TPTP Problem File: ITP008+5.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ITP008+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Ewellorder_2EWIN__WF2.p, 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 : thm_2Ewellorder_2EWIN__WF2.p [Gau20]
% : HL403501+5.p [TPAP]
% Status : Theorem
% Rating : 1.00 v8.1.0, 0.97 v7.5.0
% Syntax : Number of formulae : 6122 ( 330 unt; 0 def)
% Number of atoms : 48576 (7451 equ)
% Maximal formula atoms : 5765 ( 7 avg)
% Number of connectives : 43086 ( 632 ~; 362 |;17342 &)
% (3073 <=>;21677 =>; 0 <=; 0 <~>)
% Maximal formula depth : 363 ( 9 avg)
% Maximal term depth : 28 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 1723 (1723 usr; 200 con; 0-9 aty)
% Number of variables : 33966 (21440 !;12526 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001+2.ax').
include('Axioms/ITP001/ITP002+5.ax').
include('Axioms/ITP001/ITP003+5.ax').
include('Axioms/ITP001/ITP004+5.ax').
include('Axioms/ITP001/ITP007+5.ax').
include('Axioms/ITP001/ITP006+5.ax').
include('Axioms/ITP001/ITP005+5.ax').
include('Axioms/ITP001/ITP008+5.ax').
include('Axioms/ITP001/ITP009+5.ax').
include('Axioms/ITP001/ITP010+5.ax').
include('Axioms/ITP001/ITP012+5.ax').
include('Axioms/ITP001/ITP011+5.ax').
include('Axioms/ITP001/ITP013+5.ax').
include('Axioms/ITP001/ITP014+5.ax').
include('Axioms/ITP001/ITP015+5.ax').
include('Axioms/ITP001/ITP017+5.ax').
include('Axioms/ITP001/ITP016+5.ax').
include('Axioms/ITP001/ITP019+5.ax').
include('Axioms/ITP001/ITP018+5.ax').
include('Axioms/ITP001/ITP021+5.ax').
include('Axioms/ITP001/ITP022+5.ax').
include('Axioms/ITP001/ITP020+5.ax').
include('Axioms/ITP001/ITP024+5.ax').
include('Axioms/ITP001/ITP023+5.ax').
include('Axioms/ITP001/ITP025+5.ax').
include('Axioms/ITP001/ITP026+5.ax').
include('Axioms/ITP001/ITP027+5.ax').
include('Axioms/ITP001/ITP028+5.ax').
include('Axioms/ITP001/ITP031+5.ax').
include('Axioms/ITP001/ITP029+5.ax').
include('Axioms/ITP001/ITP033+5.ax').
include('Axioms/ITP001/ITP030+5.ax').
include('Axioms/ITP001/ITP032+5.ax').
include('Axioms/ITP001/ITP038+5.ax').
include('Axioms/ITP001/ITP035+5.ax').
include('Axioms/ITP001/ITP034+5.ax').
include('Axioms/ITP001/ITP036+5.ax').
include('Axioms/ITP001/ITP037+5.ax').
include('Axioms/ITP001/ITP039+5.ax').
include('Axioms/ITP001/ITP041+5.ax').
include('Axioms/ITP001/ITP042+5.ax').
include('Axioms/ITP001/ITP040+5.ax').
include('Axioms/ITP001/ITP044+5.ax').
include('Axioms/ITP001/ITP051+5.ax').
include('Axioms/ITP001/ITP045+5.ax').
include('Axioms/ITP001/ITP056+5.ax').
include('Axioms/ITP001/ITP046+5.ax').
include('Axioms/ITP001/ITP043+5.ax').
include('Axioms/ITP001/ITP052+5.ax').
%------------------------------------------------------------------------------
fof(ne_ty_2Ewellorder_2Ewellorder,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Ewellorder_2Ewellorder(A0)) ) ).
fof(mem_c_2Ewellorder_2EADD1,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2EADD1(A_27a),arr(A_27a,arr(ty_2Ewellorder_2Ewellorder(A_27a),ty_2Ewellorder_2Ewellorder(A_27a)))) ) ).
fof(mem_c_2Ewellorder_2EChain,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2EChain(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))) ) ).
fof(mem_c_2Ewellorder_2EelsOf,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2EelsOf(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(A_27a,bool))) ) ).
fof(mem_c_2Ewellorder_2Efinite,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Efinite(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27a),bool)) ) ).
fof(mem_c_2Ewellorder_2Efl,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Efl(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(A_27a,bool))) ) ).
fof(mem_c_2Ewellorder_2EfromNatWO,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2EfromNatWO(A_27a),arr(ty_2Enum_2Enum,ty_2Ewellorder_2Ewellorder(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)))) ) ).
fof(mem_c_2Ewellorder_2Eiseg,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Eiseg(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(A_27a,arr(A_27a,bool)))) ) ).
fof(mem_c_2Ewellorder_2Eorderiso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewellorder_2Eorderiso(A_27a,A_27b),arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27b),bool))) ) ) ).
