ITP001 Axioms: ITP054+4.ax
%------------------------------------------------------------------------------
% File : ITP054+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : string.ax [Gau19]
% : HL4054+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 208 ( 130 unt; 0 def)
% Number of atoms : 376 ( 248 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 180 ( 12 ~; 13 |; 59 &)
% ( 52 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 24 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 177 ( 177 usr; 92 con; 0-3 aty)
% Number of variables : 482 ( 473 !; 9 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).
fof(reserved_2Eho_2Ei__thm,axiom,
! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Es__thm,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).
fof(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
& p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
=> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_3D,axiom,
! [A_27a,V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
<=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).
fof(reserved_2Equant_2E_21,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(reserved_2Equant_2E_3F,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
& p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
| p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
=> p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] :
( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2ECHR_2E1,axiom,
! [X0_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),c_2Estring_2ECHR_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EORD_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Estring_2EORD_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EDEST__STRING_2E1,axiom,
! [X0_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Estring_2EDEST__STRING_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Elist_2ECONS_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EEXPLODE_2E1,axiom,
! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EEXPLODE_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EIMPLODE_2E1,axiom,
! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EIMPLODE_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EEXTRACT_2E1,axiom,
! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXTRACT_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EEXTRACT_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),X0_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2ESOME_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2ESUBSTRING_2E1,axiom,
! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ESUBSTRING_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2ESUBSTRING_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Elist_2ENULL_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Epair_2E_2C_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29,axiom,
! [X0_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2ESTR_2E1,axiom,
! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ESTR_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2ESTR_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Estring_2ESUB_2E1,axiom,
! [X0_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2ESUB_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),tyop_2Estring_2Echar),c_2Estring_2ESUB_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2ETOCHAR_2E1,axiom,
! [X0_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2ETOCHAR_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),c_2Estring_2ETOCHAR_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2Echar__size_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Estring_2Echar__size_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Estring_2Echar__size_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisAlpha_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisAlpha_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisAlpha_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisAlphaNum_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisAlphaNum_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisAlphaNum_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisAscii_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisAscii_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisAscii_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisCntrl_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisCntrl_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisCntrl_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisDigit_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisDigit_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisDigit_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisGraph_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisGraph_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisGraph_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisHexDigit_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisHexDigit_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisHexDigit_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisLower_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisLower_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisLower_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisPrint_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisPrint_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisPrint_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisPunct_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisPunct_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisPunct_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisSpace_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisSpace_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisSpace_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EisUpper_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisUpper_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),c_2Estring_2EisUpper_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EtoLower_2E1,axiom,
! [X0_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2EtoLower_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar),c_2Estring_2EtoLower_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EtoUpper_2E1,axiom,
! [X0_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2EtoUpper_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar),c_2Estring_2EtoUpper_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ETL_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3E_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Estring_2Echar,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2EFIELDS_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EFIELDS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Estring_2EFIELDS_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X1_2E0))) ).
fof(arityeq2_2Ec_2Erich__list_2ESPLITP_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erich__list_2ESPLITP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Erich__list_2ESPLITP_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),X0_2E0))) ).
fof(arityeq2_2Ec_2Estring_2ETOKENS_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2ETOKENS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Estring_2ETOKENS_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2ETRANSLATE_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ETRANSLATE_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2ETRANSLATE_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),X1_2E0))) ).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2Echar__ge_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Echar__ge_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Estring_2Echar,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),c_2Estring_2Echar__ge_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Estring_2Echar,X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2Echar__gt_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Echar__gt_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Estring_2Echar,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),c_2Estring_2Echar__gt_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Estring_2Echar,X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2Echar__le_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Echar__le_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Estring_2Echar,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),c_2Estring_2Echar__le_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Estring_2Echar,X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2Echar__lt_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Echar__lt_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Estring_2Echar,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),c_2Estring_2Echar__lt_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Estring_2Echar,X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EisPREFIX_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Elist_2EisPREFIX_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Epair_2E_2C_2E2(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))))),c_2Epair_2E_2C_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Ebool)),X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2Estring__ge_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Estring__ge_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Estring_2Estring__ge_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2Estring__gt_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Estring__gt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Estring_2Estring__gt_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2Estring__le_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Estring__le_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Estring_2Estring__le_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq2_2Ec_2Estring_2Estring__lt_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Estring_2Estring__lt_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Estring_2Echar,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Estring_2Echar,X1_2E0),s(tyop_2Estring_2Echar,X2_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Estring_2Echar,X1_2E0))),s(tyop_2Estring_2Echar,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Ecombin_2EFAIL_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum))),c_2Ecombin_2EFAIL_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0))) ).
