ITP001 Axioms: ITP054+5.ax
%------------------------------------------------------------------------------
% File : ITP054+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : string+2.ax [Gau20]
% : HL4054+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 158 ( 50 unt; 0 def)
% Number of atoms : 537 ( 142 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 388 ( 9 ~; 10 |; 64 &)
% ( 48 <=>; 257 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 118 ( 118 usr; 65 con; 0-3 aty)
% Number of variables : 272 ( 264 !; 8 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(ne_ty_2Estring_2Echar,axiom,
ne(ty_2Estring_2Echar) ).
fof(mem_c_2Estring_2ECHR,axiom,
mem(c_2Estring_2ECHR,arr(ty_2Enum_2Enum,ty_2Estring_2Echar)) ).
fof(mem_c_2Estring_2EDEST__STRING,axiom,
mem(c_2Estring_2EDEST__STRING,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))))) ).
fof(mem_c_2Estring_2EEXPLODE,axiom,
mem(c_2Estring_2EEXPLODE,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(mem_c_2Estring_2EEXTRACT,axiom,
mem(c_2Estring_2EEXTRACT,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(mem_c_2Estring_2EFIELDS,axiom,
mem(c_2Estring_2EFIELDS,arr(arr(ty_2Estring_2Echar,bool),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar))))) ).
fof(mem_c_2Estring_2EIMPLODE,axiom,
mem(c_2Estring_2EIMPLODE,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(mem_c_2Estring_2EORD,axiom,
mem(c_2Estring_2EORD,arr(ty_2Estring_2Echar,ty_2Enum_2Enum)) ).
fof(mem_c_2Estring_2ESTR,axiom,
mem(c_2Estring_2ESTR,arr(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(mem_c_2Estring_2ESUB,axiom,
mem(c_2Estring_2ESUB,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum),ty_2Estring_2Echar)) ).
fof(mem_c_2Estring_2ESUBSTRING,axiom,
mem(c_2Estring_2ESUBSTRING,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(mem_c_2Estring_2ETOCHAR,axiom,
mem(c_2Estring_2ETOCHAR,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Estring_2Echar)) ).
fof(mem_c_2Estring_2ETOKENS,axiom,
mem(c_2Estring_2ETOKENS,arr(arr(ty_2Estring_2Echar,bool),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar))))) ).
fof(mem_c_2Estring_2ETRANSLATE,axiom,
mem(c_2Estring_2ETRANSLATE,arr(arr(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)))) ).
fof(mem_c_2Estring_2Echar__ge,axiom,
mem(c_2Estring_2Echar__ge,arr(ty_2Estring_2Echar,arr(ty_2Estring_2Echar,bool))) ).
fof(mem_c_2Estring_2Echar__gt,axiom,
mem(c_2Estring_2Echar__gt,arr(ty_2Estring_2Echar,arr(ty_2Estring_2Echar,bool))) ).
fof(mem_c_2Estring_2Echar__le,axiom,
mem(c_2Estring_2Echar__le,arr(ty_2Estring_2Echar,arr(ty_2Estring_2Echar,bool))) ).
fof(mem_c_2Estring_2Echar__lt,axiom,
mem(c_2Estring_2Echar__lt,arr(ty_2Estring_2Echar,arr(ty_2Estring_2Echar,bool))) ).
fof(mem_c_2Estring_2Echar__size,axiom,
mem(c_2Estring_2Echar__size,arr(ty_2Estring_2Echar,ty_2Enum_2Enum)) ).
fof(mem_c_2Estring_2EisAlpha,axiom,
mem(c_2Estring_2EisAlpha,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisAlphaNum,axiom,
mem(c_2Estring_2EisAlphaNum,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisAscii,axiom,
mem(c_2Estring_2EisAscii,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisCntrl,axiom,
mem(c_2Estring_2EisCntrl,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisDigit,axiom,
mem(c_2Estring_2EisDigit,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisGraph,axiom,
mem(c_2Estring_2EisGraph,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisHexDigit,axiom,
mem(c_2Estring_2EisHexDigit,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisLower,axiom,
mem(c_2Estring_2EisLower,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisPrint,axiom,
mem(c_2Estring_2EisPrint,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisPunct,axiom,
mem(c_2Estring_2EisPunct,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisSpace,axiom,
mem(c_2Estring_2EisSpace,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2EisUpper,axiom,
mem(c_2Estring_2EisUpper,arr(ty_2Estring_2Echar,bool)) ).
fof(mem_c_2Estring_2Estring__ge,axiom,
mem(c_2Estring_2Estring__ge,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool))) ).
fof(mem_c_2Estring_2Estring__gt,axiom,
mem(c_2Estring_2Estring__gt,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool))) ).
fof(mem_c_2Estring_2Estring__le,axiom,
mem(c_2Estring_2Estring__le,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool))) ).
fof(mem_c_2Estring_2Estring__lt,axiom,
mem(c_2Estring_2Estring__lt,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool))) ).
fof(mem_c_2Estring_2EtoLower,axiom,
mem(c_2Estring_2EtoLower,arr(ty_2Estring_2Echar,ty_2Estring_2Echar)) ).
fof(mem_c_2Estring_2EtoUpper,axiom,
mem(c_2Estring_2EtoUpper,arr(ty_2Estring_2Echar,ty_2Estring_2Echar)) ).
fof(lameq_f1123,axiom,
! [V1n] : ap(f1123,V1n) = ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) ).
fof(ax_thm_2Estring_2Echar__TY__DEF,axiom,
? [V0rep] :
( mem(V0rep,arr(ty_2Estring_2Echar,ty_2Enum_2Enum))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Enum_2Enum,ty_2Estring_2Echar),f1123),V0rep)) ) ).
fof(lameq_f1124,axiom,
! [V2n] : ap(f1124,V2n) = ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) ).
fof(ax_thm_2Estring_2Echar__BIJ,axiom,
( ! [V0a] :
( mem(V0a,ty_2Estring_2Echar)
=> ap(c_2Estring_2ECHR,ap(c_2Estring_2EORD,V0a)) = V0a )
& ! [V1r] :
( mem(V1r,ty_2Enum_2Enum)
=> ( p(ap(f1124,V1r))
<=> ap(c_2Estring_2EORD,ap(c_2Estring_2ECHR,V1r)) = V1r ) ) ) ).
