ITP001 Axioms: ITP026+5.ax
%------------------------------------------------------------------------------
% File : ITP026+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : bit+2.ax [Gau20]
% : HL4026+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 154 ( 20 unt; 0 def)
% Number of atoms : 652 ( 113 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 526 ( 28 ~; 2 |; 33 &)
% ( 34 <=>; 429 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 51 ( 51 usr; 41 con; 0-3 aty)
% Number of variables : 371 ( 367 !; 4 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Ebit_2EBIT,axiom,
mem(c_2Ebit_2EBIT,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
fof(mem_c_2Ebit_2EBITS,axiom,
mem(c_2Ebit_2EBITS,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Ebit_2EBITV,axiom,
mem(c_2Ebit_2EBITV,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Ebit_2EBITWISE,axiom,
mem(c_2Ebit_2EBITWISE,arr(ty_2Enum_2Enum,arr(arr(bool,arr(bool,bool)),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))))) ).
fof(mem_c_2Ebit_2EBIT__MODIFY,axiom,
mem(c_2Ebit_2EBIT__MODIFY,arr(ty_2Enum_2Enum,arr(arr(ty_2Enum_2Enum,arr(bool,bool)),arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Ebit_2EBIT__REVERSE,axiom,
mem(c_2Ebit_2EBIT__REVERSE,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Ebit_2EDIVMOD__2EXP,axiom,
mem(c_2Ebit_2EDIVMOD__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Ebit_2EDIV__2EXP,axiom,
mem(c_2Ebit_2EDIV__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Ebit_2ELOG2,axiom,
mem(c_2Ebit_2ELOG2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Ebit_2ELOWEST__SET__BIT,axiom,
mem(c_2Ebit_2ELOWEST__SET__BIT,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Ebit_2EMOD__2EXP,axiom,
mem(c_2Ebit_2EMOD__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Ebit_2EMOD__2EXP__EQ,axiom,
mem(c_2Ebit_2EMOD__2EXP__EQ,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))) ).
fof(mem_c_2Ebit_2EMOD__2EXP__MAX,axiom,
mem(c_2Ebit_2EMOD__2EXP__MAX,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
fof(mem_c_2Ebit_2ESBIT,axiom,
mem(c_2Ebit_2ESBIT,arr(bool,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Ebit_2ESIGN__EXTEND,axiom,
mem(c_2Ebit_2ESIGN__EXTEND,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Ebit_2ESLICE,axiom,
mem(c_2Ebit_2ESLICE,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Ebit_2ETIMES__2EXP,axiom,
mem(c_2Ebit_2ETIMES__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(ax_thm_2Ebit_2EMOD__2EXP__def,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2EMOD__2EXP,V0x),V1n) = ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)) ) ) ).
fof(ax_thm_2Ebit_2EDIV__2EXP__def,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2EDIV__2EXP,V0x),V1n) = ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)) ) ) ).
fof(ax_thm_2Ebit_2ETIMES__2EXP__def,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2ETIMES__2EXP,V0x),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)) ) ) ).
fof(ax_thm_2Ebit_2EDIVMOD__2EXP__def,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2EDIVMOD__2EXP,V0x),V1n) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))) ) ) ).
fof(ax_thm_2Ebit_2ESBIT__def,axiom,
! [V0b] :
( mem(V0b,bool)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2ESBIT,V0b),V1n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V0b),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)),c_2Enum_2E0) ) ) ).
fof(ax_thm_2Ebit_2EBITS__def,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = ap(ap(c_2Ebit_2EMOD__2EXP,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)),ap(ap(c_2Ebit_2EDIV__2EXP,V1l),V2n)) ) ) ) ).
fof(ax_thm_2Ebit_2EBITV__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2EBITV,V0n),V1b) = ap(ap(ap(c_2Ebit_2EBITS,V1b),V1b),V0n) ) ) ).
fof(ax_thm_2Ebit_2EBIT__def,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V0b),V1n))
<=> ap(ap(ap(c_2Ebit_2EBITS,V0b),V0b),V1n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ).
