TPTP Problem File: ITP018^3.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ITP018^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Ebinary__ieee_2Eneg__ulp.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_2Ebinary__ieee_2Eneg__ulp.p [Gau19]
% : HL408501^3.p [TPAP]
% Status : Theorem
% Rating : 0.33 v8.1.0, 0.25 v7.5.0
% Syntax : Number of formulae : 32 ( 9 unt; 20 typ; 0 def)
% Number of atoms : 15 ( 5 equ; 1 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 90 ( 1 ~; 1 |; 1 &; 78 @)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 2 con; 0-3 aty)
% Number of variables : 37 ( 0 ^; 24 !; 1 ?; 37 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
thf(tyop_2Ebinary__ieee_2Efloat,type,
tyop_2Ebinary__ieee_2Efloat: $tType > $tType > $tType ).
thf(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
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_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
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_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ebinary__ieee_2Efloat__negate,type,
c_2Ebinary__ieee_2Efloat__negate:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) > ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ).
thf(c_2Ebinary__ieee_2Efloat__plus__min,type,
c_2Ebinary__ieee_2Efloat__plus__min:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) > ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ).
thf(c_2Ebinary__ieee_2Efloat__to__real,type,
c_2Ebinary__ieee_2Efloat__to__real:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) > tyop_2Erealax_2Ereal ) ).
thf(c_2Erealax_2Ereal__neg,type,
c_2Erealax_2Ereal__neg: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself @ A_27a ) ).
thf(c_2Ebinary__ieee_2Eulp,type,
c_2Ebinary__ieee_2Eulp:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) > tyop_2Erealax_2Ereal ) ).
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_2Ebinary__ieee_2Efloat__to__real__negate,axiom,
! [A_27a: $tType,A_27b: $tType,V0x: tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b] :
( ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b @ V0x ) )
= ( c_2Erealax_2Ereal__neg @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b @ V0x ) ) ) ).
thf(thm_2Ebinary__ieee_2Eulp,axiom,
! [A_27t: $tType,A_27w: $tType] :
( ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) )
= ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ).
thf(thm_2Ebool_2ETRUTH,axiom,
c_2Ebool_2ET ).
thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( V0x = V0x )
<=> c_2Ebool_2ET ) ).
thf(thm_2Ebinary__ieee_2Eneg__ulp,conjecture,
! [A_27t: $tType,A_27w: $tType] :
( ( c_2Erealax_2Ereal__neg @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) ) )
= ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ).
%------------------------------------------------------------------------------