fof(conj_thm_2Estring_2EORD__11,axiom,
! [V0a] :
( mem(V0a,ty_2Estring_2Echar)
=> ! [V1a_27] :
( mem(V1a_27,ty_2Estring_2Echar)
=> ( ap(c_2Estring_2EORD,V0a) = ap(c_2Estring_2EORD,V1a_27)
<=> V0a = V1a_27 ) ) ) ).
fof(conj_thm_2Estring_2ECHR__11,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ! [V1r_27] :
( mem(V1r_27,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1r_27),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))
=> ( ap(c_2Estring_2ECHR,V0r) = ap(c_2Estring_2ECHR,V1r_27)
<=> V0r = V1r_27 ) ) ) ) ) ).
fof(conj_thm_2Estring_2EORD__ONTO,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))
<=> ? [V1a] :
( mem(V1a,ty_2Estring_2Echar)
& V0r = ap(c_2Estring_2EORD,V1a) ) ) ) ).
fof(conj_thm_2Estring_2ECHR__ONTO,axiom,
! [V0a] :
( mem(V0a,ty_2Estring_2Echar)
=> ? [V1r] :
( mem(V1r,ty_2Enum_2Enum)
& V0a = ap(c_2Estring_2ECHR,V1r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V1r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) ) ) ).
fof(conj_thm_2Estring_2ECHR__ORD,axiom,
! [V0a] :
( mem(V0a,ty_2Estring_2Echar)
=> ap(c_2Estring_2ECHR,ap(c_2Estring_2EORD,V0a)) = V0a ) ).
fof(conj_thm_2Estring_2EORD__CHR,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))
<=> ap(c_2Estring_2EORD,ap(c_2Estring_2ECHR,V0r)) = V0r ) ) ).
fof(conj_thm_2Estring_2EORD__CHR__RWT,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))
=> ap(c_2Estring_2EORD,ap(c_2Estring_2ECHR,V0r)) = V0r ) ) ).
fof(conj_thm_2Estring_2EORD__CHR__COMPUTE,axiom,
! [V0_3E_20255] :
( mem(V0_3E_20255,bool)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Estring_2EORD,ap(c_2Estring_2ECHR,V1n)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))),V1n),ap(ap(ap(c_2Ecombin_2EFAIL(arr(ty_2Estring_2Echar,ty_2Enum_2Enum),bool),c_2Estring_2EORD),V0_3E_20255),ap(c_2Estring_2ECHR,V1n))) ) ) ).
fof(conj_thm_2Estring_2EORD__BOUND,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) ) ).
fof(conj_thm_2Estring_2Echar__nchotomy,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& V0c = ap(c_2Estring_2ECHR,V1n) ) ) ).
fof(conj_thm_2Estring_2Eranged__char__nchotomy,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& V0c = ap(c_2Estring_2ECHR,V1n)
& p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) ) ) ).
fof(ax_thm_2Estring_2EisLower__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisLower,V0c))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))),ap(c_2Estring_2EORD,V0c)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))) ) ) ) ).
fof(ax_thm_2Estring_2EisUpper__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisUpper,V0c))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))),ap(c_2Estring_2EORD,V0c)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) ) ) ) ).
fof(ax_thm_2Estring_2EisDigit__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisDigit,V0c))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))),ap(c_2Estring_2EORD,V0c)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))) ) ) ) ).
fof(ax_thm_2Estring_2EisAlpha__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisAlpha,V0c))
<=> ( p(ap(c_2Estring_2EisLower,V0c))
| p(ap(c_2Estring_2EisUpper,V0c)) ) ) ) ).
fof(ax_thm_2Estring_2EisHexDigit__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisHexDigit,V0c))
<=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))),ap(c_2Estring_2EORD,V0c)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))) )
| ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))),ap(c_2Estring_2EORD,V0c)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))) )
| ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))),ap(c_2Estring_2EORD,V0c)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) ) ) ) ) ).
fof(ax_thm_2Estring_2EisAlphaNum__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisAlphaNum,V0c))
<=> ( p(ap(c_2Estring_2EisAlpha,V0c))
| p(ap(c_2Estring_2EisDigit,V0c)) ) ) ) ).
fof(ax_thm_2Estring_2EisPrint__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisPrint,V0c))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))),ap(c_2Estring_2EORD,V0c)))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) ) ) ) ).
fof(ax_thm_2Estring_2EisSpace__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisSpace,V0c))
<=> ( ap(c_2Estring_2EORD,V0c) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))
| ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Estring_2EORD,V0c)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ) ) ) ).
fof(ax_thm_2Estring_2EisGraph__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisGraph,V0c))
<=> ( p(ap(c_2Estring_2EisPrint,V0c))
& ~ p(ap(c_2Estring_2EisSpace,V0c)) ) ) ) ).
fof(ax_thm_2Estring_2EisPunct__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisPunct,V0c))
<=> ( p(ap(c_2Estring_2EisGraph,V0c))
& ~ p(ap(c_2Estring_2EisAlphaNum,V0c)) ) ) ) ).
fof(ax_thm_2Estring_2EisAscii__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisAscii,V0c))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) ) ) ).
fof(ax_thm_2Estring_2EisCntrl__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ( p(ap(c_2Estring_2EisCntrl,V0c))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))),ap(c_2Estring_2EORD,V0c))) ) ) ) ).
fof(ax_thm_2Estring_2EtoLower__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ap(c_2Estring_2EtoLower,V0c) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Estring_2Echar),ap(c_2Estring_2EisUpper,V0c)),ap(c_2Estring_2ECHR,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))),V0c) ) ).
fof(ax_thm_2Estring_2EtoUpper__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ap(c_2Estring_2EtoUpper,V0c) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Estring_2Echar),ap(c_2Estring_2EisLower,V0c)),ap(c_2Estring_2ECHR,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Estring_2EORD,V0c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))),V0c) ) ).
fof(ax_thm_2Estring_2Echar__lt__def,axiom,
! [V0a] :
( mem(V0a,ty_2Estring_2Echar)
=> ! [V1b] :
( mem(V1b,ty_2Estring_2Echar)
=> ( p(ap(ap(c_2Estring_2Echar__lt,V0a),V1b))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Estring_2EORD,V0a)),ap(c_2Estring_2EORD,V1b))) ) ) ) ).
