ITP001 Axioms: ITP112+5.ax
%------------------------------------------------------------------------------
% File : ITP112+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 : patricia_casts+2.ax [Gau20]
% : HL4112+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 104 ( 9 unt; 0 def)
% Number of atoms : 384 ( 71 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 280 ( 0 ~; 1 |; 12 &)
% ( 12 <=>; 255 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 122 ( 122 usr; 36 con; 0-4 aty)
% Number of variables : 281 ( 275 !; 6 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(ne_ty_2Epatricia__casts_2Eword__ptree,axiom,
! [A0] :
( ne(A0)
=> ! [A1] :
( ne(A1)
=> ne(ty_2Epatricia__casts_2Eword__ptree(A0,A1)) ) ) ).
fof(mem_c_2Epatricia__casts_2EADD__LISTs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EADD__LISTs(A_27a),arr(ty_2Epatricia_2Eptree(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),A_27a)),ty_2Epatricia_2Eptree(A_27a)))) ) ).
fof(mem_c_2Epatricia__casts_2EADD__LISTw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EADD__LISTw(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),A_27b)),ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)))) ) ) ).
fof(mem_c_2Epatricia__casts_2EADDs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EADDs(A_27a),arr(ty_2Epatricia_2Eptree(A_27a),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),A_27a),ty_2Epatricia_2Eptree(A_27a)))) ) ).
fof(mem_c_2Epatricia__casts_2EADDw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EADDw(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),A_27b),ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)))) ) ) ).
fof(mem_c_2Epatricia__casts_2EDEPTHw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EDEPTHw(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),ty_2Enum_2Enum)) ) ) ).
fof(mem_c_2Epatricia__casts_2EEVERY__LEAFw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EEVERY__LEAFw(A_27a,A_27b),arr(arr(ty_2Efcp_2Ecart(bool,A_27a),arr(A_27b,bool)),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),bool))) ) ) ).
fof(mem_c_2Epatricia__casts_2EEXISTS__LEAFw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EEXISTS__LEAFw(A_27a,A_27b),arr(arr(ty_2Efcp_2Ecart(bool,A_27a),arr(A_27b,bool)),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),bool))) ) ) ).
fof(mem_c_2Epatricia__casts_2EFINDs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EFINDs(A_27a),arr(ty_2Epatricia_2Eptree(A_27a),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),A_27a))) ) ).
fof(mem_c_2Epatricia__casts_2EFINDw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EFINDw(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27b),A_27a))) ) ) ).
fof(mem_c_2Epatricia__casts_2EINSERT__PTREEs,axiom,
mem(c_2Epatricia__casts_2EINSERT__PTREEs,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),arr(ty_2Epatricia_2Eptree(ty_2Eone_2Eone),ty_2Epatricia_2Eptree(ty_2Eone_2Eone)))) ).
fof(mem_c_2Epatricia__casts_2EINSERT__PTREEw,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EINSERT__PTREEw(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone),ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone)))) ) ).
fof(mem_c_2Epatricia__casts_2EIN__PTREEs,axiom,
mem(c_2Epatricia__casts_2EIN__PTREEs,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),arr(ty_2Epatricia_2Eptree(ty_2Eone_2Eone),bool))) ).
fof(mem_c_2Epatricia__casts_2EIN__PTREEw,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EIN__PTREEw(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone),bool))) ) ).
fof(mem_c_2Epatricia__casts_2EKEYSs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EKEYSs(A_27a),arr(ty_2Epatricia_2Eptree(A_27a),ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar)))) ) ).
fof(mem_c_2Epatricia__casts_2EKEYSw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EKEYSw(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,A_27a)))) ) ) ).
fof(mem_c_2Epatricia__casts_2EPEEKs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EPEEKs(A_27a),arr(ty_2Epatricia_2Eptree(A_27a),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Eoption_2Eoption(A_27a)))) ) ).
fof(mem_c_2Epatricia__casts_2EPEEKw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EPEEKw(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Eoption_2Eoption(A_27b)))) ) ) ).
fof(mem_c_2Epatricia__casts_2EPTREE__OF__STRINGSET,axiom,
mem(c_2Epatricia__casts_2EPTREE__OF__STRINGSET,arr(ty_2Epatricia_2Eptree(ty_2Eone_2Eone),arr(arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool),ty_2Epatricia_2Eptree(ty_2Eone_2Eone)))) ).
fof(mem_c_2Epatricia__casts_2EPTREE__OF__WORDSET,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EPTREE__OF__WORDSET(A_27a),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone),arr(arr(ty_2Efcp_2Ecart(bool,A_27a),bool),ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone)))) ) ).
