TPTP Problem File: SWW919+1.p
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%------------------------------------------------------------------------------
% File : SWW919+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : lab_to_targetProof__233__tactictoe_prove_232__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : lab_to_targetProof__233__tactictoe_prove_232__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v8.2.0, 0.33 v8.1.0, 0.25 v7.5.0, 0.60 v7.4.0, 0.33 v7.3.0
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 99 ( 39 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 75 ( 4 ~; 3 |; 26 &)
% ( 20 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 47 ( 47 usr; 10 con; 0-4 aty)
% Number of variables : 130 ( 118 !; 12 ?)
% SPC : FOF_CSA_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
fof('HL_TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('HL_FALSITY',axiom,
~ p__01(s__02(cbool__00,cF__00)) ).
fof('HL_BOOL_CASES',axiom,
! [Vt] :
( s__02(cbool__00,Vt) = s__02(cbool__00,cT__00)
| s__02(cbool__00,Vt) = s__02(cbool__00,cF__00) ) ).
fof('HL_EXT',axiom,
! [V_3f2384,V_3f2380,Vf,Vg] :
( ! [Vx] : s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vf),s__02(V_3f2384,Vx))) = s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vg),s__02(V_3f2384,Vx)))
=> s__02(cfun__02(V_3f2384,V_3f2380),Vf) = s__02(cfun__02(V_3f2384,V_3f2380),Vg) ) ).
fof('thm.bool.ETA_AX',axiom,
! [V_27B_27,V_27A_27,V_27t_27,Vx] : s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) ).
fof('thm.bool.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('thm.bool.LET_THM',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27x_27] : s__02(V_27B_27,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) ).
fof('thm.bool.FORALL_SIMP',axiom,
! [V_27A_27,V_27t_27] :
( ! [V_27x_27] : p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.AND_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,cF__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cF__00)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.IMP_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,cF__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cF__00)) )
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.REFL_CLAUSE',axiom,
! [V_27A_27,V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_27)
<=> p__01(s__02(cbool__00,cT__00)) ) ).
fof('thm.bool.EQ_SYM_EQ',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27)
<=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27x_27) ) ).
fof('thm.bool.EQ_CLAUSES',axiom,
! [V_27t_27] :
( ( s__02(cbool__00,cT__00) = s__02(cbool__00,V_27t_27)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cT__00)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,cF__00) = s__02(cbool__00,V_27t_27)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cF__00)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.AND_IMP_INTRO',axiom,
! [V_27t1_27,V_27t2_27,V_27t3_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
=> ( p__01(s__02(cbool__00,V_27t2_27))
=> p__01(s__02(cbool__00,V_27t3_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27t1_27))
& p__01(s__02(cbool__00,V_27t2_27)) )
=> p__01(s__02(cbool__00,V_27t3_27)) ) ) ).
fof('thm.bool.IMP_CONG',axiom,
! [V_27x_27,V_27x_7c39_7c_27,V_27y_27,V_27y_7c39_7c_27] :
( ( s__02(cbool__00,V_27x_27) = s__02(cbool__00,V_27x_7c39_7c_27)
& ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> s__02(cbool__00,V_27y_27) = s__02(cbool__00,V_27y_7c39_7c_27) ) )
=> ( ( p__01(s__02(cbool__00,V_27x_27))
=> p__01(s__02(cbool__00,V_27y_27)) )
<=> ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> p__01(s__02(cbool__00,V_27y_7c39_7c_27)) ) ) ) ).
fof('thm.combin.I_THM',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,c_27const_2ecombin_2eI_27__01(s__02(V_27A_27,V_27x_27))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.list.MAP',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27f_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eNIL_27__00)
& ! [V_27f_27,V_27h_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eCONS_27__02(s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27h_27))),s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) ) ).
fof('thm.list.EVERY_DEF',axiom,
! [V_27A_27] :
( ! [V_27P_27] : s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(cbool__00,cT__00)
& ! [V_27P_27,V_27h_27,V_27t_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))))
<=> ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27h_27))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27)))) ) ) ) ).
fof('thm.list.list_induction',axiom,
! [V_27A_27,V_27P_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))))
& ! [V_27t_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))
=> ! [V_27h_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27)))))) ) )
=> ! [V_27l_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)))) ) ).