fof(ax_thm_2Estring_2Echar__le__def,axiom,
! [V0a] :
( mem(V0a,ty_2Estring_2Echar)
=> ! [V1b] :
( mem(V1b,ty_2Estring_2Echar)
=> ( p(ap(ap(c_2Estring_2Echar__le,V0a),V1b))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Estring_2EORD,V0a)),ap(c_2Estring_2EORD,V1b))) ) ) ) ).
fof(ax_thm_2Estring_2Echar__gt__def,axiom,
! [V0a] :
( mem(V0a,ty_2Estring_2Echar)
=> ! [V1b] :
( mem(V1b,ty_2Estring_2Echar)
=> ( p(ap(ap(c_2Estring_2Echar__gt,V0a),V1b))
<=> p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Estring_2EORD,V0a)),ap(c_2Estring_2EORD,V1b))) ) ) ) ).
fof(ax_thm_2Estring_2Echar__ge__def,axiom,
! [V0a] :
( mem(V0a,ty_2Estring_2Echar)
=> ! [V1b] :
( mem(V1b,ty_2Estring_2Echar)
=> ( p(ap(ap(c_2Estring_2Echar__ge,V0a),V1b))
<=> p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Estring_2EORD,V0a)),ap(c_2Estring_2EORD,V1b))) ) ) ) ).
fof(conj_thm_2Estring_2ECHAR__EQ__THM,axiom,
! [V0c1] :
( mem(V0c1,ty_2Estring_2Echar)
=> ! [V1c2] :
( mem(V1c2,ty_2Estring_2Echar)
=> ( V0c1 = V1c2
<=> ap(c_2Estring_2EORD,V0c1) = ap(c_2Estring_2EORD,V1c2) ) ) ) ).
fof(conj_thm_2Estring_2ECHAR__INDUCT__THM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Estring_2Echar,bool))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))
=> p(ap(V0P,ap(c_2Estring_2ECHR,V1n))) ) )
=> ! [V2c] :
( mem(V2c,ty_2Estring_2Echar)
=> p(ap(V0P,V2c)) ) ) ) ).
fof(ax_thm_2Estring_2Echar__size__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ap(c_2Estring_2Echar__size,V0c) = c_2Enum_2E0 ) ).
fof(ax_thm_2Estring_2ESUB__def,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Estring_2ESUB,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum),V0s),V1n)) = ap(ap(c_2Elist_2EEL(ty_2Estring_2Echar),V1n),V0s) ) ) ).
fof(ax_thm_2Estring_2ESTR__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ap(c_2Estring_2ESTR,V0c) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),c_2Elist_2ENIL(ty_2Estring_2Echar)) ) ).
fof(lameq_f1125,axiom,
! [V0R] : ap(f1125,V0R) = ap(c_2Erelation_2EWF(ty_2Elist_2Elist(ty_2Estring_2Echar)),V0R) ).
fof(lameq_f1126,axiom,
! [V3c] :
( mem(V3c,ty_2Estring_2Echar)
=> ! [V4v1] : ap(f1126(V3c),V4v1) = ap(ap(ap(c_2Elist_2Elist__CASE(ty_2Estring_2Echar,ty_2Estring_2Echar),V4v1),ap(c_2Ecombin_2EI(ty_2Estring_2Echar),V3c)),k(ty_2Estring_2Echar,k(ty_2Elist_2Elist(ty_2Estring_2Echar),c_2Ebool_2EARB(ty_2Estring_2Echar)))) ) ).
fof(lameq_f1127,axiom,
! [V3c] : ap(f1127,V3c) = f1126(V3c) ).
fof(lameq_f1128,axiom,
! [V2a] : ap(f1128,V2a) = ap(ap(ap(c_2Elist_2Elist__CASE(ty_2Estring_2Echar,ty_2Estring_2Echar),V2a),c_2Ebool_2EARB(ty_2Estring_2Echar)),f1127) ).
fof(ax_thm_2Estring_2ETOCHAR__primitive__def,axiom,
c_2Estring_2ETOCHAR = ap(ap(c_2Erelation_2EWFREC(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Estring_2Echar),ap(c_2Emin_2E_40(arr(ty_2Elist_2Elist(ty_2Estring_2Echar),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool))),f1125)),k(arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Estring_2Echar),f1128)) ).
fof(conj_thm_2Estring_2ETOCHAR__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool))
=> ( ( ! [V1c] :
( mem(V1c,ty_2Estring_2Echar)
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V1c),c_2Elist_2ENIL(ty_2Estring_2Echar)))) )
& p(ap(V0P,c_2Elist_2ENIL(ty_2Estring_2Echar)))
& ! [V2v6] :
( mem(V2v6,ty_2Estring_2Echar)
=> ! [V3v4] :
( mem(V3v4,ty_2Estring_2Echar)
=> ! [V4v5] :
( mem(V4v5,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V2v6),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V3v4),V4v5)))) ) ) ) )
=> ! [V5v] :
( mem(V5v,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> p(ap(V0P,V5v)) ) ) ) ).
fof(conj_thm_2Estring_2ETOCHAR__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ap(c_2Estring_2ETOCHAR,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),c_2Elist_2ENIL(ty_2Estring_2Echar))) = V0c ) ).
fof(ax_thm_2Estring_2ESUBSTRING__def,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(c_2Estring_2ESUBSTRING,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1i),V2n))) = ap(ap(ap(c_2Erich__list_2ESEG(ty_2Estring_2Echar),V2n),V1i),V0s) ) ) ) ).
fof(ax_thm_2Estring_2ETRANSLATE__def,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ! [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(c_2Estring_2ETRANSLATE,V0f),V1s) = ap(c_2Elist_2EFLAT(ty_2Estring_2Echar),ap(ap(c_2Elist_2EMAP(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),V0f),V1s)) ) ) ).
