TPTP Problem File: SWW859+1.p
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%------------------------------------------------------------------------------
% File : SWW859+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : fromSexp__81__strip_sxcons_NIL__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : fromSexp__81__strip_sxcons_NIL__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 152 ( 99 equ)
% Maximal formula atoms : 40 ( 5 avg)
% Number of connectives : 140 ( 18 ~; 5 |; 72 &)
% ( 29 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 7 avg)
% Maximal term depth : 30 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 43 ( 43 usr; 10 con; 0-5 aty)
% Number of variables : 155 ( 147 !; 8 ?)
% 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.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.EXISTS_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.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.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.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.BOUNDED_THM',axiom,
! [V_27v_27] : s__02(cbool__00,c_27const_2ebool_2eBOUNDED_27__01(s__02(cbool__00,V_27v_27))) = s__02(cbool__00,cT__00) ).
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_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.option.NOT_NONE_SOME',axiom,
! [V_27A_27,V_27x_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_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) ).
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.CONS_11',axiom,
! [V_27A_27,V_27a0_27,V_27a1_27,V_27a0_7c39_7c_27,V_27a1_7c39_7c_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)),c_27const_2elist_2eCONS_27__01(s__02(V_27A_27,V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)),c_27const_2elist_2eCONS_27__01(s__02(V_27A_27,V_27a0_7c39_7c_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_7c39_7c_27)))
<=> ( s__02(V_27A_27,V_27a0_27) = s__02(V_27A_27,V_27a0_7c39_7c_27)
& s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_7c39_7c_27) ) ) ).
fof('thm.list.NOT_NIL_CONS',axiom,
! [V_27A_27,V_27a1_27,V_27a0_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_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)),c_27const_2elist_2eCONS_27__01(s__02(V_27A_27,V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27))) ).
fof('thm.string.CHR_11',axiom,
! [V_27r_27,V_27r_7c39_7c_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27r_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_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_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_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))))))))))
=> ( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27r_7c39_7c_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_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_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_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))))))))))
=> ( s__02(c_27type_2estring_2echar_27__00,c_27const_2estring_2eCHR_27__01(s__02(c_27type_2enum_2enum_27__00,V_27r_27))) = s__02(c_27type_2estring_2echar_27__00,c_27const_2estring_2eCHR_27__01(s__02(c_27type_2enum_2enum_27__00,V_27r_7c39_7c_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27r_27) = s__02(c_27type_2enum_2enum_27__00,V_27r_7c39_7c_27) ) ) ) ).
fof('thm.simpleSexp.sexp_case_def',axiom,
! [V_27A_27] :
( ! [V_27a0_27,V_27a1_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27] : s__02(V_27A_27,c_27const_2esimpleSexp_2esexp__CASE_27__05(s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__CONS_27__02(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a0_27),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a1_27))),s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,cfun__02(c_27type_2esimpleSexp_2esexp_27__00,V_27A_27)),V_27f_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f3_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,V_27A_27),chapp__02(s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,cfun__02(c_27type_2esimpleSexp_2esexp_27__00,V_27A_27)),V_27f_27),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a0_27))),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a1_27)))
& ! [V_27a_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27] : s__02(V_27A_27,c_27const_2esimpleSexp_2esexp__CASE_27__05(s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__SYM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27))),s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,cfun__02(c_27type_2esimpleSexp_2esexp_27__00,V_27A_27)),V_27f_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f3_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27)))
& ! [V_27a_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27] : s__02(V_27A_27,c_27const_2esimpleSexp_2esexp__CASE_27__05(s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__NUM_27__01(s__02(c_27type_2enum_2enum_27__00,V_27a_27))),s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,cfun__02(c_27type_2esimpleSexp_2esexp_27__00,V_27A_27)),V_27f_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f3_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f2_27),s__02(c_27type_2enum_2enum_27__00,V_27a_27)))
& ! [V_27a_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27] : s__02(V_27A_27,c_27const_2esimpleSexp_2esexp__CASE_27__05(s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__STR_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27))),s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,cfun__02(c_27type_2esimpleSexp_2esexp_27__00,V_27A_27)),V_27f_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f3_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27A_27),V_27f3_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27))) ) ).
fof('thm.simpleSexp.sexp_11',axiom,
( ! [V_27a0_27,V_27a1_27,V_27a0_7c39_7c_27,V_27a1_7c39_7c_27] :
( s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__CONS_27__02(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a0_27),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a1_27))) = s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__CONS_27__02(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a0_7c39_7c_27),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a1_7c39_7c_27)))
<=> ( s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a0_27) = s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a0_7c39_7c_27)
& s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a1_27) = s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a1_7c39_7c_27) ) )
& ! [V_27a_27,V_27a_7c39_7c_27] :
( s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__SYM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27))) = s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__SYM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_7c39_7c_27)))
<=> s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27) = s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_7c39_7c_27) )
& ! [V_27a_27,V_27a_7c39_7c_27] :
( s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__NUM_27__01(s__02(c_27type_2enum_2enum_27__00,V_27a_27))) = s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__NUM_27__01(s__02(c_27type_2enum_2enum_27__00,V_27a_7c39_7c_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27a_27) = s__02(c_27type_2enum_2enum_27__00,V_27a_7c39_7c_27) )
& ! [V_27a_27,V_27a_7c39_7c_27] :
( s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__STR_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27))) = s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__STR_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_7c39_7c_27)))
<=> s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27) = s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_7c39_7c_27) ) ) ).