fof(mem_c_2Ewellorder_2Eorderlt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewellorder_2Eorderlt(A_27a,A_27b),arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27b),bool))) ) ) ).
fof(mem_c_2Ewellorder_2Eposet,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Eposet(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)) ) ).
fof(mem_c_2Ewellorder_2Eremove,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Eremove(A_27a),arr(A_27a,arr(ty_2Ewellorder_2Ewellorder(A_27a),ty_2Ewellorder_2Ewellorder(A_27a)))) ) ).
fof(mem_c_2Ewellorder_2EwZERO,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2EwZERO(A_27a),ty_2Ewellorder_2Ewellorder(A_27a)) ) ).
fof(mem_c_2Ewellorder_2Ewellfounded,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Ewellfounded(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)) ) ).
fof(mem_c_2Ewellorder_2Ewellorder,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Ewellorder(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)) ) ).
fof(mem_c_2Ewellorder_2Ewellorder__ABS,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Ewellorder__ABS(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),ty_2Ewellorder_2Ewellorder(A_27a))) ) ).
fof(mem_c_2Ewellorder_2Ewellorder__REP,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Ewellorder__REP(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))) ) ).
fof(mem_c_2Ewellorder_2Ewleast,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Ewleast(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(arr(A_27a,bool),ty_2Eoption_2Eoption(A_27a)))) ) ).
fof(mem_c_2Ewellorder_2Ewo2wo,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewellorder_2Ewo2wo(A_27a,A_27b),arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27b),arr(A_27a,ty_2Eoption_2Eoption(A_27b))))) ) ) ).
fof(mem_c_2Ewellorder_2Ewobound,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewellorder_2Ewobound(A_27a),arr(A_27a,arr(ty_2Ewellorder_2Ewellorder(A_27a),ty_2Ewellorder_2Ewellorder(A_27a)))) ) ).
fof(ax_thm_2Ewellorder_2Ewellfounded__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Ewellorder_2Ewellfounded(A_27a),V0R))
<=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( ? [V2w] :
( mem(V2w,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2w),V1s)) )
=> ? [V3min] :
( mem(V3min,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3min),V1s))
& ! [V4w] :
( mem(V4w,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),V4w),V3min)),V0R))
=> ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V4w),V1s)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewellorder_2Ewellfounded__WF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Ewellorder_2Ewellfounded(A_27a),V0R))
<=> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Epair_2ECURRY(A_27a,A_27a,bool),V0R))) ) ) ) ).
fof(ax_thm_2Ewellorder_2Ewellorder__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Ewellorder_2Ewellorder(A_27a),V0R))
<=> ( p(ap(c_2Ewellorder_2Ewellfounded(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0R)))
& p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0R),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))))
& p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0R),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)))) ) ) ) ) ).
fof(conj_thm_2Ewellorder_2Ewellorder__EMPTY,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(c_2Ewellorder_2Ewellorder(A_27a),c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a)))) ) ).
fof(conj_thm_2Ewellorder_2Ewellorder__SING,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ( p(ap(c_2Ewellorder_2Ewellorder(A_27a),ap(ap(c_2Epred__set_2EINSERT(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V1y)),c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a)))))
<=> V0x = V1y ) ) ) ) ).
fof(conj_thm_2Ewellorder_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_2Ewellorder_2Ewellfounded__subset,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r0] :
( mem(V0r0,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( ( p(ap(c_2Ewellorder_2Ewellfounded(A_27a),V1r))
& p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r0),V1r)) )
=> p(ap(c_2Ewellorder_2Ewellfounded(A_27a),V0r0)) ) ) ) ) ).
fof(ax_thm_2Ewellorder_2Ewellorder__TY__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ? [V0rep] :
( mem(V0rep,arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),ty_2Ewellorder_2Ewellorder(A_27a)),c_2Ewellorder_2Ewellorder(A_27a)),V0rep)) ) ) ).
fof(ax_thm_2Ewellorder_2Ewellorder__ABSREP,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0a] :
( mem(V0a,ty_2Ewellorder_2Ewellorder(A_27a))
=> ap(c_2Ewellorder_2Ewellorder__ABS(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V0a)) = V0a )
& ! [V1r] :
( mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Ewellorder_2Ewellorder(A_27a),V1r))
<=> ap(c_2Ewellorder_2Ewellorder__REP(A_27a),ap(c_2Ewellorder_2Ewellorder__ABS(A_27a),V1r)) = V1r ) ) ) ) ).
fof(conj_thm_2Ewellorder_2EmkWO__destWO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Ewellorder_2Ewellorder(A_27a))
=> ap(c_2Ewellorder_2Ewellorder__ABS(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V0a)) = V0a ) ) ).
fof(conj_thm_2Ewellorder_2EdestWO__mkWO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0r] :
( mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))
=> ( p(ap(c_2Ewellorder_2Ewellorder(A_27a),V0r))
=> ap(c_2Ewellorder_2Ewellorder__REP(A_27a),ap(c_2Ewellorder_2Ewellorder__ABS(A_27a),V0r)) = V0r ) ) ) ).