fof(conj_thm_2Estring_2ETOKENS__ind,axiom,
! [V0P_27] :
( mem(V0P_27,arr(arr(ty_2Estring_2Echar,bool),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool)))
=> ( ( ! [V1P] :
( mem(V1P,arr(ty_2Estring_2Echar,bool))
=> p(ap(ap(V0P_27,V1P),c_2Elist_2ENIL(ty_2Estring_2Echar))) )
& ! [V2P] :
( mem(V2P,arr(ty_2Estring_2Echar,bool))
=> ! [V3h] :
( mem(V3h,ty_2Estring_2Echar)
=> ! [V4t] :
( mem(V4t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V6r] :
( mem(V6r,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),V5l),V6r) = ap(ap(c_2Erich__list_2ESPLITP(ty_2Estring_2Echar),V2P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V3h),V4t))
& p(ap(c_2Elist_2ENULL(ty_2Estring_2Echar),V5l)) )
=> p(ap(ap(V0P_27,V2P),ap(c_2Elist_2ETL(ty_2Estring_2Echar),V6r))) ) ) )
& ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V8r] :
( mem(V8r,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),V7l),V8r) = ap(ap(c_2Erich__list_2ESPLITP(ty_2Estring_2Echar),V2P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V3h),V4t))
& ~ p(ap(c_2Elist_2ENULL(ty_2Estring_2Echar),V7l)) )
=> p(ap(ap(V0P_27,V2P),V8r)) ) ) ) )
=> p(ap(ap(V0P_27,V2P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V3h),V4t))) ) ) ) ) )
=> ! [V9v] :
( mem(V9v,arr(ty_2Estring_2Echar,bool))
=> ! [V10v1] :
( mem(V10v1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> p(ap(ap(V0P_27,V9v),V10v1)) ) ) ) ) ).
fof(lameq_f1129,axiom,
! [V3P] :
( mem(V3P,arr(ty_2Estring_2Echar,bool))
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V5r] : ap(f1129(V3P,V4l),V5r) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar))),ap(c_2Elist_2ENULL(ty_2Estring_2Echar),V4l)),ap(ap(c_2Estring_2ETOKENS,V3P),ap(c_2Elist_2ETL(ty_2Estring_2Echar),V5r))),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(ty_2Estring_2Echar)),V4l),ap(ap(c_2Estring_2ETOKENS,V3P),V5r))) ) ) ).
fof(lameq_f1130,axiom,
! [V3P] :
( mem(V3P,arr(ty_2Estring_2Echar,bool))
=> ! [V4l] : ap(f1130(V3P),V4l) = f1129(V3P,V4l) ) ).
fof(conj_thm_2Estring_2ETOKENS__def,axiom,
( ! [V0P] :
( mem(V0P,arr(ty_2Estring_2Echar,bool))
=> ap(ap(c_2Estring_2ETOKENS,V0P),c_2Elist_2ENIL(ty_2Estring_2Echar)) = c_2Elist_2ENIL(ty_2Elist_2Elist(ty_2Estring_2Echar)) )
& ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2h] :
( mem(V2h,ty_2Estring_2Echar)
=> ! [V3P] :
( mem(V3P,arr(ty_2Estring_2Echar,bool))
=> ap(ap(c_2Estring_2ETOKENS,V3P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V2h),V1t)) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar))),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar))),f1130(V3P))),ap(ap(c_2Erich__list_2ESPLITP(ty_2Estring_2Echar),V3P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V2h),V1t))) ) ) ) ) ).
fof(conj_thm_2Estring_2EFIELDS__ind,axiom,
! [V0P_27] :
( mem(V0P_27,arr(arr(ty_2Estring_2Echar,bool),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool)))
=> ( ( ! [V1P] :
( mem(V1P,arr(ty_2Estring_2Echar,bool))
=> p(ap(ap(V0P_27,V1P),c_2Elist_2ENIL(ty_2Estring_2Echar))) )
& ! [V2P] :
( mem(V2P,arr(ty_2Estring_2Echar,bool))
=> ! [V3h] :
( mem(V3h,ty_2Estring_2Echar)
=> ! [V4t] :
( mem(V4t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V6r] :
( mem(V6r,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),V5l),V6r) = ap(ap(c_2Erich__list_2ESPLITP(ty_2Estring_2Echar),V2P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V3h),V4t))
& p(ap(c_2Elist_2ENULL(ty_2Estring_2Echar),V5l)) )
=> p(ap(ap(V0P_27,V2P),ap(c_2Elist_2ETL(ty_2Estring_2Echar),V6r))) ) ) )
& ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V8r] :
( mem(V8r,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),V7l),V8r) = ap(ap(c_2Erich__list_2ESPLITP(ty_2Estring_2Echar),V2P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V3h),V4t))
& ~ p(ap(c_2Elist_2ENULL(ty_2Estring_2Echar),V7l))
& ~ p(ap(c_2Elist_2ENULL(ty_2Estring_2Echar),V8r)) )
=> p(ap(ap(V0P_27,V2P),ap(c_2Elist_2ETL(ty_2Estring_2Echar),V8r))) ) ) ) )
=> p(ap(ap(V0P_27,V2P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V3h),V4t))) ) ) ) ) )
=> ! [V9v] :
( mem(V9v,arr(ty_2Estring_2Echar,bool))
=> ! [V10v1] :
( mem(V10v1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> p(ap(ap(V0P_27,V9v),V10v1)) ) ) ) ) ).
fof(lameq_f1131,axiom,
! [V3P] :
( mem(V3P,arr(ty_2Estring_2Echar,bool))
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V5r] : ap(f1131(V3P,V4l),V5r) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar))),ap(c_2Elist_2ENULL(ty_2Estring_2Echar),V4l)),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Elist_2ENIL(ty_2Estring_2Echar)),ap(ap(c_2Estring_2EFIELDS,V3P),ap(c_2Elist_2ETL(ty_2Estring_2Echar),V5r)))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar))),ap(c_2Elist_2ENULL(ty_2Estring_2Echar),V5r)),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(ty_2Estring_2Echar)),V4l),c_2Elist_2ENIL(ty_2Elist_2Elist(ty_2Estring_2Echar)))),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(ty_2Estring_2Echar)),V4l),ap(ap(c_2Estring_2EFIELDS,V3P),ap(c_2Elist_2ETL(ty_2Estring_2Echar),V5r))))) ) ) ).
fof(lameq_f1132,axiom,
! [V3P] :
( mem(V3P,arr(ty_2Estring_2Echar,bool))
=> ! [V4l] : ap(f1132(V3P),V4l) = f1131(V3P,V4l) ) ).