fof('thm.labLang.line_nchotomy',axiom,
! [V_27A_27,V_27ll_27] :
( ? [V_27n_27,V_27n0_27,V_27n1_27] : s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),V_27ll_27) = s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eLabel_27__03(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27n0_27),s__02(c_27type_2enum_2enum_27__00,V_27n1_27)))
| ? [V_27a_27,V_27l_27,V_27n_27] : s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),V_27ll_27) = s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eAsm_27__03(s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27a_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27l_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
| ? [V_27a_27,V_27c_27,V_27l_27,V_27n_27] : s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),V_27ll_27) = s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eLabAsm_27__04(s__02(c_27type_2elabLang_2easm__with__lab_27__01(V_27A_27),V_27a_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27l_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ) ).
fof('thm.labLang.sec_nchotomy',axiom,
! [V_27A_27,V_27ss_27] :
? [V_27n_27,V_27l_27] : s__02(c_27type_2elabLang_2esec_27__01(V_27A_27),V_27ss_27) = s__02(c_27type_2elabLang_2esec_27__01(V_27A_27),c_27const_2elabLang_2eSection_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2eline_27__01(V_27A_27)),V_27l_27))) ).
fof('thm.lab_to_target.cbw_to_asm_def',axiom,
! [V_27A_27,V__2] :
( ! [V_27r1_27,V_27r2_27] : s__02(c_27type_2easm_2easm_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2easm_2easm_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2easm_2easm_27__01(V_27A_27))),V__2),s__02(c_27type_2enum_2enum_27__00,V_27r1_27))),s__02(c_27type_2enum_2enum_27__00,V_27r2_27))) = s__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27const_2easm_2eInst_27__01(s__02(c_27type_2easm_2einst_27__01(V_27A_27),c_27const_2easm_2eMem_27__03(s__02(c_27type_2easm_2ememop_27__00,c_27const_2easm_2eStore8_27__00),s__02(c_27type_2enum_2enum_27__00,V_27r2_27),s__02(c_27type_2easm_2eaddr_27__01(V_27A_27),c_27const_2easm_2eAddr_27__02(s__02(c_27type_2enum_2enum_27__00,V_27r1_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))))))))
=> ! [V__1] :
( ! [V_27r1_27] : s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2easm_2easm_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2easm_2easm_27__01(V_27A_27))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27r1_27))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2easm_2easm_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2easm_2easm_27__01(V_27A_27))),V__2),s__02(c_27type_2enum_2enum_27__00,V_27r1_27)))
=> ! [V__0] :
( ! [V_27a0_27] : s__02(c_27type_2easm_2easm_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2easm_2easm_27__01(V_27A_27)),V__0),s__02(c_27type_2easm_2easm_27__01(V_27A_27),V_27a0_27))) = s__02(c_27type_2easm_2easm_27__01(V_27A_27),V_27a0_27)
=> ! [V_27a_27] : s__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27const_2elab__to__target_2ecbw__to__asm_27__01(s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27a_27))) = s__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27const_2elabLang_2easm__or__cbw__CASE_27__03(s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27a_27),s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2easm_2easm_27__01(V_27A_27)),V__0),s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2easm_2easm_27__01(V_27A_27))),V__1))) ) ) ) ).
