruction limit reached!
% 62.89/10.35 % (21863)------------------------------
% 62.89/10.35 % (21863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.89/10.35 % (21863)Termination reason: Unknown
% 62.89/10.35 % (21863)Termination phase: Saturation
% 62.89/10.35
% 62.89/10.35 % (21863)Memory used [KB]: 11385
% 62.89/10.35 % (21863)Time elapsed: 1.041 s
% 62.89/10.35 % (21863)Instructions burned: 3673 (million)
% 62.89/10.35 % (21863)------------------------------
% 62.89/10.35 % (21863)------------------------------
% 62.89/10.36 % (21871)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_21337 for (2914ds/7257Mi)
% 64.96/10.70 % (21866)Instruction limit reached!
% 64.96/10.70 % (21866)------------------------------
% 64.96/10.70 % (21866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.96/10.70 % (21866)Termination reason: Unknown
% 64.96/10.70 % (21866)Termination phase: Saturation
% 64.96/10.70
% 64.96/10.70 % (21866)Memory used [KB]: 12920
% 64.96/10.70 % (21866)Time elapsed: 0.986 s
% 64.96/10.70 % (21866)Instructions burned: 3176 (million)
% 64.96/10.70 % (21866)------------------------------
% 64.96/10.70 % (21866)------------------------------
% 64.96/10.71 % (21872)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_21337 for (2910ds/3710Mi)
% 64.96/10.73 % (21869)Instruction limit reached!
% 64.96/10.73 % (21869)------------------------------
% 64.96/10.73 % (21869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.96/10.73 % (21869)Termination reason: Unknown
% 64.96/10.73 % (21869)Termination phase: Saturation
% 64.96/10.73
% 64.96/10.73 % (21869)Memory used [KB]: 13560
% 64.96/10.73 % (21869)Time elapsed: 0.735 s
% 64.96/10.73 % (21869)Instructions burned: 2326 (million)
% 64.96/10.73 % (21869)------------------------------
% 64.96/10.73 % (21869)------------------------------
% 64.96/10.74 % (21873)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_21337 for (2910ds/326Mi)
% 65.33/10.85 % (21873)Instruction limit reached!
% 65.33/10.85 % (21873)------------------------------
% 65.33/10.85 % (21873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.33/10.85 % (21873)Termination reason: Unknown
% 65.33/10.85 % (21873)Termination phase: Saturation
% 65.33/10.85
% 65.33/10.85 % (21873)Memory used [KB]: 8059
% 65.33/10.85 % (21873)Time elapsed: 0.111 s
% 65.33/10.85 % (21873)Instructions burned: 327 (million)
% 65.33/10.85 % (21873)------------------------------
% 65.33/10.85 % (21873)------------------------------
% 65.33/10.86 % (21874)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_21337 for (2909ds/1100Mi)
% 65.75/10.94 % (21865)Instruction limit reached!
% 65.75/10.94 % (21865)------------------------------
% 65.75/10.94 % (21865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.75/10.94 % (21865)Termination reason: Unknown
% 65.75/10.94 % (21865)Termination phase: Saturation
% 65.75/10.94
% 65.75/10.94 % (21865)Memory used [KB]: 12920
% 65.75/10.94 % (21865)Time elapsed: 1.420 s
% 65.75/10.94 % (21865)Instructions burned: 4638 (million)
% 65.75/10.94 % (21865)------------------------------
% 65.75/10.94 % (21865)------------------------------
% 65.75/10.96 % (21875)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_21337 for (2908ds/406Mi)
% 65.75/10.96 % (21870)Instruction limit reached!
% 65.75/10.96 % (21870)------------------------------
% 65.75/10.96 % (21870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.75/10.96 % (21870)Termination reason: Unknown
% 65.75/10.96 % (21870)Termination phase: Saturation
% 65.75/10.96
% 65.75/10.96 % (21870)Memory used [KB]: 10234
% 65.75/10.96 % (21870)Time elapsed: 0.734 s
% 65.75/10.96 % (21870)Instructions burned: 2343 (million)
% 65.75/10.96 % (21870)------------------------------
% 65.75/10.96 % (21870)------------------------------
% 65.75/10.97 % (21876)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_21337 for (2908ds/1871Mi)
% 65.75/11.02 % (21868)Instruction limit reached!
% 65.75/11.02 % (21868)------------------------------
% 65.75/11.02 % (21868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.75/11.02 % (21868)Termination reason: Unknown
% 65.75/11.02 % (21868)Termination phase: Saturation
% 65.75/11.02
% 65.75/11.02 % (21868)Memory used [KB]: 11257
% 65.75/11.02 % (21868)Time elapsed: 1.063 s
% 65.75/11.02 % (21868)Instructions burned: 3621 (million)
% 65.75/11.02 % (21868)------------------------------
% 65.75/11.02 % (21868)------------------------------
% 68.06/11.03 % (21877)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_21337 for (2907ds/1194Mi)
% 68.06/11.08 % (21875)Instruction limit reached!
% 68.06/11.08 % (21875)------------------------------
% 68.06/11.08 % (21875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.06/11.08 % (21875)Termination reason: Unknown
% 68.06/11.08 % (21875)Termination phase: Saturation
% 68.06/11.08
% 68.06/11.08 % (21875)Memory used [KB]: 8187
% 68.06/11.08 % (21875)Time elapsed: 0.130 s
% 68.06/11.08 % (21875)Instructions burned: 408 (million)
% 68.06/11.08 % (21875)------------------------------
% 68.06/11.08 % (21875)------------------------------
% 68.06/11.09 % (21878)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_21337 for (2906ds/474Mi)
% 69.02/11.20 % (21874)Instruction limit reached!
% 69.02/11.20 % (21874)------------------------------
% 69.02/11.20 % (21874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.02/11.20 % (21874)Termination reason: Unknown
% 69.02/11.20 % (21874)Termination phase: Saturation
% 69.02/11.20
% 69.02/11.20 % (21874)Memory used [KB]: 10746
% 69.02/11.20 % (21874)Time elapsed: 0.339 s
% 69.02/11.20 % (21874)Instructions burned: 1100 (million)
% 69.02/11.20 % (21874)------------------------------
% 69.02/11.20 % (21874)------------------------------
% 69.02/11.21 % (21879)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_21337 for (2905ds/3115Mi)
% 69.02/11.24 % (21878)Instruction limit reached!
% 69.02/11.24 % (21878)------------------------------
% 69.02/11.24 % (21878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.02/11.24 % (21878)Termination reason: Unknown
% 69.02/11.24 % (21878)Termination phase: Saturation
% 69.02/11.24
% 69.02/11.24 % (21878)Memory used [KB]: 8059
% 69.02/11.24 % (21878)Time elapsed: 0.144 s
% 69.02/11.24 % (21878)Instructions burned: 474 (million)
% 69.02/11.24 % (21878)------------------------------
% 69.02/11.24 % (21878)------------------------------
% 69.02/11.25 % (21880)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_21337 for (2905ds/831Mi)
% 69.98/11.40 % (21861)Instruction limit reached!
% 69.98/11.40 % (21861)------------------------------
% 69.98/11.40 % (21861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.98/11.40 % (21861)Termination reason: Unknown
% 69.98/11.40 % (21861)Termination phase: Saturation
% 69.98/11.40
% 69.98/11.40 % (21861)Memory used [KB]: 14072
% 69.98/11.40 % (21861)Time elapsed: 2.301 s
% 69.98/11.40 % (21861)Instructions burned: 7681 (million)
% 69.98/11.40 % (21861)------------------------------
% 69.98/11.40 % (21861)------------------------------
% 69.98/11.41 % (21877)Instruction limit reached!
% 69.98/11.41 % (21877)------------------------------
% 69.98/11.41 % (21877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.98/11.41 % (21877)Termination reason: Unknown
% 69.98/11.41 % (21877)Termination phase: Saturation
% 69.98/11.41
% 69.98/11.41 % (21877)Memory used [KB]: 10106
% 69.98/11.41 % (21877)Time elapsed: 0.378 s
% 69.98/11.41 % (21877)Instructions burned: 1195 (million)
% 69.98/11.41 % (21877)------------------------------
% 69.98/11.41 % (21877)------------------------------
% 69.98/11.41 % (21881)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_21337 for (2903ds/1188Mi)
% 69.98/11.42 % (21882)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_21337 for (2903ds/2868Mi)
% 69.98/11.49 % (21882)Refutation not found, incomplete strategy
% 69.98/11.49 % (21882)------------------------------
% 69.98/11.49 % (21882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.98/11.49 % (21882)Termination reason: Refutation not found, incomplete strategy
% 69.98/11.49
% 69.98/11.49
% 69.98/11.49 % (21882)Memory used [KB]: 7931
% 69.98/11.49 % (21882)Time elapsed: 0.071 s
% 69.98/11.49 % (21882)Instructions burned: 246 (million)
% 69.98/11.49 % (21882)------------------------------
% 69.98/11.49 % (21882)------------------------------
% 70.77/11.50 % (21883)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_21337 for (2902ds/1516Mi)
% 70.77/11.51 % (21880)Instruction limit reached!