fof(arityeq3_2Ec_2Erich__list_2ESEG_2E3_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Erich__list_2ESEG_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Erich__list_2ESEG_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0))) ).
fof(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Estring_2Echar,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Estring_2Echar,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),X2_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),tyop_2Estring_2Echar))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Estring_2Echar,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),X2_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0] : s(tyop_2Estring_2Echar,c_2Ecombin_2EI_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar),c_2Ecombin_2EI_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X2_2E0))) ).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool),X2_2E0))) ).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X2_2E0))) ).
fof(thm_2Estring_2EDEST__STRING__def,axiom,
( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Eoption_2ENONE_2E0)
& ! [V0c_2E0,V1rst_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1rst_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1rst_2E0))))) ) ).
fof(thm_2Estring_2Echar__TY__DEF,axiom,
! [F0_2E0] :
( ! [V1n_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))
=> ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),V0rep_2E0)))) ) ).
fof(thm_2Estring_2Echar__BIJ,axiom,
( ! [V0a_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0a_2E0))))) = s(tyop_2Estring_2Echar,V0a_2E0)
& ! [V1r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))
<=> s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V1r_2E0))))) = s(tyop_2Enum_2Enum,V1r_2E0) ) ) ).
fof(thm_2Estring_2EisLower__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisLower_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))) ) ) ).
fof(thm_2Estring_2EisUpper__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisUpper_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))) ) ) ).
fof(thm_2Estring_2EisDigit__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisDigit_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))) ) ) ).
fof(thm_2Estring_2EisAlpha__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisAlpha_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisLower_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Estring_2EisUpper_2E1(s(tyop_2Estring_2Echar,V0c_2E0)))) ) ) ).
fof(thm_2Estring_2EisHexDigit__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisHexDigit_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))) )
| ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))) )
| ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))) ) ) ) ).
fof(thm_2Estring_2EisAlphaNum__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisAlphaNum_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisAlpha_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Estring_2EisDigit_2E1(s(tyop_2Estring_2Echar,V0c_2E0)))) ) ) ).
fof(thm_2Estring_2EisPrint__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisPrint_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))) ) ) ).
fof(thm_2Estring_2EisSpace__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisSpace_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))
| ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) ) ) ) ).
fof(thm_2Estring_2EisGraph__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisGraph_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisPrint_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Estring_2EisSpace_2E1(s(tyop_2Estring_2Echar,V0c_2E0)))) ) ) ).
fof(thm_2Estring_2EisPunct__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisPunct_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisGraph_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Estring_2EisAlphaNum_2E1(s(tyop_2Estring_2Echar,V0c_2E0)))) ) ) ).
fof(thm_2Estring_2EisAscii__def,axiom,
! [V0c_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2EisAscii_2E1(s(tyop_2Estring_2Echar,V0c_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))) ).
fof(thm_2Estring_2EisCntrl__def,axiom,
! [V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2EisCntrl_2E1(s(tyop_2Estring_2Echar,V0c_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))
| p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0)))))) ) ) ).
fof(thm_2Estring_2EtoLower__def,axiom,
! [V0c_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2EtoLower_2E1(s(tyop_2Estring_2Echar,V0c_2E0))) = s(tyop_2Estring_2Echar,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Estring_2EisUpper_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))),s(tyop_2Estring_2Echar,V0c_2E0))) ).
fof(thm_2Estring_2EtoUpper__def,axiom,
! [V0c_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2EtoUpper_2E1(s(tyop_2Estring_2Echar,V0c_2E0))) = s(tyop_2Estring_2Echar,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Estring_2EisLower_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))),s(tyop_2Estring_2Echar,V0c_2E0))) ).
fof(thm_2Estring_2Echar__lt__def,axiom,
! [V0a_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Echar__lt_2E2(s(tyop_2Estring_2Echar,V0a_2E0),s(tyop_2Estring_2Echar,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0a_2E0))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V1b_2E0))))) ).
