ITP001 Axioms: ITP109+5.ax
%------------------------------------------------------------------------------
% File : ITP109+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 : int_bitwise+2.ax [Gau20]
% : HL4109+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 65 ( 23 unt; 0 def)
% Number of atoms : 241 ( 46 equ)
% Maximal formula atoms : 37 ( 3 avg)
% Number of connectives : 179 ( 3 ~; 1 |; 12 &)
% ( 12 <=>; 151 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 89 ( 89 usr; 44 con; 0-7 aty)
% Number of variables : 181 ( 181 !; 0 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Eint__bitwise_2Ebits__bitwise,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Eint__bitwise_2Ebits__bitwise(A_27a,A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27b),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27c),A_27c),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a))))) ) ) ) ).
fof(mem_c_2Eint__bitwise_2Ebits__of__int,axiom,
mem(c_2Eint__bitwise_2Ebits__of__int,arr(ty_2Einteger_2Eint,ty_2Epair_2Eprod(ty_2Elist_2Elist(bool),bool))) ).
fof(mem_c_2Eint__bitwise_2Ebits__of__num,axiom,
mem(c_2Eint__bitwise_2Ebits__of__num,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(bool))) ).
fof(mem_c_2Eint__bitwise_2Eint__and,axiom,
mem(c_2Eint__bitwise_2Eint__and,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))) ).
fof(mem_c_2Eint__bitwise_2Eint__bit,axiom,
mem(c_2Eint__bitwise_2Eint__bit,arr(ty_2Enum_2Enum,arr(ty_2Einteger_2Eint,bool))) ).
fof(mem_c_2Eint__bitwise_2Eint__bitwise,axiom,
mem(c_2Eint__bitwise_2Eint__bitwise,arr(arr(bool,arr(bool,bool)),arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)))) ).
fof(mem_c_2Eint__bitwise_2Eint__not,axiom,
mem(c_2Eint__bitwise_2Eint__not,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)) ).
fof(mem_c_2Eint__bitwise_2Eint__of__bits,axiom,
mem(c_2Eint__bitwise_2Eint__of__bits,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(bool),bool),ty_2Einteger_2Eint)) ).
fof(mem_c_2Eint__bitwise_2Eint__or,axiom,
mem(c_2Eint__bitwise_2Eint__or,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))) ).
fof(mem_c_2Eint__bitwise_2Eint__shift__left,axiom,
mem(c_2Eint__bitwise_2Eint__shift__left,arr(ty_2Enum_2Enum,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))) ).
fof(mem_c_2Eint__bitwise_2Eint__shift__right,axiom,
mem(c_2Eint__bitwise_2Eint__shift__right,arr(ty_2Enum_2Enum,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))) ).
fof(mem_c_2Eint__bitwise_2Eint__xor,axiom,
mem(c_2Eint__bitwise_2Eint__xor,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))) ).
fof(mem_c_2Eint__bitwise_2Enum__of__bits,axiom,
mem(c_2Eint__bitwise_2Enum__of__bits,arr(ty_2Elist_2Elist(bool),ty_2Enum_2Enum)) ).
fof(ax_thm_2Eint__bitwise_2Eint__not__def,axiom,
! [V0i] :
( mem(V0i,ty_2Einteger_2Eint)
=> ap(c_2Eint__bitwise_2Eint__not,V0i) = ap(ap(c_2Einteger_2Eint__sub,ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),V0i)),ap(c_2Einteger_2Eint__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__not__not,axiom,
! [V0i] :
( mem(V0i,ty_2Einteger_2Eint)
=> ap(c_2Eint__bitwise_2Eint__not,ap(c_2Eint__bitwise_2Eint__not,V0i)) = V0i ) ).
fof(ax_thm_2Eint__bitwise_2Eint__bit__def,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V0b),V1i))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Einteger_2Eint__lt,V1i),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(c_2Ebool_2E_7E,ap(ap(c_2Ebit_2EBIT,V0b),ap(c_2Einteger_2ENum,ap(c_2Eint__bitwise_2Eint__not,V1i))))),ap(ap(c_2Ebit_2EBIT,V0b),ap(c_2Einteger_2ENum,V1i)))) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__bit__not,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V0b),ap(c_2Eint__bitwise_2Eint__not,V1i)))
<=> ~ p(ap(ap(c_2Eint__bitwise_2Eint__bit,V0b),V1i)) ) ) ) ).