% 70.77/11.51 % (21880)------------------------------
% 70.77/11.51 % (21880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.77/11.51 % (21880)Termination reason: Unknown
% 70.77/11.51 % (21880)Termination phase: Saturation
% 70.77/11.51
% 70.77/11.51 % (21880)Memory used [KB]: 10106
% 70.77/11.51 % (21880)Time elapsed: 0.260 s
% 70.77/11.51 % (21880)Instructions burned: 832 (million)
% 70.77/11.51 % (21880)------------------------------
% 70.77/11.51 % (21880)------------------------------
% 70.77/11.52 % (21884)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_21337 for (2902ds/2321Mi)
% 70.77/11.56 % (21876)Instruction limit reached!
% 70.77/11.56 % (21876)------------------------------
% 70.77/11.56 % (21876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.77/11.56 % (21876)Termination reason: Unknown
% 70.77/11.56 % (21876)Termination phase: Saturation
% 70.77/11.56
% 70.77/11.56 % (21876)Memory used [KB]: 10490
% 70.77/11.56 % (21876)Time elapsed: 0.594 s
% 70.77/11.56 % (21876)Instructions burned: 1872 (million)
% 70.77/11.56 % (21876)------------------------------
% 70.77/11.56 % (21876)------------------------------
% 70.77/11.57 % (21885)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_21337 for (2901ds/2812Mi)
% 70.77/11.59 % (21884)Refutation not found, incomplete strategy
% 70.77/11.59 % (21884)------------------------------
% 70.77/11.59 % (21884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.77/11.59 % (21884)Termination reason: Refutation not found, incomplete strategy
% 70.77/11.59
% 70.77/11.59
% 70.77/11.59 % (21884)Memory used [KB]: 8059
% 70.77/11.59 % (21884)Time elapsed: 0.075 s
% 70.77/11.59 % (21884)Instructions burned: 257 (million)
% 70.77/11.59 % (21884)------------------------------
% 70.77/11.59 % (21884)------------------------------
% 71.39/11.60 % (21886)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_21337 for (2901ds/4604Mi)
% 71.59/11.79 % (21881)Instruction limit reached!
% 71.59/11.79 % (21881)------------------------------
% 71.59/11.79 % (21881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.59/11.79 % (21881)Termination reason: Unknown
% 71.59/11.79 % (21881)Termination phase: Saturation
% 71.59/11.79
% 71.59/11.79 % (21881)Memory used [KB]: 9850
% 71.59/11.79 % (21881)Time elapsed: 0.377 s
% 71.59/11.79 % (21881)Instructions burned: 1188 (million)
% 71.59/11.79 % (21881)------------------------------
% 71.59/11.79 % (21881)------------------------------
% 72.18/11.80 % (21887)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_21337 for (2899ds/2678Mi)
% 72.18/11.84 % (21872)Instruction limit reached!
% 72.18/11.84 % (21872)------------------------------
% 72.18/11.84 % (21872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.18/11.84 % (21872)Termination reason: Unknown
% 72.18/11.84 % (21872)Termination phase: Saturation
% 72.18/11.84
% 72.18/11.84 % (21872)Memory used [KB]: 13816
% 72.18/11.84 % (21872)Time elapsed: 1.127 s
% 72.18/11.84 % (21872)Instructions burned: 3713 (million)
% 72.18/11.84 % (21872)------------------------------
% 72.18/11.84 % (21872)------------------------------
% 72.18/11.85 % (21888)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_21337 for (2899ds/643Mi)
% 72.34/11.98 % (21883)Instruction limit reached!
% 72.34/11.98 % (21883)------------------------------
% 72.34/11.98 % (21883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.34/11.98 % (21883)Termination reason: Unknown
% 72.34/11.98 % (21883)Termination phase: Saturation
% 72.34/11.98
% 72.34/11.98 % (21883)Memory used [KB]: 8955
% 72.34/11.98 % (21883)Time elapsed: 0.485 s
% 72.34/11.98 % (21883)Instructions burned: 1516 (million)
% 72.34/11.98 % (21883)------------------------------
% 72.34/11.98 % (21883)------------------------------
% 72.34/11.99 % (21889)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_21337 for (2897ds/458Mi)
% 75.08/12.05 % (21888)Instruction limit reached!
% 75.08/12.05 % (21888)------------------------------
% 75.08/12.05 % (21888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.08/12.05 % (21888)Termination reason: Unknown
% 75.08/12.05 % (21888)Termination phase: Saturation
% 75.08/12.05
% 75.08/12.05 % (21888)Memory used [KB]: 9338
% 75.08/12.05 % (21888)Time elapsed: 0.197 s
% 75.08/12.05 % (21888)Instructions burned: 645 (million)
% 75.08/12.05 % (21888)------------------------------
% 75.08/12.05 % (21888)------------------------------
% 75.08/12.06 % (21890)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_21337 for (2897ds/2546Mi)
% 75.72/12.13 % (21889)Instruction limit reached!
% 75.72/12.13 % (21889)------------------------------
% 75.72/12.13 % (21889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.72/12.13 % (21889)Termination reason: Unknown
% 75.72/12.13 % (21889)Termination phase: Saturation
% 75.72/12.13
% 75.72/12.13 % (21889)Memory used [KB]: 8571
% 75.72/12.13 % (21889)Time elapsed: 0.134 s
% 75.72/12.13 % (21889)Instructions burned: 458 (million)
% 75.72/12.13 % (21889)------------------------------
% 75.72/12.13 % (21889)------------------------------
% 75.72/12.14 % (21891)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_21337 for (2896ds/1432Mi)
% 75.72/12.15 % (21879)Instruction limit reached!
% 75.72/12.15 % (21879)------------------------------
% 75.72/12.15 % (21879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.72/12.15 % (21879)Termination reason: Unknown
% 75.72/12.15 % (21879)Termination phase: Saturation
% 75.72/12.15
% 75.72/12.15 % (21879)Memory used [KB]: 12665
% 75.72/12.15 % (21879)Time elapsed: 0.946 s
% 75.72/12.15 % (21879)Instructions burned: 3115 (million)
% 75.72/12.15 % (21879)------------------------------
% 75.72/12.15 % (21879)------------------------------
% 75.72/12.16 % (21892)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_21337 for (2896ds/386Mi)
% 76.08/12.27 % (21892)Instruction limit reached!
% 76.08/12.27 % (21892)------------------------------
% 76.08/12.27 % (21892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.08/12.27 % (21892)Termination reason: Unknown
% 76.08/12.27 % (21892)Termination phase: Saturation
% 76.08/12.27
% 76.08/12.27 % (21892)Memory used [KB]: 8955
% 76.08/12.27 % (21892)Time elapsed: 0.111 s
% 76.08/12.27 % (21892)Instructions burned: 388 (million)
% 76.08/12.27 % (21892)------------------------------
% 76.08/12.27 % (21892)------------------------------
% 76.08/12.28 % (21893)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_21337 for (2894ds/360Mi)
% 76.60/12.38 % (21893)Instruction limit reached!
% 76.60/12.38 % (21893)------------------------------
% 76.60/12.38 % (21893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.60/12.38 % (21893)Termination reason: Unknown
% 76.60/12.38 % (21893)Termination phase: Saturation
% 76.60/12.38
% 76.60/12.38 % (21893)Memory used [KB]: 8827
% 76.60/12.38 % (21893)Time elapsed: 0.103 s
% 76.60/12.38 % (21893)Instructions burned: 362 (million)
% 76.60/12.38 % (21893)------------------------------
% 76.60/12.38 % (21893)------------------------------
% 76.60/12.39 % (21894)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_21337 for (2893ds/5446Mi)
% 77.11/12.47 % (21885)Instruction limit reached!
% 77.11/12.47 % (21885)------------------------------
% 77.11/12.47 % (21885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.11/12.47 % (21885)Termination reason: Unknown
% 77.11/12.47 % (21885)Termination phase: Saturation
% 77.11/12.47
% 77.11/12.47 % (21885)Memory used [KB]: 12665
% 77.11/12.47 % (21885)Time elapsed: 0.896 s
% 77.11/12.47 % (21885)Instructions burned: 2813 (million)
% 77.11/12.47 % (21885)------------------------------
% 77.11/12.47 % (21885)------------------------------
% 77.11/12.48 % (21895)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_21337 for (2892ds/2573Mi)
% 77.11/12.49 % (21891)Instruction limit reached!
% 77.11/12.49 % (21891)------------------------------
% 77.11/12.49 % (21891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.11/12.49 % (21891)Termination reason: Unknown
% 77.11/12.49 % (21891)Termination phase: Saturation
% 77.11/12.49
% 77.11/12.49 % (21891)Memory used [KB]: 10234
% 77.11/12.49 % (21891)Time elapsed: 0.388 s
% 77.11/12.49 % (21891)Instructions burned: 1432 (million)
% 77.11/12.49 % (21891)------------------------------
% 77.11/12.49 % (21891)------------------------------
% 77.85/12.50 % (21896)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_21337 for (2892ds/2655Mi)
% 77.85/12.60 % (21871)Instruction limit reached!
