TPTP Problem File: SWW898+1.p
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%------------------------------------------------------------------------------
% File : SWW898+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : clos_callProof__73__v_to_list_wfv__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : clos_callProof__73__v_to_list_wfv__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 28 ( 4 unt; 0 def)
% Number of atoms : 158 ( 58 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 139 ( 9 ~; 3 |; 64 &)
% ( 35 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 39 ( 39 usr; 12 con; 0-5 aty)
% Number of variables : 170 ( 165 !; 5 ?)
% SPC : FOF_THM_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.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('thm.bool.IMP_ANTISYM_AX',axiom,
! [V_27t1_27,V_27t2_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_27t2_27))
=> p__01(s__02(cbool__00,V_27t1_27)) )
=> s__02(cbool__00,V_27t1_27) = s__02(cbool__00,V_27t2_27) ) ) ).
fof('thm.bool.FALSITY',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,cF__00))
=> p__01(s__02(cbool__00,V_27t_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.IMP_DISJ_THM',axiom,
! [V_27A_270,V_27B_270] :
( ( p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,V_27B_270)) )
<=> ( ~ p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) ) ) ).
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.bool.UNWIND_FORALL_THM2',axiom,
! [V_27A_27,V_27f_27,V_27v_27] :
( ! [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27v_27)
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27f_27),s__02(V_27A_27,V_27x_27)))) )
<=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27f_27),s__02(V_27A_27,V_27v_27)))) ) ).
fof('thm.option.option_nchotomy',axiom,
! [V_27A_27,V_27opt_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27opt_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
| ? [V_27x_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27opt_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) ) ).
fof('thm.option.option_case_def',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27v_27,V_27f_27] : s__02(V_27B_27,c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00),s__02(V_27B_27,V_27v_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27))) = s__02(V_27B_27,V_27v_27)
& ! [V_27x_27,V_27v_27,V_27f_27] : s__02(V_27B_27,c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))),s__02(V_27B_27,V_27v_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_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.option.SOME_11',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27y_27)))
<=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27) ) ).
fof('thm.option.NOT_NONE_SOME',axiom,
! [V_27A_27,V_27x_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00) != s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) ).
fof('thm.option.IF_EQUALS_OPTION',axiom,
! [V_27A_27,V_27y_27,V_27x_27,V_27P_27] :
( ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
<=> ~ p__01(s__02(cbool__00,V_27P_27)) )
& ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
<=> p__01(s__02(cbool__00,V_27P_27)) )
& ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27y_27)))
<=> ( p__01(s__02(cbool__00,V_27P_27))
& s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27) ) )
& ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27y_27)))
<=> ( ~ p__01(s__02(cbool__00,V_27P_27))
& s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27) ) ) ) ).
fof('thm.option.IF_NONE_EQUALS_OPTION',axiom,
! [V_27A_27,V_27x_27,V_27X_27,V_27P_27] :
( ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27X_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
<=> ( p__01(s__02(cbool__00,V_27P_27))
=> p__01(s__02(cbool__00,c_27const_2eoption_2eIS__NONE_27__01(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27X_27)))) ) )
& ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27X_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
<=> ( p__01(s__02(cbool__00,c_27const_2eoption_2eIS__SOME_27__01(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27X_27))))
=> p__01(s__02(cbool__00,V_27P_27)) ) )
& ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27X_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27)))
<=> ( p__01(s__02(cbool__00,V_27P_27))
& s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27X_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) ) )
& ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27X_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27)))
<=> ( ~ p__01(s__02(cbool__00,V_27P_27))
& s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27X_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_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.closSem.v_to_list_ind',axiom,
! [V_27P_27] :
( ( ! [V_27tag_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27tag_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00))))))
& ! [V_27tag_27,V_27h_27,V_27bt_27] :
( ( s__02(c_27type_2enum_2enum_27__00,V_27tag_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebackend__common_2econs__tag_27__00)
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,V_27bt_27)))) )
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27tag_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27h_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27bt_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00)))))))))) )
& ! [V_27v_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eNumber_27__01(s__02(c_27type_2einteger_2eint_27__00,V_27v_27))))))
& ! [V_27v1_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eWord64_27__01(s__02(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_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27v1_27))))))
& ! [V_27v2_27,V_27v32_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27v2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27v32_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00))))))))
& ! [V_27v2_27,V_27v32_27,V_27v36_27,V_27v40_27,V_27v41_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27v2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27v32_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27v36_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27v40_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v41_27))))))))))))
& ! [V_27v4_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eByteVector_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_27v4_27))))))
& ! [V_27v5_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRefPtr_27__01(s__02(c_27type_2enum_2enum_27__00,V_27v5_27))))))
& ! [V_27v6_27,V_27v7_27,V_27v8_27,V_27v9_27,V_27v10_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eClosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27v6_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v7_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v8_27),s__02(c_27type_2enum_2enum_27__00,V_27v9_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27v10_27))))))
& ! [V_27v11_27,V_27v12_27,V_27v13_27,V_27v14_27,V_27v15_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRecclosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27v11_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v12_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v13_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27v14_27),s__02(c_27type_2enum_2enum_27__00,V_27v15_27)))))) )
=> ! [V_27v_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),V_27P_27),s__02(c_27type_2eclosSem_2ev_27__00,V_27v_27)))) ) ).