fof(lameq_f2674,axiom,
! [V0R] :
( mem(V0R,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ! [V1n] : ap(f2674(V0R),V1n) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0))),ap(ap(V0R,ap(ap(c_2Earithmetic_2EDIV,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1n)) ) ).
fof(lameq_f2675,axiom,
! [V0R] : ap(f2675,V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Enum_2Enum),V0R)),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f2674(V0R))) ).
fof(lameq_f2676,axiom,
! [V2bits__of__num] :
( mem(V2bits__of__num,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)))
=> ! [V3a] : ap(f2676(V2bits__of__num),V3a) = ap(c_2Ecombin_2EI(ty_2Elist_2Elist(bool)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(bool)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3a),c_2Enum_2E0)),c_2Elist_2ENIL(bool)),ap(ap(c_2Elist_2ECONS(bool),ap(c_2Earithmetic_2EODD,V3a)),ap(V2bits__of__num,ap(ap(c_2Earithmetic_2EDIV,V3a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))) ) ).
fof(lameq_f2677,axiom,
! [V2bits__of__num] : ap(f2677,V2bits__of__num) = f2676(V2bits__of__num) ).
fof(ax_thm_2Eint__bitwise_2Ebits__of__num__primitive__def,axiom,
c_2Eint__bitwise_2Ebits__of__num = ap(ap(c_2Erelation_2EWFREC(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)),ap(c_2Emin_2E_40(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))),f2675)),f2677) ).
fof(conj_thm_2Eint__bitwise_2Ebits__of__num__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( V1n != c_2Enum_2E0
=> p(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) )
=> p(ap(V0P,V1n)) ) )
=> ! [V2v] :
( mem(V2v,ty_2Enum_2Enum)
=> p(ap(V0P,V2v)) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Ebits__of__num__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Eint__bitwise_2Ebits__of__num,V0n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(bool)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0n),c_2Enum_2E0)),c_2Elist_2ENIL(bool)),ap(ap(c_2Elist_2ECONS(bool),ap(c_2Earithmetic_2EODD,V0n)),ap(c_2Eint__bitwise_2Ebits__of__num,ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ).
fof(ax_thm_2Eint__bitwise_2Ebits__of__int__def,axiom,
! [V0i] :
( mem(V0i,ty_2Einteger_2Eint)
=> ap(c_2Eint__bitwise_2Ebits__of__int,V0i) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Elist_2Elist(bool),bool)),ap(ap(c_2Einteger_2Eint__lt,V0i),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(bool),bool),ap(ap(c_2Elist_2EMAP(bool,bool),c_2Ebool_2E_7E),ap(c_2Eint__bitwise_2Ebits__of__num,ap(c_2Einteger_2ENum,ap(c_2Eint__bitwise_2Eint__not,V0i))))),c_2Ebool_2ET)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(bool),bool),ap(c_2Eint__bitwise_2Ebits__of__num,ap(c_2Einteger_2ENum,V0i))),c_2Ebool_2EF)) ) ).
fof(lameq_f2678,axiom,
! [V0R] :
( mem(V0R,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),bool)))
=> ! [V1bs] : ap(f2678(V0R),V1bs) = ap(ap(V0R,V1bs),ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2EF),V1bs)) ) ).
fof(lameq_f2679,axiom,
! [V0R] :
( mem(V0R,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),bool)))
=> ! [V2bs] : ap(f2679(V0R),V2bs) = ap(ap(V0R,V2bs),ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2ET),V2bs)) ) ).
fof(lameq_f2680,axiom,
! [V0R] : ap(f2680,V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Elist_2Elist(bool)),V0R)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(ty_2Elist_2Elist(bool)),f2678(V0R))),ap(c_2Ebool_2E_21(ty_2Elist_2Elist(bool)),f2679(V0R)))) ).