fof(mem_c_2Epatricia__casts_2EREMOVEs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EREMOVEs(A_27a),arr(ty_2Epatricia_2Eptree(A_27a),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Epatricia_2Eptree(A_27a)))) ) ).
fof(mem_c_2Epatricia__casts_2EREMOVEw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EREMOVEw(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)))) ) ) ).
fof(mem_c_2Epatricia__casts_2ESIZEw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2ESIZEw(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),ty_2Enum_2Enum)) ) ) ).
fof(mem_c_2Epatricia__casts_2ESKIP1,axiom,
mem(c_2Epatricia__casts_2ESKIP1,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(mem_c_2Epatricia__casts_2ESOME__PTREE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2ESOME__PTREE(A_27a,A_27b),arr(ty_2Epatricia_2Eptree(A_27b),ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))) ) ) ).
fof(mem_c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,axiom,
mem(c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,arr(ty_2Epatricia_2Eptree(ty_2Eone_2Eone),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool))) ).
fof(mem_c_2Epatricia__casts_2ETHE__PTREE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2ETHE__PTREE(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),ty_2Epatricia_2Eptree(A_27a))) ) ) ).
fof(mem_c_2Epatricia__casts_2ETRANSFORMw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Epatricia__casts_2ETRANSFORMw(A_27a,A_27b,A_27c),arr(arr(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),ty_2Epatricia__casts_2Eword__ptree(A_27c,A_27b)))) ) ) ) ).
fof(mem_c_2Epatricia__casts_2ETRAVERSEs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2ETRAVERSEs(A_27a),arr(ty_2Epatricia_2Eptree(A_27a),ty_2Elist_2Elist(ty_2Elist_2Elist(ty_2Estring_2Echar)))) ) ).
fof(mem_c_2Epatricia__casts_2ETRAVERSEw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2ETRAVERSEw(A_27a,A_27b),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,A_27a)))) ) ) ).
fof(mem_c_2Epatricia__casts_2EUNION__PTREEw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Epatricia__casts_2EUNION__PTREEw(A_27a,A_27b,A_27c),arr(ty_2Epatricia__casts_2Eword__ptree(A_27b,ty_2Eone_2Eone),arr(ty_2Epatricia__casts_2Eword__ptree(A_27c,ty_2Eone_2Eone),ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone)))) ) ) ) ).
fof(mem_c_2Epatricia__casts_2EWORDSET__OF__PTREE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epatricia__casts_2EWORDSET__OF__PTREE(A_27a),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Epatricia__casts_2EWordEmpty,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EWordEmpty(A_27a,A_27b),ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)) ) ) ).
fof(mem_c_2Epatricia__casts_2EWord__ptree,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),arr(arr(A_27a,ty_2Eone_2Eone),arr(ty_2Epatricia_2Eptree(A_27b),ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)))) ) ) ).
fof(mem_c_2Epatricia__casts_2Enum__to__string,axiom,
mem(c_2Epatricia__casts_2Enum__to__string,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(mem_c_2Epatricia__casts_2Estring__to__num,axiom,
mem(c_2Epatricia__casts_2Estring__to__num,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum)) ).
fof(mem_c_2Epatricia__casts_2Eword__ptree__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Epatricia__casts_2Eword__ptree__CASE(A_27a,A_27b,A_27c),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),arr(arr(arr(A_27a,ty_2Eone_2Eone),arr(ty_2Epatricia_2Eptree(A_27b),A_27c)),A_27c))) ) ) ) ).
fof(mem_c_2Epatricia__casts_2Eword__ptree__size,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epatricia__casts_2Eword__ptree__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),ty_2Enum_2Enum)))) ) ) ).
fof(ax_thm_2Epatricia__casts_2ESKIP1__def,axiom,
! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ! [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Epatricia__casts_2ESKIP1,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1s)) = V1s ) ) ).
fof(ax_thm_2Epatricia__casts_2Estring__to__num__def,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Epatricia__casts_2Estring__to__num,V0s) = ap(ap(ap(c_2EASCIInumbers_2Es2n,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)))))))))),c_2Estring_2EORD),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),ap(c_2Estring_2ECHR,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0s)) ) ).
fof(ax_thm_2Epatricia__casts_2Enum__to__string__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Epatricia__casts_2Enum__to__string,V0n) = ap(c_2Epatricia__casts_2ESKIP1,ap(ap(ap(c_2EASCIInumbers_2En2s,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)))))))))),c_2Estring_2ECHR),V0n)) ) ).