fof('thm.lab_to_target.enc_line_def',axiom,
! [V_27A_27,V__1] :
( ! [V_27l_27,V_27bs_27] : s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),c_27type_2elabLang_2eline_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2elabLang_2easm__with__lab_27__01(V_27A_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),c_27type_2elabLang_2eline_27__01(V_27A_27))),V__1),s__02(c_27type_2elabLang_2easm__with__lab_27__01(V_27A_27),V_27l_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27))) = s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eLabAsm_27__04(s__02(c_27type_2elabLang_2easm__with__lab_27__01(V_27A_27),V_27l_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27)))))
=> ! [V__0] :
( ! [V_27a_27,V_27bs_27] : s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),c_27type_2elabLang_2eline_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),c_27type_2elabLang_2eline_27__01(V_27A_27))),V__0),s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27a_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27))) = s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eAsm_27__03(s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27a_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bs_27)))))
=> ( ! [V_27enc_27,V_27skip__len_27,V_27n1_27,V_27n2_27,V_27n3_27] : s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27type_2elabLang_2eline_27__01(V_27A_27)),c_27const_2elab__to__target_2eenc__line_27__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2enum_2enum_27__00,V_27skip__len_27))),s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eLabel_27__03(s__02(c_27type_2enum_2enum_27__00,V_27n1_27),s__02(c_27type_2enum_2enum_27__00,V_27n2_27),s__02(c_27type_2enum_2enum_27__00,V_27n3_27))))) = s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eLabel_27__03(s__02(c_27type_2enum_2enum_27__00,V_27n1_27),s__02(c_27type_2enum_2enum_27__00,V_27n2_27),s__02(c_27type_2enum_2enum_27__00,V_27skip__len_27)))
& ! [V_27enc_27,V_27skip__len_27,V_27a_27,V_27v0_27,V_27v1_27] : s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27type_2elabLang_2eline_27__01(V_27A_27)),c_27const_2elab__to__target_2eenc__line_27__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2enum_2enum_27__00,V_27skip__len_27))),s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eAsm_27__03(s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27a_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27v0_27),s__02(c_27type_2enum_2enum_27__00,V_27v1_27))))) = s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),c_27type_2elabLang_2eline_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),c_27type_2elabLang_2eline_27__01(V_27A_27))),V__0),s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27a_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),chapp__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27const_2elab__to__target_2ecbw__to__asm_27__01(s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27a_27)))))))
& ! [V_27enc_27,V_27skip__len_27,V_27l_27,V_27v2_27,V_27v3_27,V_27v4_27] : s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27type_2elabLang_2eline_27__01(V_27A_27)),c_27const_2elab__to__target_2eenc__line_27__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2enum_2enum_27__00,V_27skip__len_27))),s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eLabAsm_27__04(s__02(c_27type_2elabLang_2easm__with__lab_27__01(V_27A_27),V_27l_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27v3_27),s__02(c_27type_2enum_2enum_27__00,V_27v4_27))))) = s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),c_27type_2elabLang_2eline_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2elabLang_2easm__with__lab_27__01(V_27A_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),c_27type_2elabLang_2eline_27__01(V_27A_27))),V__1),s__02(c_27type_2elabLang_2easm__with__lab_27__01(V_27A_27),V_27l_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),chapp__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27const_2elab__to__target_2elab__inst_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))),s__02(c_27type_2elabLang_2easm__with__lab_27__01(V_27A_27),V_27l_27))))))) ) ) ) ).
fof('thm.lab_to_target.enc_sec_def',axiom,
! [V_27A_27,V_27enc_27,V_27skip__len_27,V_27k_27,V_27xs_27] : s__02(c_27type_2elabLang_2esec_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elabLang_2esec_27__01(V_27A_27),c_27type_2elabLang_2esec_27__01(V_27A_27)),c_27const_2elab__to__target_2eenc__sec_27__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2enum_2enum_27__00,V_27skip__len_27))),s__02(c_27type_2elabLang_2esec_27__01(V_27A_27),c_27const_2elabLang_2eSection_27__02(s__02(c_27type_2enum_2enum_27__00,V_27k_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2eline_27__01(V_27A_27)),V_27xs_27))))) = s__02(c_27type_2elabLang_2esec_27__01(V_27A_27),c_27const_2elabLang_2eSection_27__02(s__02(c_27type_2enum_2enum_27__00,V_27k_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2eline_27__01(V_27A_27)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27type_2elabLang_2eline_27__01(V_27A_27)),c_27const_2elab__to__target_2eenc__line_27__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2enum_2enum_27__00,V_27skip__len_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2eline_27__01(V_27A_27)),V_27xs_27))))) ).
fof('thm.lab_to_target.enc_sec_list_def',axiom,
! [V_27A_27,V__0] :
( ! [V_27enc_27,V_27xs_27,V_27skip__len_27] : s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),cfun__02(c_27type_2enum_2enum_27__00,c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)))),chapp__02(s__02(cfun__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),cfun__02(c_27type_2enum_2enum_27__00,c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27))))),V__0),s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),V_27xs_27))),s__02(c_27type_2enum_2enum_27__00,V_27skip__len_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2elabLang_2esec_27__01(V_27A_27),c_27type_2elabLang_2esec_27__01(V_27A_27)),c_27const_2elab__to__target_2eenc__sec_27__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2enum_2enum_27__00,V_27skip__len_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),V_27xs_27)))
=> ! [V_27enc_27,V_27xs_27] : s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),c_27const_2elab__to__target_2eenc__sec__list_27__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),V_27xs_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),cfun__02(c_27type_2enum_2enum_27__00,c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)))),chapp__02(s__02(cfun__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),cfun__02(c_27type_2enum_2enum_27__00,c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27))))),V__0),s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),V_27xs_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),chapp__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27const_2easm_2eInst_27__01(s__02(c_27type_2easm_2einst_27__01(V_27A_27),c_27const_2easm_2eSkip_27__00))))))))) ) ).
