TPTP Problem File: SWW849+1.p
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%------------------------------------------------------------------------------
% File : SWW849+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : misc__13__map_fromAList__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : misc__13__map_fromAList__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v8.1.0, 0.25 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 26 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12 ( 1 ~; 1 |; 3 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 59 ( 57 !; 2 ?)
% SPC : FOF_CSA_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
fof('HL_TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('HL_FALSITY',axiom,
~ p__01(s__02(cbool__00,cF__00)) ).
fof('HL_BOOL_CASES',axiom,
! [Vt] :
( s__02(cbool__00,Vt) = s__02(cbool__00,cT__00)
| s__02(cbool__00,Vt) = s__02(cbool__00,cF__00) ) ).
fof('HL_EXT',axiom,
! [V_3f2384,V_3f2380,Vf,Vg] :
( ! [Vx] : s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vf),s__02(V_3f2384,Vx))) = s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vg),s__02(V_3f2384,Vx)))
=> s__02(cfun__02(V_3f2384,V_3f2380),Vf) = s__02(cfun__02(V_3f2384,V_3f2380),Vg) ) ).
fof('thm.bool.ETA_AX',axiom,
! [V_27B_27,V_27A_27,V_27t_27,Vx] : s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) ).
fof('thm.bool.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('thm.bool.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.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.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.list.MAP',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27f_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eNIL_27__00)
& ! [V_27f_27,V_27h_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eCONS_27__02(s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27h_27))),s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) ) ).
fof('thm.list.list_induction',axiom,
! [V_27A_27,V_27P_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))))
& ! [V_27t_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))
=> ! [V_27h_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27)))))) ) )
=> ! [V_27l_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)))) ) ).
fof('thm.sptree.fromAList_def',axiom,
! [V_27A_27] :
( s__02(c_27type_2esptree_2espt_27__01(V_27A_27),c_27const_2esptree_2efromAList_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2esptree_2espt_27__01(V_27A_27),c_27const_2esptree_2eLN_27__00)
& ! [V_27y_27,V_27xs_27,V_27x_27] : s__02(c_27type_2esptree_2espt_27__01(V_27A_27),c_27const_2esptree_2efromAList_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(V_27A_27,V_27y_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)),V_27xs_27))))) = s__02(c_27type_2esptree_2espt_27__01(V_27A_27),c_27const_2esptree_2einsert_27__03(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(V_27A_27,V_27y_27),s__02(c_27type_2esptree_2espt_27__01(V_27A_27),c_27const_2esptree_2efromAList_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)),V_27xs_27))))) ) ).
fof('thm.sptree.map_LN',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27t_27] :
( s__02(c_27type_2esptree_2espt_27__01(V_27B_27),c_27const_2esptree_2emap_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2esptree_2espt_27__01(V_27A_27),V_27t_27))) = s__02(c_27type_2esptree_2espt_27__01(V_27B_27),c_27const_2esptree_2eLN_27__00)
<=> s__02(c_27type_2esptree_2espt_27__01(V_27A_27),V_27t_27) = s__02(c_27type_2esptree_2espt_27__01(V_27A_27),c_27const_2esptree_2eLN_27__00) ) ).
fof('thm.sptree.map_insert',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27x_27,V_27y_27,V_27z_27] : s__02(c_27type_2esptree_2espt_27__01(V_27B_27),c_27const_2esptree_2emap_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2esptree_2espt_27__01(V_27A_27),c_27const_2esptree_2einsert_27__03(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(V_27A_27,V_27y_27),s__02(c_27type_2esptree_2espt_27__01(V_27A_27),V_27z_27))))) = s__02(c_27type_2esptree_2espt_27__01(V_27B_27),c_27const_2esptree_2einsert_27__03(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27y_27))),s__02(c_27type_2esptree_2espt_27__01(V_27B_27),c_27const_2esptree_2emap_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2esptree_2espt_27__01(V_27A_27),V_27z_27))))) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27B_27,V__1] :
( ! [V_27k_27,V_27f_27,V_27v_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27),chapp__02(s__02(cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,V_27A_27),cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(cfun__02(V_27B_27,V_27A_27),cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27k_27))),s__02(cfun__02(V_27B_27,V_27A_27),V_27f_27))),s__02(V_27B_27,V_27v_27))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27k_27),s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27B_27,V_27A_27),V_27f_27),s__02(V_27B_27,V_27v_27)))))
=> ! [V__0] :
( ! [V_27f_27,V_27k_27] : s__02(cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27))),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)))),V__0),s__02(cfun__02(V_27B_27,V_27A_27),V_27f_27))),s__02(c_27type_2enum_2enum_27__00,V_27k_27))) = s__02(cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,V_27A_27),cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(cfun__02(V_27B_27,V_27A_27),cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27k_27))),s__02(cfun__02(V_27B_27,V_27A_27),V_27f_27)))
=> ! [V_27f_27,V_27ls_27] : s__02(c_27type_2esptree_2espt_27__01(V_27A_27),c_27const_2esptree_2emap_27__02(s__02(cfun__02(V_27B_27,V_27A_27),V_27f_27),s__02(c_27type_2esptree_2espt_27__01(V_27B_27),c_27const_2esptree_2efromAList_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27B_27)),V_27ls_27))))) = s__02(c_27type_2esptree_2espt_27__01(V_27A_27),c_27const_2esptree_2efromAList_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27))),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27A_27)))),V__0),s__02(cfun__02(V_27B_27,V_27A_27),V_27f_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,V_27B_27)),V_27ls_27))))) ) ) ).
%------------------------------------------------------------------------------