fof(ax_thm_2Epatricia__casts_2EPEEKs__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(c_2Epatricia__casts_2EPEEKs(A_27a),V0t),V1w) = ap(ap(c_2Epatricia_2EPEEK(A_27a),V0t),ap(c_2Epatricia__casts_2Estring__to__num,V1w)) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EFINDs__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(c_2Epatricia__casts_2EFINDs(A_27a),V0t),V1w) = ap(c_2Eoption_2ETHE(A_27a),ap(ap(c_2Epatricia__casts_2EPEEKs(A_27a),V0t),V1w)) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EADDs__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V2d] :
( mem(V2d,A_27a)
=> ap(ap(c_2Epatricia__casts_2EADDs(A_27a),V0t),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),A_27a),V1w),V2d)) = ap(ap(c_2Epatricia_2EADD(A_27a),V0t),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),ap(c_2Epatricia__casts_2Estring__to__num,V1w)),V2d)) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EADD__LISTs__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Epatricia__casts_2EADD__LISTs(A_27a) = ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(ty_2Elist_2Elist(ty_2Estring_2Echar),A_27a),ty_2Epatricia_2Eptree(A_27a)),c_2Epatricia__casts_2EADDs(A_27a)) ) ).
fof(ax_thm_2Epatricia__casts_2EREMOVEs__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(c_2Epatricia__casts_2EREMOVEs(A_27a),V0t),V1w) = ap(ap(c_2Epatricia_2EREMOVE(A_27a),V0t),ap(c_2Epatricia__casts_2Estring__to__num,V1w)) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2ETRAVERSEs__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(A_27a))
=> ap(c_2Epatricia__casts_2ETRAVERSEs(A_27a),V0t) = ap(ap(c_2Elist_2EMAP(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Epatricia__casts_2Enum__to__string),ap(c_2Epatricia_2ETRAVERSE(A_27a),V0t)) ) ) ).
fof(ax_thm_2Epatricia__casts_2EKEYSs__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(A_27a))
=> ap(c_2Epatricia__casts_2EKEYSs(A_27a),V0t) = ap(ap(c_2Esorting_2EQSORT(ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Estring_2Estring__lt),ap(c_2Epatricia__casts_2ETRAVERSEs(A_27a),V0t)) ) ) ).
fof(ax_thm_2Epatricia__casts_2EIN__PTREEs__def,axiom,
! [V0w] :
( mem(V0w,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1t] :
( mem(V1t,ty_2Epatricia_2Eptree(ty_2Eone_2Eone))
=> ( p(ap(ap(c_2Epatricia__casts_2EIN__PTREEs,V0w),V1t))
<=> p(ap(ap(c_2Epatricia_2EIN__PTREE,ap(c_2Epatricia__casts_2Estring__to__num,V0w)),V1t)) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EINSERT__PTREEs__def,axiom,
! [V0w] :
( mem(V0w,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1t] :
( mem(V1t,ty_2Epatricia_2Eptree(ty_2Eone_2Eone))
=> ap(ap(c_2Epatricia__casts_2EINSERT__PTREEs,V0w),V1t) = ap(ap(c_2Epatricia_2EINSERT__PTREE,ap(c_2Epatricia__casts_2Estring__to__num,V0w)),V1t) ) ) ).
fof(ax_thm_2Epatricia__casts_2ESTRINGSET__OF__PTREE__def,axiom,
! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(ty_2Eone_2Eone))
=> ap(c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,V0t) = ap(c_2Elist_2ELIST__TO__SET(ty_2Elist_2Elist(ty_2Estring_2Echar)),ap(c_2Epatricia__casts_2ETRAVERSEs(ty_2Eone_2Eone),V0t)) ) ).
fof(ax_thm_2Epatricia__casts_2EPTREE__OF__STRINGSET__def,axiom,
! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(ty_2Eone_2Eone))
=> ! [V1s] :
( mem(V1s,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),bool))
=> ap(ap(c_2Epatricia__casts_2EPTREE__OF__STRINGSET,V0t),V1s) = ap(ap(c_2Epatricia_2EPTREE__OF__NUMSET,V0t),ap(ap(c_2Epred__set_2EIMAGE(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum),c_2Epatricia__casts_2Estring__to__num),V1s)) ) ) ).
fof(lameq_f2696,axiom,
! [A_27a,A_27b,V6a0] :
( mem(V6a0,arr(A_27a,ty_2Eone_2Eone))
=> ! [V7a1] : ap(f2696(A_27a,A_27b,V6a0),V7a1) = ap(ap(ap(c_2Eind__type_2ECONSTR(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b)),V6a0),V7a1)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))))) ) ).
