ITP001 Axioms: ITP033+5.ax
%------------------------------------------------------------------------------
% File : ITP033+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 : set_relation+2.ax [Gau20]
% : HL4033+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 265 ( 2 unt; 0 def)
% Number of atoms : 1512 ( 159 equ)
% Maximal formula atoms : 53 ( 5 avg)
% Number of connectives : 1270 ( 23 ~; 8 |; 189 &)
% ( 52 <=>; 998 =>; 0 <=; 0 <~>)
% Maximal formula depth : 60 ( 9 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 160 ( 160 usr; 14 con; 0-7 aty)
% Number of variables : 1035 (1008 !; 27 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Eset__relation_2ERREFL__EXP,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2ERREFL__EXP(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))))) ) ).
fof(mem_c_2Eset__relation_2ERRUNIV,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2ERRUNIV(A_27a),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) ) ).
fof(mem_c_2Eset__relation_2Eacyclic,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Eacyclic(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)) ) ).
fof(mem_c_2Eset__relation_2Eall__choices,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Eall__choices(A_27a),arr(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),bool))) ) ).
fof(mem_c_2Eset__relation_2Eantisym,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Eantisym(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)) ) ).
fof(mem_c_2Eset__relation_2Echain,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Echain(A_27a),arr(arr(A_27a,bool),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool))) ) ).
fof(mem_c_2Eset__relation_2Edomain,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Eset__relation_2Edomain(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),bool),arr(A_27a,bool))) ) ) ).
fof(mem_c_2Eset__relation_2Efchains,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Efchains(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))) ) ).
fof(mem_c_2Eset__relation_2Efinite__prefixes,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),bool),arr(arr(A_27b,bool),bool))) ) ) ).
fof(mem_c_2Eset__relation_2Eget__min,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Eget__min(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ty_2Eoption_2Eoption(A_27a)))) ) ).
fof(mem_c_2Eset__relation_2Eirreflexive,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Eirreflexive(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))) ) ).
fof(mem_c_2Eset__relation_2Elinear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Elinear__order(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))) ) ).
fof(mem_c_2Eset__relation_2Emaximal__elements,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Emaximal__elements(A_27a),arr(arr(A_27a,bool),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(A_27a,bool)))) ) ).
fof(mem_c_2Eset__relation_2Eminimal__elements,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Eminimal__elements(A_27a),arr(arr(A_27a,bool),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(A_27a,bool)))) ) ).
fof(mem_c_2Eset__relation_2Enth__min,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Enth__min(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))))) ) ).
fof(mem_c_2Eset__relation_2Enum__order,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Enum__order(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)))) ) ).
fof(mem_c_2Eset__relation_2Epartial__order,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Epartial__order(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))) ) ).
fof(mem_c_2Eset__relation_2Eper,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Eper(A_27a),arr(arr(A_27a,bool),arr(arr(arr(A_27a,bool),bool),bool))) ) ).
fof(mem_c_2Eset__relation_2Eper__restrict,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Eper__restrict(A_27a),arr(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool)))) ) ).
fof(mem_c_2Eset__relation_2Erange,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Eset__relation_2Erange(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(A_27b,A_27a),bool),arr(A_27a,bool))) ) ) ).
fof(mem_c_2Eset__relation_2Ercomp,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Eset__relation_2Ercomp(A_27a,A_27b,A_27c),arr(arr(ty_2Epair_2Eprod(A_27a,A_27c),bool),arr(arr(ty_2Epair_2Eprod(A_27c,A_27b),bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)))) ) ) ) ).
fof(mem_c_2Eset__relation_2Ereflexive,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Ereflexive(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))) ) ).
fof(mem_c_2Eset__relation_2Erel__to__reln,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))) ) ) ).
fof(mem_c_2Eset__relation_2Ereln__to__rel,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),bool),arr(A_27a,arr(A_27b,bool)))) ) ) ).
fof(mem_c_2Eset__relation_2Errestrict,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Errestrict(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)))) ) ).
fof(mem_c_2Eset__relation_2Estrict,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Estrict(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))) ) ).
fof(mem_c_2Eset__relation_2Estrict__linear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Estrict__linear__order(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))) ) ).
fof(mem_c_2Eset__relation_2Etc,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Etc(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))) ) ).
fof(mem_c_2Eset__relation_2Etransitive,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Etransitive(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)) ) ).
fof(mem_c_2Eset__relation_2Euniv__reln,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eset__relation_2Euniv__reln(A_27a),arr(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))) ) ).
fof(mem_c_2Eset__relation_2Eupper__bounds,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Eset__relation_2Eupper__bounds(A_27a,A_27b),arr(arr(A_27b,bool),arr(arr(ty_2Epair_2Eprod(A_27b,A_27a),bool),arr(A_27a,bool)))) ) ) ).
fof(conj_thm_2Eset__relation_2Erextension,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1t] :
( mem(V1t,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ( V0s = V1t
<=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),V0s))
<=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),V1t)) ) ) ) ) ) ) ) ) ).
fof(lameq_f317,axiom,
! [A_27a,A_27b,V1x] :
( mem(V1x,A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V2y] : ap(f317(A_27a,A_27b,V1x,V0r),V2y) = ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),V0r) ) ) ).
fof(lameq_f318,axiom,
! [A_27b,A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1x] : ap(f318(A_27b,A_27a,V0r),V1x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V1x),ap(c_2Ebool_2E_3F(A_27b),f317(A_27a,A_27b,V1x,V0r))) ) ).
fof(ax_thm_2Eset__relation_2Edomain__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V0r) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f318(A_27b,A_27a,V0r)) ) ) ) ).
fof(lameq_f319,axiom,
! [A_27a,A_27b,V1y] :
( mem(V1y,A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool))
=> ! [V2x] : ap(f319(A_27a,A_27b,V1y,V0r),V2x) = ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27b,A_27a)),ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V2x),V1y)),V0r) ) ) ).
fof(lameq_f320,axiom,
! [A_27b,A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool))
=> ! [V1y] : ap(f320(A_27b,A_27a,V0r),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V1y),ap(c_2Ebool_2E_3F(A_27b),f319(A_27a,A_27b,V1y,V0r))) ) ).
fof(ax_thm_2Eset__relation_2Erange__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool))
=> ap(c_2Eset__relation_2Erange(A_27a,A_27b),V0r) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f320(A_27b,A_27a,V0r)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ein__domain,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V1r)))
<=> ? [V2y] :
( mem(V2y,A_27b)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V2y)),V1r)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ein__range,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0y] :
( mem(V0y,A_27a)
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Eset__relation_2Erange(A_27a,A_27b),V1r)))
<=> ? [V2x] :
( mem(V2x,A_27b)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27b,A_27a)),ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V2x),V0y)),V1r)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ein__dom__rg,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27b)
=> ! [V2r] :
( mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),V2r))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V2r)))
& p(ap(ap(c_2Ebool_2EIN(A_27b),V1y),ap(c_2Eset__relation_2Erange(A_27b,A_27a),V2r))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Edomain__mono,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1r_27] :
( mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27b)),V0r),V1r_27))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V0r)),ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V1r_27))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Erange__mono,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1r_27] :
( mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27b)),V0r),V1r_27))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(c_2Eset__relation_2Erange(A_27b,A_27a),V0r)),ap(c_2Eset__relation_2Erange(A_27b,A_27a),V1r_27))) ) ) ) ) ) ).
fof(lameq_f321,axiom,
! [A_27a,V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] : ap(f321(A_27a,V1s,V0r,V2x),V3y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)),ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)))) ) ) ) ).
fof(lameq_f322,axiom,
! [A_27a,V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2x] : ap(f322(A_27a,V1s,V0r),V2x) = f321(A_27a,V1s,V0r,V2x) ) ) ).
fof(ax_thm_2Eset__relation_2Errestrict__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f322(A_27a,V1s,V0r))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ein__rrestrict,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ! [V2r] :
( mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V3s] :
( mem(V3s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V1y)),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V2r),V3s)))
<=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V1y)),V2r))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V3s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V1y),V3s)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ein__rrestrict__alt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Epair_2Eprod(A_27a,A_27a))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),V0x),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r),V2s)))
<=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),V0x),V1r))
& p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2EFST(A_27a,A_27a),V0x)),V2s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2ESND(A_27a,A_27a),V0x)),V2s)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Errestrict__SUBSET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s)),V0r)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Errestrict__union,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ap(ap(c_2Eset__relation_2Errestrict(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r1),V1r2)),V2s) = ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r1),V2s)),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r2),V2s)) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Errestrict__rrestrict,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,arr(A_27a,bool))
=> ! [V2y] :
( mem(V2y,arr(A_27a,bool))
=> ap(ap(c_2Eset__relation_2Errestrict(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1x)),V2y) = ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),ap(ap(c_2Epred__set_2EINTER(A_27a),V1x),V2y)) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Edomain__rrestrict__SUBSET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s))),V1s)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Erange__rrestrict__SUBSET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s))),V1s)) ) ) ) ).