fof(lameq_f2681,axiom,
! [V5v] :
( mem(V5v,bool)
=> ! [V3num__of__bits] :
( mem(V3num__of__bits,arr(ty_2Elist_2Elist(bool),ty_2Enum_2Enum))
=> ! [V6bs] : ap(f2681(V5v,V3num__of__bits),V6bs) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V5v),ap(c_2Ecombin_2EI(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(V3num__of__bits,V6bs))))),ap(c_2Ecombin_2EI(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(V3num__of__bits,V6bs)))) ) ) ).
fof(lameq_f2682,axiom,
! [V3num__of__bits] :
( mem(V3num__of__bits,arr(ty_2Elist_2Elist(bool),ty_2Enum_2Enum))
=> ! [V5v] : ap(f2682(V3num__of__bits),V5v) = f2681(V5v,V3num__of__bits) ) ).
fof(lameq_f2683,axiom,
! [V3num__of__bits] :
( mem(V3num__of__bits,arr(ty_2Elist_2Elist(bool),ty_2Enum_2Enum))
=> ! [V4a] : ap(f2683(V3num__of__bits),V4a) = ap(ap(ap(c_2Elist_2Elist__CASE(bool,ty_2Enum_2Enum),V4a),ap(c_2Ecombin_2EI(ty_2Enum_2Enum),c_2Enum_2E0)),f2682(V3num__of__bits)) ) ).
fof(lameq_f2684,axiom,
! [V3num__of__bits] : ap(f2684,V3num__of__bits) = f2683(V3num__of__bits) ).
fof(ax_thm_2Eint__bitwise_2Enum__of__bits__primitive__def,axiom,
c_2Eint__bitwise_2Enum__of__bits = ap(ap(c_2Erelation_2EWFREC(ty_2Elist_2Elist(bool),ty_2Enum_2Enum),ap(c_2Emin_2E_40(arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),bool))),f2680)),f2684) ).
fof(conj_thm_2Eint__bitwise_2Enum__of__bits__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(bool),bool))
=> ( ( p(ap(V0P,c_2Elist_2ENIL(bool)))
& ! [V1bs] :
( mem(V1bs,ty_2Elist_2Elist(bool))
=> ( p(ap(V0P,V1bs))
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2EF),V1bs))) ) )
& ! [V2bs] :
( mem(V2bs,ty_2Elist_2Elist(bool))
=> ( p(ap(V0P,V2bs))
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2ET),V2bs))) ) ) )
=> ! [V3v] :
( mem(V3v,ty_2Elist_2Elist(bool))
=> p(ap(V0P,V3v)) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Enum__of__bits__def,axiom,
( ap(c_2Eint__bitwise_2Enum__of__bits,c_2Elist_2ENIL(bool)) = c_2Enum_2E0
& ! [V0bs] :
( mem(V0bs,ty_2Elist_2Elist(bool))
=> ap(c_2Eint__bitwise_2Enum__of__bits,ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2EF),V0bs)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eint__bitwise_2Enum__of__bits,V0bs)) )
& ! [V1bs] :
( mem(V1bs,ty_2Elist_2Elist(bool))
=> ap(c_2Eint__bitwise_2Enum__of__bits,ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2ET),V1bs)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eint__bitwise_2Enum__of__bits,V1bs))) ) ) ).
fof(ax_thm_2Eint__bitwise_2Eint__of__bits__def,axiom,
! [V0bs] :
( mem(V0bs,ty_2Elist_2Elist(bool))
=> ! [V1rest] :
( mem(V1rest,bool)
=> ap(c_2Eint__bitwise_2Eint__of__bits,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(bool),bool),V0bs),V1rest)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Einteger_2Eint),V1rest),ap(c_2Eint__bitwise_2Eint__not,ap(c_2Einteger_2Eint__of__num,ap(c_2Eint__bitwise_2Enum__of__bits,ap(ap(c_2Elist_2EMAP(bool,bool),c_2Ebool_2E_7E),V0bs))))),ap(c_2Einteger_2Eint__of__num,ap(c_2Eint__bitwise_2Enum__of__bits,V0bs))) ) ) ).