fof(lameq_f2697,axiom,
! [A_27b,A_27a,V6a0] : ap(f2697(A_27b,A_27a),V6a0) = f2696(A_27a,A_27b,V6a0) ).
fof(lameq_f2698,axiom,
! [A_27a,A_27b,V4a0] :
( mem(V4a0,arr(A_27a,ty_2Eone_2Eone))
=> ! [V3a0_27] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))))
=> ! [V5a1] : ap(f2698(A_27a,A_27b,V4a0,V3a0_27),V5a1) = ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b)))),V3a0_27),ap(ap(f2697(A_27b,A_27a),V4a0),V5a1)) ) ) ).
fof(lameq_f2699,axiom,
! [A_27b,A_27a,V3a0_27] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))))
=> ! [V4a0] : ap(f2699(A_27b,A_27a,V3a0_27),V4a0) = ap(c_2Ebool_2E_3F(ty_2Epatricia_2Eptree(A_27b)),f2698(A_27a,A_27b,V4a0,V3a0_27)) ) ).
fof(lameq_f2700,axiom,
! [A_27b,A_27a,V2_27word__ptree_27] :
( mem(V2_27word__ptree_27,arr(ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))),bool))
=> ! [V3a0_27] : ap(f2700(A_27b,A_27a,V2_27word__ptree_27),V3a0_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_3F(arr(A_27a,ty_2Eone_2Eone)),f2699(A_27b,A_27a,V3a0_27))),ap(V2_27word__ptree_27,V3a0_27)) ) ).
fof(lameq_f2701,axiom,
! [A_27b,A_27a,V1a0_27] :
( mem(V1a0_27,ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))))
=> ! [V2_27word__ptree_27] : ap(f2701(A_27b,A_27a,V1a0_27),V2_27word__ptree_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b)))),f2700(A_27b,A_27a,V2_27word__ptree_27))),ap(V2_27word__ptree_27,V1a0_27)) ) ).
fof(lameq_f2702,axiom,
! [A_27b,A_27a,V1a0_27] : ap(f2702(A_27b,A_27a),V1a0_27) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))),bool)),f2701(A_27b,A_27a,V1a0_27)) ).
fof(ax_thm_2Epatricia__casts_2Eword__ptree__TY__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ? [V0rep] :
( mem(V0rep,arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b)))))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))),ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),f2702(A_27b,A_27a)),V0rep)) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2Eword__ptree__case__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0a0] :
( mem(V0a0,arr(A_27a,ty_2Eone_2Eone))
=> ! [V1a1] :
( mem(V1a1,ty_2Epatricia_2Eptree(A_27b))
=> ! [V2f] :
( mem(V2f,arr(arr(A_27a,ty_2Eone_2Eone),arr(ty_2Epatricia_2Eptree(A_27b),A_27c)))
=> ap(ap(c_2Epatricia__casts_2Eword__ptree__CASE(A_27a,A_27b,A_27c),ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),V0a0),V1a1)),V2f) = ap(ap(V2f,V0a0),V1a1) ) ) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2Eword__ptree__size__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1f1] :
( mem(V1f1,arr(A_27b,ty_2Enum_2Enum))
=> ! [V2a0] :
( mem(V2a0,arr(A_27a,ty_2Eone_2Eone))
=> ! [V3a1] :
( mem(V3a1,ty_2Epatricia_2Eptree(A_27b))
=> ap(ap(ap(c_2Epatricia__casts_2Eword__ptree__size(A_27a,A_27b),V0f),V1f1),ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),V2a0),V3a1)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epatricia_2Eptree__size(A_27b),V1f1),V3a1)) ) ) ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2Edatatype__word__ptree,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0word__ptree] :
( mem(V0word__ptree,arr(arr(arr(A_27a,ty_2Eone_2Eone),arr(ty_2Epatricia_2Eptree(A_27b),ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),bool))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(V0word__ptree,c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b)))) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2Eword__ptree__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a0] :
( mem(V0a0,arr(A_27a,ty_2Eone_2Eone))
=> ! [V1a1] :
( mem(V1a1,ty_2Epatricia_2Eptree(A_27b))
=> ! [V2a0_27] :
( mem(V2a0_27,arr(A_27a,ty_2Eone_2Eone))
=> ! [V3a1_27] :
( mem(V3a1_27,ty_2Epatricia_2Eptree(A_27b))
=> ( ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),V0a0),V1a1) = ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),V2a0_27),V3a1_27)