fof(thm_2Estring_2Echar__le__def,axiom,
! [V0a_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Echar__le_2E2(s(tyop_2Estring_2Echar,V0a_2E0),s(tyop_2Estring_2Echar,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0a_2E0))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V1b_2E0))))) ).
fof(thm_2Estring_2Echar__gt__def,axiom,
! [V0a_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Echar__gt_2E2(s(tyop_2Estring_2Echar,V0a_2E0),s(tyop_2Estring_2Echar,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0a_2E0))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V1b_2E0))))) ).
fof(thm_2Estring_2Echar__ge__def,axiom,
! [V0a_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Echar__ge_2E2(s(tyop_2Estring_2Echar,V0a_2E0),s(tyop_2Estring_2Echar,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0a_2E0))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V1b_2E0))))) ).
fof(thm_2Estring_2Echar__size__def,axiom,
! [V0c_2E0] : s(tyop_2Enum_2Enum,c_2Estring_2Echar__size_2E1(s(tyop_2Estring_2Echar,V0c_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ).
fof(thm_2Estring_2ESUB__def,axiom,
! [V0s_2E0,V1n_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2ESUB_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Estring_2Echar,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) ).
fof(thm_2Estring_2ESTR__def,axiom,
! [V0c_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ESTR_2E1(s(tyop_2Estring_2Echar,V0c_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) ).
fof(thm_2Estring_2ETOCHAR__primitive__def,axiom,
! [F0_2E0,F3_2E0,F2_2E0,F1_2E0] :
( ! [V0R_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0R_2E0)))
=> ( ! [V5v2_2E0,V6v3_2E0] : s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),F3_2E0),s(tyop_2Estring_2Echar,V5v2_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V6v3_2E0))) = s(tyop_2Estring_2Echar,c_2Ebool_2EARB_2E0)
=> ( ! [V3c_2E0,V4v1_2E0] : s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),F2_2E0),s(tyop_2Estring_2Echar,V3c_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4v1_2E0))) = s(tyop_2Estring_2Echar,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4v1_2E0),s(tyop_2Estring_2Echar,c_2Ecombin_2EI_2E1(s(tyop_2Estring_2Echar,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),F3_2E0)))
=> ( ! [V1TOCHAR_2E0,V2a_2E0] : s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),V1TOCHAR_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2a_2E0))) = s(tyop_2Estring_2Echar,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2a_2E0),s(tyop_2Estring_2Echar,c_2Ebool_2EARB_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),F2_2E0)))
=> s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),c_2Estring_2ETOCHAR_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Estring_2Echar)),F1_2E0))) ) ) ) ) ).
fof(thm_2Estring_2ESUBSTRING__def,axiom,
! [V0s_2E0,V1i_2E0,V2n_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ESUBSTRING_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Erich__list_2ESEG_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) ).
fof(thm_2Estring_2ETRANSLATE__def,axiom,
! [V0f_2E0,V1s_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ETRANSLATE_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V0f_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V0f_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))))) ).
fof(thm_2Estring_2EIMPLODE__def,axiom,
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0)
& ! [V0c_2E0,V1cs_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1cs_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1cs_2E0))))) ) ).
fof(thm_2Estring_2EEXPLODE__def,axiom,
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0)
& ! [V0c_2E0,V1s_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))))) ) ).
fof(thm_2Estring_2EEXTRACT__primitive__def,axiom,
! [F4_2E0,F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
( ! [V3s_2E0,V5i_2E0,V7n_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),F4_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0))),s(tyop_2Enum_2Enum,V5i_2E0))),s(tyop_2Enum_2Enum,V7n_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ESUBSTRING_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V5i_2E0),s(tyop_2Enum_2Enum,V7n_2E0)))))))))
=> ( ! [V3s_2E0,V5i_2E0,V6v3_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),F3_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0))),s(tyop_2Enum_2Enum,V5i_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V6v3_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V6v3_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ESUBSTRING_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V5i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0))),s(tyop_2Enum_2Enum,V5i_2E0))))))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),F4_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0))),s(tyop_2Enum_2Enum,V5i_2E0)))))
=> ( ! [V3s_2E0,V4v1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),F2_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V4v1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V4v1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),F3_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0)))))
=> ( ! [V1EXTRACT_2E0,V2a_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V1EXTRACT_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),V2a_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),V2a_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),F2_2E0)))
=> ( ! [V0R_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),V0R_2E0)))
=> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EEXTRACT_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),F1_2E0))) ) ) ) ) ) ).