fof('thm.labProps.line_ok_pre_def',axiom,
! [V_27A_27,V_27v9_27,V_27v8_27,V_27v4_27,V_27v3_27,V_27v2_27,V_27v11_27,V_27v10_27,V_27l_27,V_27c_27,V_27bytes_27,V_27b_27] :
( s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elabLang_2eline_27__01(V_27A_27),cbool__00),c_27const_2elabProps_2eline__ok__pre_27__01(s__02(c_27type_2easm_2easm__config_27__01(V_27A_27),V_27c_27))),s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eAsm_27__03(s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27b_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27bytes_27),s__02(c_27type_2enum_2enum_27__00,V_27l_27))))) = s__02(cbool__00,c_27const_2easm_2easm__ok_27__02(s__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27const_2elab__to__target_2ecbw__to__asm_27__01(s__02(c_27type_2elabLang_2easm__or__cbw_27__01(V_27A_27),V_27b_27))),s__02(c_27type_2easm_2easm__config_27__01(V_27A_27),V_27c_27)))
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elabLang_2eline_27__01(V_27A_27),cbool__00),c_27const_2elabProps_2eline__ok__pre_27__01(s__02(c_27type_2easm_2easm__config_27__01(V_27A_27),V_27c_27))),s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eLabel_27__03(s__02(c_27type_2enum_2enum_27__00,V_27v2_27),s__02(c_27type_2enum_2enum_27__00,V_27v3_27),s__02(c_27type_2enum_2enum_27__00,V_27v4_27))))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elabLang_2eline_27__01(V_27A_27),cbool__00),c_27const_2elabProps_2eline__ok__pre_27__01(s__02(c_27type_2easm_2easm__config_27__01(V_27A_27),V_27c_27))),s__02(c_27type_2elabLang_2eline_27__01(V_27A_27),c_27const_2elabLang_2eLabAsm_27__04(s__02(c_27type_2elabLang_2easm__with__lab_27__01(V_27A_27),V_27v8_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v9_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27v10_27),s__02(c_27type_2enum_2enum_27__00,V_27v11_27))))) = s__02(cbool__00,cT__00) ) ).
fof('thm.labProps.sec_ok_pre_def',axiom,
! [V_27A_27,V_27c_27,V_27k_27,V_27ls_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elabLang_2esec_27__01(V_27A_27),cbool__00),c_27const_2elabProps_2esec__ok__pre_27__01(s__02(c_27type_2easm_2easm__config_27__01(V_27A_27),V_27c_27))),s__02(c_27type_2elabLang_2esec_27__01(V_27A_27),c_27const_2elabLang_2eSection_27__02(s__02(c_27type_2enum_2enum_27__00,V_27k_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2eline_27__01(V_27A_27)),V_27ls_27))))) = s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2elabLang_2eline_27__01(V_27A_27),cbool__00),c_27const_2elabProps_2eline__ok__pre_27__01(s__02(c_27type_2easm_2easm__config_27__01(V_27A_27),V_27c_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2eline_27__01(V_27A_27)),V_27ls_27))) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27code_27,V_27enc_27,V_27c_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2elabLang_2esec_27__01(V_27A_27),cbool__00),c_27const_2elabProps_2esec__ok__pre_27__01(s__02(c_27type_2easm_2easm__config_27__01(V_27A_27),V_27c_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),V_27code_27))))
=> p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2elabLang_2esec_27__01(V_27A_27),cbool__00),c_27const_2elabProps_2esec__ok__pre_27__01(s__02(c_27type_2easm_2easm__config_27__01(V_27A_27),V_27c_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),c_27const_2elab__to__target_2eenc__sec__list_27__02(s__02(cfun__02(c_27type_2easm_2easm_27__01(V_27A_27),c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))))),V_27enc_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2elabLang_2esec_27__01(V_27A_27)),V_27code_27)))))) ) ).
%------------------------------------------------------------------------------