fof(conj_thm_2Estring_2EFIELDS__def,axiom,
( ! [V0P] :
( mem(V0P,arr(ty_2Estring_2Echar,bool))
=> ap(ap(c_2Estring_2EFIELDS,V0P),c_2Elist_2ENIL(ty_2Estring_2Echar)) = ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Elist_2ENIL(ty_2Estring_2Echar)),c_2Elist_2ENIL(ty_2Elist_2Elist(ty_2Estring_2Echar))) )
& ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2h] :
( mem(V2h,ty_2Estring_2Echar)
=> ! [V3P] :
( mem(V3P,arr(ty_2Estring_2Echar,bool))
=> ap(ap(c_2Estring_2EFIELDS,V3P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V2h),V1t)) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar))),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar))),f1132(V3P))),ap(ap(c_2Erich__list_2ESPLITP(ty_2Estring_2Echar),V3P),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V2h),V1t))) ) ) ) ) ).
fof(ax_thm_2Estring_2EIMPLODE__def,axiom,
( ap(c_2Estring_2EIMPLODE,c_2Elist_2ENIL(ty_2Estring_2Echar)) = c_2Elist_2ENIL(ty_2Estring_2Echar)
& ! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ! [V1cs] :
( mem(V1cs,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring_2EIMPLODE,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1cs)) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),ap(c_2Estring_2EIMPLODE,V1cs)) ) ) ) ).
fof(ax_thm_2Estring_2EEXPLODE__def,axiom,
( ap(c_2Estring_2EEXPLODE,c_2Elist_2ENIL(ty_2Estring_2Echar)) = c_2Elist_2ENIL(ty_2Estring_2Echar)
& ! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ! [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring_2EEXPLODE,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1s)) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),ap(c_2Estring_2EEXPLODE,V1s)) ) ) ) ).
fof(conj_thm_2Estring_2EIMPLODE__EXPLODE__I,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(c_2Estring_2EEXPLODE,V0s) = V0s
& ap(c_2Estring_2EIMPLODE,V0s) = V0s ) ) ).
fof(conj_thm_2Estring_2EIMPLODE__EXPLODE,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring_2EIMPLODE,ap(c_2Estring_2EEXPLODE,V0s)) = V0s ) ).
fof(conj_thm_2Estring_2EEXPLODE__IMPLODE,axiom,
! [V0cs] :
( mem(V0cs,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring_2EEXPLODE,ap(c_2Estring_2EIMPLODE,V0cs)) = V0cs ) ).
fof(conj_thm_2Estring_2EEXPLODE__ONTO,axiom,
! [V0cs] :
( mem(V0cs,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ? [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
& V0cs = ap(c_2Estring_2EEXPLODE,V1s) ) ) ).
fof(conj_thm_2Estring_2EIMPLODE__ONTO,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ? [V1cs] :
( mem(V1cs,ty_2Elist_2Elist(ty_2Estring_2Echar))
& V0s = ap(c_2Estring_2EIMPLODE,V1cs) ) ) ).
fof(conj_thm_2Estring_2EEXPLODE__11,axiom,
! [V0s1] :
( mem(V0s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s2] :
( mem(V1s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(c_2Estring_2EEXPLODE,V0s1) = ap(c_2Estring_2EEXPLODE,V1s2)
<=> V0s1 = V1s2 ) ) ) ).
fof(conj_thm_2Estring_2EIMPLODE__11,axiom,
! [V0cs1] :
( mem(V0cs1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1cs2] :
( mem(V1cs2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(c_2Estring_2EIMPLODE,V0cs1) = ap(c_2Estring_2EIMPLODE,V1cs2)
<=> V0cs1 = V1cs2 ) ) ) ).
fof(conj_thm_2Estring_2ESTRING__ACYCLIC,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1c] :
( mem(V1c,ty_2Estring_2Echar)
=> ( ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V1c),V0s) != V0s
& V0s != ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V1c),V0s) ) ) ) ).
fof(lameq_f1133,axiom,
! [V0R] : ap(f1133,V0R) = ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum)))),V0R) ).
fof(lameq_f1134,axiom,
! [V5i] :
( mem(V5i,ty_2Enum_2Enum)
=> ! [V3s] :
( mem(V3s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V7n] : ap(f1134(V5i,V3s),V7n) = ap(c_2Ecombin_2EI(ty_2Elist_2Elist(ty_2Estring_2Echar)),ap(c_2Estring_2ESUBSTRING,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V3s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V5i),V7n)))) ) ) ).
fof(lameq_f1135,axiom,
! [V5i] :
( mem(V5i,ty_2Enum_2Enum)
=> ! [V3s] :
( mem(V3s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V6v3] : ap(f1135(V5i,V3s),V6v3) = ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)),V6v3),ap(c_2Ecombin_2EI(ty_2Elist_2Elist(ty_2Estring_2Echar)),ap(c_2Estring_2ESUBSTRING,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V3s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V5i),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),V3s)),V5i)))))),f1134(V5i,V3s)) ) ) ).
fof(lameq_f1136,axiom,
! [V3s] :
( mem(V3s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V5i] : ap(f1136(V3s),V5i) = f1135(V5i,V3s) ) ).
fof(lameq_f1137,axiom,
! [V3s] :
( mem(V3s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V4v1] : ap(f1137(V3s),V4v1) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum)),V4v1),f1136(V3s)) ) ).
fof(lameq_f1138,axiom,
! [V3s] : ap(f1138,V3s) = f1137(V3s) ).
fof(lameq_f1139,axiom,
! [V2a] : ap(f1139,V2a) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),V2a),f1138) ).
fof(ax_thm_2Estring_2EEXTRACT__primitive__def,axiom,
c_2Estring_2EEXTRACT = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),ty_2Elist_2Elist(ty_2Estring_2Echar)),ap(c_2Emin_2E_40(arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),bool))),f1133)),k(arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),ty_2Elist_2Elist(ty_2Estring_2Echar)),f1139)) ).
fof(conj_thm_2Estring_2EEXTRACT__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),bool))
=> ( ( ! [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),V1s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum)),V2i),c_2Eoption_2ENONE(ty_2Enum_2Enum))))) ) )
& ! [V3s] :
( mem(V3s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V4i] :
( mem(V4i,ty_2Enum_2Enum)
=> ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),V3s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum)),V4i),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V5n))))) ) ) ) )
=> ! [V6v] :
( mem(V6v,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V7v1] :
( mem(V7v1,ty_2Enum_2Enum)
=> ! [V8v2] :
( mem(V8v2,ty_2Eoption_2Eoption(ty_2Enum_2Enum))
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),V6v),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum)),V7v1),V8v2)))) ) ) ) ) ) ).