<=> ( V0a0 = V2a0_27
& V1a1 = V3a1_27 ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2Eword__ptree__nchotomy,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0ww] :
( mem(V0ww,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ? [V1f] :
( mem(V1f,arr(A_27a,ty_2Eone_2Eone))
& ? [V2p] :
( mem(V2p,ty_2Epatricia_2Eptree(A_27b))
& V0ww = ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),V1f),V2p) ) ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2Eword__ptree__Axiom,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(arr(A_27a,ty_2Eone_2Eone),arr(ty_2Epatricia_2Eptree(A_27b),A_27c)))
=> ? [V1fn] :
( mem(V1fn,arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),A_27c))
& ! [V2a0] :
( mem(V2a0,arr(A_27a,ty_2Eone_2Eone))
=> ! [V3a1] :
( mem(V3a1,ty_2Epatricia_2Eptree(A_27b))
=> ap(V1fn,ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),V2a0),V3a1)) = ap(ap(V0f,V2a0),V3a1) ) ) ) ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2Eword__ptree__induction,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),bool))
=> ( ! [V1f] :
( mem(V1f,arr(A_27a,ty_2Eone_2Eone))
=> ! [V2p] :
( mem(V2p,ty_2Epatricia_2Eptree(A_27b))
=> p(ap(V0P,ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),V1f),V2p))) ) )
=> ! [V3w] :
( mem(V3w,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> p(ap(V0P,V3w)) ) ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2Eword__ptree__case__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f_27] :
( mem(V0f_27,arr(arr(A_27a,ty_2Eone_2Eone),arr(ty_2Epatricia_2Eptree(A_27b),A_27c)))
=> ! [V1M] :
( mem(V1M,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ! [V2M_27] :
( mem(V2M_27,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ! [V3f] :
( mem(V3f,arr(arr(A_27a,ty_2Eone_2Eone),arr(ty_2Epatricia_2Eptree(A_27b),A_27c)))
=> ( ( V1M = V2M_27
& ! [V4a0] :
( mem(V4a0,arr(A_27a,ty_2Eone_2Eone))
=> ! [V5a1] :
( mem(V5a1,ty_2Epatricia_2Eptree(A_27b))
=> ( V2M_27 = ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),V4a0),V5a1)
=> ap(ap(V3f,V4a0),V5a1) = ap(ap(V0f_27,V4a0),V5a1) ) ) ) )
=> ap(ap(c_2Epatricia__casts_2Eword__ptree__CASE(A_27a,A_27b,A_27c),V1M),V3f) = ap(ap(c_2Epatricia__casts_2Eword__ptree__CASE(A_27a,A_27b,A_27c),V2M_27),V0f_27) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2Eword__ptree__case__eq,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0x] :
( mem(V0x,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ! [V1f] :
( mem(V1f,arr(arr(A_27a,ty_2Eone_2Eone),arr(ty_2Epatricia_2Eptree(A_27b),A_27c)))
=> ! [V2v] :
( mem(V2v,A_27c)
=> ( ap(ap(c_2Epatricia__casts_2Eword__ptree__CASE(A_27a,A_27b,A_27c),V0x),V1f) = V2v
<=> ? [V3f_27] :
( mem(V3f_27,arr(A_27a,ty_2Eone_2Eone))
& ? [V4p] :
( mem(V4p,ty_2Epatricia_2Eptree(A_27b))
& V0x = ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),V3f_27),V4p)
& ap(ap(V1f,V3f_27),V4p) = V2v ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2ETHE__PTREE__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,arr(A_27b,ty_2Eone_2Eone))
=> ! [V1t] :
( mem(V1t,ty_2Epatricia_2Eptree(A_27a))
=> ap(c_2Epatricia__casts_2ETHE__PTREE(A_27a,A_27b),ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27b,A_27a),V0a),V1t)) = V1t ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2ESOME__PTREE__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(A_27b))
=> ap(c_2Epatricia__casts_2ESOME__PTREE(A_27a,A_27b),V0t) = ap(ap(c_2Epatricia__casts_2EWord__ptree(A_27a,A_27b),ap(c_2Ecombin_2EK(ty_2Eone_2Eone,A_27a),c_2Eone_2Eone)),V0t) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EWordEmpty__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Epatricia__casts_2EWordEmpty(A_27a,A_27b) = ap(c_2Epatricia__casts_2ESOME__PTREE(A_27a,A_27b),c_2Epatricia_2EEmpty(A_27b)) ) ) ).