% 77.85/12.60 % (21871)------------------------------
% 77.85/12.60 % (21871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.85/12.60 % (21871)Termination reason: Unknown
% 77.85/12.60 % (21871)Termination phase: Saturation
% 77.85/12.60
% 77.85/12.60 % (21871)Memory used [KB]: 17782
% 77.85/12.60 % (21871)Time elapsed: 2.237 s
% 77.85/12.60 % (21871)Instructions burned: 7257 (million)
% 77.85/12.60 % (21871)------------------------------
% 77.85/12.60 % (21871)------------------------------
% 75.92/12.61 % (21887)Instruction limit reached!
% 75.92/12.61 % (21887)------------------------------
% 75.92/12.61 % (21887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.92/12.61 % (21887)Termination reason: Unknown
% 75.92/12.61 % (21887)Termination phase: Saturation
% 75.92/12.61
% 75.92/12.61 % (21887)Memory used [KB]: 10618
% 75.92/12.61 % (21887)Time elapsed: 0.817 s
% 75.92/12.61 % (21887)Instructions burned: 2681 (million)
% 75.92/12.61 % (21887)------------------------------
% 75.92/12.61 % (21887)------------------------------
% 75.92/12.61 % (21897)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_21337 for (2891ds/2781Mi)
% 75.92/12.62 % (21898)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_21337 for (2891ds/307Mi)
% 78.29/12.71 % (21898)Instruction limit reached!
% 78.29/12.71 % (21898)------------------------------
% 78.29/12.71 % (21898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.29/12.71 % (21898)Termination reason: Unknown
% 78.29/12.71 % (21898)Termination phase: Saturation
% 78.29/12.71
% 78.29/12.71 % (21898)Memory used [KB]: 7803
% 78.29/12.71 % (21898)Time elapsed: 0.092 s
% 78.29/12.71 % (21898)Instructions burned: 310 (million)
% 78.29/12.71 % (21898)------------------------------
% 78.29/12.71 % (21898)------------------------------
% 78.29/12.72 % (21899)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_21337 for (2890ds/1548Mi)
% 78.49/12.86 % (21890)Instruction limit reached!
% 78.49/12.86 % (21890)------------------------------
% 78.49/12.86 % (21890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.49/12.86 % (21890)Termination reason: Unknown
% 78.49/12.86 % (21890)Termination phase: Saturation
% 78.49/12.86
% 78.49/12.86 % (21890)Memory used [KB]: 11513
% 78.49/12.86 % (21890)Time elapsed: 0.829 s
% 78.49/12.86 % (21890)Instructions burned: 2549 (million)
% 78.49/12.86 % (21890)------------------------------
% 78.49/12.86 % (21890)------------------------------
% 78.49/12.87 % (21900)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_21337 for (2889ds/5214Mi)
% 79.39/12.96 % (21886)Instruction limit reached!
% 79.39/12.96 % (21886)------------------------------
% 79.39/12.96 % (21886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.39/12.96 % (21886)Termination reason: Unknown
% 79.39/12.96 % (21886)Termination phase: Saturation
% 79.39/12.96
% 79.39/12.96 % (21886)Memory used [KB]: 16119
% 79.39/12.96 % (21886)Time elapsed: 1.361 s
% 79.39/12.96 % (21886)Instructions burned: 4604 (million)
% 79.39/12.96 % (21886)------------------------------
% 79.39/12.96 % (21886)------------------------------
% 79.39/12.97 % (21901)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_21337 for (2887ds/3201Mi)
% 82.03/13.06 % (21901)First to succeed.
% 82.03/13.06 % (21901)Refutation found. Thanks to Tanya!
% 82.03/13.06 % SZS status Theorem for DTF2THF_21337
% 82.03/13.06 % SZS output start Proof for DTF2THF_21337
% 82.03/13.06 thf(type_def_5, type, itself: ($tType) > $tType).
% 82.03/13.06 thf(type_def_7, type, sum_sum: ($tType * $tType) > $tType).
% 82.03/13.06 thf(type_def_8, type, set: ($tType) > $tType).
% 82.03/13.06 thf(type_def_9, type, n: $tType).
% 82.03/13.06 thf(type_def_10, type, t: $tType).
% 82.03/13.06 thf(type_def_11, type, dtree: $tType).
% 82.03/13.06 thf(func_def_0, type, sum_sum: ($tType * $tType) > $tType).
% 82.03/13.06 thf(func_def_1, type, dtree: $tType).
% 82.03/13.06 thf(func_def_2, type, set: ($tType) > $tType).
% 82.03/13.06 thf(func_def_3, type, t: $tType).
% 82.03/13.06 thf(func_def_4, type, n: $tType).
% 82.03/13.06 thf(func_def_5, type, itself: ($tType) > $tType).
% 82.03/13.06 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 82.03/13.06 thf(func_def_7, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 82.03/13.06 thf(func_def_8, type, complete_Sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 82.03/13.06 thf(func_def_9, type, comple1141879883l_ccpo: !>[X0: $tType]:(itself @ X0 > $o)).
% 82.03/13.06 thf(func_def_10, type, comple187826305attice: !>[X0: $tType]:(itself @ X0 > $o)).
% 82.03/13.06 thf(func_def_11, type, condit378418413attice: !>[X0: $tType]:(itself @ X0 > $o)).
% 82.03/13.06 thf(func_def_12, type, bNF_Greatest_image2p: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > (X0 > X2 > $o) > X1 > X3 > $o)).
% 82.03/13.06 thf(func_def_13, type, basic_setl: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > set @ X0)).
% 82.03/13.06 thf(func_def_14, type, basic_setr: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > set @ X1)).
% 82.03/13.06 thf(func_def_15, type, complete_Sup_Sup: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_16, type, node: n > set @ sum_sum @ t @ dtree > dtree).
% 82.03/13.06 thf(func_def_17, type, cont: dtree > set @ sum_sum @ t @ dtree).
% 82.03/13.06 thf(func_def_18, type, root: dtree > n).
% 82.03/13.06 thf(func_def_19, type, gram_L861583724lle_Fr: set @ n > dtree > set @ t).
% 82.03/13.06 thf(func_def_20, type, gram_L1580978439le_Itr: set @ n > dtree > set @ n).
% 82.03/13.06 thf(func_def_21, type, gram_L1333338417e_inFr: set @ n > dtree > t > $o).
% 82.03/13.06 thf(func_def_22, type, gram_L805317441_inFr2: set @ n > dtree > t > $o).
% 82.03/13.06 thf(func_def_23, type, gram_L830233218_inItr: set @ n > dtree > n > $o).
% 82.03/13.06 thf(func_def_24, type, gram_L716654942_subtr: set @ n > dtree > dtree > $o).
% 82.03/13.06 thf(func_def_25, type, gram_L1283001940subtr2: set @ n > dtree > dtree > $o).
% 82.03/13.06 thf(func_def_26, type, the: !>[X0: $tType]:((X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_27, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 82.03/13.06 thf(func_def_28, type, rel_pred_comp: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X1 > $o) > X0 > $o)).
% 82.03/13.06 thf(func_def_29, type, bot_bot: !>[X0: $tType]:(X0)).
% 82.03/13.06 thf(func_def_30, type, type2: !>[X0: $tType]:(itself @ X0)).
% 82.03/13.06 thf(func_def_31, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 82.03/13.06 thf(func_def_32, type, image: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 82.03/13.06 thf(func_def_33, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 82.03/13.06 thf(func_def_34, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 82.03/13.06 thf(func_def_35, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 82.03/13.06 thf(func_def_36, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_37, type, vimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1 > set @ X0)).
% 82.03/13.06 thf(func_def_38, type, sum_Inl: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X0 @ X1)).
% 82.03/13.06 thf(func_def_39, type, sum_Inr: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X1 @ X0)).
% 82.03/13.06 thf(func_def_40, type, sum_Suml: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > sum_sum @ X0 @ X2 > X1)).
% 82.03/13.06 thf(func_def_41, type, sum_rec_set_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1 > $o)).
% 82.03/13.06 thf(func_def_42, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1)).
% 82.03/13.06 thf(func_def_43, type, sum_case_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1)).
% 82.03/13.06 thf(func_def_44, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 82.03/13.06 thf(func_def_45, type, ns: set @ n).
% 82.03/13.06 thf(func_def_46, type, tr: dtree).
% 82.03/13.06 thf(func_def_65, type, sP0: (set @ n > dtree > n > $o) > $o).
% 82.03/13.06 thf(func_def_66, type, sP1: (set @ n > dtree > dtree > $o) > $o).
% 82.03/13.06 thf(func_def_67, type, sP2: (set @ n > dtree > t > $o) > $o).