fof(lameq_f323,axiom,
! [A_27b,A_27a,A_27c,V2x] :
( mem(V2x,A_27a)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool))
=> ! [V3y] :
( mem(V3y,A_27b)
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool))
=> ! [V4z] : ap(f323(A_27b,A_27a,A_27c,V2x,V0r1,V3y,V1r2),V4z) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27c)),ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2x),V4z)),V0r1)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27c,A_27b)),ap(ap(c_2Epair_2E_2C(A_27c,A_27b),V4z),V3y)),V1r2)) ) ) ) ) ).
fof(lameq_f324,axiom,
! [A_27a,A_27c,A_27b,V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] : ap(f324(A_27a,A_27c,A_27b,V0r1,V1r2,V2x),V3y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),ap(c_2Ebool_2E_3F(A_27c),f323(A_27b,A_27a,A_27c,V2x,V0r1,V3y,V1r2))) ) ) ) ).
fof(lameq_f325,axiom,
! [A_27b,A_27c,A_27a,V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool))
=> ! [V2x] : ap(f325(A_27b,A_27c,A_27a,V0r1,V1r2),V2x) = f324(A_27a,A_27c,A_27b,V0r1,V1r2,V2x) ) ) ).
fof(ax_thm_2Eset__relation_2Ercomp__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool))
=> ap(ap(c_2Eset__relation_2Ercomp(A_27a,A_27b,A_27c),V0r1),V1r2) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f325(A_27b,A_27c,A_27a,V0r1,V1r2))) ) ) ) ) ) ).
fof(lameq_f326,axiom,
! [A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] : ap(f326(A_27a,V0r,V1x),V2y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(A_27a),V1x),V2y)))) ) ) ).
fof(lameq_f327,axiom,
! [A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] : ap(f327(A_27a,V0r),V1x) = f326(A_27a,V0r,V1x) ) ).
fof(ax_thm_2Eset__relation_2Estrict__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(c_2Eset__relation_2Estrict(A_27a),V0r) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f327(A_27a,V0r))) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__rrestrict,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ap(c_2Eset__relation_2Estrict(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s)) = ap(ap(c_2Eset__relation_2Errestrict(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r)),V1s) ) ) ) ).
fof(lameq_f328,axiom,
! [A_27a,V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1x1] :
( mem(V1x1,A_27a)
=> ! [V2x2] : ap(f328(A_27a,V0xs,V1x1),V2x2) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x1),V2x2)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V1x1),V0xs)),ap(ap(c_2Ebool_2EIN(A_27a),V2x2),V0xs))) ) ) ).
fof(lameq_f329,axiom,
! [A_27a,V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1x1] : ap(f329(A_27a,V0xs),V1x1) = f328(A_27a,V0xs,V1x1) ) ).
fof(ax_thm_2Eset__relation_2Euniv__reln__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ap(c_2Eset__relation_2Euniv__reln(A_27a),V0xs) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f329(A_27a,V0xs))) ) ) ).
fof(lameq_f330,axiom,
! [A_27b,A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V2e] :
( mem(V2e,A_27b)
=> ! [V3e_27] : ap(f330(A_27b,A_27a,V0r,V2e),V3e_27) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V3e_27),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3e_27),V2e)),V0r)) ) ) ).
fof(ax_thm_2Eset__relation_2Efinite__prefixes__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27b,bool))
=> ( p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s))
<=> ! [V2e] :
( mem(V2e,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27b),V2e),V1s))
=> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f330(A_27b,A_27a,V0r,V2e)))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefixes__subset__s,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2s_27] :
( mem(V2s_27,arr(A_27b,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),V2s_27),V1s)) )
=> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V2s_27)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefixes__subset__r,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1r_27] :
( mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V2s] :
( mem(V2s,arr(A_27b,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V2s))
& p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27b)),V1r_27),V0r)) )
=> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V1r_27),V2s)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefixes__subset__rs,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2r_27] :
( mem(V2r_27,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V3s_27] :
( mem(V3s_27,arr(A_27b,bool))
=> ( p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27b)),V2r_27),V0r))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),V3s_27),V1s))
=> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V2r_27),V3s_27)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefixes__subset,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2s_27] :
( mem(V2s_27,arr(A_27a,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V0r),V1s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s_27),V1s)) )
=> ( p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V0r),V2s_27))
& p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V2s_27)),V2s_27)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefixes__union,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V2s1] :
( mem(V2s1,arr(A_27b,bool))
=> ! [V3s2] :
( mem(V3s2,arr(A_27b,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r1),V2s1))
& p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V1r2),V3s2)) )
=> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27b)),V0r1),V1r2)),ap(ap(c_2Epred__set_2EINTER(A_27b),V2s1),V3s2))) ) ) ) ) ) ) ) ).
fof(lameq_f331,axiom,
! [A_27b,A_27c,V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27b,A_27c),bool))
=> ! [V4x] :
( mem(V4x,A_27b)
=> ! [V3s2] :
( mem(V3s2,arr(A_27c,bool))
=> ! [V5y] : ap(f331(A_27b,A_27c,V1r2,V4x,V3s2),V5y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27c),V5y),V3s2)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27b,A_27c)),ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V4x),V5y)),V1r2)) ) ) ) ).
fof(lameq_f332,axiom,
! [A_27c,A_27b,V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27b,A_27c),bool))
=> ! [V3s2] :
( mem(V3s2,arr(A_27c,bool))
=> ! [V4x] : ap(f332(A_27c,A_27b,V1r2,V3s2),V4x) = ap(ap(c_2Epair_2E_2C(A_27b,bool),V4x),ap(c_2Ebool_2E_3F(A_27c),f331(A_27b,A_27c,V1r2,V4x,V3s2))) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefixes__comp,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27b,A_27c),bool))
=> ! [V2s1] :
( mem(V2s1,arr(A_27b,bool))
=> ! [V3s2] :
( mem(V3s2,arr(A_27c,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r1),V2s1))
& p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27b,A_27c),V1r2),V3s2))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(c_2Epred__set_2EGSPEC(A_27b,A_27b),f332(A_27c,A_27b,V1r2,V3s2))),V2s1)) )
=> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27c),ap(ap(c_2Eset__relation_2Ercomp(A_27a,A_27c,A_27b),V0r1),V1r2)),V3s2)) ) ) ) ) ) ) ) ) ).
fof(lameq_f333,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V6y] : ap(f333(A_27b,A_27a,V0f,V5x,V1r),V6y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27b,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27b,A_27b),ap(V0f,V5x)),ap(V0f,V6y))),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V5x),V6y)),V1r)) ) ) ) ).
fof(lameq_f334,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V5x] : ap(f334(A_27b,A_27a,V0f,V1r),V5x) = f333(A_27b,A_27a,V0f,V5x,V1r) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefixes__inj__image,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ( ( ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( ap(V0f,V3x) = ap(V0f,V4y)
=> V3x = V4y ) ) )
& p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V1r),V2s)) )
=> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27b,A_27b),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27b,A_27b),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27b,A_27b),bool)),f334(A_27b,A_27a,V0f,V1r)))),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s))) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefixes__range,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2t] :
( mem(V2t,arr(A_27b,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s))
& p(ap(ap(c_2Epred__set_2EDISJOINT(A_27b),V2t),ap(c_2Eset__relation_2Erange(A_27b,A_27a),V0r))) )
=> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),ap(ap(c_2Epred__set_2EUNION(A_27b),V1s),V2t))) ) ) ) ) ) ) ).
fof(lameq_f335,axiom,
! [A_27a,V3a0] :
( mem(V3a0,ty_2Epair_2Eprod(A_27a,A_27a))
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V5y] : ap(f335(A_27a,V3a0,V4x,V0r),V5y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Epair_2Eprod(A_27a,A_27a)),V3a0),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V5y))),ap(V0r,ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V5y))) ) ) ) ).