fof(ax_thm_2Ebit_2ESLICE__def,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Ebit_2EMOD__2EXP,ap(c_2Enum_2ESUC,V0h)),V2n)),ap(ap(c_2Ebit_2EMOD__2EXP,V1l),V2n)) ) ) ) ).
fof(ax_thm_2Ebit_2ELOG2__def,axiom,
c_2Ebit_2ELOG2 = ap(c_2Elogroot_2ELOG,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ).
fof(lameq_f249,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] : ap(f249(V0n),V1i) = ap(ap(c_2Ebit_2EBIT,V1i),V0n) ) ).
fof(ax_thm_2Ebit_2ELOWEST__SET__BIT__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ebit_2ELOWEST__SET__BIT,V0n) = ap(c_2Ewhile_2ELEAST,f249(V0n)) ) ).
fof(ax_thm_2Ebit_2EBIT__REVERSE__def,axiom,
( ! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2EBIT__REVERSE,c_2Enum_2E0),V0x) = c_2Enum_2E0 )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2EBIT__REVERSE,ap(c_2Enum_2ESUC,V1n)),V2x) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Ebit_2EBIT__REVERSE,V1n),V2x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V1n),V2x)),c_2Enum_2E0)) ) ) ) ).
fof(ax_thm_2Ebit_2EBITWISE__def,axiom,
( ! [V0op] :
( mem(V0op,arr(bool,arr(bool,bool)))
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ap(ap(ap(ap(c_2Ebit_2EBITWISE,c_2Enum_2E0),V0op),V1x),V2y) = c_2Enum_2E0 ) ) )
& ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4op] :
( mem(V4op,arr(bool,arr(bool,bool)))
=> ! [V5x] :
( mem(V5x,ty_2Enum_2Enum)
=> ! [V6y] :
( mem(V6y,ty_2Enum_2Enum)
=> ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V3n)),V4op),V5x),V6y) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V3n),V4op),V5x),V6y)),ap(ap(c_2Ebit_2ESBIT,ap(ap(V4op,ap(ap(c_2Ebit_2EBIT,V3n),V5x)),ap(ap(c_2Ebit_2EBIT,V3n),V6y))),V3n)) ) ) ) ) ) ).
fof(ax_thm_2Ebit_2EBIT__MODIFY__def,axiom,
( ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool)))
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBIT__MODIFY,c_2Enum_2E0),V0f),V1x) = c_2Enum_2E0 ) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3f] :
( mem(V3f,arr(ty_2Enum_2Enum,arr(bool,bool)))
=> ! [V4x] :
( mem(V4x,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBIT__MODIFY,ap(c_2Enum_2ESUC,V2n)),V3f),V4x) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBIT__MODIFY,V2n),V3f),V4x)),ap(ap(c_2Ebit_2ESBIT,ap(ap(V3f,V2n),ap(ap(c_2Ebit_2EBIT,V2n),V4x))),V2n)) ) ) ) ) ).
fof(lameq_f250,axiom,
! [V0l] :
( mem(V0l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V3m] : ap(f250(V0l,V2n,V1h),V3m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,V0l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2n)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1h)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0l))),V3m)),V3m) ) ) ) ).
fof(ax_thm_2Ebit_2ESIGN__EXTEND__def,axiom,
! [V0l] :
( mem(V0l,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2ESIGN__EXTEND,V0l),V1h),V2n) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f250(V0l,V2n,V1h)),ap(ap(c_2Earithmetic_2EMOD,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0l))) ) ) ) ).
fof(ax_thm_2Ebit_2EMOD__2EXP__EQ__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Ebit_2EMOD__2EXP__EQ,V0n),V1a),V2b))
<=> ap(ap(c_2Ebit_2EMOD__2EXP,V0n),V1a) = ap(ap(c_2Ebit_2EMOD__2EXP,V0n),V2b) ) ) ) ) ).
fof(ax_thm_2Ebit_2EMOD__2EXP__MAX__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EMOD__2EXP__MAX,V0n),V1a))
<=> ap(ap(c_2Ebit_2EMOD__2EXP,V0n),V1a) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ).