fof(thm_2Estring_2Estring__le__def,axiom,
! [V0s1_2E0,V1s2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__le_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0))))
<=> ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0)))) ) ) ).
fof(thm_2Estring_2Estring__gt__def,axiom,
! [V0s1_2E0,V1s2_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Estring__gt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0))) = s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0))) ).
fof(thm_2Estring_2Estring__ge__def,axiom,
! [V0s1_2E0,V1s2_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Estring__ge_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0))) = s(tyop_2Emin_2Ebool,c_2Estring_2Estring__le_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0))) ).
fof(thm_2Estring_2EIMPLODE__STRING,axiom,
! [V0clist_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0clist_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0clist_2E0))) ).
fof(thm_2Estring_2EEXPLODE__DEST__STRING,axiom,
! [F1_2E0,F0_2E0] :
( ! [V2c_2E0,V3t_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),F1_2E0),s(tyop_2Estring_2Echar,V2c_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3t_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3t_2E0)))))
=> ( ! [V1v_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V1v_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V1v_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),F1_2E0)))
=> ! [V0s_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),F0_2E0))) ) ) ).
fof(thm_2Estring_2EIMPLODE__EQ__THM,axiom,
! [V0c_2E0,V1s_2E0,V2l_2E0] :
( ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))))) )
& ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))))) ) ) ).
fof(thm_2Estring_2EEXPLODE__EQ__THM,axiom,
! [V0s_2E0,V1h_2E0,V2t_2E0] :
( ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V1h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V1h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0))))) )
& ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V1h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V1h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0))))) ) ) ).
fof(thm_2Estring_2EEXPLODE__EQ__NIL,axiom,
! [V0s_2E0] :
( ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0)
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) )
& ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) ) ) ).
fof(thm_2Estring_2EIMPLODE__EQ__EMPTYSTRING,axiom,
! [V0l_2E0] :
( ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0)
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) )
& ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) ) ) ).
fof(thm_2Estring_2EIMPLODE__EQNS,axiom,
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0)
& ! [V0c_2E0,V1cs_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1cs_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1cs_2E0))))) ) ).
fof(thm_2Estring_2EEXPLODE__EQNS,axiom,
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0)
& ! [V0c_2E0,V1s_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))))) ) ).
fof(thm_2Estring_2EDEST__STRING__LEMS,axiom,
! [V0t_2E0,V1c_2E0,V2s_2E0] :
( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Eoption_2ENONE_2E0)
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) )
& ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Estring_2Echar,V1c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0t_2E0)))))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V1c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0t_2E0))) ) ) ).
fof(thm_2Estring_2ESTRLEN__EXPLODE__THM,axiom,
! [V0s_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))))) ).
fof(thm_2Estring_2EORD__11,axiom,
! [V0a_2E0,V1a_27_2E0] :
( s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V1a_27_2E0)))
<=> s(tyop_2Estring_2Echar,V0a_2E0) = s(tyop_2Estring_2Echar,V1a_27_2E0) ) ).
fof(thm_2Estring_2ECHR__11,axiom,
! [V0r_2E0,V1r_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_27_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))
=> ( s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V0r_2E0))) = s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V1r_27_2E0)))
<=> s(tyop_2Enum_2Enum,V0r_2E0) = s(tyop_2Enum_2Enum,V1r_27_2E0) ) ) ) ).
fof(thm_2Estring_2EORD__ONTO,axiom,
! [V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))
<=> ? [V1a_2E0] : s(tyop_2Enum_2Enum,V0r_2E0) = s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V1a_2E0))) ) ).
fof(thm_2Estring_2ECHR__ONTO,axiom,
! [V0a_2E0] :
? [V1r_2E0] :
( s(tyop_2Estring_2Echar,V0a_2E0) = s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V1r_2E0)))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))) ) ).
fof(thm_2Estring_2ECHR__ORD,axiom,
! [V0a_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0a_2E0))))) = s(tyop_2Estring_2Echar,V0a_2E0) ).
fof(thm_2Estring_2EORD__CHR,axiom,
! [V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))
<=> s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V0r_2E0))))) = s(tyop_2Enum_2Enum,V0r_2E0) ) ).