fof(lameq_f336,axiom,
! [A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V3a0] :
( mem(V3a0,ty_2Epair_2Eprod(A_27a,A_27a))
=> ! [V4x] : ap(f336(A_27a,V0r,V3a0),V4x) = ap(c_2Ebool_2E_3F(A_27a),f335(A_27a,V3a0,V4x,V0r)) ) ) ).
fof(lameq_f337,axiom,
! [A_27a,V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27a)
=> ! [V2tc_27] :
( mem(V2tc_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V8z] : ap(f337(A_27a,V6x,V7y,V2tc_27),V8z) = ap(ap(c_2Ebool_2E_2F_5C,ap(V2tc_27,ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6x),V8z))),ap(V2tc_27,ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V8z),V7y))) ) ) ) ).
fof(lameq_f338,axiom,
! [A_27a,V3a0] :
( mem(V3a0,ty_2Epair_2Eprod(A_27a,A_27a))
=> ! [V2tc_27] :
( mem(V2tc_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] : ap(f338(A_27a,V3a0,V2tc_27,V6x),V7y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Epair_2Eprod(A_27a,A_27a)),V3a0),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6x),V7y))),ap(c_2Ebool_2E_3F(A_27a),f337(A_27a,V6x,V7y,V2tc_27))) ) ) ) ).
fof(lameq_f339,axiom,
! [A_27a,V2tc_27] :
( mem(V2tc_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V3a0] :
( mem(V3a0,ty_2Epair_2Eprod(A_27a,A_27a))
=> ! [V6x] : ap(f339(A_27a,V2tc_27,V3a0),V6x) = ap(c_2Ebool_2E_3F(A_27a),f338(A_27a,V3a0,V2tc_27,V6x)) ) ) ).
fof(lameq_f340,axiom,
! [A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2tc_27] :
( mem(V2tc_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V3a0] : ap(f340(A_27a,V0r,V2tc_27),V3a0) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(A_27a),f336(A_27a,V0r,V3a0))),ap(c_2Ebool_2E_3F(A_27a),f339(A_27a,V2tc_27,V3a0)))),ap(V2tc_27,V3a0)) ) ) ).
fof(lameq_f341,axiom,
! [A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1a0] :
( mem(V1a0,ty_2Epair_2Eprod(A_27a,A_27a))
=> ! [V2tc_27] : ap(f341(A_27a,V0r,V1a0),V2tc_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27a)),f340(A_27a,V0r,V2tc_27))),ap(V2tc_27,V1a0)) ) ) ).
fof(lameq_f342,axiom,
! [A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1a0] : ap(f342(A_27a,V0r),V1a0) = ap(c_2Ebool_2E_21(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f341(A_27a,V0r,V1a0)) ) ).
fof(lameq_f343,axiom,
! [A_27a,V0r] : ap(f343(A_27a),V0r) = f342(A_27a,V0r) ).
fof(ax_thm_2Eset__relation_2Etc__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Eset__relation_2Etc(A_27a) = f343(A_27a) ) ).
fof(conj_thm_2Eset__relation_2Etc__rules,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) ) ) )
& ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( ? [V5z] :
( mem(V5z,A_27a)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x),V5z)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V5z),V4y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) )
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x),V4y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__cases,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
<=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r))
| ? [V3z] :
( mem(V3z,A_27a)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V3z)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3z),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1tc_27] :
( mem(V1tc_27,arr(A_27a,arr(A_27a,bool)))
=> ( ( ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
=> p(ap(ap(V1tc_27,V2x),V3y)) ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( ? [V6z] :
( mem(V6z,A_27a)
& p(ap(ap(V1tc_27,V4x),V6z))
& p(ap(ap(V1tc_27,V6z),V5y)) )
=> p(ap(ap(V1tc_27,V4x),V5y)) ) ) ) )
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8y] :
( mem(V8y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
=> p(ap(ap(V1tc_27,V7x),V8y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__closure,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),ap(c_2Eset__relation_2Etc(A_27a),V1s)))
=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Eset__relation_2Etc(A_27a),V0r)),ap(c_2Eset__relation_2Etc(A_27a),V1s))) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Esubset__tc,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),ap(c_2Eset__relation_2Etc(A_27a),V0r))) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__idemp,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(c_2Eset__relation_2Etc(A_27a),ap(c_2Eset__relation_2Etc(A_27a),V0r)) = ap(c_2Eset__relation_2Etc(A_27a),V0r) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__mono,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),V1s))
=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Eset__relation_2Etc(A_27a),V0r)),ap(c_2Eset__relation_2Etc(A_27a),V1s))) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__strongind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1tc_27] :
( mem(V1tc_27,arr(A_27a,arr(A_27a,bool)))
=> ( ( ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
=> p(ap(ap(V1tc_27,V2x),V3y)) ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( ? [V6z] :
( mem(V6z,A_27a)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V6z)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
& p(ap(ap(V1tc_27,V4x),V6z))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6z),V5y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
& p(ap(ap(V1tc_27,V6z),V5y)) )
=> p(ap(ap(V1tc_27,V4x),V5y)) ) ) ) )
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8y] :
( mem(V8y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
=> p(ap(ap(V1tc_27,V7x),V8y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__cases__right,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
<=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r))
| ? [V3z] :
( mem(V3z,A_27a)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V3z)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3z),V2y)),V0r)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__cases__left,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
<=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r))
| ? [V3z] :
( mem(V3z,A_27a)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V3z)),V0r))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3z),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__ind__left,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1tc_27] :
( mem(V1tc_27,arr(A_27a,arr(A_27a,bool)))
=> ( ( ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
=> p(ap(ap(V1tc_27,V2x),V3y)) ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( ? [V6z] :
( mem(V6z,A_27a)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V6z)),V0r))
& p(ap(ap(V1tc_27,V6z),V5y)) )
=> p(ap(ap(V1tc_27,V4x),V5y)) ) ) ) )
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8y] :
( mem(V8y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
=> p(ap(ap(V1tc_27,V7x),V8y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__strongind__left,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1tc_27] :
( mem(V1tc_27,arr(A_27a,arr(A_27a,bool)))
=> ( ( ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
=> p(ap(ap(V1tc_27,V2x),V3y)) ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( ? [V6z] :
( mem(V6z,A_27a)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V6z)),V0r))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6z),V5y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
& p(ap(ap(V1tc_27,V6z),V5y)) )
=> p(ap(ap(V1tc_27,V4x),V5y)) ) ) ) )
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8y] :
( mem(V8y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
=> p(ap(ap(V1tc_27,V7x),V8y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__ind__right,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1tc_27] :
( mem(V1tc_27,arr(A_27a,arr(A_27a,bool)))
=> ( ( ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
=> p(ap(ap(V1tc_27,V2x),V3y)) ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( ? [V6z] :
( mem(V6z,A_27a)
& p(ap(ap(V1tc_27,V4x),V6z))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6z),V5y)),V0r)) )
=> p(ap(ap(V1tc_27,V4x),V5y)) ) ) ) )
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8y] :
( mem(V8y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
=> p(ap(ap(V1tc_27,V7x),V8y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ertc__ind__right,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1tc_27] :
( mem(V1tc_27,arr(A_27a,arr(A_27a,bool)))
=> ( ( ! [V2x] :
( mem(V2x,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)))
| p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r))) )
=> p(ap(ap(V1tc_27,V2x),V2x)) ) )
& ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( ? [V5z] :
( mem(V5z,A_27a)
& p(ap(ap(V1tc_27,V3x),V5z))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V5z),V4y)),V0r)) )
=> p(ap(ap(V1tc_27,V3x),V4y)) ) ) ) )
=> ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6x),V7y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
=> p(ap(ap(V1tc_27,V6x),V7y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__strongind__right,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1tc_27] :
( mem(V1tc_27,arr(A_27a,arr(A_27a,bool)))
=> ( ( ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
=> p(ap(ap(V1tc_27,V2x),V3y)) ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( ? [V6z] :
( mem(V6z,A_27a)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V6z)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
& p(ap(ap(V1tc_27,V4x),V6z))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6z),V5y)),V0r)) )
=> p(ap(ap(V1tc_27,V4x),V5y)) ) ) ) )
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8y] :
( mem(V8y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
=> p(ap(ap(V1tc_27,V7x),V8y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__union,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r1)))
=> ! [V3r2] :
( mem(V3r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r1),V3r2)))) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__implication,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r1))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V1r2)) ) ) )
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V5y)),ap(c_2Eset__relation_2Etc(A_27a),V0r1)))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V5y)),ap(c_2Eset__relation_2Etc(A_27a),V1r2))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__empty,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ~ p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V1y)),ap(c_2Eset__relation_2Etc(A_27a),c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a))))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__empty__eqn,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Eset__relation_2Etc(A_27a),c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a))) = c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a)) ) ).