fof(conj_thm_2Ebit_2ELESS__MULT__MONO2,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ! [V3y] :
( mem(V3y,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0a),V2x))
& p(ap(ap(c_2Eprim__rec_2E_3C,V1b),V3y)) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0a),V1b)),ap(ap(c_2Earithmetic_2E_2A,V2x),V3y))) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ELOG2__UNIQUE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1p] :
( mem(V1p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1p)),V0n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V1p)))) )
=> ap(c_2Ebit_2ELOG2,V0n) = V1p ) ) ) ).
fof(conj_thm_2Ebit_2ELOG2__TWOEXP,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ebit_2ELOG2,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) = V0n ) ).
fof(conj_thm_2Ebit_2EDIVMOD__2EXP,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2EDIVMOD__2EXP,V0x),V1n) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Ebit_2EDIV__2EXP,V0x),V1n)),ap(ap(c_2Ebit_2EMOD__2EXP,V0x),V1n)) ) ) ).
fof(conj_thm_2Ebit_2ESUC__SUB,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0a)),V0a) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ).
fof(conj_thm_2Ebit_2EDIV__MULT__1,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),V1n))
=> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,V1n),V0r)),V1n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ).
fof(conj_thm_2Ebit_2ENOT__ZERO__ADD1,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ( V0m != c_2Enum_2E0
=> ? [V1p] :
( mem(V1p,ty_2Enum_2Enum)
& V0m = ap(c_2Enum_2ESUC,V1p) ) ) ) ).
fof(conj_thm_2Ebit_2EZERO__LT__TWOEXP,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) ) ).
fof(conj_thm_2Ebit_2EONE__LE__TWOEXP,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) ) ).
fof(conj_thm_2Ebit_2ETWOEXP__NOT__ZERO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n) != c_2Enum_2E0 ) ).
fof(conj_thm_2Ebit_2EMOD__2EXP__LT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V1k),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) ) ) ).
fof(conj_thm_2Ebit_2ETWOEXP__DIVISION,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EDIV,V1k),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EMOD,V1k),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) ) ) ).
fof(conj_thm_2Ebit_2ETWOEXP__MONO,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0a),V1b))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))) ) ) ) ).
fof(conj_thm_2Ebit_2ETWOEXP__MONO2,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))) ) ) ) ).
fof(conj_thm_2Ebit_2EEXP__SUB__LESS__EQ,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,V0a),V1b))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a))) ) ) ).
fof(conj_thm_2Ebit_2EMOD__LEQ,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMOD,V0a),V1b)),V0a)) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__THM,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l))) ) ) ) ).
fof(conj_thm_2Ebit_2EBITSLT__THM,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)))) ) ) ) ).
fof(conj_thm_2Ebit_2EBITSLT__THM2,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__THM2,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EMOD,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__LEQ,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)),V2n)) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__COMP__THM,axiom,
! [V0h1] :
( mem(V0h1,ty_2Enum_2Enum)
=> ! [V1l1] :
( mem(V1l1,ty_2Enum_2Enum)
=> ! [V2h2] :
( mem(V2h2,ty_2Enum_2Enum)
=> ! [V3l2] :
( mem(V3l2,ty_2Enum_2Enum)
=> ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1)),V0h1))
=> ap(ap(ap(c_2Ebit_2EBITS,V2h2),V3l2),ap(ap(ap(c_2Ebit_2EBITS,V0h1),V1l1),V4n)) = ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1)),ap(ap(c_2Earithmetic_2E_2B,V3l2),V1l1)),V4n) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__DIV__THM,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EDIV,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2x)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V3n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),ap(ap(c_2Earithmetic_2E_2B,V1l),V3n)),V2x) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__LT__HIGH,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h))))
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = ap(ap(c_2Earithmetic_2EDIV,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__ZERO,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0h),V1l))
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__ZERO2,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),c_2Enum_2E0) = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Ebit_2EBITS__ZERO3,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1n) = ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h))) ) ) ).