% 82.03/13.06 thf(func_def_68, type, sP3: (set @ n > dtree > t > $o) > $o).
% 82.03/13.06 thf(func_def_69, type, sP4: (set @ n > dtree > dtree > $o) > $o).
% 82.03/13.06 thf(func_def_70, type, sK5: (set @ n > dtree > n > $o) > dtree).
% 82.03/13.06 thf(func_def_71, type, sK6: (set @ n > dtree > n > $o) > set @ n).
% 82.03/13.06 thf(func_def_72, type, sK7: (set @ n > dtree > n > $o) > dtree).
% 82.03/13.06 thf(func_def_73, type, sK8: (set @ n > dtree > n > $o) > n).
% 82.03/13.06 thf(func_def_74, type, sK9: (set @ n > dtree > n > $o) > dtree).
% 82.03/13.06 thf(func_def_75, type, sK10: (set @ n > dtree > n > $o) > set @ n).
% 82.03/13.06 thf(func_def_76, type, sK11: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_77, type, sK12: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_78, type, sK13: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 82.03/13.06 thf(func_def_79, type, sK14: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 82.03/13.06 thf(func_def_80, type, sK15: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_81, type, sK16: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X1)).
% 82.03/13.06 thf(func_def_82, type, sK17: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_83, type, sK18: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > set @ X0) > X0 > X1)).
% 82.03/13.06 thf(func_def_84, type, sK19: dtree > dtree > set @ n > dtree).
% 82.03/13.06 thf(func_def_85, type, sK20: !>[X0: $tType, X1: $tType]:(X1 > (X0 > X1) > set @ X0 > X0)).
% 82.03/13.06 thf(func_def_86, type, sK21: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 82.03/13.06 thf(func_def_87, type, sK22: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_88, type, sK23: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 82.03/13.06 thf(func_def_89, type, sK24: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_90, type, sK25: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X0)).
% 82.03/13.06 thf(func_def_91, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(X0 > X1 > (X2 > X3 > $o) > (X3 > X0) > (X2 > X1) > X2)).
% 82.03/13.06 thf(func_def_92, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(X0 > X1 > (X2 > X3 > $o) > (X3 > X0) > (X2 > X1) > X3)).
% 82.03/13.06 thf(func_def_93, type, sK28: n > dtree > set @ n > dtree).
% 82.03/13.06 thf(func_def_94, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:($o > (sum_sum @ X0 @ X1 > X2) > X2 > X1)).
% 82.03/13.06 thf(func_def_95, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType]:($o > (sum_sum @ X0 @ X1 > X2) > X2 > X0)).
% 82.03/13.06 thf(func_def_96, type, sK31: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 82.03/13.06 thf(func_def_97, type, sK32: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X1)).
% 82.03/13.06 thf(func_def_98, type, sK33: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_99, type, sK34: (set @ n > dtree > dtree > $o) > set @ n).
% 82.03/13.06 thf(func_def_100, type, sK35: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_101, type, sK36: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_102, type, sK37: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_103, type, sK38: (set @ n > dtree > dtree > $o) > set @ n).
% 82.03/13.06 thf(func_def_104, type, sK39: t > dtree > set @ n > dtree).
% 82.03/13.06 thf(func_def_105, type, sK40: !>[X0: $tType, X1: $tType]:(X1 > (X1 > X0) > set @ X1 > X1)).
% 82.03/13.06 thf(func_def_106, type, sK41: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_107, type, sK42: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > (X0 > $o) > X1)).
% 82.03/13.06 thf(func_def_108, type, sK43: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_109, type, sK44: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_110, type, sK45: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_111, type, sK46: !>[X0: $tType, X1: $tType]:((X1 > $o) > sum_sum @ X1 @ X0 > X1)).
% 82.03/13.06 thf(func_def_112, type, sK47: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 82.03/13.06 thf(func_def_113, type, sK48: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 82.03/13.06 thf(func_def_114, type, sK49: (set @ n > dtree > t > $o) > dtree).
% 82.03/13.06 thf(func_def_115, type, sK50: (set @ n > dtree > t > $o) > dtree).
% 82.03/13.06 thf(func_def_116, type, sK51: (set @ n > dtree > t > $o) > set @ n).
% 82.03/13.06 thf(func_def_117, type, sK52: (set @ n > dtree > t > $o) > t).
% 82.03/13.06 thf(func_def_118, type, sK53: (set @ n > dtree > t > $o) > dtree).
% 82.03/13.06 thf(func_def_119, type, sK54: (set @ n > dtree > t > $o) > set @ n).
% 82.03/13.06 thf(func_def_120, type, sK55: (set @ n > dtree > t > $o) > t).
% 82.03/13.06 thf(func_def_121, type, sK56: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 82.03/13.06 thf(func_def_122, type, sK57: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 82.03/13.06 thf(func_def_123, type, sK58: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_124, type, sK59: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_125, type, sK60: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > X0 > X1)).
% 82.03/13.06 thf(func_def_126, type, sK61: !>[X0: $tType]:(set @ set @ X0 > X0 > set @ X0)).
% 82.03/13.06 thf(func_def_127, type, sK62: dtree > dtree > set @ n > dtree).
% 82.03/13.06 thf(func_def_128, type, sK63: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_129, type, sK64: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_130, type, sK65: !>[X0: $tType, X1: $tType]:((X1 > $o) > sum_sum @ X0 @ X1 > X1)).
% 82.03/13.06 thf(func_def_131, type, sK66: (set @ n > dtree > t > $o) > dtree).
% 82.03/13.06 thf(func_def_132, type, sK67: (set @ n > dtree > t > $o) > set @ n).
% 82.03/13.06 thf(func_def_133, type, sK68: (set @ n > dtree > t > $o) > dtree).
% 82.03/13.06 thf(func_def_134, type, sK69: (set @ n > dtree > t > $o) > t).
% 82.03/13.06 thf(func_def_135, type, sK70: (set @ n > dtree > t > $o) > dtree).
% 82.03/13.06 thf(func_def_136, type, sK71: (set @ n > dtree > t > $o) > set @ n).
% 82.03/13.06 thf(func_def_137, type, sK72: (set @ n > dtree > t > $o) > t).
% 82.03/13.06 thf(func_def_138, type, sK73: t > dtree > set @ n > dtree).
% 82.03/13.06 thf(func_def_139, type, sK74: t > dtree > set @ n > dtree).
% 82.03/13.06 thf(func_def_140, type, sK75: t > dtree > set @ n > set @ n).
% 82.03/13.06 thf(func_def_141, type, sK76: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 82.03/13.06 thf(func_def_142, type, sK77: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 82.03/13.06 thf(func_def_143, type, sK78: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 82.03/13.06 thf(func_def_144, type, sK79: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 82.03/13.06 thf(func_def_145, type, sK80: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_146, type, sK81: (set @ n > dtree > dtree > $o) > set @ n).
% 82.03/13.06 thf(func_def_147, type, sK82: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_148, type, sK83: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_149, type, sK84: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_150, type, sK85: (set @ n > dtree > dtree > $o) > set @ n).
% 82.03/13.06 thf(func_def_151, type, sK86: n > dtree > set @ n > dtree).
% 82.03/13.06 thf(func_def_152, type, sK87: (set @ n > dtree > dtree > $o) > set @ n).
% 82.03/13.06 thf(func_def_153, type, sK88: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_154, type, sK89: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_155, type, sK90: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_156, type, sK91: (set @ n > dtree > dtree > $o) > set @ n).
% 82.03/13.06 thf(func_def_157, type, sK92: (set @ n > dtree > dtree > $o) > dtree).
% 82.03/13.06 thf(func_def_158, type, sK93: t > dtree > set @ n > dtree).
% 82.03/13.06 thf(func_def_160, type, sK95: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X1 > X1)).
% 82.03/13.06 thf(func_def_161, type, sK96: !>[X0: $tType]:((X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_162, type, sK97: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1 > X1)).
% 82.03/13.06 thf(func_def_163, type, sK98: !>[X0: $tType]:(X0 > set @ set @ X0 > set @ X0)).
% 82.03/13.06 thf(func_def_164, type, sK99: !>[X0: $tType]:((X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_165, type, sK100: !>[X0: $tType, X1: $tType]:((X1 > set @ X0) > set @ X1 > X0 > X1)).
% 82.03/13.06 thf(func_def_166, type, sK101: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_167, type, sK102: !>[X0: $tType]:(X0 > set @ X0 > X0 > set @ X0 > set @ X0)).
% 82.03/13.06 thf(func_def_168, type, sK103: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 82.03/13.06 thf(func_def_169, type, sK104: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1)).
% 82.03/13.06 thf(func_def_170, type, sK105: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 82.03/13.06 thf(func_def_171, type, sK106: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 82.03/13.06 thf(func_def_172, type, sK107: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1)).
% 82.03/13.06 thf(func_def_173, type, sK108: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0)).