fof(conj_thm_2Eset__relation_2Etc__domain__range,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r))) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Errestrict__tc,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,arr(A_27a,bool))
=> ! [V2e] :
( mem(V2e,A_27a)
=> ! [V3e_27] :
( mem(V3e_27,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2e),V3e_27)),ap(c_2Eset__relation_2Etc(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1x))))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2e),V3e_27)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__SWAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(c_2Eset__relation_2Etc(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP(A_27a,A_27a)),V0r)) = ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP(A_27a,A_27a)),ap(c_2Eset__relation_2Etc(A_27a),V0r)) ) ) ).
fof(ax_thm_2Eset__relation_2Eacyclic__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r))
<=> ! [V1x] :
( mem(V1x,A_27a)
=> ~ p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V1x)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eacyclic__subset,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r1))
& p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V1r2),V0r1)) )
=> p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r2)) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eacyclic__rrestrict,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r))
=> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s))) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eacyclic__irreflexive,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r))
=> ~ p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V1x)),V0r)) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eacyclic__SWAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP(A_27a,A_27a)),V0r)))
<=> p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eacyclic__bigunion,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0rs] :
( mem(V0rs,arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool))
=> ( ( ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2r_27] :
( mem(V2r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(ap(c_2Ebool_2EIN(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V1r),V0rs))
& p(ap(ap(c_2Ebool_2EIN(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V2r_27),V0rs))
& V1r != V2r_27 )
=> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r))),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V2r_27)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V2r_27)))) ) ) )
& ! [V3r] :
( mem(V3r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Ebool_2EIN(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3r),V0rs))
=> p(ap(c_2Eset__relation_2Eacyclic(A_27a),V3r)) ) ) )
=> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(c_2Epred__set_2EBIGUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0rs))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eacyclic__union,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1r_27] :
( mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r))),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r_27)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r_27))))
& p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r))
& p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r_27)) )
=> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),V1r_27))) ) ) ) ) ).
fof(ax_thm_2Eset__relation_2Ereflexive__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0r),V1s))
<=> ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),V0r)) ) ) ) ) ) ) ).
fof(ax_thm_2Eset__relation_2Eirreflexive__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Eirreflexive(A_27a),V0r),V1s))
<=> ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
=> ~ p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),V0r)) ) ) ) ) ) ) ).
fof(ax_thm_2Eset__relation_2Etransitive__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r))
<=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ! [V3z] :
( mem(V3z,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2y),V3z)),V0r)) )
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V3z)),V0r)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etransitive__tc,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r))
=> ap(c_2Eset__relation_2Etc(A_27a),V0r) = V0r ) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__transitive,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> p(ap(c_2Eset__relation_2Etransitive(A_27a),ap(c_2Eset__relation_2Etc(A_27a),V0r))) ) ) ).
fof(ax_thm_2Eset__relation_2Eantisym__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Eantisym(A_27a),V0r))
<=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2y),V1x)),V0r)) )
=> V1x = V2y ) ) ) ) ) ) ).
fof(ax_thm_2Eset__relation_2Epartial__order__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))
<=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)),V1s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r)),V1s))
& p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r))
& p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0r),V1s))
& p(ap(c_2Eset__relation_2Eantisym(A_27a),V0r)) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eantisym__subset,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Eantisym(A_27a),V0t))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V1s),V0t))
=> p(ap(c_2Eset__relation_2Eantisym(A_27a),V1s)) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Epartial__order__dom__rng,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
& p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) )
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Epartial__order__subset,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2s_27] :
( mem(V2s_27,arr(A_27a,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s_27),V1s)) )
=> p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V2s_27)),V2s_27)) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__partial__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))),V1s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))),V1s))
& p(ap(c_2Eset__relation_2Etransitive(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r)))
& p(ap(c_2Eset__relation_2Eantisym(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__partial__order__acyclic,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))
=> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))) ) ) ) ) ).
fof(ax_thm_2Eset__relation_2Elinear__order__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s))
<=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)),V1s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r)),V1s))
& p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r))
& p(ap(c_2Eset__relation_2Eantisym(A_27a),V0r))
& ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)) )
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
| p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),V0r)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order__subset,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2s_27] :
( mem(V2s_27,arr(A_27a,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s_27),V1s)) )
=> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V2s_27)),V2s_27)) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Epartial__order__linear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s))
=> p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) ) ) ) ) ).
fof(ax_thm_2Eset__relation_2Estrict__linear__order__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),V1s))
<=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)),V1s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r)),V1s))
& p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r))
& ! [V2x] :
( mem(V2x,A_27a)
=> ~ p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),V0r)) )
& ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V1s))
& V3x != V4y )
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x),V4y)),V0r))
| p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4y),V3x)),V0r)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__linear__order__dom__rng,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
& p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),V1s)) )
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order__dom__rng,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))
& p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) )
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)) ) ) ) ) ) ) ) ).
fof(lameq_f344,axiom,
! [A_27b,A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1x] : ap(f344(A_27b,A_27a,V0r),V1x) = f317(A_27a,A_27b,V1x,V0r) ) ).
fof(ax_thm_2Eset__relation_2Ereln__to__rel__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r) = f344(A_27b,A_27a,V0r) ) ) ) ).
fof(lameq_f345,axiom,
! [A_27a,A_27b,V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] : ap(f345(A_27a,A_27b,V0R,V1x),V2y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),ap(ap(V0R,V1x),V2y)) ) ) ).
fof(lameq_f346,axiom,
! [A_27b,A_27a,V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1x] : ap(f346(A_27b,A_27a,V0R),V1x) = f345(A_27a,A_27b,V0R,V1x) ) ).
fof(ax_thm_2Eset__relation_2Erel__to__reln__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V0R) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f346(A_27b,A_27a,V0R))) ) ) ) ).
fof(lameq_f347,axiom,
! [A_27a,V1x] :
( mem(V1x,A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V2y] : ap(f347(A_27a,V1x,V0s),V2y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)),ap(ap(c_2Ebool_2EIN(A_27a),V2y),V0s)) ) ) ).
fof(lameq_f348,axiom,
! [A_27a,V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1x] : ap(f348(A_27a,V0s),V1x) = f347(A_27a,V1x,V0s) ) ).
fof(ax_thm_2Eset__relation_2ERRUNIV__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ap(c_2Eset__relation_2ERRUNIV(A_27a),V0s) = f348(A_27a,V0s) ) ) ).
fof(lameq_f349,axiom,
! [A_27a,V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] : ap(f349(A_27a,V1s,V2x),V3y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V2x),V3y)),ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))) ) ) ).
fof(lameq_f350,axiom,
! [A_27a,V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] : ap(f350(A_27a,V1s),V2x) = f349(A_27a,V1s,V2x) ) ).
fof(ax_thm_2Eset__relation_2ERREFL__EXP__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),V0R),V1s) = ap(ap(c_2Erelation_2ERUNION(A_27a,A_27a),V0R),f350(A_27a,V1s)) ) ) ) ).
fof(conj_thm_2Eset__relation_2ERREFL__EXP__RSUBSET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),V0R),ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),V0R),V1s))) ) ) ) ).
fof(conj_thm_2Eset__relation_2ERREFL__EXP__UNIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),V0R),c_2Epred__set_2EUNIV(A_27a)) = V0R ) ) ).
fof(conj_thm_2Eset__relation_2EREL__RESTRICT__UNIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V0R),c_2Epred__set_2EUNIV(A_27a)) = V0R ) ) ).
fof(conj_thm_2Eset__relation_2Ein__rel__to__reln,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0xy] :
( mem(V0xy,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V1R] :
( mem(V1R,arr(A_27a,arr(A_27b,bool)))
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V0xy),ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R)))
<=> p(ap(ap(V1R,ap(c_2Epair_2EFST(A_27a,A_27b),V0xy)),ap(c_2Epair_2ESND(A_27a,A_27b),V0xy))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ereln__to__rel__app,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27b)
=> ( p(ap(ap(ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r),V1x),V2y))
<=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),V0r)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Eset__relation_2Erel__to__reln(A_27a,A_27b) = c_2Epair_2EUNCURRY(A_27a,A_27b,bool) ) ) ).