fof(thm_2Estring_2EORD__CHR__RWT,axiom,
! [V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))
=> s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V0r_2E0))))) = s(tyop_2Enum_2Enum,V0r_2E0) ) ).
fof(thm_2Estring_2EORD__CHR__COMPUTE,axiom,
! [V0_3E_20255_2E0,V1n_2E0] : s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Ecombin_2EFAIL_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Estring_2EORD_2E0),s(tyop_2Emin_2Ebool,V0_3E_20255_2E0))),s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))) ).
fof(thm_2Estring_2EORD__BOUND,axiom,
! [V0c_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))) ).
fof(thm_2Estring_2Echar__nchotomy,axiom,
! [V0c_2E0] :
? [V1n_2E0] : s(tyop_2Estring_2Echar,V0c_2E0) = s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) ).
fof(thm_2Estring_2Eranged__char__nchotomy,axiom,
! [V0a_2E0] :
? [V1r_2E0] :
( s(tyop_2Estring_2Echar,V0a_2E0) = s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V1r_2E0)))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))) ) ).
fof(thm_2Estring_2ECHAR__EQ__THM,axiom,
! [V0c1_2E0,V1c2_2E0] :
( s(tyop_2Estring_2Echar,V0c1_2E0) = s(tyop_2Estring_2Echar,V1c2_2E0)
<=> s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c1_2E0))) = s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V1c2_2E0))) ) ).
fof(thm_2Estring_2ECHAR__INDUCT__THM,axiom,
! [V0P_2E0] :
( ! [V1n_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) )
=> ! [V2c_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Estring_2Echar,V2c_2E0)))) ) ).
fof(thm_2Estring_2ETOCHAR__ind,axiom,
! [V0P_2E0] :
( ( ! [V1c_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V1c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))))
& ! [V2v6_2E0,V3v4_2E0,V4v5_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V2v6_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3v4_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4v5_2E0)))))))) )
=> ! [V5v_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5v_2E0)))) ) ).
fof(thm_2Estring_2ETOCHAR__def,axiom,
! [V0c_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2ETOCHAR_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))))) = s(tyop_2Estring_2Echar,V0c_2E0) ).
fof(thm_2Estring_2ETOKENS__ind,axiom,
! [V0P_27_2E0] :
( ( ! [V1P_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V1P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))))
& ! [V2P_2E0,V3h_2E0,V4t_2E0] :
( ( ! [V5l_2E0,V6r_2E0] :
( ( s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5l_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V6r_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erich__list_2ESPLITP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0)))))
& p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5l_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V6r_2E0)))))) )
& ! [V7l_2E0,V8r_2E0] :
( ( s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7l_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V8r_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erich__list_2ESPLITP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0)))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7l_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V8r_2E0)))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0)))))) ) )
=> ! [V9v_2E0,V10v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V9v_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V10v1_2E0)))) ) ).
fof(thm_2Estring_2ETOKENS__def,axiom,
! [F0_2E0] :
( ! [V3P_2E0,V4l_2E0,V5r_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4l_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5r_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4l_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2ETOKENS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5r_2E0))))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4l_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2ETOKENS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5r_2E0)))))))
=> ( ! [V0P_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2ETOKENS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ENIL_2E0)
& ! [V1t_2E0,V2h_2E0,V3P_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2ETOKENS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V2h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erich__list_2ESPLITP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V2h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))))) ) ) ).
fof(thm_2Estring_2EFIELDS__ind,axiom,
! [V0P_27_2E0] :
( ( ! [V1P_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V1P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))))
& ! [V2P_2E0,V3h_2E0,V4t_2E0] :
( ( ! [V5l_2E0,V6r_2E0] :
( ( s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5l_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V6r_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erich__list_2ESPLITP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0)))))
& p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5l_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V6r_2E0)))))) )
& ! [V7l_2E0,V8r_2E0] :
( ( s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7l_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V8r_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erich__list_2ESPLITP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0)))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7l_2E0))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V8r_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V8r_2E0)))))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0)))))) ) )
=> ! [V9v_2E0,V10v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_27_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V9v_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V10v1_2E0)))) ) ).