% 82.03/13.06 thf(func_def_174, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(X0 > (X1 > X2) > (X0 > X1 > $o) > X1 > (X0 > X3) > X1)).
% 82.03/13.06 thf(func_def_175, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(X2 > (X2 > X1 > $o) > (X2 > X3) > X1 > (X1 > X0) > X2)).
% 82.03/13.06 thf(func_def_176, type, sK111: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_177, type, sK112: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > set @ X0)).
% 82.03/13.06 thf(func_def_178, type, sK113: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_179, type, sK114: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > X0 > X1)).
% 82.03/13.06 thf(func_def_180, type, sK115: !>[X0: $tType, X1: $tType]:(sum_sum @ X1 @ X0 > X1 > X1)).
% 82.03/13.06 thf(func_def_181, type, sK116: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > set @ X0) > X1)).
% 82.03/13.06 thf(func_def_182, type, sK117: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > set @ X0) > X0)).
% 82.03/13.06 thf(func_def_183, type, sK118: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > set @ X0) > X0)).
% 82.03/13.06 thf(func_def_184, type, sK119: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_185, type, sK120: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > set @ X0) > X1)).
% 82.03/13.06 thf(func_def_186, type, sK121: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_187, type, sK122: !>[X0: $tType]:(set @ set @ X0 > set @ X0)).
% 82.03/13.06 thf(func_def_188, type, sK123: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_189, type, sK124: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_190, type, sK125: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_191, type, sK126: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > set @ X0) > X1)).
% 82.03/13.06 thf(func_def_192, type, sK127: !>[X0: $tType]:(set @ X0 > X0)).
% 82.03/13.06 thf(func_def_193, type, sK128: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > X1)).
% 82.03/13.06 thf(func_def_194, type, sK129: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > set @ X0) > X1)).
% 82.03/13.06 thf(func_def_195, type, sK130: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > set @ X0) > X0)).
% 82.03/13.06 thf(func_def_196, type, sK131: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > set @ X0) > X0)).
% 82.03/13.06 thf(func_def_197, type, sK132: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > set @ X0)).
% 82.03/13.06 thf(func_def_198, type, sK133: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_199, type, sK134: !>[X0: $tType]:(set @ set @ X0 > (X0 > $o) > X0)).
% 82.03/13.06 thf(func_def_200, type, sK135: !>[X0: $tType]:(X0 > X0)).
% 82.03/13.06 thf(func_def_201, type, sK136: !>[X0: $tType]:(set @ set @ X0 > set @ X0)).
% 82.03/13.06 thf(func_def_202, type, ph137: !>[X0: $tType]:(X0)).
% 82.03/13.06 thf(func_def_203, type, sK138: n).
% 82.03/13.06 thf(func_def_204, type, sK139: dtree).
% 82.03/13.06 thf(func_def_205, type, sK140: n).
% 82.03/13.06 thf(func_def_206, type, sK141: set @ n > n).
% 82.03/13.06 thf(f2630,plain,(
% 82.03/13.06 $false),
% 82.03/13.06 inference(avatar_sat_refutation,[status(thm)],[f2392,f2396,f2403,f2512,f2522,f2581,f2629])).
% 82.03/13.06 thf(f2629,plain,(
% 82.03/13.06 ~spl94_4 | ~spl94_5 | ~spl94_7),
% 82.03/13.06 inference(avatar_contradiction_clause,[status(thm)],[f2628])).
% 82.03/13.06 thf(f2628,plain,(
% 82.03/13.06 $false | (~spl94_4 | ~spl94_5 | ~spl94_7)),
% 82.03/13.06 inference(trivial_inequality_removal,[status(thm)],[f2627])).
% 82.03/13.06 thf(f2627,plain,(
% 82.03/13.06 ($false = $true) | (~spl94_4 | ~spl94_5 | ~spl94_7)),
% 82.03/13.06 inference(forward_demodulation,[status(thm)],[f2626,f2402])).
% 82.03/13.06 thf(f2402,plain,(
% 82.03/13.06 ($false = (gram_L830233218_inItr @ ns @ tr @ sK138)) | ~spl94_7),
% 82.03/13.06 inference(avatar_component_clause,[status(thm)],[f2401])).
% 82.03/13.06 thf(f2401,definition,(
% 82.03/13.06 spl94_7 <=> ($false = (gram_L830233218_inItr @ ns @ tr @ sK138))),
% 82.03/13.06 introduced(definition,[new_symbols(naming,[spl94_7])],[avatar_definition])).
% 82.03/13.06 thf(f2626,plain,(
% 82.03/13.06 ((gram_L830233218_inItr @ ns @ tr @ sK138) = $true) | (~spl94_4 | ~spl94_5)),
% 82.03/13.06 inference(forward_demodulation,[status(thm)],[f2625,f2391])).
% 82.03/13.06 thf(f2391,plain,(
% 82.03/13.06 (sK138 = (root @ sK139)) | ~spl94_4),
% 82.03/13.06 inference(avatar_component_clause,[status(thm)],[f2390])).
% 82.03/13.06 thf(f2390,definition,(
% 82.03/13.06 spl94_4 <=> (sK138 = (root @ sK139))),
% 82.03/13.06 introduced(definition,[new_symbols(naming,[spl94_4])],[avatar_definition])).
% 82.03/13.06 thf(f2625,plain,(
% 82.03/13.06 ($true = (gram_L830233218_inItr @ ns @ tr @ (root @ sK139))) | (~spl94_4 | ~spl94_5)),
% 82.03/13.06 inference(subsumption_resolution,[status(thm)],[f2624,f2558])).
% 82.03/13.06 thf(f2558,plain,(
% 82.03/13.06 ($true = (member @ n @ sK138 @ ns)) | (~spl94_4 | ~spl94_5)),
% 82.03/13.06 inference(forward_demodulation,[status(thm)],[f2554,f2391])).
% 82.03/13.06 thf(f2554,plain,(
% 82.03/13.06 ($true = (member @ n @ (root @ sK139) @ ns)) | ~spl94_5),
% 82.03/13.06 inference(trivial_inequality_removal,[status(thm)],[f2553])).
% 82.03/13.06 thf(f2553,plain,(
% 82.03/13.06 ($true != $true) | ($true = (member @ n @ (root @ sK139) @ ns)) | ~spl94_5),
% 82.03/13.06 inference(superposition,[status(thm)],[f1524,f2395])).
% 82.03/13.06 thf(f2395,plain,(
% 82.03/13.06 ((gram_L1283001940subtr2 @ ns @ sK139 @ tr) = $true) | ~spl94_5),
% 82.03/13.06 inference(avatar_component_clause,[status(thm)],[f2394])).
% 82.03/13.06 thf(f2394,definition,(
% 82.03/13.06 spl94_5 <=> ((gram_L1283001940subtr2 @ ns @ sK139 @ tr) = $true)),
% 82.03/13.06 introduced(definition,[new_symbols(naming,[spl94_5])],[avatar_definition])).
% 82.03/13.06 thf(f1524,plain,(
% 82.03/13.06 ( ! [X2 : dtree,X0 : set @ n,X1 : dtree] : (($true != (gram_L1283001940subtr2 @ X0 @ X1 @ X2)) | ((member @ n @ (root @ X1) @ X0) = $true)) )),
% 82.03/13.06 inference(definition_unfolding,[status(thm)],[f1156,f1275])).
% 82.03/13.06 thf(f1275,plain,(
% 82.03/13.06 (gram_L716654942_subtr = gram_L1283001940subtr2)),
% 82.03/13.06 inference(cnf_transformation,[status(thm)],[f15])).
% 82.03/13.06 thf(f15,axiom,(
% 82.03/13.06 (gram_L716654942_subtr = gram_L1283001940subtr2)),
% 82.03/13.06 file('/export/starexec/sandbox2/tmp/tmp.40Ab8elA6V/DTF2THF_21337.p',fact_14_subtr__subtr2)).
% 82.03/13.06 thf(f1156,plain,(
% 82.03/13.06 ( ! [X2 : dtree,X0 : set @ n,X1 : dtree] : (($true != (gram_L716654942_subtr @ X0 @ X1 @ X2)) | ((member @ n @ (root @ X1) @ X0) = $true)) )),
% 82.03/13.06 inference(cnf_transformation,[status(thm)],[f803])).
% 82.03/13.06 thf(f803,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : dtree] : (($true != (gram_L716654942_subtr @ X0 @ X1 @ X2)) | ((member @ n @ (root @ X1) @ X0) = $true))),
% 82.03/13.06 inference(ennf_transformation,[status(thm)],[f641])).
% 82.03/13.06 thf(f641,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : dtree] : (($true = (gram_L716654942_subtr @ X0 @ X1 @ X2)) => ((member @ n @ (root @ X1) @ X0) = $true))),
% 82.03/13.06 inference(fool_elimination,[status(thm)],[f640])).