fof(conj_thm_2Ebit_2EBITS__ZERO4,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),V0h))
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))) = ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2D,V0h),V1l)),c_2Enum_2E0),V2a) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__ZEROL,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h))))
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1a) = V1a ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__LOG2__ZERO__ID,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Ebit_2ELOG2,V0n)),c_2Enum_2E0),V0n) = V0n ) ) ).
fof(conj_thm_2Ebit_2EBITS__LT__LOW,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)))
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__ZERO,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ~ p(ap(ap(c_2Ebit_2EBIT,V0b),c_2Enum_2E0)) ) ).
fof(conj_thm_2Ebit_2EBIT__B,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> p(ap(ap(c_2Ebit_2EBIT,V0b),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b))) ) ).
fof(conj_thm_2Ebit_2EBIT__TWO__POW,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)))
<=> V1m = V0n ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__B__NEQ,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( V0a != V1b
=> ~ p(ap(ap(c_2Ebit_2EBIT,V0a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__COMP__THM2,axiom,
! [V0h1] :
( mem(V0h1,ty_2Enum_2Enum)
=> ! [V1l1] :
( mem(V1l1,ty_2Enum_2Enum)
=> ! [V2h2] :
( mem(V2h2,ty_2Enum_2Enum)
=> ! [V3l2] :
( mem(V3l2,ty_2Enum_2Enum)
=> ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V2h2),V3l2),ap(ap(ap(c_2Ebit_2EBITS,V0h1),V1l1),V4n)) = ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2EMIN,V0h1),ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1))),ap(ap(c_2Earithmetic_2E_2B,V3l2),V1l1)),V4n) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ENOT__MOD2__LEM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) != c_2Enum_2E0
<=> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ).
fof(conj_thm_2Ebit_2ENOT__MOD2__LEM2,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) != ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
<=> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Ebit_2EODD__MOD2__LEM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EODD,V0n))
<=> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ).
fof(conj_thm_2Ebit_2EDIV__MULT__THM,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)) = ap(ap(c_2Earithmetic_2E_2D,V1n),ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))) ) ) ).
fof(conj_thm_2Ebit_2EDIV__MULT__THM2,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) ) ).
fof(conj_thm_2Ebit_2ELESS__EQ__EXP__MULT,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b))
=> ? [V2p] :
( mem(V2p,ty_2Enum_2Enum)
& ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b) = ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)) ) ) ) ) ).
fof(conj_thm_2Ebit_2ESLICE__THM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2ESLICE,V1h),V2l),V0n) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2EBITS,V1h),V2l),V0n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2l)) ) ) ) ).
fof(conj_thm_2Ebit_2ESLICELT__THM,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__SLICE__THM,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__SLICE__THM2,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1h2] :
( mem(V1h2,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0h),V1h2))
=> ap(ap(ap(c_2Ebit_2EBITS,V1h2),V2l),ap(ap(ap(c_2Ebit_2ESLICE,V0h),V2l),V3n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V2l),V3n) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ESLICE__ZERO__THM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2ESLICE,V1h),c_2Enum_2E0),V0n) = ap(ap(ap(c_2Ebit_2EBITS,V1h),c_2Enum_2E0),V0n) ) ) ).
fof(conj_thm_2Ebit_2EMOD__2EXP__MONO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V1h))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMOD,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2l))),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V1h))))) ) ) ) ) ).
fof(conj_thm_2Ebit_2ESLICE__COMP__THM,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1m)),V0h))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V1m)) )
=> ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2ESLICE,V0h),ap(c_2Enum_2ESUC,V1m)),V3n)),ap(ap(ap(c_2Ebit_2ESLICE,V1m),V2l),V3n)) = ap(ap(ap(c_2Ebit_2ESLICE,V0h),V2l),V3n) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ESLICE__COMP__RWT,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1m_27] :
( mem(V1m_27,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3l] :
( mem(V3l,ty_2Enum_2Enum)
=> ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V3l),V2m))
& V1m_27 = ap(ap(c_2Earithmetic_2E_2B,V2m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V0h)) )
=> ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1m_27),V4n)),ap(ap(ap(c_2Ebit_2ESLICE,V2m),V3l),V4n)) = ap(ap(ap(c_2Ebit_2ESLICE,V0h),V3l),V4n) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ESLICE__ZERO,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0h),V1l))
=> ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n) = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Ebit_2ESLICE__ZERO2,axiom,
! [V0l] :
( mem(V0l,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2ESLICE,V1h),V0l),c_2Enum_2E0) = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Ebit_2EBITS__SUM,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ! [V3b] :
( mem(V3b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3b),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)))
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))),V3b)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__SUM2,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ! [V3b] :
( mem(V3b,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))),V3b)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V3b) ) ) ) ) ).
