TPTP Problem File: SWW866+1.p
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%------------------------------------------------------------------------------
% File : SWW866+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : typeSysProps__43__tenv_ctor_ok_lookup__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : typeSysProps__43__tenv_ctor_ok_lookup__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 72 ( 20 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 61 ( 4 ~; 1 |; 20 &)
% ( 17 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% 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.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
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.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.pair.UNCURRY_DEF',axiom,
! [V_27C_27,V_27A_27,V_27B_27,V_27f_27,V_27x_27,V_27y_27] : s__02(V_27C_27,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27C_27),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_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_27x_27),s__02(V_27B_27,V_27y_27))))) = s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27B_27,V_27C_27),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_27),s__02(V_27A_27,V_27x_27))),s__02(V_27B_27,V_27y_27))) ).
fof('thm.namespaceProps.nsLookup_nsAll',axiom,
! [V_27A_27,V_27B_27,V_27C_27,V_27env_27,V_27x_27,V_27P_27,V_27v_27] :
( ( p__01(s__02(cbool__00,c_27const_2enamespace_2ensAll_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cfun__02(V_27C_27,cbool__00)),V_27P_27),s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27),V_27env_27))))
& s__02(c_27type_2eoption_2eoption_27__01(V_27C_27),c_27const_2enamespace_2ensLookup_27__02(s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27),V_27env_27),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),V_27x_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27C_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27C_27,V_27v_27))) )
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27C_27,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cfun__02(V_27C_27,cbool__00)),V_27P_27),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),V_27x_27))),s__02(V_27C_27,V_27v_27)))) ) ).
fof('thm.typeSoundInvariants.tenv_ctor_ok_def',axiom,
! [V_27A_27,V_27B_27,V_27C_27,V__3] :
( ! [V_27tvs_27,V_27ts_27,V_27tn_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(V_27C_27,cbool__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),cfun__02(V_27C_27,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),cfun__02(V_27C_27,cbool__00))),V__3),s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27tvs_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27ts_27))),s__02(V_27C_27,V_27tn_27))) = s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2east_2et_27__00,cbool__00),c_27const_2etypeSystem_2echeck__freevars_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27tvs_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27ts_27)))
=> ! [V__2] :
( ! [V_27tvs_27,V_27ts_27] : s__02(cfun__02(V_27C_27,cbool__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),cfun__02(V_27C_27,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),cfun__02(V_27C_27,cbool__00))),V__2),s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27tvs_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27ts_27))) = s__02(cfun__02(V_27C_27,cbool__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),cfun__02(V_27C_27,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),cfun__02(V_27C_27,cbool__00))),V__3),s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27tvs_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27ts_27)))
=> ! [V__1] :
( ! [V_27tvs_27] : s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27),cbool__00)),V__1),s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27tvs_27))) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27),cbool__00),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),cfun__02(V_27C_27,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),cfun__02(V_27C_27,cbool__00))),V__2),s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27tvs_27)))))
=> ! [V__0] :
( ! [V_27id_27] : s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27)),cbool__00),chapp__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27)),cbool__00)),V__0),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),V_27id_27))) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27)),cbool__00),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27),cbool__00)),V__1)))
=> ! [V_27tenvC_27] : s__02(cbool__00,c_27const_2etypeSoundInvariants_2etenv__ctor__ok_27__01(s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27))),V_27tenvC_27))) = s__02(cbool__00,c_27const_2enamespace_2ensAll_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_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(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27))),V_27tenvC_27))) ) ) ) ) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27B_27,V_27C_27,V_27tenvC_27,V_27cn_27,V_27tvs_27,V_27ts_27,V_27tn_27] :
( ( p__01(s__02(cbool__00,c_27const_2etypeSoundInvariants_2etenv__ctor__ok_27__01(s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27))),V_27tenvC_27))))
& s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_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(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27))),V_27tenvC_27),s__02(c_27type_2enamespace_2eid_27__02(V_27A_27,V_27B_27),V_27cn_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27))),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27tvs_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27ts_27),s__02(V_27C_27,V_27tn_27))))))) )
=> p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2east_2et_27__00,cbool__00),c_27const_2etypeSystem_2echeck__freevars_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),V_27tvs_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2et_27__00),V_27ts_27)))) ) ).
%------------------------------------------------------------------------------