fof(ax_thm_2Epatricia__casts_2EPEEKw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Epatricia__casts_2EPEEKw(A_27a,A_27b),V0t),V1w) = ap(ap(c_2Epatricia_2EPEEK(A_27b),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V0t)),ap(c_2Ewords_2Ew2n(A_27a),V1w)) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EFINDw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27b,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27b))
=> ap(ap(c_2Epatricia__casts_2EFINDw(A_27a,A_27b),V0t),V1w) = ap(c_2Eoption_2ETHE(A_27a),ap(ap(c_2Epatricia__casts_2EPEEKw(A_27b,A_27a),V0t),V1w)) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EADDw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2d] :
( mem(V2d,A_27b)
=> ap(ap(c_2Epatricia__casts_2EADDw(A_27a,A_27b),V0t),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27a),A_27b),V1w),V2d)) = ap(c_2Epatricia__casts_2ESOME__PTREE(A_27a,A_27b),ap(ap(c_2Epatricia_2EADD(A_27b),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V0t)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27b),ap(c_2Ewords_2Ew2n(A_27a),V1w)),V2d))) ) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EADD__LISTw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Epatricia__casts_2EADD__LISTw(A_27a,A_27b) = ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),A_27b),ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),c_2Epatricia__casts_2EADDw(A_27a,A_27b)) ) ) ).
fof(ax_thm_2Epatricia__casts_2EREMOVEw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Epatricia__casts_2EREMOVEw(A_27a,A_27b),V0t),V1w) = ap(c_2Epatricia__casts_2ESOME__PTREE(A_27a,A_27b),ap(ap(c_2Epatricia_2EREMOVE(A_27b),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V0t)),ap(c_2Ewords_2Ew2n(A_27a),V1w))) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2ETRAVERSEw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ap(c_2Epatricia__casts_2ETRAVERSEw(A_27a,A_27b),V0t) = ap(ap(c_2Elist_2EMAP(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a)),c_2Ewords_2En2w(A_27a)),ap(c_2Epatricia_2ETRAVERSE(A_27b),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V0t))) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EKEYSw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ap(c_2Epatricia__casts_2EKEYSw(A_27a,A_27b),V0t) = ap(ap(c_2Esorting_2EQSORT(ty_2Efcp_2Ecart(bool,A_27a)),c_2Ewords_2Eword__lo(A_27a)),ap(c_2Epatricia__casts_2ETRAVERSEw(A_27a,A_27b),V0t)) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2ETRANSFORMw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1t] :
( mem(V1t,ty_2Epatricia__casts_2Eword__ptree(A_27c,A_27a))
=> ap(ap(c_2Epatricia__casts_2ETRANSFORMw(A_27a,A_27b,A_27c),V0f),V1t) = ap(c_2Epatricia__casts_2ESOME__PTREE(A_27c,A_27b),ap(ap(c_2Epatricia_2ETRANSFORM(A_27b,A_27a),V0f),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27a,A_27c),V1t))) ) ) ) ) ) ).
fof(lameq_f2703,axiom,
! [A_27a,A_27b,V2k] :
( mem(V2k,ty_2Enum_2Enum)
=> ! [V0P] :
( mem(V0P,arr(ty_2Efcp_2Ecart(bool,A_27a),arr(A_27b,bool)))
=> ! [V3d] : ap(f2703(A_27a,A_27b,V2k,V0P),V3d) = ap(ap(V0P,ap(c_2Ewords_2En2w(A_27a),V2k)),V3d) ) ) ).
fof(lameq_f2704,axiom,
! [A_27b,A_27a,V0P] :
( mem(V0P,arr(ty_2Efcp_2Ecart(bool,A_27a),arr(A_27b,bool)))
=> ! [V2k] : ap(f2704(A_27b,A_27a,V0P),V2k) = f2703(A_27a,A_27b,V2k,V0P) ) ).
