TPTP Problem File: ITP008+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP008+2 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Ewellorder_2EWIN__WF2.p, bushy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Ewellorder_2EWIN__WF2.p [Gau19]
% : HL403501+2.p [TPAP]
% Status : CounterSatisfiable
% Rating : 0.00 v8.1.0, 0.92 v7.5.0
% Syntax : Number of formulae : 26 ( 2 unt; 0 def)
% Number of atoms : 79 ( 8 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 53 ( 0 ~; 0 |; 0 &)
% ( 4 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 20 ( 20 usr; 2 con; 0-3 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% SPC : FOF_CSA_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001+2.ax').
%------------------------------------------------------------------------------
fof(ne_ty_2Epair_2Eprod,axiom,
! [A0] :
( ne(A0)
=> ! [A1] :
( ne(A1)
=> ne(ty_2Epair_2Eprod(A0,A1)) ) ) ).
fof(mem_c_2Epair_2E_2C,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))) ) ) ).
fof(mem_c_2Epair_2ECURRY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),arr(A_27a,arr(A_27b,A_27c)))) ) ) ) ).
fof(mem_c_2Erelation_2EWF,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Erelation_2EWF(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) ).
fof(mem_c_2Emin_2E_3D,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ) ).
fof(ax_eq_p,axiom,
! [A] :
( ne(A)
=> ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ) ).
fof(ne_ty_2Ewellorder_2Ewellorder,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Ewellorder_2Ewellorder(A0)) ) ).
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_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_2Ebool_2EIN,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))) ) ).
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_2Ebool_2E_21,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ) ).
fof(ax_all_p,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ) ).
fof(ax_thm_2Ebool_2EETA__AX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,arr(A_27a,A_27b))
=> f31(A_27b,A_27a,V0t) = V0t ) ) ) ).
fof(ax_thm_2Epair_2ECURRY__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27b)
=> ap(ap(ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),V0f),V1x),V2y) = ap(V0f,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) ) ) ) ) ) ) ).
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(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(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))) ) ) ).
%------------------------------------------------------------------------------