% 82.03/13.06 thf(f640,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : dtree] : ((gram_L716654942_subtr @ X0 @ X1 @ X2) => (member @ n @ (root @ X1) @ X0))),
% 82.03/13.06 inference(rectify,[status(thm)],[f7])).
% 82.03/13.06 thf(f7,axiom,(
% 82.03/13.06 ! [X6 : set @ n,X9 : dtree,X10 : dtree] : ((gram_L716654942_subtr @ X6 @ X9 @ X10) => (member @ n @ (root @ X9) @ X6))),
% 82.03/13.06 file('/export/starexec/sandbox2/tmp/tmp.40Ab8elA6V/DTF2THF_21337.p',fact_6_subtr__rootL__in)).
% 82.03/13.06 thf(f2624,plain,(
% 82.03/13.06 ($true = (gram_L830233218_inItr @ ns @ tr @ (root @ sK139))) | ($true != (member @ n @ sK138 @ ns)) | (~spl94_4 | ~spl94_5)),
% 82.03/13.06 inference(forward_demodulation,[status(thm)],[f2617,f2391])).
% 82.03/13.06 thf(f2617,plain,(
% 82.03/13.06 ($true != (member @ n @ (root @ sK139) @ ns)) | ($true = (gram_L830233218_inItr @ ns @ tr @ (root @ sK139))) | ~spl94_5),
% 82.03/13.06 inference(trivial_inequality_removal,[status(thm)],[f2614])).
% 82.03/13.06 thf(f2614,plain,(
% 82.03/13.06 ($true = (gram_L830233218_inItr @ ns @ tr @ (root @ sK139))) | ($true != $true) | ($true != (member @ n @ (root @ sK139) @ ns)) | ~spl94_5),
% 82.03/13.06 inference(superposition,[status(thm)],[f2556,f1449])).
% 82.03/13.06 thf(f1449,plain,(
% 82.03/13.06 ( ! [X0 : dtree,X1 : set @ n] : (($true = (gram_L830233218_inItr @ X1 @ X0 @ (root @ X0))) | ($true != (member @ n @ (root @ X0) @ X1))) )),
% 82.03/13.06 inference(cnf_transformation,[status(thm)],[f823])).
% 82.03/13.06 thf(f823,plain,(
% 82.03/13.06 ! [X0 : dtree,X1 : set @ n] : (($true != (member @ n @ (root @ X0) @ X1)) | ($true = (gram_L830233218_inItr @ X1 @ X0 @ (root @ X0))))),
% 82.03/13.06 inference(ennf_transformation,[status(thm)],[f571])).
% 82.03/13.06 thf(f571,plain,(
% 82.03/13.06 ! [X0 : dtree,X1 : set @ n] : (($true = (member @ n @ (root @ X0) @ X1)) => ($true = (gram_L830233218_inItr @ X1 @ X0 @ (root @ X0))))),
% 82.03/13.06 inference(fool_elimination,[status(thm)],[f570])).
% 82.03/13.06 thf(f570,plain,(
% 82.03/13.06 ! [X0 : dtree,X1 : set @ n] : ((member @ n @ (root @ X0) @ X1) => (gram_L830233218_inItr @ X1 @ X0 @ (root @ X0)))),
% 82.03/13.06 inference(rectify,[status(thm)],[f1])).
% 82.03/13.06 thf(f1,axiom,(
% 82.03/13.06 ! [X5 : dtree,X6 : set @ n] : ((member @ n @ (root @ X5) @ X6) => (gram_L830233218_inItr @ X6 @ X5 @ (root @ X5)))),
% 82.03/13.06 file('/export/starexec/sandbox2/tmp/tmp.40Ab8elA6V/DTF2THF_21337.p',fact_0_inItr_OBase)).
% 82.03/13.06 thf(f2556,plain,(
% 82.03/13.06 ( ! [X0 : n] : (($true != (gram_L830233218_inItr @ ns @ sK139 @ X0)) | ((gram_L830233218_inItr @ ns @ tr @ X0) = $true)) ) | ~spl94_5),
% 82.03/13.06 inference(trivial_inequality_removal,[status(thm)],[f2550])).
% 82.03/13.06 thf(f2550,plain,(
% 82.03/13.06 ( ! [X0 : n] : (($true != (gram_L830233218_inItr @ ns @ sK139 @ X0)) | ((gram_L830233218_inItr @ ns @ tr @ X0) = $true) | ($true != $true)) ) | ~spl94_5),
% 82.03/13.06 inference(superposition,[status(thm)],[f1559,f2395])).
% 82.03/13.06 thf(f1559,plain,(
% 82.03/13.06 ( ! [X2 : n,X3 : dtree,X0 : set @ n,X1 : dtree] : (($true != (gram_L1283001940subtr2 @ X0 @ X1 @ X3)) | ($true != (gram_L830233218_inItr @ X0 @ X1 @ X2)) | ($true = (gram_L830233218_inItr @ X0 @ X3 @ X2))) )),
% 82.03/13.06 inference(definition_unfolding,[status(thm)],[f1280,f1275])).
% 82.03/13.06 thf(f1280,plain,(
% 82.03/13.06 ( ! [X2 : n,X3 : dtree,X0 : set @ n,X1 : dtree] : (($true != (gram_L716654942_subtr @ X0 @ X1 @ X3)) | ($true = (gram_L830233218_inItr @ X0 @ X3 @ X2)) | ($true != (gram_L830233218_inItr @ X0 @ X1 @ X2))) )),
% 82.03/13.06 inference(cnf_transformation,[status(thm)],[f973])).
% 82.03/13.06 thf(f973,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : n,X3 : dtree] : (($true != (gram_L716654942_subtr @ X0 @ X1 @ X3)) | ($true = (gram_L830233218_inItr @ X0 @ X3 @ X2)) | ($true != (gram_L830233218_inItr @ X0 @ X1 @ X2)))),
% 82.03/13.06 inference(flattening,[status(thm)],[f972])).
% 82.03/13.06 thf(f972,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : n,X3 : dtree] : ((($true = (gram_L830233218_inItr @ X0 @ X3 @ X2)) | ($true != (gram_L716654942_subtr @ X0 @ X1 @ X3))) | ($true != (gram_L830233218_inItr @ X0 @ X1 @ X2)))),
% 82.03/13.06 inference(ennf_transformation,[status(thm)],[f347])).
% 82.03/13.06 thf(f347,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : n,X3 : dtree] : (($true = (gram_L830233218_inItr @ X0 @ X1 @ X2)) => (($true = (gram_L716654942_subtr @ X0 @ X1 @ X3)) => ($true = (gram_L830233218_inItr @ X0 @ X3 @ X2))))),
% 82.03/13.06 inference(fool_elimination,[status(thm)],[f346])).
% 82.03/13.06 thf(f346,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : n,X3 : dtree] : ((gram_L830233218_inItr @ X0 @ X1 @ X2) => ((gram_L716654942_subtr @ X0 @ X1 @ X3) => (gram_L830233218_inItr @ X0 @ X3 @ X2)))),
% 82.03/13.06 inference(rectify,[status(thm)],[f4])).
% 82.03/13.06 thf(f4,axiom,(
% 82.03/13.06 ! [X6 : set @ n,X5 : dtree,X7 : n,X9 : dtree] : ((gram_L830233218_inItr @ X6 @ X5 @ X7) => ((gram_L716654942_subtr @ X6 @ X5 @ X9) => (gram_L830233218_inItr @ X6 @ X9 @ X7)))),
% 82.03/13.06 file('/export/starexec/sandbox2/tmp/tmp.40Ab8elA6V/DTF2THF_21337.p',fact_3_subtr__inItr)).
% 82.03/13.06 thf(f2581,plain,(
% 82.03/13.06 ~spl94_4 | ~spl94_5 | ~spl94_6),
% 82.03/13.06 inference(avatar_contradiction_clause,[status(thm)],[f2580])).
% 82.03/13.06 thf(f2580,plain,(
% 82.03/13.06 $false | (~spl94_4 | ~spl94_5 | ~spl94_6)),
% 82.03/13.06 inference(subsumption_resolution,[status(thm)],[f2573,f2391])).
% 82.03/13.06 thf(f2573,plain,(
% 82.03/13.06 (sK138 != (root @ sK139)) | (~spl94_5 | ~spl94_6)),
% 82.03/13.06 inference(trivial_inequality_removal,[status(thm)],[f2563])).
% 82.03/13.06 thf(f2563,plain,(
% 82.03/13.06 ($false = $true) | (sK138 != (root @ sK139)) | (~spl94_5 | ~spl94_6)),
% 82.03/13.06 inference(superposition,[status(thm)],[f2395,f2399])).
% 82.03/13.06 thf(f2399,plain,(
% 82.03/13.06 ( ! [X1 : dtree] : (($false = (gram_L1283001940subtr2 @ ns @ X1 @ tr)) | (sK138 != (root @ X1))) ) | ~spl94_6),
% 82.03/13.06 inference(avatar_component_clause,[status(thm)],[f2398])).
