TPTP Problem File: SWW864+1.p
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%------------------------------------------------------------------------------
% File : SWW864+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : semanticPrimitivesProps__20__do_con_check_build_conv__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : semanticPrimitivesProps__20__do_con_check_build_conv__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 62 ( 34 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 44 ( 4 ~; 2 |; 6 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 101 ( 95 !; 6 ?)
% 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.EXISTS_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.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.bool.EXISTS_REFL',axiom,
! [V_27A_27,V_27a_27] :
? [V_27x_27] : s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_27) ).
fof('thm.pair.ABS_PAIR_THM',axiom,
! [V_27A_27,V_27B_27,V_27x_27] :
? [V_27q_27,V_27r_27] : s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27x_27) = s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27q_27),s__02(V_27B_27,V_27r_27))) ).
fof('thm.pair.pair_case_thm',axiom,
! [V_27A_27,V_27B_27,V_27C_27,V_27y_27,V_27x_27,V_27f_27] : s__02(V_27A_27,c_27const_2epair_2epair__CASE_27__02(s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(V_27B_27,V_27x_27),s__02(V_27C_27,V_27y_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27C_27,V_27A_27),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_27),s__02(V_27B_27,V_27x_27))),s__02(V_27C_27,V_27y_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.semanticPrimitives.do_con_check_def',axiom,
! [V_27A_27,V_27B_27,V_27D_27,V_27C_27,V__3] :
( ! [V_27l_27,V_27l_7c39_7c_27,V_27ns_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27D_27,cbool__00),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(V_27D_27,cbool__00)),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(V_27C_27,cfun__02(V_27D_27,cbool__00))),V__3),s__02(V_27C_27,V_27l_27))),s__02(V_27C_27,V_27l_7c39_7c_27))),s__02(V_27D_27,V_27ns_27))))
<=> s__02(V_27C_27,V_27l_27) = s__02(V_27C_27,V_27l_7c39_7c_27) )
=> ! [V__2] :
( ! [V_27l_27,V_27l_7c39_7c_27] : s__02(cfun__02(V_27D_27,cbool__00),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(V_27D_27,cbool__00)),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(V_27C_27,cfun__02(V_27D_27,cbool__00))),V__2),s__02(V_27C_27,V_27l_27))),s__02(V_27C_27,V_27l_7c39_7c_27))) = s__02(cfun__02(V_27D_27,cbool__00),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(V_27D_27,cbool__00)),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(V_27C_27,cfun__02(V_27D_27,cbool__00))),V__3),s__02(V_27C_27,V_27l_27))),s__02(V_27C_27,V_27l_7c39_7c_27)))
=> ! [V__1] :
( ! [V_27l_27,V_27v_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27),cbool__00),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27),cbool__00)),V__1),s__02(V_27C_27,V_27l_27))),s__02(c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27),V_27v_27))) = s__02(cbool__00,c_27const_2epair_2epair__CASE_27__02(s__02(c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27),V_27v_27),s__02(cfun__02(V_27C_27,cfun__02(V_27D_27,cbool__00)),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(V_27C_27,cfun__02(V_27D_27,cbool__00))),V__2),s__02(V_27C_27,V_27l_27)))))
=> ! [V__0] :
( ! [V_27cenv_27,V_27l_27,V_27n_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cbool__00),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27)),cfun__02(V_27C_27,cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cbool__00))),V__0),s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27)),V_27cenv_27))),s__02(V_27C_27,V_27l_27))),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),V_27n_27))) = s__02(cbool__00,c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27)),c_27const_2enamespace_2ensLookup_27__02(s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27)),V_27cenv_27),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),V_27n_27))),s__02(cbool__00,cF__00),s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27),cbool__00),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27),cbool__00)),V__1),s__02(V_27C_27,V_27l_27)))))
=> ! [V_27cenv_27,V_27n__opt_27,V_27l_27] : s__02(cbool__00,c_27const_2esemanticPrimitives_2edo__con__check_27__03(s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27)),V_27cenv_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27)),V_27n__opt_27),s__02(V_27C_27,V_27l_27))) = s__02(cbool__00,c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27)),V_27n__opt_27),s__02(cbool__00,cT__00),s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cbool__00),chapp__02(s__02(cfun__02(V_27C_27,cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27)),cfun__02(V_27C_27,cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cbool__00))),V__0),s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,c_27type_2epair_2eprod_27__02(V_27C_27,V_27D_27)),V_27cenv_27))),s__02(V_27C_27,V_27l_27))))) ) ) ) ) ).
fof('thm.semanticPrimitives.build_conv_def',axiom,
! [V_27A_27,V_27B_27,V__3] :
( ! [V_27id_27,V_27vs_27,V_27t_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)))),V__3),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27id_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27))),s__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,V_27t_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00,c_27const_2esemanticPrimitives_2eConv_27__02(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2esemanticPrimitives_2etid__or__exn_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27const_2enamespace_2eid__to__n_27__01(s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27id_27))),s__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,V_27t_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27)))))
=> ! [V__2] :
( ! [V_27id_27,V_27vs_27,V_27len_27] : s__02(cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)))),chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))))),V__2),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27id_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27))),s__02(V_27B_27,V_27len_27))) = s__02(cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)))),V__3),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27id_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27)))
=> ! [V__1] :
( ! [V_27id_27,V_27vs_27,V_27v_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)))),V__1),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27id_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27))),s__02(c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00),V_27v_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2epair_2epair__CASE_27__02(s__02(c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00),V_27v_27),s__02(cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)))),chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(V_27B_27,cfun__02(c_27type_2esemanticPrimitives_2etid__or__exn_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))))),V__2),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27id_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27)))))
=> ! [V__0] :
( ! [V_27envC_27,V_27vs_27,V_27id_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)))),V__0),s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),V_27envC_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27))),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27id_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),c_27const_2enamespace_2ensLookup_27__02(s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),V_27envC_27),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27id_27))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2eoption_2eNONE_27__00),s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)))),V__1),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27id_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27)))))
=> ! [V_27envC_27,V_27cn_27,V_27vs_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2esemanticPrimitives_2ebuild__conv_27__03(s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),V_27envC_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))),V_27cn_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))),V_27cn_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00,c_27const_2esemanticPrimitives_2eConv_27__02(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),c_27const_2eoption_2eNONE_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27))))),s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00))),chapp__02(s__02(cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00)))),V__0),s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),V_27envC_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27))))) ) ) ) ) ).
fof(conjecture,conjecture,
! [V_27B_27,V_27A_27,V_27tenvC_27,V_27cn_27,V_27vs_27,V_27l_27] :
( p__01(s__02(cbool__00,c_27const_2esemanticPrimitives_2edo__con__check_27__03(s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),V_27tenvC_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))),V_27cn_27),s__02(V_27B_27,V_27l_27))))
=> ? [V_27v_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2esemanticPrimitives_2ebuild__conv_27__03(s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2epair_2eprod_27__02(V_27B_27,c_27type_2esemanticPrimitives_2etid__or__exn_27__00)),V_27tenvC_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enamespace_2eid_27__02(V_27A_27,c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))),V_27cn_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2ev_27__00),V_27vs_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2esemanticPrimitives_2ev_27__00),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00,V_27v_27))) ) ).
%------------------------------------------------------------------------------