TPTP Problem File: SWW927+1.p
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%------------------------------------------------------------------------------
% File : SWW927+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : data_to_word_memoryProof__204__tactictoe_prove_203__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : data_to_word_memoryProof__204__tactictoe_prove_203__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 66 ( 23 unt; 0 def)
% Number of atoms : 275 ( 124 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 233 ( 24 ~; 12 |; 111 &)
% ( 56 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 49 ( 49 usr; 9 con; 0-3 aty)
% Number of variables : 205 ( 204 !; 1 ?)
% 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.LET_THM',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27x_27] : s__02(V_27B_27,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,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_27x_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.CONJ_ASSOC',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.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.OR_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,cT__00)) )
& ( ( 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,V_27t_27)) )
& ( ( 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,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.NOT_CLAUSES',axiom,
( ! [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,cF__00)) )
& ( ~ p__01(s__02(cbool__00,cF__00))
<=> 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.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.DE_MORGAN_THM',axiom,
! [V_27A_270,V_27B_270] :
( ( ~ ( p__01(s__02(cbool__00,V_27A_270))
& p__01(s__02(cbool__00,V_27B_270)) )
<=> ( ~ p__01(s__02(cbool__00,V_27A_270))
| ~ p__01(s__02(cbool__00,V_27B_270)) ) )
& ( ~ ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) )
<=> ( ~ p__01(s__02(cbool__00,V_27A_270))
& ~ p__01(s__02(cbool__00,V_27B_270)) ) ) ) ).
fof('thm.bool.IMP_DISJ_THM',axiom,
! [V_27A_270,V_27B_270] :
( ( p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,V_27B_270)) )
<=> ( ~ p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) ) ) ).
fof('thm.bool.IMP_F_EQ_F',axiom,
! [V_27t_27] :
( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cF__00)) )
<=> s__02(cbool__00,V_27t_27) = s__02(cbool__00,cF__00) ) ).
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.combin.I_THM',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,c_27const_2ecombin_2eI_27__01(s__02(V_27A_27,V_27x_27))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.arithmetic.NORM_0',axiom,
s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) ).
fof('thm.arithmetic.ADD_CLAUSES',axiom,
! [V_27n_27,V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ) ).
fof('thm.arithmetic.ADD_SYM',axiom,
! [V_27m_27,V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ).
fof('thm.arithmetic.ADD_COMM',axiom,
! [V_27m_27,V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ).
fof('thm.arithmetic.ADD_ASSOC',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))) ).
fof('thm.arithmetic.LESS_EQ',axiom,
! [V_27m_27,V_27n_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ).
fof('thm.arithmetic.ZERO_LESS_EQ',axiom,
! [V_27n_27] : p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) ).
fof('thm.arithmetic.NOT_LESS',axiom,
! [V_27m_27,V_27n_27] :
( ~ p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
<=> p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))) ) ).
fof('thm.arithmetic.MULT_CLAUSES',axiom,
! [V_27m_27,V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ) ).
fof('thm.arithmetic.LESS_EQ_TRANS',axiom,
! [V_27m_27,V_27n_27,V_27p_27] :
( ( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27)))) )
=> p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27)))) ) ).
fof('thm.arithmetic.EQ_LESS_EQ',axiom,
! [V_27m_27,V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,V_27m_27) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
<=> ( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))) ) ) ).
fof('thm.arithmetic.ADD_MONO_LESS_EQ',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27))) ).
fof('thm.arithmetic.SUC_ONE_ADD',axiom,
! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ).
fof('thm.arithmetic.SUB_RIGHT_LESS_EQ',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))) ).
fof('thm.arithmetic.SUB_RIGHT_LESS',axiom,
! [V_27m_27,V_27n_27,V_27p_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))
<=> ( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))))
& p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27p_27)))) ) ) ).
fof('thm.arithmetic.DIV2_def',axiom,
! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))) ).
fof('thm.arithmetic.SUB_ELIM_THM',axiom,
! [V_27b_27,V_27a_27,V_27P_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27a_27),s__02(c_27type_2enum_2enum_27__00,V_27b_27))))))
<=> ! [V_27d_27] :
( ( s__02(c_27type_2enum_2enum_27__00,V_27b_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27a_27),s__02(c_27type_2enum_2enum_27__00,V_27d_27)))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))) )
& ( s__02(c_27type_2enum_2enum_27__00,V_27a_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27b_27),s__02(c_27type_2enum_2enum_27__00,V_27d_27)))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2enum_2enum_27__00,V_27d_27)))) ) ) ) ).
fof('thm.numeral.numeral_suc',axiom,
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ) ).
fof('thm.numeral.numeral_distrib',axiom,
( ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& ! [V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [V_27n_27,V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) )
& ! [V_27n_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cF__00)
& ! [V_27n_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,cF__00)
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,cT__00)
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cT__00)
& ! [V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) )
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))) ) ).
fof('thm.numeral.numeral_eq',axiom,
! [V_27n_27,V_27m_27] :
( ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) ) ) ).
fof('thm.numeral.numeral_lt',axiom,
! [V_27n_27,V_27m_27] :
( s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))
<=> ~ p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) )
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ) ).
fof('thm.numeral.numeral_lte',axiom,
! [V_27n_27,V_27m_27] :
( s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))
<=> ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) )
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ) ).
fof('thm.numeral.numeral_sub',axiom,
! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiSUB_27__03(s__02(cbool__00,cT__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) ).
fof('thm.numeral.numeral_evenodd',axiom,
! [V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))) ) ).
fof('thm.numeral.numeral_div2',axiom,
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ) ).