fof(conj_thm_2Estring_2EEXTRACT__def,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ap(c_2Estring_2EEXTRACT,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),V0s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum)),V1i),c_2Eoption_2ENONE(ty_2Enum_2Enum)))) = ap(c_2Estring_2ESUBSTRING,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1i),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),V0s)),V1i))))
& ap(c_2Estring_2EEXTRACT,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum))),V0s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Eoption_2Eoption(ty_2Enum_2Enum)),V1i),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V2n)))) = ap(c_2Estring_2ESUBSTRING,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1i),V2n))) ) ) ) ) ).
fof(conj_thm_2Estring_2ESTRLEN__EXPLODE__THM,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),V0s) = ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),ap(c_2Estring_2EEXPLODE,V0s)) ) ).
fof(ax_thm_2Estring_2EDEST__STRING__def,axiom,
( ap(c_2Estring_2EDEST__STRING,c_2Elist_2ENIL(ty_2Estring_2Echar)) = c_2Eoption_2ENONE(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)))
& ! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ! [V1rst] :
( mem(V1rst,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring_2EDEST__STRING,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1rst)) = ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))),ap(ap(c_2Epair_2E_2C(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),V0c),V1rst)) ) ) ) ).
fof(conj_thm_2Estring_2EDEST__STRING__LEMS,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2s] :
( mem(V2s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(c_2Estring_2EDEST__STRING,V2s) = c_2Eoption_2ENONE(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)))
<=> V2s = c_2Elist_2ENIL(ty_2Estring_2Echar) )
& ( ap(c_2Estring_2EDEST__STRING,V2s) = ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))),ap(ap(c_2Epair_2E_2C(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),V0c),V1t))
<=> V2s = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1t) ) ) ) ) ) ).
fof(conj_thm_2Estring_2EEXPLODE__EQNS,axiom,
( ap(c_2Estring_2EEXPLODE,c_2Elist_2ENIL(ty_2Estring_2Echar)) = c_2Elist_2ENIL(ty_2Estring_2Echar)
& ! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ! [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring_2EEXPLODE,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1s)) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),ap(c_2Estring_2EEXPLODE,V1s)) ) ) ) ).
fof(conj_thm_2Estring_2EIMPLODE__EQNS,axiom,
( ap(c_2Estring_2EIMPLODE,c_2Elist_2ENIL(ty_2Estring_2Echar)) = c_2Elist_2ENIL(ty_2Estring_2Echar)
& ! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ! [V1cs] :
( mem(V1cs,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring_2EIMPLODE,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1cs)) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),ap(c_2Estring_2EIMPLODE,V1cs)) ) ) ) ).
fof(conj_thm_2Estring_2EIMPLODE__EQ__EMPTYSTRING,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(c_2Estring_2EIMPLODE,V0l) = c_2Elist_2ENIL(ty_2Estring_2Echar)
<=> V0l = c_2Elist_2ENIL(ty_2Estring_2Echar) )
& ( c_2Elist_2ENIL(ty_2Estring_2Echar) = ap(c_2Estring_2EIMPLODE,V0l)
<=> V0l = c_2Elist_2ENIL(ty_2Estring_2Echar) ) ) ) ).
fof(conj_thm_2Estring_2EEXPLODE__EQ__NIL,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(c_2Estring_2EEXPLODE,V0s) = c_2Elist_2ENIL(ty_2Estring_2Echar)
<=> V0s = c_2Elist_2ENIL(ty_2Estring_2Echar) )
& ( c_2Elist_2ENIL(ty_2Estring_2Echar) = ap(c_2Estring_2EEXPLODE,V0s)
<=> V0s = c_2Elist_2ENIL(ty_2Estring_2Echar) ) ) ) ).
fof(conj_thm_2Estring_2EEXPLODE__EQ__THM,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1h] :
( mem(V1h,ty_2Estring_2Echar)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V1h),V2t) = ap(c_2Estring_2EEXPLODE,V0s)
<=> V0s = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V1h),ap(c_2Estring_2EIMPLODE,V2t)) )
& ( ap(c_2Estring_2EEXPLODE,V0s) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V1h),V2t)
<=> V0s = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V1h),ap(c_2Estring_2EIMPLODE,V2t)) ) ) ) ) ) ).
fof(conj_thm_2Estring_2EIMPLODE__EQ__THM,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ! [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1s) = ap(c_2Estring_2EIMPLODE,V2l)
<=> V2l = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),ap(c_2Estring_2EEXPLODE,V1s)) )
& ( ap(c_2Estring_2EIMPLODE,V2l) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1s)
<=> V2l = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),ap(c_2Estring_2EEXPLODE,V1s)) ) ) ) ) ) ).
fof(lameq_f1140,axiom,
! [V2c] :
( mem(V2c,ty_2Estring_2Echar)
=> ! [V3t] : ap(f1140(V2c),V3t) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V2c),ap(c_2Estring_2EEXPLODE,V3t)) ) ).
fof(lameq_f1141,axiom,
! [V2c] : ap(f1141,V2c) = f1140(V2c) ).
fof(lameq_f1142,axiom,
! [V1v] : ap(f1142,V1v) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),V1v),f1141) ).
fof(conj_thm_2Estring_2EEXPLODE__DEST__STRING,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring_2EEXPLODE,V0s) = ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),ty_2Elist_2Elist(ty_2Estring_2Echar)),ap(c_2Estring_2EDEST__STRING,V0s)),c_2Elist_2ENIL(ty_2Estring_2Echar)),f1142) ) ).
fof(conj_thm_2Estring_2EIMPLODE__STRING,axiom,
! [V0clist] :
( mem(V0clist,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring_2EIMPLODE,V0clist) = ap(ap(ap(c_2Elist_2EFOLDR(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Elist_2ECONS(ty_2Estring_2Echar)),c_2Elist_2ENIL(ty_2Estring_2Echar)),V0clist) ) ).
fof(conj_thm_2Estring_2ESTRLEN__EQ__0,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),V0l) = c_2Enum_2E0
<=> V0l = c_2Elist_2ENIL(ty_2Estring_2Echar) ) ) ).
fof(conj_thm_2Estring_2ESTRLEN__THM,axiom,
( ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),c_2Elist_2ENIL(ty_2Estring_2Echar)) = c_2Enum_2E0
& ! [V0h] :
( mem(V0h,ty_2Estring_2Echar)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0h),V1t)) = ap(c_2Enum_2ESUC,ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),V1t)) ) ) ) ).
