TPTP Problem File: ITP008^3.p
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% File : ITP008^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic 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]
% : HL403501^3.p [TPAP]
% Status : Theorem
% Rating : 0.67 v8.2.0, 1.00 v8.1.0, 0.75 v7.5.0
% Syntax : Number of formulae : 30 ( 8 unt; 18 typ; 0 def)
% Number of atoms : 22 ( 4 equ; 1 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 95 ( 1 ~; 1 |; 1 &; 84 @)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 1 con; 0-6 aty)
% Number of variables : 48 ( 4 ^; 30 !; 1 ?; 48 :)
% ( 13 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
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thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(tyop_2Ewellorder_2Ewellorder,type,
tyop_2Ewellorder_2Ewellorder: $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Epair_2E_2C,type,
c_2Epair_2E_2C:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Epair_2ECURRY,type,
c_2Epair_2ECURRY:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27c ) > A_27a > A_27b > A_27c ) ).
thf(c_2Ebool_2EIN,type,
c_2Ebool_2EIN:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
thf(c_2Erelation_2EWF,type,
c_2Erelation_2EWF:
!>[A_27a: $tType] : ( ( A_27a > A_27a > $o ) > $o ) ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Eset__relation_2Estrict,type,
c_2Eset__relation_2Estrict:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) ).
thf(c_2Ewellorder_2Ewellfounded,type,
c_2Ewellorder_2Ewellfounded:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > $o ) ).
thf(c_2Ewellorder_2Ewellorder__REP,type,
c_2Ewellorder_2Ewellorder__REP:
!>[A_27a: $tType] : ( ( tyop_2Ewellorder_2Ewellorder @ A_27a ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2Ebool_2EETA__AX,axiom,
! [A_27a: $tType,A_27b: $tType,V0t: A_27a > A_27b] :
( ( ^ [V1x: A_27a] : ( V0t @ V1x ) )
= V0t ) ).
thf(thm_2Epair_2ECURRY__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27c,V1x: A_27a,V2y: A_27b] :
( ( c_2Epair_2ECURRY @ A_27a @ A_27b @ A_27c @ V0f @ V1x @ V2y )
= ( V0f @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ V1x @ V2y ) ) ) ).
thf(thm_2Ewellorder_2Ewellfounded__WF,axiom,
! [A_27a: $tType,V0R: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o] :
( ( c_2Ewellorder_2Ewellfounded @ A_27a @ V0R )
= ( c_2Erelation_2EWF @ A_27a @ ( c_2Epair_2ECURRY @ A_27a @ A_27a @ $o @ V0R ) ) ) ).
thf(thm_2Ewellorder_2EWIN__WF,axiom,
! [A_27a: $tType,V0w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( c_2Ewellorder_2Ewellfounded @ A_27a
@ ^ [V1p: tyop_2Epair_2Eprod @ A_27a @ A_27a] : ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ V1p @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0w ) ) ) ) ).
thf(thm_2Ewellorder_2EWIN__WF2,conjecture,
! [A_27a: $tType,V0w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( c_2Erelation_2EWF @ A_27a
@ ^ [V1x: A_27a,V2y: A_27a] : ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1x @ V2y ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0w ) ) ) ) ).
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