fof(conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b) = c_2Epair_2ECURRY(A_27a,A_27b,bool) ) ) ).
fof(conj_thm_2Eset__relation_2Erel__to__reln__inv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V0R)) = V0R ) ) ) ).
fof(conj_thm_2Eset__relation_2Ereln__to__rel__inv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r)) = V0r ) ) ) ).
fof(conj_thm_2Eset__relation_2Ereln__to__rel__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ( ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r1) = ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V1r2)
<=> V0r1 = V1r2 ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Erel__to__reln__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27b,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27a,arr(A_27b,bool)))
=> ( ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V0R1) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R2)
<=> V0R1 = V1R2 ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Erel__to__reln__swap,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1R] :
( mem(V1R,arr(A_27a,arr(A_27b,bool)))
=> ( V0r = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R)
<=> ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r) = V1R ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Edomain__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V0r) = ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Erange__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool))
=> ap(c_2Eset__relation_2Erange(A_27a,A_27b),V0r) = ap(c_2Erelation_2ERRANGE(A_27b,A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27b,A_27a),V0r)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(c_2Eset__relation_2Estrict(A_27a),V0r) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Erelation_2ESTRORD(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) ) ) ).
fof(conj_thm_2Eset__relation_2Errestrict__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),V1s)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ercomp__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool))
=> ap(ap(c_2Eset__relation_2Ercomp(A_27a,A_27b,A_27c),V0r1),V1r2) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),ap(ap(c_2Erelation_2EO(A_27a,A_27c,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27c,A_27b),V1r2)),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27c),V0r1))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Euniv__reln__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ap(c_2Eset__relation_2Euniv__reln(A_27a),V0s) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Eset__relation_2ERRUNIV(A_27a),V0s)) ) ) ).
fof(conj_thm_2Eset__relation_2Etc__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(c_2Eset__relation_2Etc(A_27a),V0r) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) ) ) ).
fof(conj_thm_2Eset__relation_2Eacyclic__reln__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r))
<=> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eirreflexive__reln__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Eirreflexive(A_27a),V0r),V1s))
<=> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),V1s))) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eirreflexive__reln__to__rel__conv__UNIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Eset__relation_2Eirreflexive(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a)))
<=> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ereflexive__reln__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0r),V1s))
<=> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),V1s))) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ereflexive__reln__to__rel__conv__UNIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a)))
<=> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Etransitive__reln__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r))
<=> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eantisym__reln__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Eantisym(A_27a),V0r))
<=> p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Epartial__order__reln__to__rel__conv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))
<=> ( p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),ap(c_2Eset__relation_2ERRUNIV(A_27a),V1s)))
& p(ap(c_2Erelation_2EWeakOrder(A_27a),ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),V1s))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Epartial__order__reln__to__rel__conv__UNIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a)))
<=> p(ap(c_2Erelation_2EWeakOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order__reln__to__rel__conv__UNIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a)))
<=> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__linear__order__reln__to__rel__conv__UNIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a)))
<=> p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ereln__rel__conv__thms,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0xy] :
( mem(V0xy,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V1R] :
( mem(V1R,arr(A_27a,arr(A_27b,bool)))
=> ! [V2r] :
( mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27b)
=> ! [V5r1] :
( mem(V5r1,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V6r2] :
( mem(V6r2,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V7R1] :
( mem(V7R1,arr(A_27a,arr(A_27b,bool)))
=> ! [V8R2] :
( mem(V8R2,arr(A_27a,arr(A_27b,bool)))
=> ! [V9R] :
( mem(V9R,arr(A_27a,arr(A_27a,bool)))
=> ! [V10r] :
( mem(V10r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool))
=> ! [V11r] :
( mem(V11r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V12s] :
( mem(V12s,arr(A_27a,bool))
=> ! [V13r1] :
( mem(V13r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool))
=> ! [V14r2] :
( mem(V14r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool))
=> ( ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V0xy),ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R)))
<=> p(ap(ap(V1R,ap(c_2Epair_2EFST(A_27a,A_27b),V0xy)),ap(c_2Epair_2ESND(A_27a,A_27b),V0xy))) )
& ( p(ap(ap(ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V2r),V3x),V4y))
<=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V4y)),V2r)) )
& ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R)) = V1R
& ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V2r)) = V2r
& ( ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V5r1) = ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V6r2)
<=> V5r1 = V6r2 )
& ( ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V7R1) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V8R2)
<=> V7R1 = V8R2 )
& ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),V9R),c_2Epred__set_2EUNIV(A_27a)) = V9R
& ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V9R),c_2Epred__set_2EUNIV(A_27a)) = V9R
& ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V2r) = ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V2r))
& ap(c_2Eset__relation_2Erange(A_27a,A_27b),V10r) = ap(c_2Erelation_2ERRANGE(A_27b,A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27b,A_27a),V10r))
& ap(c_2Eset__relation_2Estrict(A_27a),V11r) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Erelation_2ESTRORD(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)))
& ap(ap(c_2Eset__relation_2Errestrict(A_27a),V11r),V12s) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)),V12s))
& ap(ap(c_2Eset__relation_2Ercomp(A_27a,A_27b,A_27c),V13r1),V14r2) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),ap(ap(c_2Erelation_2EO(A_27a,A_27c,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27c,A_27b),V14r2)),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27c),V13r1)))
& ap(c_2Eset__relation_2Euniv__reln(A_27a),V12s) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Eset__relation_2ERRUNIV(A_27a),V12s))
& ap(c_2Eset__relation_2Etc(A_27a),V11r) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)))
& ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),V11r))
<=> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)))) )
& ( p(ap(ap(c_2Eset__relation_2Eirreflexive(A_27a),V11r),V12s))
<=> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)),V12s))) )
& ( p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V11r),V12s))
<=> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)),V12s))) )
& ( p(ap(c_2Eset__relation_2Etransitive(A_27a),V11r))
<=> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) )
& ( p(ap(c_2Eset__relation_2Eantisym(A_27a),V11r))
<=> p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) )
& ( p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V11r),c_2Epred__set_2EUNIV(A_27a)))
<=> p(ap(c_2Erelation_2EWeakOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) )
& ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V11r),c_2Epred__set_2EUNIV(A_27a)))
<=> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) )
& ( p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V11r),c_2Epred__set_2EUNIV(A_27a)))
<=> p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eacyclic__WF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
& p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r)),V0s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r)),V0s)) )
=> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V1r))) ) ) ) ) ).
fof(lameq_f351,axiom,
! [A_27a,V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3x_27] : ap(f351(A_27a,V1r,V0xs,V2x),V3x_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x_27),V0xs)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3x_27)),V1r))),ap(ap(c_2Emin_2E_3D(A_27a),V2x),V3x_27)) ) ) ) ).
fof(lameq_f352,axiom,
! [A_27a,V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2x] : ap(f352(A_27a,V0xs,V1r),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0xs)),ap(c_2Ebool_2E_21(A_27a),f351(A_27a,V1r,V0xs,V2x)))) ) ) ).
fof(ax_thm_2Eset__relation_2Emaximal__elements__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0xs),V1r) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f352(A_27a,V0xs,V1r)) ) ) ) ).
fof(lameq_f353,axiom,
! [A_27a,V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3x_27] : ap(f353(A_27a,V1r,V0xs,V2x),V3x_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x_27),V0xs)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x_27),V2x)),V1r))),ap(ap(c_2Emin_2E_3D(A_27a),V2x),V3x_27)) ) ) ) ).
fof(lameq_f354,axiom,
! [A_27a,V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2x] : ap(f354(A_27a,V0xs,V1r),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0xs)),ap(c_2Ebool_2E_21(A_27a),f353(A_27a,V1r,V0xs,V2x)))) ) ) ).
fof(ax_thm_2Eset__relation_2Eminimal__elements__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0xs),V1r) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f354(A_27a,V0xs,V1r)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eminimal__elements__subset,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1lo] :
( mem(V1lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1lo)),V0s)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eminimal__elements__SWAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0xs),ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP(A_27a,A_27a)),V1r)) = ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0xs),V1r) ) ) ) ).