fof(conj_thm_2Estring_2ESTRLEN__DEF,axiom,
( ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),c_2Elist_2ENIL(ty_2Estring_2Echar)) = c_2Enum_2E0
& ! [V0h] :
( mem(V0h,ty_2Estring_2Echar)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0h),V1t)) = ap(c_2Enum_2ESUC,ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),V1t)) ) ) ) ).
fof(conj_thm_2Estring_2ESTRCAT__def,axiom,
( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),c_2Elist_2ENIL(ty_2Estring_2Echar)),V0l) = V0l )
& ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V3h] :
( mem(V3h,ty_2Estring_2Echar)
=> ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V3h),V1l1)),V2l2) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V3h),ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V1l1),V2l2)) ) ) ) ) ).
fof(conj_thm_2Estring_2ESTRCAT,axiom,
! [V0s1] :
( mem(V0s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s2] :
( mem(V1s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0s1),V1s2) = ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0s1),V1s2) ) ) ).
fof(conj_thm_2Estring_2ESTRCAT__EQNS,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1c] :
( mem(V1c,ty_2Estring_2Echar)
=> ! [V2s1] :
( mem(V2s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V3s2] :
( mem(V3s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),c_2Elist_2ENIL(ty_2Estring_2Echar)),V0s) = V0s
& ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0s),c_2Elist_2ENIL(ty_2Estring_2Echar)) = V0s
& ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V1c),V2s1)),V3s2) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V1c),ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V2s1),V3s2)) ) ) ) ) ) ).
fof(conj_thm_2Estring_2ESTRCAT__ASSOC,axiom,
! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2l3] :
( mem(V2l3,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0l1),ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V1l2),V2l3)) = ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0l1),V1l2)),V2l3) ) ) ) ).
fof(conj_thm_2Estring_2ESTRCAT__11,axiom,
( ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2l3] :
( mem(V2l3,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0l1),V1l2) = ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0l1),V2l3)
<=> V1l2 = V2l3 ) ) ) )
& ! [V3l1] :
( mem(V3l1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V4l2] :
( mem(V4l2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V5l3] :
( mem(V5l3,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V4l2),V3l1) = ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V5l3),V3l1)
<=> V4l2 = V5l3 ) ) ) ) ) ).
fof(conj_thm_2Estring_2ESTRCAT__ACYCLIC,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s1] :
( mem(V1s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( V0s = ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0s),V1s1)
<=> V1s1 = c_2Elist_2ENIL(ty_2Estring_2Echar) )
& ( V0s = ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V1s1),V0s)
<=> V1s1 = c_2Elist_2ENIL(ty_2Estring_2Echar) ) ) ) ) ).
fof(conj_thm_2Estring_2ESTRCAT__EXPLODE,axiom,
! [V0s1] :
( mem(V0s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s2] :
( mem(V1s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0s1),V1s2) = ap(ap(ap(c_2Elist_2EFOLDR(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Elist_2ECONS(ty_2Estring_2Echar)),V1s2),ap(c_2Estring_2EEXPLODE,V0s1)) ) ) ).
fof(conj_thm_2Estring_2ESTRCAT__EQ__EMPTY,axiom,
! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0l1),V1l2) = c_2Elist_2ENIL(ty_2Estring_2Echar)
<=> ( V0l1 = c_2Elist_2ENIL(ty_2Estring_2Echar)
& V1l2 = c_2Elist_2ENIL(ty_2Estring_2Echar) ) ) ) ) ).
fof(conj_thm_2Estring_2ESTRLEN__CAT,axiom,
! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0l1),V1l2)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),V0l1)),ap(c_2Elist_2ELENGTH(ty_2Estring_2Echar),V1l2)) ) ) ).
fof(lameq_f1143,axiom,
! [V8c1] :
( mem(V8c1,ty_2Estring_2Echar)
=> ! [V6c2] :
( mem(V6c2,ty_2Estring_2Echar)
=> ! [V7t2] :
( mem(V7t2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V9t1] : ap(f1143(V8c1,V6c2,V7t2),V9t1) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Estring_2Echar),V8c1),V6c2)),ap(ap(c_2Elist_2EisPREFIX(ty_2Estring_2Echar),V9t1),V7t2)) ) ) ) ).
fof(lameq_f1144,axiom,
! [V6c2] :
( mem(V6c2,ty_2Estring_2Echar)
=> ! [V7t2] :
( mem(V7t2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V8c1] : ap(f1144(V6c2,V7t2),V8c1) = f1143(V8c1,V6c2,V7t2) ) ) ).
fof(lameq_f1145,axiom,
! [V6c2] :
( mem(V6c2,ty_2Estring_2Echar)
=> ! [V4v2] :
( mem(V4v2,ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ! [V7t2] : ap(f1145(V6c2,V4v2),V7t2) = ap(ap(c_2Epair_2Epair__CASE(bool,ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),V4v2),f1144(V6c2,V7t2)) ) ) ).
fof(lameq_f1146,axiom,
! [V4v2] :
( mem(V4v2,ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ! [V6c2] : ap(f1146(V4v2),V6c2) = f1145(V6c2,V4v2) ) ).
fof(lameq_f1147,axiom,
! [V4v2] :
( mem(V4v2,ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ! [V5v3] : ap(f1147(V4v2),V5v3) = ap(ap(c_2Epair_2Epair__CASE(bool,ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),V5v3),f1146(V4v2)) ) ).
fof(lameq_f1148,axiom,
! [V3v1] :
( mem(V3v1,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))))
=> ! [V4v2] : ap(f1148(V3v1),V4v2) = ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),bool),V3v1),c_2Ebool_2EF),f1147(V4v2)) ) ).
fof(lameq_f1149,axiom,
! [V2v] :
( mem(V2v,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))))
=> ! [V3v1] : ap(f1149(V2v),V3v1) = ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),bool),V2v),c_2Ebool_2ET),f1148(V3v1)) ) ).
fof(lameq_f1150,axiom,
! [V2v] : ap(f1150,V2v) = f1149(V2v) ).
fof(conj_thm_2Estring_2EisPREFIX__DEF,axiom,
! [V0s1] :
( mem(V0s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s2] :
( mem(V1s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( p(ap(ap(c_2Elist_2EisPREFIX(ty_2Estring_2Echar),V0s1),V1s2))
<=> p(ap(ap(c_2Epair_2Epair__CASE(bool,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)))),ap(ap(c_2Epair_2E_2C(ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)))),ap(c_2Estring_2EDEST__STRING,V0s1)),ap(c_2Estring_2EDEST__STRING,V1s2))),f1150)) ) ) ) ).
