TPTP Problem File: SWW848+1.p
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%------------------------------------------------------------------------------
% File : SWW848+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : misc__12__ALOOKUP_MAP_gen__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : misc__12__ALOOKUP_MAP_gen__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 27 ( 6 unt; 0 def)
% Number of atoms : 72 ( 39 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 50 ( 5 ~; 2 |; 15 &)
% ( 12 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 102 ( 97 !; 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.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.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.EXCLUDED_MIDDLE',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,V_27t_27))
| ~ 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.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.COND_CLAUSES',axiom,
! [V_27A_27,V_27t1_27,V_27t2_27] :
( s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cT__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t1_27)
& s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cF__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t2_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.COND_CONG',axiom,
! [V_27A_27,V_27P_27,V_27Q_27,V_27x_27,V_27x_7c39_7c_27,V_27y_27,V_27y_7c39_7c_27] :
( ( s__02(cbool__00,V_27P_27) = s__02(cbool__00,V_27Q_27)
& ( p__01(s__02(cbool__00,V_27Q_27))
=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_7c39_7c_27) )
& ( ~ p__01(s__02(cbool__00,V_27Q_27))
=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27y_7c39_7c_27) ) )
=> s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(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(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27Q_27),s__02(V_27A_27,V_27x_7c39_7c_27),s__02(V_27A_27,V_27y_7c39_7c_27))) ) ).
fof('thm.bool.UNWIND_THM2',axiom,
! [V_27A_27,V_27P_27,V_27a_27] :
( ? [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_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_27x_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_27a_27)))) ) ).
fof('thm.bool.bool_case_thm',axiom,
! [V_27A_27] :
( ! [V_27t1_27,V_27t2_27] : s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cT__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t1_27)
& ! [V_27t1_27,V_27t2_27] : s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cF__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t2_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.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.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.OPTION_MAP_DEF',axiom,
! [V_27A_27,V_27B_27] :
( ! [V_27f_27,V_27x_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eOPTION__MAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_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_27B_27),c_27const_2eoption_2eSOME_27__01(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)))))
& ! [V_27f_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eOPTION__MAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_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_27B_27),c_27const_2eoption_2eNONE_27__00) ) ).
fof('thm.option.OPTION_MAP_EQ_SOME',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27x_27,V_27y_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eOPTION__MAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27x_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27B_27,V_27y_27)))
<=> ? [V_27z_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_27z_27)))
& s__02(V_27B_27,V_27y_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_27z_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.alist.ALOOKUP_def',axiom,
! [V_27A_27,V_27B_27] :
( ! [V_27q_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ealist_2eALOOKUP_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27A_27)),c_27const_2elist_2eNIL_27__00),s__02(V_27B_27,V_27q_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
& ! [V_27y_27,V_27x_27,V_27t_27,V_27q_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(V_27B_27,V_27x_27) = s__02(V_27B_27,V_27q_27) )
& s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ealist_2eALOOKUP_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27A_27)),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27A_27),c_27const_2epair_2e_2c_27__02(s__02(V_27B_27,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(V_27B_27,V_27A_27)),V_27t_27))),s__02(V_27B_27,V_27q_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),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(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ealist_2eALOOKUP_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27A_27)),V_27t_27),s__02(V_27B_27,V_27q_27))))) ) ) ).
fof(conjecture,conjecture,
! [V_27C_27,V_27B_27,V_27A_27,V__1] :
( ! [V_27f_27,V_27x0_27,V_27y_27] : s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27),chapp__02(s__02(cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27)))),V__1),s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_27))),s__02(V_27A_27,V_27x0_27))),s__02(V_27B_27,V_27y_27))) = s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27x0_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_27x0_27))),s__02(V_27B_27,V_27y_27)))))
=> ! [V__0] :
( ! [V_27f_27,V_27x0_27] : s__02(cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27)))),V__0),s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_27))),s__02(V_27A_27,V_27x0_27))) = s__02(cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27)))),V__1),s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_27))),s__02(V_27A_27,V_27x0_27)))
=> ! [V_27f_27,V_27al_27,V_27x_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27C_27),c_27const_2ealist_2eALOOKUP_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27)),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2epair_2eprod_27__02(V_27A_27,V_27C_27)))),V__0),s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27)),V_27al_27))),s__02(V_27A_27,V_27x_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27C_27),c_27const_2eoption_2eOPTION__MAP_27__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(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2ealist_2eALOOKUP_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27)),V_27al_27),s__02(V_27A_27,V_27x_27))))) ) ) ).
%------------------------------------------------------------------------------