% 82.03/13.06 thf(f2398,definition,(
% 82.03/13.06 spl94_6 <=> ! [X1 : dtree] : (($false = (gram_L1283001940subtr2 @ ns @ X1 @ tr)) | (sK138 != (root @ X1)))),
% 82.03/13.06 introduced(definition,[new_symbols(naming,[spl94_6])],[avatar_definition])).
% 82.03/13.06 thf(f2522,plain,(
% 82.03/13.06 ~spl94_3 | ~spl94_7),
% 82.03/13.06 inference(avatar_contradiction_clause,[status(thm)],[f2521])).
% 82.03/13.06 thf(f2521,plain,(
% 82.03/13.06 $false | (~spl94_3 | ~spl94_7)),
% 82.03/13.06 inference(trivial_inequality_removal,[status(thm)],[f2518])).
% 82.03/13.06 thf(f2518,plain,(
% 82.03/13.06 ($false = $true) | (~spl94_3 | ~spl94_7)),
% 82.03/13.06 inference(backward_demodulation,[status(thm)],[f2388,f2402])).
% 82.03/13.06 thf(f2388,plain,(
% 82.03/13.06 ((gram_L830233218_inItr @ ns @ tr @ sK138) = $true) | ~spl94_3),
% 82.03/13.06 inference(avatar_component_clause,[status(thm)],[f2387])).
% 82.03/13.06 thf(f2387,definition,(
% 82.03/13.06 spl94_3 <=> ((gram_L830233218_inItr @ ns @ tr @ sK138) = $true)),
% 82.03/13.06 introduced(definition,[new_symbols(naming,[spl94_3])],[avatar_definition])).
% 82.03/13.06 thf(f2512,plain,(
% 82.03/13.06 ~spl94_3 | ~spl94_6),
% 82.03/13.06 inference(avatar_contradiction_clause,[status(thm)],[f2511])).
% 82.03/13.06 thf(f2511,plain,(
% 82.03/13.06 $false | (~spl94_3 | ~spl94_6)),
% 82.03/13.06 inference(trivial_inequality_removal,[status(thm)],[f2507])).
% 82.03/13.06 thf(f2507,plain,(
% 82.03/13.06 ($true != $true) | (sK138 != sK138) | (~spl94_3 | ~spl94_6)),
% 82.03/13.06 inference(superposition,[status(thm)],[f2506,f2388])).
% 82.03/13.06 thf(f2506,plain,(
% 82.03/13.06 ( ! [X0 : n] : (((gram_L830233218_inItr @ ns @ tr @ X0) != $true) | (sK138 != X0)) ) | ~spl94_6),
% 82.03/13.06 inference(duplicate_literal_removal,[status(thm)],[f2505])).
% 82.03/13.06 thf(f2505,plain,(
% 82.03/13.06 ( ! [X0 : n] : (((gram_L830233218_inItr @ ns @ tr @ X0) != $true) | ((gram_L830233218_inItr @ ns @ tr @ X0) != $true) | (sK138 != X0)) ) | ~spl94_6),
% 82.03/13.06 inference(superposition,[status(thm)],[f2467,f1479])).
% 82.03/13.06 thf(f1479,plain,(
% 82.03/13.06 ( ! [X2 : n,X0 : set @ n,X1 : dtree] : (((root @ (sK86 @ X2 @ X1 @ X0)) = X2) | ($true != (gram_L830233218_inItr @ X0 @ X1 @ X2))) )),
% 82.03/13.06 inference(cnf_transformation,[status(thm)],[f1115])).
% 82.03/13.06 thf(f1115,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : n] : (($true != (gram_L830233218_inItr @ X0 @ X1 @ X2)) | (((root @ (sK86 @ X2 @ X1 @ X0)) = X2) & ($true = (gram_L716654942_subtr @ X0 @ (sK86 @ X2 @ X1 @ X0) @ X1))))),
% 82.03/13.06 inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f934,f1114])).
% 82.03/13.06 thf(f1114,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : n] : (? [X3 : dtree] : (((root @ X3) = X2) & ((gram_L716654942_subtr @ X0 @ X3 @ X1) = $true)) => (((root @ (sK86 @ X2 @ X1 @ X0)) = X2) & ($true = (gram_L716654942_subtr @ X0 @ (sK86 @ X2 @ X1 @ X0) @ X1))))),
% 82.03/13.06 introduced(definition,[],[choice_axiom])).
% 82.03/13.06 thf(f934,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : n] : (($true != (gram_L830233218_inItr @ X0 @ X1 @ X2)) | ? [X3 : dtree] : (((root @ X3) = X2) & ((gram_L716654942_subtr @ X0 @ X3 @ X1) = $true)))),
% 82.03/13.06 inference(ennf_transformation,[status(thm)],[f661])).
% 82.03/13.06 thf(f661,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : n] : (($true = (gram_L830233218_inItr @ X0 @ X1 @ X2)) => ? [X3 : dtree] : (((root @ X3) = X2) & ((gram_L716654942_subtr @ X0 @ X3 @ X1) = $true)))),
% 82.03/13.06 inference(fool_elimination,[status(thm)],[f660])).
% 82.03/13.06 thf(f660,plain,(
% 82.03/13.06 ! [X0 : set @ n,X1 : dtree,X2 : n] : ((gram_L830233218_inItr @ X0 @ X1 @ X2) => ? [X3 : dtree] : ((gram_L716654942_subtr @ X0 @ X3 @ X1) & ((root @ X3) = X2)))),
% 82.03/13.06 inference(rectify,[status(thm)],[f3])).
% 82.03/13.06 thf(f3,axiom,(
% 82.03/13.06 ! [X6 : set @ n,X5 : dtree,X7 : n] : ((gram_L830233218_inItr @ X6 @ X5 @ X7) => ? [X8 : dtree] : ((gram_L716654942_subtr @ X6 @ X8 @ X5) & ((root @ X8) = X7)))),
% 82.03/13.06 file('/export/starexec/sandbox2/tmp/tmp.40Ab8elA6V/DTF2THF_21337.p',fact_2_inItr__subtr)).
% 82.03/13.06 thf(f2467,plain,(
% 82.03/13.06 ( ! [X0 : n] : ((sK138 != (root @ (sK86 @ X0 @ tr @ ns))) | ((gram_L830233218_inItr @ ns @ tr @ X0) != $true)) ) | ~spl94_6),
% 82.03/13.06 inference(trivial_inequality_removal,[status(thm)],[f2463])).
% 82.03/13.06 thf(f2463,plain,(
% 82.03/13.06 ( ! [X0 : n] : (((gram_L830233218_inItr @ ns @ tr @ X0) != $true) | ($false = $true) | (sK138 != (root @ (sK86 @ X0 @ tr @ ns)))) ) | ~spl94_6),
% 82.03/13.06 inference(superposition,[status(thm)],[f1626,f2399])).
% 82.03/13.06 thf(f1626,plain,(
% 82.03/13.06 ( ! [X2 : n,X0 : set @ n,X1 : dtree] : (($true = (gram_L1283001940subtr2 @ X0 @ (sK86 @ X2 @ X1 @ X0) @ X1)) | ($true != (gram_L830233218_inItr @ X0 @ X1 @ X2))) )),
% 82.03/13.06 inference(definition_unfolding,[status(thm)],[f1478,f1275])).
% 82.03/13.06 thf(f1478,plain,(
% 82.03/13.06 ( ! [X2 : n,X0 : set @ n,X1 : dtree] : (($true != (gram_L830233218_inItr @ X0 @ X1 @ X2)) | ($true = (gram_L716654942_subtr @ X0 @ (sK86 @ X2 @ X1 @ X0) @ X1))) )),
% 82.03/13.06 inference(cnf_transformation,[status(thm)],[f1115])).
% 82.03/13.06 thf(f2403,plain,(
% 82.03/13.06 spl94_6 | spl94_7),
% 82.03/13.06 inference(avatar_split_clause,[status(thm)],[f2380,f2401,f2398])).
% 82.03/13.06 thf(f2380,plain,(
% 82.03/13.06 ( ! [X1 : dtree] : (($false = (gram_L1283001940subtr2 @ ns @ X1 @ tr)) | ($false = (gram_L830233218_inItr @ ns @ tr @ sK138)) | (sK138 != (root @ X1))) )),
% 82.03/13.06 inference(equality_proxy_clausification,[status(thm)],[f2379])).
% 82.03/13.06 thf(f2379,plain,(
% 82.03/13.06 ( ! [X1 : dtree] : (($false = (gram_L1283001940subtr2 @ ns @ X1 @ tr)) | ($false = ((root @ X1) = sK138)) | ($false = (gram_L830233218_inItr @ ns @ tr @ sK138))) )),
% 82.03/13.06 inference(binary_proxy_clausification,[status(thm)],[f2378])).