fof(conj_thm_2Eset__relation_2Emaximal__union,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2r1] :
( mem(V2r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V3r2] :
( mem(V3r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V1s),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V2r1),V3r2))))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V1s),V2r1)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V1s),V3r2))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eminimal__union,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2r1] :
( mem(V2r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V3r2] :
( mem(V3r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1s),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V2r1),V3r2))))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1s),V2r1)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1s),V3r2))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eminimal__elements__mono,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1r_27] :
( mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2xs] :
( mem(V2xs,arr(A_27a,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),V1r_27))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2xs),V1r_27)),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2xs),V0r))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eminimal__elements__rrestrict,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0xs),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r),V0xs)) = ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0xs),V1r) ) ) ) ).
fof(conj_thm_2Eset__relation_2EWF__has__minimal__path,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ( p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2s))
=> ? [V3y] :
( mem(V3y,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2s),V0r)))
& ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V1x)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))
| V3y = V1x ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__acyclic__has__maximal,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> ( V0s != c_2Epred__set_2EEMPTY(A_27a)
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r))
=> ? [V2x] :
( mem(V2x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__acyclic__has__minimal,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> ( V0s != c_2Epred__set_2EEMPTY(A_27a)
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r))
=> ? [V2x] :
( mem(V2x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Emaximal__TC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r)),V0s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r)),V0s)) )
=> ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),ap(c_2Eset__relation_2Etc(A_27a),V1r)) = ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eminimal__TC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r)),V0s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r)),V0s)) )
=> ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),ap(c_2Eset__relation_2Etc(A_27a),V1r)) = ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__acyclic__has__minimal__path,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
& p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) )
=> ? [V3y] :
( mem(V3y,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),ap(c_2Eset__relation_2Etc(A_27a),V1r))) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__acyclic__has__maximal__path,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
& p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r))) )
=> ? [V3y] :
( mem(V3y,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),ap(c_2Eset__relation_2Etc(A_27a),V1r))) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefix__po__has__minimal__path,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3s_27] :
( mem(V3s_27,arr(A_27a,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))
& p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V0r),V1s))
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V3s_27),V0r)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V3s_27))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V3s_27),V1s)) )
=> ? [V4x_27] :
( mem(V4x_27,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V4x_27),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V3s_27),V0r)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x_27),V2x)),V0r)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eempty__strict__linear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),c_2Epred__set_2EEMPTY(A_27a)))
<=> V0r = c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eempty__linear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),c_2Epred__set_2EEMPTY(A_27a)))
<=> V0r = c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a)) ) ) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order__restrict,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2s_27] :
( mem(V2s_27,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s))
=> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r),V2s_27)),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2s_27))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__linear__order__restrict,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2s_27] :
( mem(V2s_27,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V1r),V0s))
=> p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r),V2s_27)),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2s_27))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order__dom__rg,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0lo] :
( mem(V0lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1X] :
( mem(V1X,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0lo),V1X))
=> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0lo)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0lo)) = V1X ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order__refl,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0lo] :
( mem(V0lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1X] :
( mem(V1X,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0lo),V1X))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1X))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),V0lo)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order__in__set,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0lo] :
( mem(V0lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1X] :
( mem(V1X,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0lo),V1X))
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0lo))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1X))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1X)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2EIN__MIN__LO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1X] :
( mem(V1X,arr(A_27a,bool))
=> ! [V2lo] :
( mem(V2lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1X))
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V2lo),V1X))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1X),V2lo)))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V0x)),V2lo)) ) ) ) ) ) ) ) ) ).
fof(lameq_f355,axiom,
! [A_27a,V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] : ap(f355(A_27a,V1s,V2x),V3y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),c_2Epred__set_2EEMPTY(A_27a))))) ) ) ).
fof(conj_thm_2Eset__relation_2Eextend__linear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ( ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
& p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) )
=> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),A_27a),f355(A_27a,V1s,V2x)))),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),c_2Epred__set_2EEMPTY(A_27a))))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__linear__order__acyclic,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),V1s))
=> p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r)) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__linear__order__union__acyclic,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r1] :
( mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1r2] :
( mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r1),V2s))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r2)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r2))),V2s)) )
=> ( p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r1),V1r2)))
<=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V1r2),V0r1)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Estrict__linear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s))
=> p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r)),V1s)) ) ) ) ) ).
fof(lameq_f356,axiom,
! [A_27a,V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] : ap(f356(A_27a,V1s),V2x) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),V1s))
=> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),A_27a),f356(A_27a,V1s)))),V1s)) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__strict__linear__order__has__maximal,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
& p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V1r),V0s))
& V0s != c_2Epred__set_2EEMPTY(A_27a) )
=> ? [V2x] :
( mem(V2x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__strict__linear__order__has__minimal,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
& p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V1r),V0s))
& V0s != c_2Epred__set_2EEMPTY(A_27a) )
=> ? [V2x] :
( mem(V2x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__linear__order__has__maximal,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
& p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s))
& V0s != c_2Epred__set_2EEMPTY(A_27a) )
=> ? [V2x] :
( mem(V2x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__linear__order__has__minimal,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
& p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s))
& V0s != c_2Epred__set_2EEMPTY(A_27a) )
=> ? [V2x] :
( mem(V2x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Emaximal__linear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V0s))
& p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r))) )
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),V1r)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eminimal__linear__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V0s))
& p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) )
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V1r)) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eminimal__linear__order__unique,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2s_27] :
( mem(V2s_27,arr(A_27a,bool))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2s_27),V0r)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2s_27),V0r)))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s_27),V1s)) )
=> V3x = V4y ) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Efinite__prefix__linear__order__has__unique__minimal,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ! [V3s_27] :
( mem(V3s_27,arr(A_27a,bool))
=> ( ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V2s))
& p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V1r),V2s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V3s_27))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V3s_27),V2s)) )
=> p(ap(c_2Epred__set_2ESING(A_27a),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V3s_27),V1r))) ) ) ) ) ) ) ).
fof(lameq_f357,axiom,
! [A_27a,V9y] :
( mem(V9y,A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a)))
=> ! [V8x] :
( mem(V8x,A_27a)
=> ! [V10m] :
( mem(V10m,ty_2Enum_2Enum)
=> ! [V11n] : ap(f357(A_27a,V9y,V0f,V8x,V10m),V11n) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,V10m),V11n)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(V0f,V10m)),ap(c_2Eoption_2ESOME(A_27a),V8x))),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(V0f,V11n)),ap(c_2Eoption_2ESOME(A_27a),V9y)))) ) ) ) ) ).
fof(lameq_f358,axiom,
! [A_27a,V8x] :
( mem(V8x,A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a)))
=> ! [V9y] :
( mem(V9y,A_27a)
=> ! [V10m] : ap(f358(A_27a,V8x,V0f,V9y),V10m) = ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f357(A_27a,V9y,V0f,V8x,V10m)) ) ) ) ).
fof(lameq_f359,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a)))
=> ! [V8x] :
( mem(V8x,A_27a)
=> ! [V9y] : ap(f359(A_27a,V0f,V8x),V9y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V8x),V9y)),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f358(A_27a,V8x,V0f,V9y))) ) ) ).
fof(lameq_f360,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a)))
=> ! [V8x] : ap(f360(A_27a,V0f),V8x) = f359(A_27a,V0f,V8x) ) ).
fof(lameq_f361,axiom,
! [A_27a,V13y] :
( mem(V13y,A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a)))
=> ! [V12x] :
( mem(V12x,A_27a)
=> ! [V14m] :
( mem(V14m,ty_2Enum_2Enum)
=> ! [V15n] : ap(f361(A_27a,V13y,V0f,V12x,V14m),V15n) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,V14m),V15n)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(V0f,V14m)),ap(c_2Eoption_2ESOME(A_27a),V12x))),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(V0f,V15n)),ap(c_2Eoption_2ESOME(A_27a),V13y)))) ) ) ) ) ).
fof(lameq_f362,axiom,
! [A_27a,V12x] :
( mem(V12x,A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a)))
=> ! [V13y] :
( mem(V13y,A_27a)
=> ! [V14m] : ap(f362(A_27a,V12x,V0f,V13y),V14m) = ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f361(A_27a,V13y,V0f,V12x,V14m)) ) ) ) ).
fof(lameq_f363,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a)))
=> ! [V12x] :
( mem(V12x,A_27a)
=> ! [V13y] : ap(f363(A_27a,V0f,V12x),V13y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V12x),V13y)),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f362(A_27a,V12x,V0f,V13y))) ) ) ).
fof(lameq_f364,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a)))
=> ! [V12x] : ap(f364(A_27a,V0f),V12x) = f363(A_27a,V0f,V12x) ) ).