fof(conj_thm_2Eint__bitwise_2Ebits__bitwise__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0P] :
( mem(V0P,arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27b),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27c),A_27c),bool))))
=> ( ( ! [V1f] :
( mem(V1f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V2r1] :
( mem(V2r1,A_27b)
=> ! [V3r2] :
( mem(V3r2,A_27c)
=> p(ap(ap(ap(V0P,V1f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),c_2Elist_2ENIL(A_27b)),V2r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),c_2Elist_2ENIL(A_27c)),V3r2))) ) ) )
& ! [V4f] :
( mem(V4f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V5r1] :
( mem(V5r1,A_27b)
=> ! [V6b2] :
( mem(V6b2,A_27c)
=> ! [V7bs2] :
( mem(V7bs2,ty_2Elist_2Elist(A_27c))
=> ! [V8r2] :
( mem(V8r2,A_27c)
=> ( p(ap(ap(ap(V0P,V4f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),c_2Elist_2ENIL(A_27b)),V5r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),V7bs2),V8r2)))
=> p(ap(ap(ap(V0P,V4f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),c_2Elist_2ENIL(A_27b)),V5r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),ap(ap(c_2Elist_2ECONS(A_27c),V6b2),V7bs2)),V8r2))) ) ) ) ) ) )
& ! [V9f] :
( mem(V9f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V10b1] :
( mem(V10b1,A_27b)
=> ! [V11bs1] :
( mem(V11bs1,ty_2Elist_2Elist(A_27b))
=> ! [V12r1] :
( mem(V12r1,A_27b)
=> ! [V13r2] :
( mem(V13r2,A_27c)
=> ( p(ap(ap(ap(V0P,V9f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),V11bs1),V12r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),c_2Elist_2ENIL(A_27c)),V13r2)))
=> p(ap(ap(ap(V0P,V9f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V10b1),V11bs1)),V12r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),c_2Elist_2ENIL(A_27c)),V13r2))) ) ) ) ) ) )
& ! [V14f] :
( mem(V14f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V15b1] :
( mem(V15b1,A_27b)
=> ! [V16bs1] :
( mem(V16bs1,ty_2Elist_2Elist(A_27b))
=> ! [V17r1] :
( mem(V17r1,A_27b)
=> ! [V18b2] :
( mem(V18b2,A_27c)
=> ! [V19bs2] :
( mem(V19bs2,ty_2Elist_2Elist(A_27c))
=> ! [V20r2] :
( mem(V20r2,A_27c)
=> ( p(ap(ap(ap(V0P,V14f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),V16bs1),V17r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),V19bs2),V20r2)))
=> p(ap(ap(ap(V0P,V14f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V15b1),V16bs1)),V17r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),ap(ap(c_2Elist_2ECONS(A_27c),V18b2),V19bs2)),V20r2))) ) ) ) ) ) ) ) ) )
=> ! [V21v] :
( mem(V21v,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V22v1] :
( mem(V22v1,ty_2Elist_2Elist(A_27b))
=> ! [V23v2] :
( mem(V23v2,A_27b)
=> ! [V24v3] :
( mem(V24v3,ty_2Elist_2Elist(A_27c))
=> ! [V25v4] :
( mem(V25v4,A_27c)
=> p(ap(ap(ap(V0P,V21v),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),V22v1),V23v2)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),V24v3),V25v4))) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f2685,axiom,
! [A_27c,A_27b,A_27a,V4r1] :
( mem(V4r1,A_27b)
=> ! [V5f] :
( mem(V5f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V7b2] :
( mem(V7b2,A_27c)
=> ! [V8bs] :
( mem(V8bs,ty_2Elist_2Elist(A_27a))
=> ! [V9r] : ap(f2685(A_27c,A_27b,A_27a,V4r1,V5f,V7b2,V8bs),V9r) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),A_27a),ap(ap(c_2Elist_2ECONS(A_27a),ap(ap(V5f,V4r1),V7b2)),V8bs)),V9r) ) ) ) ) ).