fof(ax_thm_2Epatricia__casts_2EEVERY__LEAFw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Efcp_2Ecart(bool,A_27a),arr(A_27b,bool)))
=> ! [V1t] :
( mem(V1t,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ( p(ap(ap(c_2Epatricia__casts_2EEVERY__LEAFw(A_27a,A_27b),V0P),V1t))
<=> p(ap(ap(c_2Epatricia_2EEVERY__LEAF(A_27b),f2704(A_27b,A_27a,V0P)),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V1t))) ) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EEXISTS__LEAFw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Efcp_2Ecart(bool,A_27a),arr(A_27b,bool)))
=> ! [V1t] :
( mem(V1t,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ( p(ap(ap(c_2Epatricia__casts_2EEXISTS__LEAFw(A_27a,A_27b),V0P),V1t))
<=> p(ap(ap(c_2Epatricia_2EEXISTS__LEAF(A_27b),f2704(A_27b,A_27a,V0P)),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V1t))) ) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2ESIZEw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ap(c_2Epatricia__casts_2ESIZEw(A_27a,A_27b),V0t) = ap(c_2Epatricia_2ESIZE(A_27b),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V0t)) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EDEPTHw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))
=> ap(c_2Epatricia__casts_2EDEPTHw(A_27a,A_27b),V0t) = ap(c_2Epatricia_2EDEPTH(A_27b),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V0t)) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EIN__PTREEw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone))
=> ( p(ap(ap(c_2Epatricia__casts_2EIN__PTREEw(A_27a),V0w),V1t))
<=> p(ap(ap(c_2Epatricia_2EIN__PTREE,ap(c_2Ewords_2Ew2n(A_27a),V0w)),ap(c_2Epatricia__casts_2ETHE__PTREE(ty_2Eone_2Eone,A_27a),V1t))) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EINSERT__PTREEw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone))
=> ap(ap(c_2Epatricia__casts_2EINSERT__PTREEw(A_27a),V0w),V1t) = ap(c_2Epatricia__casts_2ESOME__PTREE(A_27a,ty_2Eone_2Eone),ap(ap(c_2Epatricia_2EINSERT__PTREE,ap(c_2Ewords_2Ew2n(A_27a),V0w)),ap(c_2Epatricia__casts_2ETHE__PTREE(ty_2Eone_2Eone,A_27a),V1t))) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EWORDSET__OF__PTREE__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone))
=> ap(c_2Epatricia__casts_2EWORDSET__OF__PTREE(A_27a),V0t) = ap(c_2Elist_2ELIST__TO__SET(ty_2Efcp_2Ecart(bool,A_27a)),ap(c_2Epatricia__casts_2ETRAVERSEw(A_27a,ty_2Eone_2Eone),V0t)) ) ) ).
fof(ax_thm_2Epatricia__casts_2EUNION__PTREEw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0t1] :
( mem(V0t1,ty_2Epatricia__casts_2Eword__ptree(A_27b,ty_2Eone_2Eone))
=> ! [V1t2] :
( mem(V1t2,ty_2Epatricia__casts_2Eword__ptree(A_27c,ty_2Eone_2Eone))
=> ap(ap(c_2Epatricia__casts_2EUNION__PTREEw(A_27a,A_27b,A_27c),V0t1),V1t2) = ap(c_2Epatricia__casts_2ESOME__PTREE(A_27a,ty_2Eone_2Eone),ap(ap(c_2Epatricia_2EUNION__PTREE,ap(c_2Epatricia__casts_2ETHE__PTREE(ty_2Eone_2Eone,A_27b),V0t1)),ap(c_2Epatricia__casts_2ETHE__PTREE(ty_2Eone_2Eone,A_27c),V1t2))) ) ) ) ) ) ).
fof(ax_thm_2Epatricia__casts_2EPTREE__OF__WORDSET__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone))
=> ! [V1s] :
( mem(V1s,arr(ty_2Efcp_2Ecart(bool,A_27a),bool))
=> ap(ap(c_2Epatricia__casts_2EPTREE__OF__WORDSET(A_27a),V0t),V1s) = ap(c_2Epatricia__casts_2ESOME__PTREE(A_27a,ty_2Eone_2Eone),ap(ap(c_2Epatricia_2EPTREE__OF__NUMSET,ap(c_2Epatricia__casts_2ETHE__PTREE(ty_2Eone_2Eone,A_27a),V0t)),ap(ap(c_2Epred__set_2EIMAGE(ty_2Efcp_2Ecart(bool,A_27a),ty_2Enum_2Enum),c_2Ewords_2Ew2n(A_27a)),V1s))) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2EADD__INSERT__STRING,axiom,
! [V0w] :
( mem(V0w,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1v] :
( mem(V1v,ty_2Eone_2Eone)
=> ! [V2t] :
( mem(V2t,ty_2Epatricia_2Eptree(ty_2Eone_2Eone))
=> ap(ap(c_2Epatricia__casts_2EADDs(ty_2Eone_2Eone),V2t),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Eone_2Eone),V0w),V1v)) = ap(ap(c_2Epatricia__casts_2EADDs(ty_2Eone_2Eone),V2t),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Eone_2Eone),V0w),c_2Eone_2Eone)) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2El2n__APPEND,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(ap(c_2Enumposrep_2El2n,V0b),ap(ap(c_2Elist_2EAPPEND(ty_2Enum_2Enum),V1l1),V2l2)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Enumposrep_2El2n,V0b),V1l1)),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V0b),ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),V1l1))),ap(ap(c_2Enumposrep_2El2n,V0b),V2l2))) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2El2n__LENGTH,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Enumposrep_2El2n,V0b),V1l)),ap(ap(c_2Earithmetic_2EEXP,V0b),ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),V1l)))) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2El2n__11,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b))