fof(conj_thm_2Eset__relation_2Enat__order__iso__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a)))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( ( ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ( ( ap(V0f,V3m) = ap(V0f,V2n)
& ap(V0f,V3m) != c_2Eoption_2ENONE(A_27a) )
=> V3m = V2n ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s))
=> ? [V5m] :
( mem(V5m,ty_2Enum_2Enum)
& ap(V0f,V5m) = ap(c_2Eoption_2ESOME(A_27a),V4x) ) ) )
& ! [V6m] :
( mem(V6m,ty_2Enum_2Enum)
=> ! [V7x] :
( mem(V7x,A_27a)
=> ( ap(V0f,V6m) = ap(c_2Eoption_2ESOME(A_27a),V7x)
=> p(ap(ap(c_2Ebool_2EIN(A_27a),V7x),V1s)) ) ) ) )
=> ( p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f360(A_27a,V0f)))),V1s))
& p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f364(A_27a,V0f)))),V1s)) ) ) ) ) ) ).
fof(ax_thm_2Eset__relation_2Echain__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(ap(c_2Eset__relation_2Echain(A_27a),V0s),V1r))
<=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V0s)) )
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V1r))
| p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),V1r)) ) ) ) ) ) ) ) ) ).
fof(lameq_f365,axiom,
! [A_27a,A_27b,V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27b,bool))
=> ! [V3y] : ap(f365(A_27a,A_27b,V1r,V2x,V0s),V3y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27b),V3y),V0s)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27b,A_27a)),ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V3y),V2x)),V1r)) ) ) ) ).
fof(lameq_f366,axiom,
! [A_27b,A_27a,V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool))
=> ! [V0s] :
( mem(V0s,arr(A_27b,bool))
=> ! [V2x] : ap(f366(A_27b,A_27a,V1r,V0s),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Eset__relation_2Erange(A_27a,A_27b),V1r))),ap(c_2Ebool_2E_21(A_27b),f365(A_27a,A_27b,V1r,V2x,V0s)))) ) ) ).
fof(ax_thm_2Eset__relation_2Eupper__bounds__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27b,bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool))
=> ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27b),V0s),V1r) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f366(A_27b,A_27a,V1r,V0s)) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eupper__bounds__lem,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x1] :
( mem(V2x1,A_27a)
=> ! [V3x2] :
( mem(V3x2,A_27a)
=> ( ( p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x1),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V1s),V0r)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x1),V3x2)),V0r)) )
=> p(ap(ap(c_2Ebool_2EIN(A_27a),V3x2),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V1s),V0r))) ) ) ) ) ) ) ).
fof(lameq_f367,axiom,
! [A_27a,V1k] :
( mem(V1k,arr(A_27a,bool))
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2C] : ap(f367(A_27a,V1k,V0r),V2C) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eset__relation_2Echain(A_27a),V2C),V0r)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2C),V1k)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V2C),V0r)),V2C)),V1k)),c_2Epred__set_2EEMPTY(A_27a)))))),ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V2C),V0r)),V2C))),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V2C),V0r)),V2C)),V1k)),V0r))) ) ) ).
fof(lameq_f368,axiom,
! [A_27a,V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1k] : ap(f368(A_27a,V0r),V1k) = ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),V1k),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eset__relation_2Echain(A_27a),V1k),V0r)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V1k),c_2Epred__set_2EEMPTY(A_27a)))),ap(c_2Ebool_2E_21(arr(A_27a,bool)),f367(A_27a,V1k,V0r))))) ) ).
fof(ax_thm_2Eset__relation_2Efchains__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(c_2Eset__relation_2Efchains(A_27a),V0r) = ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f368(A_27a,V0r)) ) ) ).
fof(conj_thm_2Eset__relation_2Ezorns__lemma,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( ( V1s != c_2Epred__set_2EEMPTY(A_27a)
& p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))
& ! [V2t] :
( mem(V2t,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Echain(A_27a),V2t),V0r))
=> ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V2t),V0r) != c_2Epred__set_2EEMPTY(A_27a) ) ) )
=> ? [V3x] :
( mem(V3x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V1s),V0r))) ) ) ) ) ) ).
fof(ax_thm_2Eset__relation_2Eper__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1xss] :
( mem(V1xss,arr(arr(A_27a,bool),bool))
=> ( p(ap(ap(c_2Eset__relation_2Eper(A_27a),V0xs),V1xss))
<=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V1xss)),V0xs))
& ~ p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),c_2Epred__set_2EEMPTY(A_27a)),V1xss))
& ! [V2xs1] :
( mem(V2xs1,arr(A_27a,bool))
=> ! [V3xs2] :
( mem(V3xs2,arr(A_27a,bool))
=> ( ( p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2xs1),V1xss))
& p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V3xs2),V1xss))
& V2xs1 != V3xs2 )
=> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2xs1),V3xs2)) ) ) ) ) ) ) ) ) ).
fof(lameq_f369,axiom,
! [A_27a,V1xs] :
( mem(V1xs,arr(A_27a,bool))
=> ! [V0xss] :
( mem(V0xss,arr(arr(A_27a,bool),bool))
=> ! [V2xs_27] : ap(f369(A_27a,V1xs,V0xss),V2xs_27) = ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),ap(ap(c_2Epred__set_2EINTER(A_27a),V2xs_27),V1xs)),ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2xs_27),V0xss)) ) ) ).
fof(ax_thm_2Eset__relation_2Eper__restrict__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xss] :
( mem(V0xss,arr(arr(A_27a,bool),bool))
=> ! [V1xs] :
( mem(V1xs,arr(A_27a,bool))
=> ap(ap(c_2Eset__relation_2Eper__restrict(A_27a),V0xss),V1xs) = ap(ap(c_2Epred__set_2EDELETE(arr(A_27a,bool)),ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f369(A_27a,V1xs,V0xss))),c_2Epred__set_2EEMPTY(A_27a)) ) ) ) ).
fof(lameq_f370,axiom,
! [A_27a,V2e] :
( mem(V2e,A_27a)
=> ! [V4es] : ap(f370(A_27a,V2e),V4es) = ap(ap(c_2Epred__set_2EDELETE(A_27a),V4es),V2e) ) ).
fof(lameq_f371,axiom,
! [A_27a,V2e] :
( mem(V2e,A_27a)
=> ! [V1xss] :
( mem(V1xss,arr(arr(A_27a,bool),bool))
=> ! [V3es] : ap(f371(A_27a,V2e,V1xss),V3es) = ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),V3es),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V3es),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27a,bool),arr(A_27a,bool)),f370(A_27a,V2e)),V1xss))),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V3es),c_2Epred__set_2EEMPTY(A_27a))))) ) ) ).
fof(conj_thm_2Eset__relation_2Eper__delete,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1xss] :
( mem(V1xss,arr(arr(A_27a,bool),bool))
=> ! [V2e] :
( mem(V2e,A_27a)
=> ( p(ap(ap(c_2Eset__relation_2Eper(A_27a),V0xs),V1xss))
=> p(ap(ap(c_2Eset__relation_2Eper(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0xs),V2e)),ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f371(A_27a,V2e,V1xss)))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Eper__restrict__per,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(arr(A_27a,bool),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2s_27] :
( mem(V2s_27,arr(A_27a,bool))
=> ( p(ap(ap(c_2Eset__relation_2Eper(A_27a),V1s),V0r))
=> p(ap(ap(c_2Eset__relation_2Eper(A_27a),V2s_27),ap(ap(c_2Eset__relation_2Eper__restrict(A_27a),V0r),V2s_27))) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Ecountable__per,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,arr(A_27a,bool))
=> ! [V1xss] :
( mem(V1xss,arr(arr(A_27a,bool),bool))
=> ( ( p(ap(c_2Epred__set_2Ecountable(A_27a),V0xs))
& p(ap(ap(c_2Eset__relation_2Eper(A_27a),V0xs),V1xss)) )
=> p(ap(c_2Epred__set_2Ecountable(arr(A_27a,bool)),V1xss)) ) ) ) ) ).
fof(lameq_f372,axiom,
! [A_27a,V0xss] :
( mem(V0xss,arr(arr(A_27a,bool),bool))
=> ! [V1choice] :
( mem(V1choice,arr(arr(A_27a,bool),A_27a))
=> ! [V2xs] : ap(f372(A_27a,V0xss,V1choice),V2xs) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2xs),V0xss)),ap(ap(c_2Ebool_2EIN(A_27a),ap(V1choice,V2xs)),V2xs)) ) ) ).