fof(ax_thm_2Ewellorder_2EelsOf__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Ewellorder_2Ewellorder(A_27a))
=> ap(c_2Ewellorder_2EelsOf(A_27a),V0w) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V0w))),ap(c_2Eset__relation_2Erange(A_27a,A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V0w))) ) ) ).
fof(conj_thm_2Ewellorder_2EWIN__elsOf,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ! [V2w] :
( mem(V2w,ty_2Ewellorder_2Ewellorder(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_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V2w))))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Ewellorder_2EelsOf(A_27a),V2w)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V1y),ap(c_2Ewellorder_2EelsOf(A_27a),V2w))) ) ) ) ) ) ) ).
fof(conj_thm_2Ewellorder_2EWLE__elsOf,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ! [V2w] :
( mem(V2w,ty_2Ewellorder_2Ewellorder(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_2Ewellorder_2Ewellorder__REP(A_27a),V2w)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Ewellorder_2EelsOf(A_27a),V2w)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V1y),ap(c_2Ewellorder_2EelsOf(A_27a),V2w))) ) ) ) ) ) ) ).
fof(conj_thm_2Ewellorder_2EWIN__trichotomy,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Ewellorder_2Ewellorder(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Ewellorder_2EelsOf(A_27a),V0w)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),ap(c_2Ewellorder_2EelsOf(A_27a),V0w))) )
=> ( 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_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V0w))))
| V1x = V2y
| 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)),ap(c_2Eset__relation_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V0w)))) ) ) ) ) ) ) ).
fof(conj_thm_2Ewellorder_2EWIN__REFL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1w] :
( mem(V1w,ty_2Ewellorder_2Ewellorder(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),V0x)),ap(c_2Eset__relation_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V1w))))
<=> $false ) ) ) ) ).
fof(conj_thm_2Ewellorder_2EWLE__TRANS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ! [V2w] :
( mem(V2w,ty_2Ewellorder_2Ewellorder(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),V0x),V1y)),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V2w)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1y),V3z)),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V2w))) )
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V3z)),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V2w))) ) ) ) ) ) ) ).
fof(conj_thm_2Ewellorder_2EWLE__ANTISYM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ! [V2w] :
( mem(V2w,ty_2Ewellorder_2Ewellorder(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_2Ewellorder_2Ewellorder__REP(A_27a),V2w)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1y),V0x)),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V2w))) )
=> V0x = V1y ) ) ) ) ) ).
fof(conj_thm_2Ewellorder_2EWIN__WLE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ! [V2w] :
( mem(V2w,ty_2Ewellorder_2Ewellorder(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_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V2w))))
=> 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_2Ewellorder_2Ewellorder__REP(A_27a),V2w))) ) ) ) ) ) ).
fof(conj_thm_2Ewellorder_2EelsOf__WLE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1w] :
( mem(V1w,ty_2Ewellorder_2Ewellorder(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Ewellorder_2EelsOf(A_27a),V1w)))
<=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V0x)),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V1w))) ) ) ) ) ).
fof(conj_thm_2Ewellorder_2Etransitive__strict,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_2Eset__relation_2Eantisym(A_27a),V0r)) )
=> p(ap(c_2Eset__relation_2Etransitive(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))) ) ) ) ).
fof(conj_thm_2Ewellorder_2EWIN__TRANS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ! [V2w] :
( mem(V2w,ty_2Ewellorder_2Ewellorder(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),V0x),V1y)),ap(c_2Eset__relation_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V2w))))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1y),V3z)),ap(c_2Eset__relation_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V2w)))) )
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V3z)),ap(c_2Eset__relation_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V2w)))) ) ) ) ) ) ) ).
fof(lameq_f1018,axiom,
! [A_27a,V0w] :
( mem(V0w,ty_2Ewellorder_2Ewellorder(A_27a))
=> ! [V1p] : ap(f1018(A_27a,V0w),V1p) = ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),V1p),ap(c_2Eset__relation_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V0w))) ) ).
fof(conj_thm_2Ewellorder_2EWIN__WF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Ewellorder_2Ewellorder(A_27a))
=> p(ap(c_2Ewellorder_2Ewellfounded(A_27a),f1018(A_27a,V0w))) ) ) ).
fof(lameq_f1019,axiom,
! [A_27a,V1x] :
( mem(V1x,A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Ewellorder_2Ewellorder(A_27a))
=> ! [V2y] : ap(f1019(A_27a,V1x,V0w),V2y) = 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_2Estrict(A_27a),ap(c_2Ewellorder_2Ewellorder__REP(A_27a),V0w))) ) ) ).
fof(lameq_f1020,axiom,
! [A_27a,V0w] :
( mem(V0w,ty_2Ewellorder_2Ewellorder(A_27a))
=> ! [V1x] : ap(f1020(A_27a,V0w),V1x) = f1019(A_27a,V1x,V0w) ) ).
fof(conj_thm_2Ewellorder_2EWIN__WF2,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Ewellorder_2Ewellorder(A_27a))
=> p(ap(c_2Erelation_2EWF(A_27a),f1020(A_27a,V0w))) ) ) ).
%------------------------------------------------------------------------------