fof(conj_thm_2Ebit_2ESLICE__COMP__THM2,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ! [V3y] :
( mem(V3y,ty_2Enum_2Enum)
=> ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0h),V2x))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V3y),V1l)) )
=> ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),ap(ap(ap(c_2Ebit_2ESLICE,V2x),V3y),V4n)) = ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V4n) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__SUM3,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V2b))) = ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__MUL,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V2b))) = ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,V1a),V2b)) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__COMP__THM3,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1m)),V0h))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V1m)) )
=> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2EBITS,V0h),ap(c_2Enum_2ESUC,V1m)),V3n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V1m)),V2l)))),ap(ap(ap(c_2Ebit_2EBITS,V1m),V2l),V3n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V2l),V3n) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ENOT__BIT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Ebit_2EBIT,V0n),V1a))
<=> ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Ebit_2ENOT__BITS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ( ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) != c_2Enum_2E0
<=> ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ).
fof(conj_thm_2Ebit_2ENOT__BITS2,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ( ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) != ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
<=> ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SLICE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Ebit_2EBIT,V0n),V1a))
<=> p(ap(ap(c_2Ebit_2EBIT,V0n),V2b)) )
<=> ap(ap(ap(c_2Ebit_2ESLICE,V0n),V0n),V1a) = ap(ap(ap(c_2Ebit_2ESLICE,V0n),V0n),V2b) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SLICE__LEM,axiom,
! [V0y] :
( mem(V0y,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V1x),V2n)),ap(ap(c_2Earithmetic_2E_2B,V1x),V0y)) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2ESLICE,V1x),V1x),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0y)) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SLICE__THM,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V0x),V1n)),V0x) = ap(ap(ap(c_2Ebit_2ESLICE,V0x),V0x),V1n) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SLICE__THM2,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V0b),V1n))
<=> ap(ap(ap(c_2Ebit_2ESLICE,V0b),V0b),V1n) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SLICE__THM3,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Ebit_2EBIT,V0b),V1n))
<=> ap(ap(ap(c_2Ebit_2ESLICE,V0b),V0b),V1n) = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SLICE__THM4,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V0b),ap(ap(ap(c_2Ebit_2ESLICE,V1h),V2l),V3n)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V0b))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V0b),V1h))
& p(ap(ap(c_2Ebit_2EBIT,V0b),V3n)) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ESBIT__DIV,axiom,
! [V0b] :
( mem(V0b,bool)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1m))
=> ap(ap(c_2Ebit_2ESBIT,V0b),ap(ap(c_2Earithmetic_2E_2D,V1m),V2n)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Ebit_2ESBIT,V0b),V1m)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2n)) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__SUC,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),ap(c_2Enum_2ESUC,V0h)))
=> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0h)),V2n)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l))),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)) = ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0h)),V1l),V2n) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__SUC__THM,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0h)),V1l),V2n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0h)),V1l)),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0h)),V2n)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l))),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n))) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__BITS__THM,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ! [V3b] :
( mem(V3b,ty_2Enum_2Enum)
=> ( ! [V4x] :
( mem(V4x,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),V4x))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V4x),V0h)) )
=> ( p(ap(ap(c_2Ebit_2EBIT,V4x),V2a))
<=> p(ap(ap(c_2Ebit_2EBIT,V4x),V3b)) ) ) )
<=> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2a) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V3b) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITS__ZERO5,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2i),V0n))
=> ~ p(ap(ap(c_2Ebit_2EBIT,V2i),V1m)) ) )
=> ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1m) = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Ebit_2EBIT0__ODD,axiom,
ap(c_2Ebit_2EBIT,c_2Enum_2E0) = c_2Earithmetic_2EODD ).