fof('thm.simpleSexp.sexp_distinct',axiom,
( ! [V_27a1_27,V_27a0_27,V_27a_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__CONS_27__02(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a0_27),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a1_27))) != s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__SYM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27)))
& ! [V_27a1_27,V_27a0_27,V_27a_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__CONS_27__02(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a0_27),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a1_27))) != s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__NUM_27__01(s__02(c_27type_2enum_2enum_27__00,V_27a_27)))
& ! [V_27a1_27,V_27a0_27,V_27a_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__CONS_27__02(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a0_27),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27a1_27))) != s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__STR_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27)))
& ! [V_27a_7c39_7c_27,V_27a_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__SYM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27))) != s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__NUM_27__01(s__02(c_27type_2enum_2enum_27__00,V_27a_7c39_7c_27)))
& ! [V_27a_7c39_7c_27,V_27a_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__SYM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_27))) != s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__STR_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_7c39_7c_27)))
& ! [V_27a_7c39_7c_27,V_27a_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__NUM_27__01(s__02(c_27type_2enum_2enum_27__00,V_27a_27))) != s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__STR_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27a_7c39_7c_27))) ) ).
fof('thm.simpleSexp.sexp_nchotomy',axiom,
! [V_27ss_27] :
( ? [V_27s_27,V_27s0_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27ss_27) = s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__CONS_27__02(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27s_27),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27s0_27)))
| ? [V_27s_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27ss_27) = s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__SYM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27s_27)))
| ? [V_27n_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27ss_27) = s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__NUM_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
| ? [V_27s_27] : s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27ss_27) = s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__STR_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27s_27))) ) ).
fof('thm.simpleSexp.strip_sxcons_def',axiom,
! [V__4] :
( ! [V_27v9_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00))),V__4),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27v9_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2eoption_2eNONE_27__00)
=> ! [V__3] :
( ! [V_27v8_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00))),V__3),s__02(c_27type_2enum_2enum_27__00,V_27v8_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2eoption_2eNONE_27__00)
=> ! [V__2] :
( ! [V_27s0_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27s0_27) = s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27const_2elist_2eCONS_27__01(s__02(c_27type_2estring_2echar_27__00,c_27const_2estring_2eCHR_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_2eBIT2_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_2eBIT2_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27const_2elist_2eCONS_27__01(s__02(c_27type_2estring_2echar_27__00,c_27const_2estring_2eCHR_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_2eBIT2_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_2eBIT2_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27const_2elist_2eCONS_27__01(s__02(c_27type_2estring_2echar_27__00,c_27const_2estring_2eCHR_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_2eBIT1_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_2eBIT2_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27const_2elist_2eNIL_27__00))))))) )
& s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00))),V__2),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27s0_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00),c_27const_2elist_2eNIL_27__00))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2eoption_2eNONE_27__00))) )
=> ! [V__1] :
( ! [V_27h_27,V_27t_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),chapp__02(s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00))),chapp__02(s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,cfun__02(c_27type_2esimpleSexp_2esexp_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)))),V__1),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27h_27))),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27t_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2eoption_2eOPTION__MAP_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00),c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2elist_2eCONS_27__01(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27h_27))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2esimpleSexp_2estrip__sxcons_27__01(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27t_27)))))
=> ! [V__0] :
( ! [V_27h_27] : s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00))),chapp__02(s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,cfun__02(c_27type_2esimpleSexp_2esexp_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)))),V__0),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27h_27))) = s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00))),chapp__02(s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,cfun__02(c_27type_2esimpleSexp_2esexp_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)))),V__1),s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27h_27)))
=> ! [V_27s_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2esimpleSexp_2estrip__sxcons_27__01(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27s_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2esimpleSexp_2esexp__CASE_27__05(s__02(c_27type_2esimpleSexp_2esexp_27__00,V_27s_27),s__02(cfun__02(c_27type_2esimpleSexp_2esexp_27__00,cfun__02(c_27type_2esimpleSexp_2esexp_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)))),V__0),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00))),V__2),s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00))),V__3),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00))),V__4))) ) ) ) ) ) ).
fof(conjecture,conjecture,
s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2esimpleSexp_2estrip__sxcons_27__01(s__02(c_27type_2esimpleSexp_2esexp_27__00,c_27const_2esimpleSexp_2eSX__SYM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27const_2elist_2eCONS_27__01(s__02(c_27type_2estring_2echar_27__00,c_27const_2estring_2eCHR_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_2eBIT2_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_2eBIT2_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27const_2elist_2eCONS_27__01(s__02(c_27type_2estring_2echar_27__00,c_27const_2estring_2eCHR_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_2eBIT2_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_2eBIT2_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)),c_27const_2elist_2eCONS_27__01(s__02(c_27type_2estring_2echar_27__00,c_27const_2estring_2eCHR_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_2eBIT1_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_2eBIT2_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27const_2elist_2eNIL_27__00))))))))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esimpleSexp_2esexp_27__00),c_27const_2elist_2eNIL_27__00))) ).
%------------------------------------------------------------------------------