fof(thm_2Estring_2EFIELDS__def,axiom,
! [F0_2E0] :
( ! [V3P_2E0,V4l_2E0,V5r_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4l_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5r_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4l_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EFIELDS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5r_2E0))))))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5r_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4l_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4l_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EFIELDS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5r_2E0)))))))))))
=> ( ! [V0P_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EFIELDS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ENIL_2E0)))
& ! [V1t_2E0,V2h_2E0,V3P_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EFIELDS_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V2h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erich__list_2ESPLITP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V2h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))))) ) ) ).
fof(thm_2Estring_2EIMPLODE__EXPLODE__I,axiom,
! [V0s_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0)
& s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) ) ).
fof(thm_2Estring_2EIMPLODE__EXPLODE,axiom,
! [V0s_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) ).
fof(thm_2Estring_2EEXPLODE__IMPLODE,axiom,
! [V0cs_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0cs_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0cs_2E0) ).
fof(thm_2Estring_2EEXPLODE__ONTO,axiom,
! [V0cs_2E0] :
? [V1s_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0cs_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))) ).
fof(thm_2Estring_2EIMPLODE__ONTO,axiom,
! [V0s_2E0] :
? [V1cs_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1cs_2E0))) ).
fof(thm_2Estring_2EEXPLODE__11,axiom,
! [V0s2_2E0,V1s1_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s2_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s2_2E0) ) ).
fof(thm_2Estring_2EIMPLODE__11,axiom,
! [V0cs2_2E0,V1cs1_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1cs1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0cs2_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1cs1_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0cs2_2E0) ) ).
fof(thm_2Estring_2ESTRING__ACYCLIC,axiom,
! [V0s_2E0,V1c_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V1c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) != s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0)
& s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) != s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V1c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) ) ).
fof(thm_2Estring_2EEXTRACT__ind,axiom,
! [V0P_2E0] :
( ( ! [V1s_2E0,V2i_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))))))))
& ! [V3s_2E0,V4i_2E0,V5n_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V5n_2E0)))))))))) )
=> ! [V6v_2E0,V7v1_2E0,V8v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V6v_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V7v1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V8v2_2E0)))))))) ) ).
fof(thm_2Estring_2EEXTRACT__def,axiom,
! [V0s_2E0,V1n_2E0,V2i_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXTRACT_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ESUBSTRING_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))),s(tyop_2Enum_2Enum,V2i_2E0)))))))))
& s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXTRACT_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2ESUBSTRING_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) ) ).
fof(thm_2Estring_2ESTRLEN__EQ__0,axiom,
! [V0l_2E0] :
( s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) ) ).
fof(thm_2Estring_2ESTRLEN__THM,axiom,
( s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V0h_2E0,V1t_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))) ) ).
fof(thm_2Estring_2ESTRLEN__DEF,axiom,
( s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V0h_2E0,V1t_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))) ) ).
fof(thm_2Estring_2ESTRCAT__def,axiom,
( ! [V0l_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l_2E0)
& ! [V1l1_2E0,V2l2_2E0,V3h_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3h_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l2_2E0))))) ) ).
fof(thm_2Estring_2ESTRCAT,axiom,
! [V0s2_2E0,V1s1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s2_2E0))) ).
fof(thm_2Estring_2ESTRCAT__EQNS,axiom,
! [V0s2_2E0,V1s1_2E0,V2s_2E0,V3c_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s_2E0)
& s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s_2E0)
& s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s2_2E0))))) ) ).
fof(thm_2Estring_2ESTRCAT__ASSOC,axiom,
! [V0l1_2E0,V1l2_2E0,V2l3_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l2_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l3_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l2_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l3_2E0))) ).
fof(thm_2Estring_2ESTRCAT__11,axiom,
( ! [V0l1_2E0,V1l2_2E0,V2l3_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l3_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l2_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2l3_2E0) )
& ! [V3l1_2E0,V4l2_2E0,V5l3_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4l2_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3l1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5l3_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3l1_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4l2_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5l3_2E0) ) ) ).
fof(thm_2Estring_2ESTRCAT__ACYCLIC,axiom,
! [V0s_2E0,V1s1_2E0] :
( ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) )
& ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0)))
<=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) ) ) ).
fof(thm_2Estring_2ESTRCAT__EXPLODE,axiom,
! [V0s1_2E0,V1s2_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0))))) ).