fof(conj_thm_2Ebit_2EBITV__THM,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebit_2EBITV,V1n),V0b) = ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V0b),V1n)),c_2Enum_2E0) ) ) ).
fof(conj_thm_2Ebit_2EADD__BIT0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))
<=> ~ ( p(ap(ap(c_2Ebit_2EBIT,c_2Enum_2E0),V0m))
<=> p(ap(ap(c_2Ebit_2EBIT,c_2Enum_2E0),V1n)) ) ) ) ) ).
fof(conj_thm_2Ebit_2EADD__BITS__SUC,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),V1a)),ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),V2b))),ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V2b))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) ) ) ).
fof(conj_thm_2Ebit_2EADD__BIT__SUC,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V2b)))),ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V1a)),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V2b))),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V1a)),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V2b))))) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITWISE__LT__2EXP,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1op] :
( mem(V1op,arr(bool,arr(bool,bool)))
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ! [V3b] :
( mem(V3b,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V0n),V1op),V2a),V3b)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITWISE__THM,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2op] :
( mem(V2op,arr(bool,arr(bool,bool)))
=> ! [V3a] :
( mem(V3a,ty_2Enum_2Enum)
=> ! [V4b] :
( mem(V4b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n))
=> ( p(ap(ap(c_2Ebit_2EBIT,V0x),ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b)))
<=> p(ap(ap(V2op,ap(ap(c_2Ebit_2EBIT,V0x),V3a)),ap(ap(c_2Ebit_2EBIT,V0x),V4b))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITWISE__COR,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2op] :
( mem(V2op,arr(bool,arr(bool,bool)))
=> ! [V3a] :
( mem(V3a,ty_2Enum_2Enum)
=> ! [V4b] :
( mem(V4b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n))
=> ( p(ap(ap(V2op,ap(ap(c_2Ebit_2EBIT,V0x),V3a)),ap(ap(c_2Ebit_2EBIT,V0x),V4b)))
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITWISE__NOT__COR,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2op] :
( mem(V2op,arr(bool,arr(bool,bool)))
=> ! [V3a] :
( mem(V3a,ty_2Enum_2Enum)
=> ! [V4b] :
( mem(V4b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n))
=> ( ~ p(ap(ap(V2op,ap(ap(c_2Ebit_2EBIT,V0x),V3a)),ap(ap(c_2Ebit_2EBIT,V0x),V4b)))
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0 ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBITWISE__BITS,axiom,
! [V0wl] :
( mem(V0wl,ty_2Enum_2Enum)
=> ! [V1op] :
( mem(V1op,arr(bool,arr(bool,bool)))
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ! [V3b] :
( mem(V3b,ty_2Enum_2Enum)
=> ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0wl)),V1op),ap(ap(ap(c_2Ebit_2EBITS,V0wl),c_2Enum_2E0),V2a)),ap(ap(ap(c_2Ebit_2EBITS,V0wl),c_2Enum_2E0),V3b)) = ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0wl)),V1op),V2a),V3b) ) ) ) ) ).
fof(conj_thm_2Ebit_2ENOT__BIT__GT__TWOEXP,axiom,
! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0i)))
=> ~ p(ap(ap(c_2Ebit_2EBIT,V0i),V1n)) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__IMP__GE__TWOEXP,axiom,
! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V0i),V1n))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0i)),V1n)) ) ) ) ).
fof(lameq_f251,axiom,
! [V3x] : ap(f251,V3x) = k(bool,ap(c_2Ebool_2E_7E,V3x)) ).