fof(lameq_f373,axiom,
! [A_27a,V0xss] :
( mem(V0xss,arr(arr(A_27a,bool),bool))
=> ! [V1choice] : ap(f373(A_27a,V0xss),V1choice) = ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27a,bool),A_27a),V1choice),V0xss)),ap(c_2Ebool_2E_21(arr(A_27a,bool)),f372(A_27a,V0xss,V1choice))) ) ).
fof(ax_thm_2Eset__relation_2Eall__choices__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xss] :
( mem(V0xss,arr(arr(A_27a,bool),bool))
=> ap(c_2Eset__relation_2Eall__choices(A_27a),V0xss) = ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(arr(A_27a,bool),A_27a)),f373(A_27a,V0xss)) ) ) ).
fof(conj_thm_2Eset__relation_2Eall__choices__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,arr(A_27a,bool))
=> ! [V1s] :
( mem(V1s,arr(arr(A_27a,bool),bool))
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V0x),ap(c_2Eset__relation_2Eall__choices(A_27a),V1s)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V0x)) )
=> ? [V3z] :
( mem(V3z,arr(A_27a,bool))
& p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V3z),V1s))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V3z)) ) ) ) ) ) ) ).
fof(lameq_f374,axiom,
! [A_27a,V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] : ap(f374(A_27a,V1s,V0f,V2x),V3y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)),ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V2x)),ap(V0f,V3y))))) ) ) ) ).
fof(lameq_f375,axiom,
! [A_27a,V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2x] : ap(f375(A_27a,V1s,V0f),V2x) = f374(A_27a,V1s,V0f,V2x) ) ) ).
fof(ax_thm_2Eset__relation_2Enum__order__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ap(ap(c_2Eset__relation_2Enum__order(A_27a),V0f),V1s) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f375(A_27a,V1s,V0f))) ) ) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order__num__order,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t] :
( mem(V2t,arr(ty_2Enum_2Enum,bool))
=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,ty_2Enum_2Enum),V0f),V1s),V2t))
=> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Eset__relation_2Enum__order(A_27a),V0f),V1s)),V1s)) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Enum__order__finite__prefix,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t] :
( mem(V2t,arr(ty_2Enum_2Enum,bool))
=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,ty_2Enum_2Enum),V0f),V1s),V2t))
=> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),ap(ap(c_2Eset__relation_2Enum__order(A_27a),V0f),V1s)),V1s)) ) ) ) ) ) ).
fof(lameq_f376,axiom,
! [A_27a,V3mins] : ap(f376(A_27a),V3mins) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Epred__set_2ESING(A_27a),V3mins)),ap(c_2Eoption_2ESOME(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V3mins))),c_2Eoption_2ENONE(A_27a)) ).
fof(ax_thm_2Eset__relation_2Eget__min__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r_27] :
( mem(V0r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2r] :
( mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(ap(c_2Eset__relation_2Eget__min(A_27a),V0r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V1s),V2r)) = ap(ap(c_2Ebool_2ELET(arr(A_27a,bool),ty_2Eoption_2Eoption(A_27a)),f376(A_27a)),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1s),V2r)),V0r_27)) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Enth__min__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),arr(ty_2Enum_2Enum,bool))))
=> ( ( ! [V1r_27] :
( mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ! [V3r] :
( mem(V3r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> p(ap(ap(ap(V0P,V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V2s),V3r)),c_2Enum_2E0)) ) ) )
& ! [V4r_27] :
( mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V5s] :
( mem(V5s,arr(A_27a,bool))
=> ! [V6r] :
( mem(V6r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V7n] :
( mem(V7n,ty_2Enum_2Enum)
=> ( ! [V8min] :
( mem(V8min,ty_2Eoption_2Eoption(A_27a))
=> ( ( V8min = ap(ap(c_2Eset__relation_2Eget__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V5s),V6r))
& V8min != c_2Eoption_2ENONE(A_27a) )
=> p(ap(ap(ap(V0P,V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V5s),ap(c_2Eoption_2ETHE(A_27a),V8min))),V6r)),V7n)) ) )
=> p(ap(ap(ap(V0P,V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V5s),V6r)),ap(c_2Enum_2ESUC,V7n))) ) ) ) ) ) )
=> ! [V9v] :
( mem(V9v,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V10v1] :
( mem(V10v1,arr(A_27a,bool))
=> ! [V11v2] :
( mem(V11v2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V12v3] :
( mem(V12v3,ty_2Enum_2Enum)
=> p(ap(ap(ap(V0P,V9v),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V10v1),V11v2)),V12v3)) ) ) ) ) ) ) ) ).
fof(lameq_f377,axiom,
! [A_27a,V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V5r] :
( mem(V5r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V3s] :
( mem(V3s,arr(A_27a,bool))
=> ! [V4r_27] :
( mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V7min] : ap(f377(A_27a,V6n,V5r,V3s,V4r_27),V7min) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),V7min),c_2Eoption_2ENONE(A_27a))),c_2Eoption_2ENONE(A_27a)),ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V3s),ap(c_2Eoption_2ETHE(A_27a),V7min))),V5r)),V6n)) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Enth__min__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r_27] :
( mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2r] :
( mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V0s),V2r)),c_2Enum_2E0) = ap(ap(c_2Eset__relation_2Eget__min(A_27a),V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V0s),V2r)) ) ) )
& ! [V3s] :
( mem(V3s,arr(A_27a,bool))
=> ! [V4r_27] :
( mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V5r] :
( mem(V5r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3s),V5r)),ap(c_2Enum_2ESUC,V6n)) = ap(ap(c_2Ebool_2ELET(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)),f377(A_27a,V6n,V5r,V3s,V4r_27)),ap(ap(c_2Eset__relation_2Eget__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3s),V5r))) ) ) ) ) ) ) ).
fof(lameq_f378,axiom,
! [A_27a,V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V5r] :
( mem(V5r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V3s] :
( mem(V3s,arr(A_27a,bool))
=> ! [V4r_27] :
( mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V7min] : ap(f378(A_27a,V6n,V5r,V3s,V4r_27),V7min) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),V7min),c_2Eoption_2ENONE(A_27a))),c_2Eoption_2ENONE(A_27a)),ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V3s),ap(c_2Eoption_2ETHE(A_27a),V7min))),V5r)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) ) ).
fof(lameq_f379,axiom,
! [A_27a,V11n] :
( mem(V11n,ty_2Enum_2Enum)
=> ! [V10r] :
( mem(V10r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V8s] :
( mem(V8s,arr(A_27a,bool))
=> ! [V9r_27] :
( mem(V9r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V12min] : ap(f379(A_27a,V11n,V10r,V8s,V9r_27),V12min) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),V12min),c_2Eoption_2ENONE(A_27a))),c_2Eoption_2ENONE(A_27a)),ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V9r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V8s),ap(c_2Eoption_2ETHE(A_27a),V12min))),V10r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V11n)))) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Enth__min__def__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1r_27] :
( mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V2r] :
( mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V0s),V2r)),c_2Enum_2E0) = ap(ap(c_2Eset__relation_2Eget__min(A_27a),V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V0s),V2r)) ) ) )
& ! [V3s] :
( mem(V3s,arr(A_27a,bool))
=> ! [V4r_27] :
( mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V5r] :
( mem(V5r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3s),V5r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))) = ap(ap(c_2Ebool_2ELET(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)),f378(A_27a,V6n,V5r,V3s,V4r_27)),ap(ap(c_2Eset__relation_2Eget__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3s),V5r))) ) ) ) )
& ! [V8s] :
( mem(V8s,arr(A_27a,bool))
=> ! [V9r_27] :
( mem(V9r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V10r] :
( mem(V10r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V11n] :
( mem(V11n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V9r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V8s),V10r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V11n))) = ap(ap(c_2Ebool_2ELET(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)),f379(A_27a,V11n,V10r,V8s,V9r_27)),ap(ap(c_2Eset__relation_2Eget__min(A_27a),V9r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V8s),V10r))) ) ) ) ) ) ) ).
fof(conj_thm_2Eset__relation_2Elinear__order__of__countable__po,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( ( p(ap(c_2Epred__set_2Ecountable(A_27a),V1s))
& p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))
& p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V0r),V1s)) )
=> ? [V2r_27] :
( mem(V2r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
& p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V2r_27),V1s))
& p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V2r_27),V1s))
& p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),V2r_27)) ) ) ) ) ) ).
%------------------------------------------------------------------------------