& p(ap(ap(c_2Elist_2EEVERY(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_3E,V0b)),V1l1))
& p(ap(ap(c_2Elist_2EEVERY(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_3E,V0b)),V2l2)) )
=> ( ap(ap(c_2Enumposrep_2El2n,V0b),ap(ap(c_2Elist_2EAPPEND(ty_2Enum_2Enum),V1l1),ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Elist_2ENIL(ty_2Enum_2Enum)))) = ap(ap(c_2Enumposrep_2El2n,V0b),ap(ap(c_2Elist_2EAPPEND(ty_2Enum_2Enum),V2l2),ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Elist_2ENIL(ty_2Enum_2Enum))))
<=> V1l1 = V2l2 ) ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2EEVERY__MAP__ORD,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> p(ap(ap(c_2Elist_2EEVERY(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_3E,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(ap(c_2Elist_2EMAP(ty_2Estring_2Echar,ty_2Enum_2Enum),c_2Estring_2EORD),V0l))) ) ).
fof(conj_thm_2Epatricia__casts_2EMAP__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( ap(V0f,V3x) = ap(V0f,V4y)
<=> V3x = V4y ) ) )
=> ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l1) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l2)
<=> V1l1 = V2l2 ) ) ) ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2EREVERSE__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2EREVERSE(A_27a),V0l1) = ap(c_2Elist_2EREVERSE(A_27a),V1l2)
<=> V0l1 = V1l2 ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2Estring__to__num__11,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(c_2Epatricia__casts_2Estring__to__num,V0s) = ap(c_2Epatricia__casts_2Estring__to__num,V1t)
<=> V0s = V1t ) ) ) ).
fof(conj_thm_2Epatricia__casts_2EIMAGE__string__to__num,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( ( V0n = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| ( 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,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),V0n))
& ap(ap(c_2Earithmetic_2EDIV,V0n),ap(ap(c_2Earithmetic_2EEXP,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(ap(c_2Elogroot_2ELOG,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)))))))))),V0n))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) )
<=> p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0n),ap(ap(c_2Epred__set_2EIMAGE(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum),c_2Epatricia__casts_2Estring__to__num),c_2Epred__set_2EUNIV(ty_2Elist_2Elist(ty_2Estring_2Echar))))) ) ) ).
fof(conj_thm_2Epatricia__casts_2Estring__to__num__num__to__string,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0n),ap(ap(c_2Epred__set_2EIMAGE(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum),c_2Epatricia__casts_2Estring__to__num),c_2Epred__set_2EUNIV(ty_2Elist_2Elist(ty_2Estring_2Echar)))))
=> ap(c_2Epatricia__casts_2Estring__to__num,ap(c_2Epatricia__casts_2Enum__to__string,V0n)) = V0n ) ) ).
fof(conj_thm_2Epatricia__casts_2Enum__to__string__string__to__num,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Epatricia__casts_2Enum__to__string,ap(c_2Epatricia__casts_2Estring__to__num,V0s)) = V0s ) ).
fof(conj_thm_2Epatricia__casts_2EADD__INSERT__WORD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1v] :
( mem(V1v,ty_2Eone_2Eone)
=> ! [V2t] :
( mem(V2t,ty_2Epatricia__casts_2Eword__ptree(A_27a,ty_2Eone_2Eone))
=> ap(ap(c_2Epatricia__casts_2EADDw(A_27a,ty_2Eone_2Eone),V2t),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27a),ty_2Eone_2Eone),V0w),V1v)) = ap(ap(c_2Epatricia__casts_2EADDw(A_27a,ty_2Eone_2Eone),V2t),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27a),ty_2Eone_2Eone),V0w),c_2Eone_2Eone)) ) ) ) ) ).
fof(conj_thm_2Epatricia__casts_2ETHE__PTREE__SOME__PTREE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,ty_2Epatricia_2Eptree(A_27a))
=> ap(c_2Epatricia__casts_2ETHE__PTREE(A_27a,A_27b),ap(c_2Epatricia__casts_2ESOME__PTREE(A_27b,A_27a),V0t)) = V0t ) ) ) ).
%------------------------------------------------------------------------------