fof(conj_thm_2Ebit_2EBITWISE__ONE__COMP__LEM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0n)),f251),V1a),V2b) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1a)) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__COMPLEMENT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V1i),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)))))
<=> ( ( ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) = c_2Enum_2E0
& V1i = V0n )
| ( ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) != c_2Enum_2E0
& p(ap(ap(c_2Eprim__rec_2E_3C,V1i),V0n))
& ~ p(ap(ap(c_2Ebit_2EBIT,V1i),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__OF__BITS__THM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ! [V3a] :
( mem(V3a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V2l),V0n)),V1h))
=> ( p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(ap(c_2Ebit_2EBITS,V1h),V2l),V3a)))
<=> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V2l),V0n)),V3a)) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SHIFT__THM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2s] :
( mem(V2s,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V0n),V2s)),ap(ap(c_2Earithmetic_2E_2A,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2s))))
<=> p(ap(ap(c_2Ebit_2EBIT,V0n),V1a)) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SHIFT__THM2,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2s] :
( mem(V2s,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2s),V0n))
=> ( p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2E_2A,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2s))))
<=> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,V0n),V2s)),V1a)) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SHIFT__THM3,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2s] :
( mem(V2s,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V2s))
=> ~ p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2E_2A,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2s)))) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__OF__BITS__THM2,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0h),ap(ap(c_2Earithmetic_2E_2B,V1l),V2x)))
=> ~ p(ap(ap(c_2Ebit_2EBIT,V2x),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V3n))) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__DIV2,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2EDIV,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))
<=> p(ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V1i)) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SHIFT__THM4,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V1i),ap(ap(c_2Earithmetic_2EDIV,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))
<=> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V1i),V0n)),V2a)) ) ) ) ) ).
fof(conj_thm_2Ebit_2EDIV__LT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) ) ) ) ) ).
fof(conj_thm_2Ebit_2EMOD__ZERO__GT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ( ( V1a != c_2Enum_2E0
& ap(ap(c_2Earithmetic_2EMOD,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) = c_2Enum_2E0 )
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),V1a)) ) ) ) ).
fof(conj_thm_2Ebit_2EDIV__GT0,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EDIV,V0a),V1b))) ) ) ) ).
fof(conj_thm_2Ebit_2EDIV__SUB1,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)),V0a))
& ap(ap(c_2Earithmetic_2EMOD,V0a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)) = c_2Enum_2E0 )
=> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EDIV,V0a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V0a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__EXP__SUB1,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V0b),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0b),V1n)) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SHIFT__THM5,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ! [V3a] :
( mem(V3a,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2i),V0n)),V1m))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) )
=> ( p(ap(ap(c_2Ebit_2EBIT,V2i),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)),ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EDIV,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EMOD,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),c_2Enum_2E0)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)))))
<=> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V2i),V0n)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)),ap(ap(c_2Earithmetic_2EMOD,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))))) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ESBIT__MULT,axiom,
! [V0b] :
( mem(V0b,bool)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Ebit_2ESBIT,V0b),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)) = ap(ap(c_2Ebit_2ESBIT,V0b),ap(ap(c_2Earithmetic_2E_2B,V2n),V1m)) ) ) ) ).
fof(conj_thm_2Ebit_2EBITWISE__EVAL,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1op] :
( mem(V1op,arr(bool,arr(bool,bool)))
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ! [V3b] :
( mem(V3b,ty_2Enum_2Enum)
=> ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0n)),V1op),V2a),V3b) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(ap(ap(c_2Ebit_2EBITWISE,V0n),V1op),ap(ap(c_2Earithmetic_2EDIV,V2a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EDIV,V3b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Ebit_2ESBIT,ap(ap(V1op,ap(c_2Earithmetic_2EODD,V2a)),ap(c_2Earithmetic_2EODD,V3b))),c_2Enum_2E0)) ) ) ) ) ).
fof(conj_thm_2Ebit_2EMOD__PLUS__RIGHT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1j] :
( mem(V1j,ty_2Enum_2Enum)
=> ! [V2k] :
( mem(V2k,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1j),ap(ap(c_2Earithmetic_2EMOD,V2k),V0n))),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1j),V2k)),V0n) ) ) ) ) ).
fof(conj_thm_2Ebit_2EMOD__PLUS__LEFT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1j] :
( mem(V1j,ty_2Enum_2Enum)
=> ! [V2k] :
( mem(V2k,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V2k),V0n)),V1j)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2k),V1j)),V0n) ) ) ) ) ).