fof(conj_thm_2Estring_2EisPREFIX__IND,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool)))
=> ( ! [V1s1] :
( mem(V1s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2s2] :
( mem(V2s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ! [V3c] :
( mem(V3c,ty_2Estring_2Echar)
=> ! [V4t1] :
( mem(V4t1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V5t2] :
( mem(V5t2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( ap(c_2Estring_2EDEST__STRING,V1s1) = ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))),ap(ap(c_2Epair_2E_2C(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),V3c),V4t1))
& ap(c_2Estring_2EDEST__STRING,V2s2) = ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar))),ap(ap(c_2Epair_2E_2C(ty_2Estring_2Echar,ty_2Elist_2Elist(ty_2Estring_2Echar)),V3c),V5t2)) )
=> p(ap(ap(V0P,V4t1),V5t2)) ) ) ) )
=> p(ap(ap(V0P,V1s1),V2s2)) ) ) )
=> ! [V6v] :
( mem(V6v,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V7v1] :
( mem(V7v1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> p(ap(ap(V0P,V6v),V7v1)) ) ) ) ) ).
fof(conj_thm_2Estring_2EisPREFIX__STRCAT,axiom,
! [V0s1] :
( mem(V0s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s2] :
( mem(V1s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( p(ap(ap(c_2Elist_2EisPREFIX(ty_2Estring_2Echar),V0s1),V1s2))
<=> ? [V2s3] :
( mem(V2s3,ty_2Elist_2Elist(ty_2Estring_2Echar))
& V1s2 = ap(ap(c_2Elist_2EAPPEND(ty_2Estring_2Echar),V0s1),V2s3) ) ) ) ) ).
fof(conj_thm_2Estring_2Estring__lt__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool)))
=> ( ( ! [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> p(ap(ap(V0P,V1s),c_2Elist_2ENIL(ty_2Estring_2Echar))) )
& ! [V2c] :
( mem(V2c,ty_2Estring_2Echar)
=> ! [V3s] :
( mem(V3s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> p(ap(ap(V0P,c_2Elist_2ENIL(ty_2Estring_2Echar)),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V2c),V3s))) ) )
& ! [V4c1] :
( mem(V4c1,ty_2Estring_2Echar)
=> ! [V5s1] :
( mem(V5s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V6c2] :
( mem(V6c2,ty_2Estring_2Echar)
=> ! [V7s2] :
( mem(V7s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( p(ap(ap(V0P,V5s1),V7s2))
=> p(ap(ap(V0P,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V4c1),V5s1)),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V6c2),V7s2))) ) ) ) ) ) )
=> ! [V8v] :
( mem(V8v,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V9v1] :
( mem(V9v1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> p(ap(ap(V0P,V8v),V9v1)) ) ) ) ) ).
fof(conj_thm_2Estring_2Estring__lt__def,axiom,
( ! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( p(ap(ap(c_2Estring_2Estring__lt,V0s),c_2Elist_2ENIL(ty_2Estring_2Echar)))
<=> $false ) )
& ! [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2c] :
( mem(V2c,ty_2Estring_2Echar)
=> ( p(ap(ap(c_2Estring_2Estring__lt,c_2Elist_2ENIL(ty_2Estring_2Echar)),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V2c),V1s)))
<=> $true ) ) )
& ! [V3s2] :
( mem(V3s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V4s1] :
( mem(V4s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V5c2] :
( mem(V5c2,ty_2Estring_2Echar)
=> ! [V6c1] :
( mem(V6c1,ty_2Estring_2Echar)
=> ( p(ap(ap(c_2Estring_2Estring__lt,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V6c1),V4s1)),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V5c2),V3s2)))
<=> ( p(ap(ap(c_2Estring_2Echar__lt,V6c1),V5c2))
| ( V6c1 = V5c2
& p(ap(ap(c_2Estring_2Estring__lt,V4s1),V3s2)) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Estring_2Estring__le__def,axiom,
! [V0s1] :
( mem(V0s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s2] :
( mem(V1s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( p(ap(ap(c_2Estring_2Estring__le,V0s1),V1s2))
<=> ( V0s1 = V1s2
| p(ap(ap(c_2Estring_2Estring__lt,V0s1),V1s2)) ) ) ) ) ).
fof(ax_thm_2Estring_2Estring__gt__def,axiom,
! [V0s1] :
( mem(V0s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s2] :
( mem(V1s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( p(ap(ap(c_2Estring_2Estring__gt,V0s1),V1s2))
<=> p(ap(ap(c_2Estring_2Estring__lt,V1s2),V0s1)) ) ) ) ).
fof(ax_thm_2Estring_2Estring__ge__def,axiom,
! [V0s1] :
( mem(V0s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s2] :
( mem(V1s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( p(ap(ap(c_2Estring_2Estring__ge,V0s1),V1s2))
<=> p(ap(ap(c_2Estring_2Estring__le,V1s2),V0s1)) ) ) ) ).
fof(conj_thm_2Estring_2Estring__lt__nonrefl,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ~ p(ap(ap(c_2Estring_2Estring__lt,V0s),V0s)) ) ).
fof(conj_thm_2Estring_2Estring__lt__antisym,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ~ ( p(ap(ap(c_2Estring_2Estring__lt,V0s),V1t))
& p(ap(ap(c_2Estring_2Estring__lt,V1t),V0s)) ) ) ) ).
fof(conj_thm_2Estring_2Estring__lt__cases,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( V0s = V1t
| p(ap(ap(c_2Estring_2Estring__lt,V0s),V1t))
| p(ap(ap(c_2Estring_2Estring__lt,V1t),V0s)) ) ) ) ).
fof(conj_thm_2Estring_2Estring__lt__trans,axiom,
! [V0s1] :
( mem(V0s1,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1s2] :
( mem(V1s2,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2s3] :
( mem(V2s3,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ( p(ap(ap(c_2Estring_2Estring__lt,V0s1),V1s2))
& p(ap(ap(c_2Estring_2Estring__lt,V1s2),V2s3)) )
=> p(ap(ap(c_2Estring_2Estring__lt,V0s1),V2s3)) ) ) ) ) ).
%------------------------------------------------------------------------------