TPTP Problem File: SWW861+1.p
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%------------------------------------------------------------------------------
% File : SWW861+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : namespaceProps__19__nsMap_nsEmpty__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : namespaceProps__19__nsMap_nsEmpty__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 42 ( 20 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 33 ( 3 ~; 1 |; 14 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 50 !; 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.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.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.namespace.namespace_11',axiom,
! [V_27M_27,V_27N_27,V_27V_27,V_27a0_27,V_27a1_27,V_27a0_7c39_7c_27,V_27a1_7c39_7c_27] :
( s__02(c_27type_2enamespace_2enamespace_27__03(V_27M_27,V_27N_27,V_27V_27),c_27const_2enamespace_2eBind_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27N_27,V_27V_27)),V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27M_27,c_27type_2enamespace_2enamespace_27__03(V_27M_27,V_27N_27,V_27V_27))),V_27a1_27))) = s__02(c_27type_2enamespace_2enamespace_27__03(V_27M_27,V_27N_27,V_27V_27),c_27const_2enamespace_2eBind_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27N_27,V_27V_27)),V_27a0_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27M_27,c_27type_2enamespace_2enamespace_27__03(V_27M_27,V_27N_27,V_27V_27))),V_27a1_7c39_7c_27)))
<=> ( s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27N_27,V_27V_27)),V_27a0_27) = s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27N_27,V_27V_27)),V_27a0_7c39_7c_27)
& s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27M_27,c_27type_2enamespace_2enamespace_27__03(V_27M_27,V_27N_27,V_27V_27))),V_27a1_27) = s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27M_27,c_27type_2enamespace_2enamespace_27__03(V_27M_27,V_27N_27,V_27V_27))),V_27a1_7c39_7c_27) ) ) ).
fof('thm.namespace.nsEmpty_def',axiom,
! [V_27A_27,V_27B_27,V_27C_27] : s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2enamespace_2ensEmpty_27__00) = s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2enamespace_2eBind_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))),c_27const_2elist_2eNIL_27__00))) ).
fof('thm.termination.nsMap_def',axiom,
! [V_27C_27,V_27A_27,V_27B_27,V_27D_27,V__3] :
( ! [V_27mn_27,V_27f_27,V_27e_27] : s__02(c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27)),chapp__02(s__02(cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))),chapp__02(s__02(cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27)))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))))),V__3),s__02(V_27A_27,V_27mn_27))),s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27))),s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),V_27e_27))) = s__02(c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27)),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27mn_27),s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2enamespace_2ensMap_27__02(s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27),s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),V_27e_27)))))
=> ! [V__2] :
( ! [V_27f_27,V_27mn_27] : s__02(cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27)))),chapp__02(s__02(cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(V_27A_27,cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))))),V__2),s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27))),s__02(V_27A_27,V_27mn_27))) = s__02(cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))),chapp__02(s__02(cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27)))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))))),V__3),s__02(V_27A_27,V_27mn_27))),s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27)))
=> ! [V__1] :
( ! [V_27n_27,V_27f_27,V_27x_27] : s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),chapp__02(s__02(cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)),chapp__02(s__02(cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27))),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)))),V__1),s__02(V_27B_27,V_27n_27))),s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27))),s__02(V_27D_27,V_27x_27))) = 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_27n_27),s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27),s__02(V_27D_27,V_27x_27)))))
=> ! [V__0] :
( ! [V_27f_27,V_27n_27] : s__02(cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27))),chapp__02(s__02(cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(V_27B_27,cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)))),V__0),s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27))),s__02(V_27B_27,V_27n_27))) = s__02(cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)),chapp__02(s__02(cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27))),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)))),V__1),s__02(V_27B_27,V_27n_27))),s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27)))
=> ! [V_27v_27,V_27m_27,V_27f_27] : s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2enamespace_2ensMap_27__02(s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27),s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27const_2enamespace_2eBind_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27D_27)),V_27v_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27))),V_27m_27))))) = s__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2enamespace_2eBind_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(V_27B_27,cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27))),chapp__02(s__02(cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(V_27B_27,cfun__02(V_27D_27,c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27)))),V__0),s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27D_27)),V_27v_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27)),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(V_27A_27,cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27)))),chapp__02(s__02(cfun__02(cfun__02(V_27D_27,V_27C_27),cfun__02(V_27A_27,cfun__02(c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27),c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27C_27))))),V__2),s__02(cfun__02(V_27D_27,V_27C_27),V_27f_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27A_27,c_27type_2enamespace_2enamespace_27__03(V_27A_27,V_27B_27,V_27D_27))),V_27m_27))))) ) ) ) ) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27C_27,V_27D_27,V_27B_27,V_27f_27] : s__02(c_27type_2enamespace_2enamespace_27__03(V_27C_27,V_27D_27,V_27B_27),c_27const_2enamespace_2ensMap_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2enamespace_2enamespace_27__03(V_27C_27,V_27D_27,V_27A_27),c_27const_2enamespace_2ensEmpty_27__00))) = s__02(c_27type_2enamespace_2enamespace_27__03(V_27C_27,V_27D_27,V_27B_27),c_27const_2enamespace_2ensEmpty_27__00) ).
%------------------------------------------------------------------------------