TPTP Problem File: ITP018^2.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ITP018^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory 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]
% : HL408501^2.p [TPAP]
% Status : Theorem
% Rating : 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0
% Syntax : Number of formulae : 54 ( 9 unt; 26 typ; 0 def)
% Number of atoms : 92 ( 13 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 239 ( 0 ~; 0 |; 0 &; 219 @)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 11 con; 0-2 aty)
% Number of variables : 49 ( 0 ^; 49 !; 0 ?; 49 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001^2.ax').
%------------------------------------------------------------------------------
thf(tp_ty_2Erealax_2Ereal,type,
ty_2Erealax_2Ereal: del ).
thf(stp_ty_2Erealax_2Ereal,type,
tp__ty_2Erealax_2Ereal: $tType ).
thf(stp_inj_ty_2Erealax_2Ereal,type,
inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
thf(stp_surj_ty_2Erealax_2Ereal,type,
surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).
thf(stp_inj_surj_ty_2Erealax_2Ereal,axiom,
! [X: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ X ) )
= X ) ).
thf(stp_inj_mem_ty_2Erealax_2Ereal,axiom,
! [X: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ X ) @ ty_2Erealax_2Ereal ) ).
thf(stp_iso_mem_ty_2Erealax_2Ereal,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Erealax_2Ereal )
=> ( X
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ X ) ) ) ) ).
thf(tp_c_2Erealax_2Ereal__neg,type,
c_2Erealax_2Ereal__neg: $i ).
thf(mem_c_2Erealax_2Ereal__neg,axiom,
mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ).
thf(stp_fo_c_2Erealax_2Ereal__neg,type,
fo__c_2Erealax_2Ereal__neg: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
thf(stp_eq_fo_c_2Erealax_2Ereal__neg,axiom,
! [X0: tp__ty_2Erealax_2Ereal] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Ereal__neg @ X0 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ X0 ) ) ) ).
thf(tp_ty_2Ebinary__ieee_2Efloat,type,
ty_2Ebinary__ieee_2Efloat: del > del > del ).
thf(tp_c_2Ebinary__ieee_2Efloat__negate,type,
c_2Ebinary__ieee_2Efloat__negate: del > del > $i ).
thf(mem_c_2Ebinary__ieee_2Efloat__negate,axiom,
! [A_27t: del,A_27w: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ).
thf(tp_ty_2Epair_2Eprod,type,
ty_2Epair_2Eprod: del > del > del ).
thf(tp_ty_2Ebool_2Eitself,type,
ty_2Ebool_2Eitself: del > del ).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__min,type,
c_2Ebinary__ieee_2Efloat__plus__min: del > del > $i ).
thf(mem_c_2Ebinary__ieee_2Efloat__plus__min,axiom,
! [A_27t: del,A_27w: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ).
thf(tp_c_2Ebinary__ieee_2Efloat__to__real,type,
c_2Ebinary__ieee_2Efloat__to__real: del > del > $i ).
thf(mem_c_2Ebinary__ieee_2Efloat__to__real,axiom,
! [A_27t: del,A_27w: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ty_2Erealax_2Ereal ) ) ).
thf(tp_c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value: del > $i ).
thf(mem_c_2Ebool_2Ethe__value,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) ).
thf(tp_c_2Ebinary__ieee_2Eulp,type,
c_2Ebinary__ieee_2Eulp: del > del > $i ).
thf(mem_c_2Ebinary__ieee_2Eulp,axiom,
! [A_27t: del,A_27w: del] : ( mem @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ty_2Erealax_2Ereal ) ) ).
thf(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
thf(mem_c_2Ebool_2ET,axiom,
mem @ c_2Ebool_2ET @ bool ).
thf(ax_true_p,axiom,
p @ c_2Ebool_2ET ).
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_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(conj_thm_2Ebinary__ieee_2Efloat__to__real__negate,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) )
=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b ) @ V0x ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ V0x ) ) ) ) ) ).
thf(conj_thm_2Ebinary__ieee_2Eulp,axiom,
! [A_27t: del,A_27w: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ETRUTH,axiom,
$true ).
thf(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( V0x = V0x )
<=> $true ) ) ).
thf(conj_thm_2Ebinary__ieee_2Eneg__ulp,conjecture,
! [A_27t: del,A_27w: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------