fof('thm.closSem.v_to_list_def',axiom,
! [V__0] :
( ! [V_27h_27,V_27t_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)))),V__0),s__02(c_27type_2eclosSem_2ev_27__00,V_27h_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27t_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27h_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27t_27)))))
=> ( ! [V_27tag_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(c_27type_2enum_2enum_27__00,V_27tag_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebackend__common_2enil__tag_27__00) )
& s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27tag_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00))) )
& ! [V_27tag_27,V_27h_27,V_27bt_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(c_27type_2enum_2enum_27__00,V_27tag_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebackend__common_2econs__tag_27__00) )
& s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27tag_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27h_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27bt_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00))))))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,V_27bt_27))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)))),V__0),s__02(c_27type_2eclosSem_2ev_27__00,V_27h_27))))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00))) )
& ! [V_27v_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eNumber_27__01(s__02(c_27type_2einteger_2eint_27__00,V_27v_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00)
& ! [V_27v1_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eWord64_27__01(s__02(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_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27v1_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00)
& ! [V_27v32_27,V_27v2_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27v2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27v32_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00))))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00)
& ! [V_27v41_27,V_27v40_27,V_27v36_27,V_27v32_27,V_27v2_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27v2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27v32_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27v36_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27v40_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v41_27))))))))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00)
& ! [V_27v4_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eByteVector_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_27v4_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00)
& ! [V_27v5_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRefPtr_27__01(s__02(c_27type_2enum_2enum_27__00,V_27v5_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00)
& ! [V_27v9_27,V_27v8_27,V_27v7_27,V_27v6_27,V_27v10_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eClosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27v6_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v7_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v8_27),s__02(c_27type_2enum_2enum_27__00,V_27v9_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27v10_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00)
& ! [V_27v15_27,V_27v14_27,V_27v13_27,V_27v12_27,V_27v11_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRecclosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27v11_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v12_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v13_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27v14_27),s__02(c_27type_2enum_2enum_27__00,V_27v15_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eNONE_27__00) ) ) ).
fof('thm.clos_callProof.wfv_def',axiom,
! [V__0] :
( ! [V_27g_27,V_27l_27,V_27a_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00))),V__0),s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2eclosSem_2ev_27__00,V_27a_27))) = s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2eclosSem_2ev_27__00,V_27a_27)))
=> ( ! [V_27v3_27,V_27v2_27,V_27v1_27,V_27v0_27,V_27l_27,V_27g_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eClosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),c_27const_2eoption_2eNONE_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v1_27),s__02(c_27type_2enum_2enum_27__00,V_27v2_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27v3_27))))) = s__02(cbool__00,cF__00)
& ! [V_27v7_27,V_27v6_27,V_27v5_27,V_27v4_27,V_27l_27,V_27g_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRecclosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),c_27const_2eoption_2eNONE_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v4_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27v5_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27v6_27),s__02(c_27type_2enum_2enum_27__00,V_27v7_27))))) = s__02(cbool__00,cF__00)
& ! [V_27vs_27,V_27n_27,V_27loc_27,V_27l_27,V_27g_27,V_27env_27,V_27bod_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eClosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2enum_2enum_27__00,V_27loc_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27env_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27bod_27))))))
<=> ( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00))),V__0),s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs_27))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00))),V__0),s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27env_27))))
& ? [V_27fns2_27] : p__01(s__02(cbool__00,c_27const_2eclos__callProof_2erecclosure__rel_27__05(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27),s__02(c_27type_2enum_2enum_27__00,V_27loc_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27bod_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),c_27const_2elist_2eNIL_27__00))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27fns2_27)))) ) )
& ! [V_27vs_27,V_27loc_27,V_27l_27,V_27i_27,V_27g_27,V_27fns_27,V_27env_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRecclosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2enum_2enum_27__00,V_27loc_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27env_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27fns_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27))))))
<=> ( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00))),V__0),s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs_27))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00))),V__0),s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27env_27))))
& ? [V_27fns2_27] : p__01(s__02(cbool__00,c_27const_2eclos__callProof_2erecclosure__rel_27__05(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27),s__02(c_27type_2enum_2enum_27__00,V_27loc_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27fns_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27fns2_27)))) ) )
& ! [V_27vs_27,V_27v8_27,V_27l_27,V_27g_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27v8_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs_27))))) = s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00))),V__0),s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27vs_27)))
& ! [V_27v9_27,V_27v15_27,V_27v10_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27v9_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27v10_27))),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eNumber_27__01(s__02(c_27type_2einteger_2eint_27__00,V_27v15_27))))) = s__02(cbool__00,cT__00)
& ! [V_27v9_27,V_27v16_27,V_27v10_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27v9_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27v10_27))),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eWord64_27__01(s__02(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_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27v16_27))))) = s__02(cbool__00,cT__00)
& ! [V_27v9_27,V_27v19_27,V_27v10_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27v9_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27v10_27))),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eByteVector_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_27v19_27))))) = s__02(cbool__00,cT__00)
& ! [V_27v9_27,V_27v20_27,V_27v10_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27v9_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27v10_27))),s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRefPtr_27__01(s__02(c_27type_2enum_2enum_27__00,V_27v20_27))))) = s__02(cbool__00,cT__00) ) ) ).
fof(conjecture,conjecture,
! [V_27g1_27,V_27l1_27,V_27h_27,V_27x_27] :
( ( s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2ev__to__list_27__01(s__02(c_27type_2eclosSem_2ev_27__00,V_27h_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27x_27)))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l1_27))),s__02(c_27type_2eclosSem_2ev_27__00,V_27h_27)))) )
=> p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),c_27const_2eclos__callProof_2ewfv_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esptree_2espt_27__01(c_27type_2eone_2eone_27__00),c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)))),V_27g1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27l1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27x_27)))) ) ).
%------------------------------------------------------------------------------