TPTP Problem File: ITP018_2.p
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%------------------------------------------------------------------------------
% 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 : 0.22 v8.2.0, 0.20 v8.1.0, 0.18 v7.5.0
% Syntax : Number of formulae : 60 ( 19 unt; 30 typ; 0 def)
% Number of atoms : 97 ( 16 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 23 ( 0 ~; 0 |; 0 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 44 ( 44 fml; 0 var)
% Number of types : 5 ( 3 usr)
% Number of type conns : 31 ( 21 >; 10 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 0 ?; 49 :)
% SPC : TF0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001_2.ax').
%------------------------------------------------------------------------------
tff(tp_ty_2Erealax_2Ereal,type,
ty_2Erealax_2Ereal: del ).
tff(stp_ty_2Erealax_2Ereal,type,
tp__ty_2Erealax_2Ereal: $tType ).
tff(stp_inj_ty_2Erealax_2Ereal,type,
inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
tff(stp_surj_ty_2Erealax_2Ereal,type,
surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).
tff(stp_inj_surj_ty_2Erealax_2Ereal,axiom,
! [X: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X)) = X ).
tff(stp_inj_mem_ty_2Erealax_2Ereal,axiom,
! [X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X),ty_2Erealax_2Ereal) ).
tff(stp_iso_mem_ty_2Erealax_2Ereal,axiom,
! [X: $i] :
( mem(X,ty_2Erealax_2Ereal)
=> ( X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)) ) ) ).
tff(tp_c_2Erealax_2Ereal__neg,type,
c_2Erealax_2Ereal__neg: $i ).
tff(mem_c_2Erealax_2Ereal__neg,axiom,
mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
tff(stp_fo_c_2Erealax_2Ereal__neg,type,
fo__c_2Erealax_2Ereal__neg: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
tff(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)) ).
tff(tp_ty_2Ebinary__ieee_2Efloat,type,
ty_2Ebinary__ieee_2Efloat: ( del * del ) > del ).
tff(tp_c_2Ebinary__ieee_2Efloat__negate,type,
c_2Ebinary__ieee_2Efloat__negate: ( del * del ) > $i ).
tff(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))) ).
tff(tp_ty_2Epair_2Eprod,type,
ty_2Epair_2Eprod: ( del * del ) > del ).
tff(tp_ty_2Ebool_2Eitself,type,
ty_2Ebool_2Eitself: del > del ).
tff(tp_c_2Ebinary__ieee_2Efloat__plus__min,type,
c_2Ebinary__ieee_2Efloat__plus__min: ( del * del ) > $i ).
tff(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))) ).
tff(tp_c_2Ebinary__ieee_2Efloat__to__real,type,
c_2Ebinary__ieee_2Efloat__to__real: ( del * del ) > $i ).
tff(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)) ).
tff(tp_c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value: del > $i ).
tff(mem_c_2Ebool_2Ethe__value,axiom,
! [A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)) ).
tff(tp_c_2Ebinary__ieee_2Eulp,type,
c_2Ebinary__ieee_2Eulp: ( del * del ) > $i ).
tff(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)) ).
tff(stp_o,type,
tp__o: $tType ).
tff(stp_inj_o,type,
inj__o: tp__o > $i ).
tff(stp_surj_o,type,
surj__o: $i > tp__o ).
tff(stp_inj_surj_o,axiom,
! [X: tp__o] : surj__o(inj__o(X)) = X ).
tff(stp_inj_mem_o,axiom,
! [X: tp__o] : mem(inj__o(X),bool) ).
tff(stp_iso_mem_o,axiom,
! [X: $i] :
( mem(X,bool)
=> ( X = inj__o(surj__o(X)) ) ) ).
tff(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
tff(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool) ).
tff(stp_fo_c_2Ebool_2ET,type,
fo__c_2Ebool_2ET: tp__o ).
tff(stp_eq_fo_c_2Ebool_2ET,axiom,
inj__o(fo__c_2Ebool_2ET) = c_2Ebool_2ET ).
tff(ax_true_p,axiom,
p(c_2Ebool_2ET) ).
tff(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
tff(mem_c_2Emin_2E_3D,axiom,
! [A_27a: del] : mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ).
tff(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 ) ) ) ) ).
tff(tp_c_2Ebool_2E_21,type,
c_2Ebool_2E_21: del > $i ).
tff(mem_c_2Ebool_2E_21,axiom,
! [A_27a: del] : mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ).
tff(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)) ) ) ) ).
tff(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))) ) ) ).
tff(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))))) ).
tff(conj_thm_2Ebool_2ETRUTH,axiom,
$true ).
tff(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ( ( V0x = V0x )
<=> $true ) ) ).
tff(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)))))) ).
%------------------------------------------------------------------------------