fof(thm_2Estring_2ESTRCAT__EQ__EMPTY,axiom,
! [V0l1_2E0,V1l2_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0)
<=> ( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l1_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0)
& s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l2_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0) ) ) ).
fof(thm_2Estring_2ESTRLEN__CAT,axiom,
! [V0l1_2E0,V1l2_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1l2_2E0))))) ).
fof(thm_2Estring_2EisPREFIX__DEF,axiom,
! [F4_2E0,F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
( ! [V6c2_2E0,V7t2_2E0,V8c1_2E0,V9t1_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)))),F4_2E0),s(tyop_2Estring_2Echar,V6c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7t2_2E0))),s(tyop_2Estring_2Echar,V8c1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V9t1_2E0))))
<=> ( s(tyop_2Estring_2Echar,V8c1_2E0) = s(tyop_2Estring_2Echar,V6c2_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V9t1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7t2_2E0)))) ) )
=> ( ! [V4v2_2E0,V6c2_2E0,V7t2_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool))),F3_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V4v2_2E0))),s(tyop_2Estring_2Echar,V6c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7t2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V4v2_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)))),F4_2E0),s(tyop_2Estring_2Echar,V6c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7t2_2E0)))))
=> ( ! [V4v2_2E0,V5v3_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V4v2_2E0))),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V5v3_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V5v3_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool))),F3_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V4v2_2E0)))))
=> ( ! [V3v1_2E0,V4v2_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),V3v1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V4v2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),V3v1_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V4v2_2E0)))))
=> ( ! [V2v_2E0,V3v1_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),V2v_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),V3v1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),V2v_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),V3v1_2E0)))))
=> ! [V0s1_2E0,V1s2_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Epair_2E_2C_2E2(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0))))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Ebool)),F0_2E0))) ) ) ) ) ) ).
fof(thm_2Estring_2EisPREFIX__IND,axiom,
! [V0P_2E0] :
( ! [V1s1_2E0,V2s2_2E0] :
( ! [V3c_2E0,V4t1_2E0,V5t2_2E0] :
( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Estring_2Echar,V3c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t1_2E0)))))
& s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epair_2E_2C_2E2(s(tyop_2Estring_2Echar,V3c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5t2_2E0))))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5t2_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s2_2E0)))) )
=> ! [V6v_2E0,V7v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V6v_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7v1_2E0)))) ) ).
fof(thm_2Estring_2EisPREFIX__STRCAT,axiom,
! [V0s1_2E0,V1s2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0))))
<=> ? [V2s3_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s3_2E0))) ) ).
fof(thm_2Estring_2Estring__lt__ind,axiom,
! [V0P_2E0] :
( ( ! [V1s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))))
& ! [V2c_2E0,V3s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s_2E0))))))
& ! [V4c1_2E0,V5s1_2E0,V6c2_2E0,V7s2_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5s1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7s2_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V4c1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5s1_2E0))))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V6c2_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V7s2_2E0)))))) ) )
=> ! [V8v_2E0,V9v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V8v_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V9v1_2E0)))) ) ).
fof(thm_2Estring_2Estring__lt__def,axiom,
( ! [V0s_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ! [V1s_2E0,V2c_2E0] : s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ! [V3s2_2E0,V4s1_2E0,V5c2_2E0,V6c1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V6c1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4s1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V5c2_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Estring_2Echar__lt_2E2(s(tyop_2Estring_2Echar,V6c1_2E0),s(tyop_2Estring_2Echar,V5c2_2E0))))
| ( s(tyop_2Estring_2Echar,V6c1_2E0) = s(tyop_2Estring_2Echar,V5c2_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3s2_2E0)))) ) ) ) ) ).
fof(thm_2Estring_2Estring__lt__nonrefl,axiom,
! [V0s_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0)))) ).
fof(thm_2Estring_2Estring__lt__antisym,axiom,
! [V0s_2E0,V1t_2E0] :
~ ( p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0)))) ) ).
fof(thm_2Estring_2Estring__lt__cases,axiom,
! [V0s_2E0,V1t_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0)))) ) ).
fof(thm_2Estring_2Estring__lt__trans,axiom,
! [V0s1_2E0,V1s2_2E0,V2s3_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s2_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s3_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Estring_2Estring__lt_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2s3_2E0)))) ) ).
fof(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
=> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).
%------------------------------------------------------------------------------