TPTP Problem File: ITP008^2.p
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% File : ITP008^2 : TPTP v8.2.0. 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 : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 43 ( 1 unt; 20 typ; 0 def)
% Number of atoms : 133 ( 8 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 295 ( 0 ~; 0 |; 0 &; 271 @)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 25 usr; 8 con; 0-3 aty)
% Number of variables : 56 ( 4 ^; 52 !; 0 ?; 56 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
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include('Axioms/ITP001/ITP001^2.ax').
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thf(tp_ty_2Epair_2Eprod,type,
ty_2Epair_2Eprod: del > del > del ).
thf(tp_c_2Epair_2E_2C,type,
c_2Epair_2E_2C: del > del > $i ).
thf(mem_c_2Epair_2E_2C,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) ).
thf(tp_c_2Epair_2ECURRY,type,
c_2Epair_2ECURRY: del > del > del > $i ).
thf(mem_c_2Epair_2ECURRY,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Erelation_2EWF,type,
c_2Erelation_2EWF: del > $i ).
thf(mem_c_2Erelation_2EWF,axiom,
! [A_27a: del] : ( mem @ ( c_2Erelation_2EWF @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
thf(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
thf(mem_c_2Emin_2E_3D,axiom,
! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
thf(ax_eq_p,axiom,
! [A: del,X: $i] :
( ( mem @ X @ A )
=> ! [Y: $i] :
( ( mem @ Y @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
<=> ( X = Y ) ) ) ) ).
thf(tp_ty_2Ewellorder_2Ewellorder,type,
ty_2Ewellorder_2Ewellorder: del > del ).
thf(tp_c_2Ewellorder_2Ewellorder__REP,type,
c_2Ewellorder_2Ewellorder__REP: del > $i ).
thf(mem_c_2Ewellorder_2Ewellorder__REP,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a ) @ ( arr @ ( ty_2Ewellorder_2Ewellorder @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Eset__relation_2Estrict,type,
c_2Eset__relation_2Estrict: del > $i ).
thf(mem_c_2Eset__relation_2Estrict,axiom,
! [A_27a: del] : ( 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 ) ) ) ).
thf(tp_c_2Ebool_2EIN,type,
c_2Ebool_2EIN: del > $i ).
thf(mem_c_2Ebool_2EIN,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2EIN @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
thf(tp_c_2Ewellorder_2Ewellfounded,type,
c_2Ewellorder_2Ewellfounded: del > $i ).
thf(mem_c_2Ewellorder_2Ewellfounded,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewellorder_2Ewellfounded @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ bool ) ) ).
thf(tp_c_2Ebool_2E_21,type,
c_2Ebool_2E_21: del > $i ).
thf(mem_c_2Ebool_2E_21,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
thf(ax_all_p,axiom,
! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
<=> ! [X: $i] :
( ( mem @ X @ A )
=> ( p @ ( ap @ Q @ X ) ) ) ) ) ).
thf(ax_thm_2Ebool_2EETA__AX,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( arr @ A_27a @ A_27b ) )
=> ( ( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0t @ V1x ) )
= V0t ) ) ).
thf(ax_thm_2Epair_2ECURRY__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2y: $i] :
( ( 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 ) ) ) ) ) ) ).
thf(conj_thm_2Ewellorder_2Ewellfounded__WF,axiom,
! [A_27a: del,V0R: $i] :
( ( 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 ) ) ) ) ) ).
thf(conj_thm_2Ewellorder_2EWIN__WF,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Ewellorder_2Ewellorder @ A_27a ) )
=> ( p
@ ( ap @ ( c_2Ewellorder_2Ewellfounded @ A_27a )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27a )
@ ^ [V1p: $i] : ( 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 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewellorder_2EWIN__WF2,conjecture,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Ewellorder_2Ewellorder @ A_27a ) )
=> ( p
@ ( ap @ ( c_2Erelation_2EWF @ A_27a )
@ ( lam @ A_27a
@ ^ [V1x: $i] :
( lam @ A_27a
@ ^ [V2y: $i] : ( 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 ) ) ) ) ) ) ) ) ).
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