fof('thm.pred_set.NOT_IN_EMPTY',axiom,
! [V_27A_27,V_27x_27] : ~ p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eEMPTY_27__00)))) ).
fof('thm.pred_set.IN_INSERT',axiom,
! [V_27A_27,V_27x_27,V_27y_27,V_27s_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eINSERT_27__02(s__02(V_27A_27,V_27y_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27))))))
<=> ( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27)
| p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27)))) ) ) ).
fof('thm.fcp.CART_EQ',axiom,
! [V_27A_27,V_27B_27,V_27x_27,V_27y_27] :
( s__02(c_27type_2efcp_2ecart_27__02(V_27A_27,V_27B_27),V_27x_27) = s__02(c_27type_2efcp_2ecart_27__02(V_27A_27,V_27B_27),V_27y_27)
<=> ! [V_27i_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27B_27),c_27const_2ebool_2ethe__value_27__00))))))
=> s__02(V_27A_27,c_27const_2efcp_2efcp__index_27__02(s__02(c_27type_2efcp_2ecart_27__02(V_27A_27,V_27B_27),V_27x_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27))) = s__02(V_27A_27,c_27const_2efcp_2efcp__index_27__02(s__02(c_27type_2efcp_2ecart_27__02(V_27A_27,V_27B_27),V_27y_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27))) ) ) ).
fof('thm.fcp.FCP_BETA',axiom,
! [V_27B_27,V_27A_27,V_27g_27,V_27i_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27B_27),c_27const_2ebool_2ethe__value_27__00))))))
=> s__02(V_27A_27,c_27const_2efcp_2efcp__index_27__02(s__02(c_27type_2efcp_2ecart_27__02(V_27A_27,V_27B_27),c_27const_2efcp_2eFCP_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27g_27))),s__02(c_27type_2enum_2enum_27__00,V_27i_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27g_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27))) ) ).
fof('thm.words.word_and_def',axiom,
! [V_27A_27,V__0] :
( ! [V_27v_27,V_27w_27,V_27i_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),V__0),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))),s__02(c_27type_2enum_2enum_27__00,V_27i_27))))
<=> ( p__01(s__02(cbool__00,c_27const_2efcp_2efcp__index_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27))))
& p__01(s__02(cbool__00,c_27const_2efcp_2efcp__index_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27)))) ) )
=> ! [V_27v_27,V_27w_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__and_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2efcp_2eFCP_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),V__0),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))))) ) ).
fof('thm.words.word_or_def',axiom,
! [V_27A_27,V__0] :
( ! [V_27v_27,V_27w_27,V_27i_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),V__0),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))),s__02(c_27type_2enum_2enum_27__00,V_27i_27))))
<=> ( p__01(s__02(cbool__00,c_27const_2efcp_2efcp__index_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27))))
| p__01(s__02(cbool__00,c_27const_2efcp_2efcp__index_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27)))) ) )
=> ! [V_27v_27,V_27w_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__or_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2efcp_2eFCP_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),V__0),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))))) ) ).
fof('thm.words.BIT_SET_def',axiom,
! [V_27n_27,V_27i_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) )
& s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2ewords_2eBIT__SET_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eEMPTY_27__00),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eINSERT_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2ewords_2eBIT__SET_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27i_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2ewords_2eBIT__SET_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27i_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))) ) ).
fof('thm.words.word_lsl_def',axiom,
! [V_27A_27,V__0] :
( ! [V_27w_27,V_27n_27,V_27i_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),V__0),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27i_27))))
<=> ( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27))))
& p__01(s__02(cbool__00,c_27const_2efcp_2efcp__index_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))) ) )
=> ! [V_27w_27,V_27n_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__lsl_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2efcp_2eFCP_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),V__0),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ) ).
fof('thm.words.DIMINDEX_GT_0',axiom,
! [V_27A_27] : p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00)))))) ).
fof('thm.words.WORD_OR_ASSOC',axiom,
! [V_27A_27,V_27a_27,V_27b_27,V_27c_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__or_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__or_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27a_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27b_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27c_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__or_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27a_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__or_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27b_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27c_27))))) ).
fof('thm.words.WORD_OR_COMM',axiom,
! [V_27A_27,V_27a_27,V_27b_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__or_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27a_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27b_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__or_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27b_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27a_27))) ).
fof('thm.words.word_index',axiom,
! [V_27A_27,V_27n_27,V_27i_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
=> s__02(cbool__00,c_27const_2efcp_2efcp__index_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27i_27))) = s__02(cbool__00,c_27const_2ebit_2eBIT_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ) ).
fof('thm.words.BIT_SET',axiom,
! [V_27i_27,V_27n_27] : s__02(cbool__00,c_27const_2ebit_2eBIT_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2ewords_2eBIT__SET_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ).
fof('thm.data_to_word.make_header_def',axiom,
! [V_27A_27,V__0] :
( ! [V_27len_27,V_27tag_27,V_27l_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27)))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27len_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27tag_27))),s__02(c_27type_2enum_2enum_27__00,V_27l_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__or_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__lsl_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,V_27len_27))),s__02(c_27type_2enum_2enum_27__00,V_27l_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__or_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__lsl_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27tag_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
=> ! [V_27conf_27,V_27tag_27,V_27len_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2edata__to__word_2emake__header_27__03(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27tag_27),s__02(c_27type_2enum_2enum_27__00,V_27len_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27)))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27len_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27tag_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))),s__02(c_27type_2enum_2enum_27__00,c_27const_2edata__to__word_2econfig__len__size_27__01(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))))) ) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27c_27,V_27w_27,V_27n_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__and_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2edata__to__word_2emake__header_27__03(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27c_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))) ).
%------------------------------------------------------------------------------