fof(conj_thm_2Ebit_2EMOD__PLUS__1,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n) = c_2Enum_2E0
<=> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0n ) ) ) ) ).
fof(conj_thm_2Ebit_2EMOD__ADD__1,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n) != c_2Enum_2E0
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__REVERSE__THM,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n))
=> ( p(ap(ap(c_2Ebit_2EBIT,V0x),ap(ap(c_2Ebit_2EBIT__REVERSE,V1n),V2a)))
<=> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x)),V2a)) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ELOG2__LE__MONO,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x))
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),V1y))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ebit_2ELOG2,V0x)),ap(c_2Ebit_2ELOG2,V1y))) ) ) ) ) ).
fof(conj_thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2,axiom,
( ! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)),V1y))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(c_2Ebit_2ELOG2,V1y))) ) ) )
& ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ! [V3x] :
( mem(V3x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3x))
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V3x),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2y)))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ebit_2ELOG2,V3x)),V2y)) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ENOT__BIT__GT__LOG2,axiom,
! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ebit_2ELOG2,V1n)),V0i))
=> ~ p(ap(ap(c_2Ebit_2EBIT,V0i),V1n)) ) ) ) ).
fof(conj_thm_2Ebit_2ENOT__BIT__GT__BITWISE,axiom,
! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2op] :
( mem(V2op,arr(bool,arr(bool,bool)))
=> ! [V3a] :
( mem(V3a,ty_2Enum_2Enum)
=> ! [V4b] :
( mem(V4b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0i))
=> ~ p(ap(ap(c_2Ebit_2EBIT,V0i),ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b))) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2ELT__TWOEXP,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)))
<=> ( V0x = c_2Enum_2E0
| p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ebit_2ELOG2,V0x)),V1n)) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__MODIFY__THM,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,arr(bool,bool)))
=> ! [V3a] :
( mem(V3a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n))
=> ( p(ap(ap(c_2Ebit_2EBIT,V0x),ap(ap(ap(c_2Ebit_2EBIT__MODIFY,V1n),V2f),V3a)))
<=> p(ap(ap(V2f,V0x),ap(ap(c_2Ebit_2EBIT,V0x),V3a))) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__SIGN__EXTEND,axiom,
! [V0l] :
( mem(V0l,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ( V0l != c_2Enum_2E0
=> ( p(ap(ap(c_2Ebit_2EBIT,V3i),ap(ap(ap(c_2Ebit_2ESIGN__EXTEND,V0l),V1h),V2n)))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Earithmetic_2E_3C_3D,V0l),V1h)),ap(ap(c_2Eprim__rec_2E_3C,V3i),V0l))),ap(ap(c_2Ebit_2EBIT,V3i),ap(ap(c_2Earithmetic_2EMOD,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0l)))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,V3i),V1h)),ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,V0l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2n)))) ) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EBIT__LOG2,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( V0n != c_2Enum_2E0
=> p(ap(ap(c_2Ebit_2EBIT,ap(c_2Ebit_2ELOG2,V0n)),V0n)) ) ) ).
fof(conj_thm_2Ebit_2EEXISTS__BIT__IN__RANGE,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( V2n != c_2Enum_2E0
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),V2n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))) )
=> ? [V3i] :
( mem(V3i,ty_2Enum_2Enum)
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V3i))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V1b))
& p(ap(ap(c_2Ebit_2EBIT,V3i),V2n)) ) ) ) ) ) ).
fof(conj_thm_2Ebit_2EEXISTS__BIT__LT,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( V1n != c_2Enum_2E0
& p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b))) )
=> ? [V2i] :
( mem(V2i,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V2i),V0b))
& p(ap(ap(c_2Ebit_2EBIT,V2i),V1n)) ) ) ) ) ).
fof(conj_thm_2Ebit_2ELEAST__THM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1P] :
( mem(V1P,arr(ty_2Enum_2Enum,bool))
=> ( ( ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V0n))
=> ~ p(ap(V1P,V2m)) ) )
& p(ap(V1P,V0n)) )
=> ap(c_2Ewhile_2ELEAST,V1P) = V0n ) ) ) ).
%------------------------------------------------------------------------------