% 82.03/13.06 thf(f2378,plain,(
% 82.03/13.06 ( ! [X1 : dtree] : ((((gram_L1283001940subtr2 @ ns @ X1 @ tr) & ((root @ X1) = sK138)) = $false) | ($false = (gram_L830233218_inItr @ ns @ tr @ sK138))) )),
% 82.03/13.06 inference(beta_eta_normalization,[status(thm)],[f2377])).
% 82.03/13.06 thf(f2377,plain,(
% 82.03/13.06 ( ! [X1 : dtree] : (($false = ((^[Y0 : dtree]: ((gram_L1283001940subtr2 @ ns @ Y0 @ tr) & ((root @ Y0) = sK138))) @ X1)) | ($false = (gram_L830233218_inItr @ ns @ tr @ sK138))) )),
% 82.03/13.06 inference(pi_clausification,[status(thm)],[f2376])).
% 82.03/13.06 thf(f2376,plain,(
% 82.03/13.06 ($false = (?? @ dtree @ (^[Y0 : dtree]: ((gram_L1283001940subtr2 @ ns @ Y0 @ tr) & ((root @ Y0) = sK138))))) | ($false = (gram_L830233218_inItr @ ns @ tr @ sK138))),
% 82.03/13.06 inference(binary_proxy_clausification,[status(thm)],[f2374])).
% 82.03/13.06 thf(f2374,plain,(
% 82.03/13.06 ((gram_L830233218_inItr @ ns @ tr @ sK138) != (?? @ dtree @ (^[Y0 : dtree]: ((gram_L1283001940subtr2 @ ns @ Y0 @ tr) & ((root @ Y0) = sK138)))))),
% 82.03/13.06 inference(beta_eta_normalization,[status(thm)],[f2373])).
% 82.03/13.06 thf(f2373,plain,(
% 82.03/13.06 ((gram_L830233218_inItr @ ns @ tr @ sK138) != ((^[Y0 : n]: (?? @ dtree @ (^[Y1 : dtree]: ((gram_L1283001940subtr2 @ ns @ Y1 @ tr) & ((root @ Y1) = Y0))))) @ sK138))),
% 82.03/13.06 inference(negative_extensionality,[status(thm)],[f2355])).
% 82.03/13.06 thf(f2355,plain,(
% 82.03/13.06 ((gram_L830233218_inItr @ ns @ tr) != (^[Y0 : n]: (?? @ dtree @ (^[Y1 : dtree]: ((gram_L1283001940subtr2 @ ns @ Y1 @ tr) & ((root @ Y1) = Y0))))))),
% 82.03/13.06 inference(equality_resolution,[status(thm)],[f1568])).
% 82.03/13.06 thf(f1568,plain,(
% 82.03/13.06 ((collect @ n @ (gram_L830233218_inItr @ ns @ tr)) != (collect @ n @ (^[Y0 : n]: (?? @ dtree @ (^[Y1 : dtree]: ((gram_L1283001940subtr2 @ ns @ Y1 @ tr) & ((root @ Y1) = Y0)))))))),
% 82.03/13.06 inference(definition_unfolding,[status(thm)],[f1309,f1275])).
% 82.03/13.06 thf(f1309,plain,(
% 82.03/13.06 ((collect @ n @ (gram_L830233218_inItr @ ns @ tr)) != (collect @ n @ (^[Y0 : n]: (?? @ dtree @ (^[Y1 : dtree]: ((gram_L716654942_subtr @ ns @ Y1 @ tr) & ((root @ Y1) = Y0)))))))),
% 82.03/13.06 inference(cnf_transformation,[status(thm)],[f732])).
% 82.03/13.06 thf(f732,plain,(
% 82.03/13.06 ((collect @ n @ (gram_L830233218_inItr @ ns @ tr)) != (collect @ n @ (^[Y0 : n]: (?? @ dtree @ (^[Y1 : dtree]: ((gram_L716654942_subtr @ ns @ Y1 @ tr) & ((root @ Y1) = Y0)))))))),
% 82.03/13.06 inference(flattening,[status(thm)],[f297])).
% 82.03/13.06 thf(f297,plain,(
% 82.03/13.06 ~((collect @ n @ (gram_L830233218_inItr @ ns @ tr)) = (collect @ n @ (^[Y0 : n]: (?? @ dtree @ (^[Y1 : dtree]: ((gram_L716654942_subtr @ ns @ Y1 @ tr) & ((root @ Y1) = Y0)))))))),
% 82.03/13.06 inference(fool_elimination,[status(thm)],[f296])).
% 82.03/13.06 thf(f296,plain,(
% 82.03/13.06 ~((collect @ n @ (gram_L830233218_inItr @ ns @ tr)) = (collect @ n @ (^[X0 : n] : (? [X1 : dtree] : (((root @ X1) = X0) & (gram_L716654942_subtr @ ns @ X1 @ tr))))))),
% 82.03/13.06 inference(rectify,[status(thm)],[f276])).
% 82.03/13.06 thf(f276,negated_conjecture,(
% 82.03/13.06 ~((collect @ n @ (gram_L830233218_inItr @ ns @ tr)) = (collect @ n @ (^[X18 : n] : (? [X19 : dtree] : (((root @ X19) = X18) & (gram_L716654942_subtr @ ns @ X19 @ tr))))))),
% 82.03/13.06 inference(negated_conjecture,[status(cth)],[f275])).
% 82.03/13.06 thf(f275,conjecture,(
% 82.03/13.06 ((collect @ n @ (gram_L830233218_inItr @ ns @ tr)) = (collect @ n @ (^[X18 : n] : (? [X19 : dtree] : (((root @ X19) = X18) & (gram_L716654942_subtr @ ns @ X19 @ tr))))))),
% 82.03/13.06 file('/export/starexec/sandbox2/tmp/tmp.40Ab8elA6V/DTF2THF_21337.p',conj_0)).
% 82.03/13.06 thf(f2396,plain,(
% 82.03/13.06 spl94_3 | spl94_5),
% 82.03/13.06 inference(avatar_split_clause,[status(thm)],[f2384,f2394,f2387])).
% 82.03/13.06 thf(f2384,plain,(
% 82.03/13.06 ((gram_L830233218_inItr @ ns @ tr @ sK138) = $true) | ((gram_L1283001940subtr2 @ ns @ sK139 @ tr) = $true)),
% 82.03/13.06 inference(binary_proxy_clausification,[status(thm)],[f2382])).
% 82.03/13.06 thf(f2382,plain,(
% 82.03/13.06 ($true = ((gram_L1283001940subtr2 @ ns @ sK139 @ tr) & ((root @ sK139) = sK138))) | ((gram_L830233218_inItr @ ns @ tr @ sK138) = $true)),
% 82.03/13.06 inference(beta_eta_normalization,[status(thm)],[f2381])).
% 82.03/13.06 thf(f2381,plain,(
% 82.03/13.06 ((gram_L830233218_inItr @ ns @ tr @ sK138) = $true) | ($true = ((^[Y0 : dtree]: ((gram_L1283001940subtr2 @ ns @ Y0 @ tr) & ((root @ Y0) = sK138))) @ sK139))),
% 82.03/13.06 inference(sigma_clausification,[status(thm)],[f2375])).
% 82.03/13.06 thf(f2375,plain,(
% 82.03/13.06 ((gram_L830233218_inItr @ ns @ tr @ sK138) = $true) | ($true = (?? @ dtree @ (^[Y0 : dtree]: ((gram_L1283001940subtr2 @ ns @ Y0 @ tr) & ((root @ Y0) = sK138)))))),
% 82.03/13.06 inference(binary_proxy_clausification,[status(thm)],[f2374])).
% 82.03/13.06 thf(f2392,plain,(
% 82.03/13.06 spl94_3 | spl94_4),
% 82.03/13.06 inference(avatar_split_clause,[status(thm)],[f2385,f2390,f2387])).
% 82.03/13.06 thf(f2385,plain,(
% 82.03/13.06 (sK138 = (root @ sK139)) | ((gram_L830233218_inItr @ ns @ tr @ sK138) = $true)),
% 82.03/13.06 inference(equality_proxy_clausification,[status(thm)],[f2383])).
% 82.03/13.06 thf(f2383,plain,(
% 82.03/13.06 ((gram_L830233218_inItr @ ns @ tr @ sK138) = $true) | ($true = ((root @ sK139) = sK138))),
% 82.03/13.06 inference(binary_proxy_clausification,[status(thm)],[f2382])).
% 82.03/13.06 % SZS output end Proof for DTF2THF_21337
% 82.03/13.06 % (21901)------------------------------
% 82.03/13.06 % (21901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.03/13.06 % (21901)Termination reason: Refutation
% 82.03/13.06
% 82.03/13.06 % (21901)Memory used [KB]: 7931
% 82.03/13.06 % (21901)Time elapsed: 0.087 s
% 82.03/13.06 % (21901)Instructions burned: 272 (million)
% 82.03/13.06 % (21901)------------------------------
% 82.03/13.06 % (21901)------------------------------
% 82.03/13.06 % (21435)Success in time 11.298 s
%------------------------------------------------------------------------------