fof(lameq_f2686,axiom,
! [A_27b,A_27c,A_27a,V4r1] :
( mem(V4r1,A_27b)
=> ! [V5f] :
( mem(V5f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V7b2] :
( mem(V7b2,A_27c)
=> ! [V8bs] : ap(f2686(A_27b,A_27c,A_27a,V4r1,V5f,V7b2),V8bs) = f2685(A_27c,A_27b,A_27a,V4r1,V5f,V7b2,V8bs) ) ) ) ).
fof(lameq_f2687,axiom,
! [A_27c,A_27b,A_27a,V14b1] :
( mem(V14b1,A_27b)
=> ! [V12f] :
( mem(V12f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V10r2] :
( mem(V10r2,A_27c)
=> ! [V15bs] :
( mem(V15bs,ty_2Elist_2Elist(A_27a))
=> ! [V16r] : ap(f2687(A_27c,A_27b,A_27a,V14b1,V12f,V10r2,V15bs),V16r) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),A_27a),ap(ap(c_2Elist_2ECONS(A_27a),ap(ap(V12f,V14b1),V10r2)),V15bs)),V16r) ) ) ) ) ).
fof(lameq_f2688,axiom,
! [A_27b,A_27c,A_27a,V14b1] :
( mem(V14b1,A_27b)
=> ! [V12f] :
( mem(V12f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V10r2] :
( mem(V10r2,A_27c)
=> ! [V15bs] : ap(f2688(A_27b,A_27c,A_27a,V14b1,V12f,V10r2),V15bs) = f2687(A_27c,A_27b,A_27a,V14b1,V12f,V10r2,V15bs) ) ) ) ).
fof(lameq_f2689,axiom,
! [A_27c,A_27b,A_27a,V23b1] :
( mem(V23b1,A_27b)
=> ! [V19f] :
( mem(V19f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V22b2] :
( mem(V22b2,A_27c)
=> ! [V24bs] :
( mem(V24bs,ty_2Elist_2Elist(A_27a))
=> ! [V25r] : ap(f2689(A_27c,A_27b,A_27a,V23b1,V19f,V22b2,V24bs),V25r) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),A_27a),ap(ap(c_2Elist_2ECONS(A_27a),ap(ap(V19f,V23b1),V22b2)),V24bs)),V25r) ) ) ) ) ).
fof(lameq_f2690,axiom,
! [A_27b,A_27c,A_27a,V23b1] :
( mem(V23b1,A_27b)
=> ! [V19f] :
( mem(V19f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V22b2] :
( mem(V22b2,A_27c)
=> ! [V24bs] : ap(f2690(A_27b,A_27c,A_27a,V23b1,V19f,V22b2),V24bs) = f2689(A_27c,A_27b,A_27a,V23b1,V19f,V22b2,V24bs) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Ebits__bitwise__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ( ! [V0r2] :
( mem(V0r2,A_27c)
=> ! [V1r1] :
( mem(V1r1,A_27b)
=> ! [V2f] :
( mem(V2f,arr(A_27b,arr(A_27c,A_27a)))
=> ap(ap(ap(c_2Eint__bitwise_2Ebits__bitwise(A_27a,A_27b,A_27c),V2f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),c_2Elist_2ENIL(A_27b)),V1r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),c_2Elist_2ENIL(A_27c)),V0r2)) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),A_27a),c_2Elist_2ENIL(A_27a)),ap(ap(V2f,V1r1),V0r2)) ) ) )
& ! [V3r2] :
( mem(V3r2,A_27c)
=> ! [V4r1] :
( mem(V4r1,A_27b)
=> ! [V5f] :
( mem(V5f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V6bs2] :
( mem(V6bs2,ty_2Elist_2Elist(A_27c))
=> ! [V7b2] :
( mem(V7b2,A_27c)
=> ap(ap(ap(c_2Eint__bitwise_2Ebits__bitwise(A_27a,A_27b,A_27c),V5f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),c_2Elist_2ENIL(A_27b)),V4r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),ap(ap(c_2Elist_2ECONS(A_27c),V7b2),V6bs2)),V3r2)) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a)),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(A_27a),A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a)),f2686(A_27b,A_27c,A_27a,V4r1,V5f,V7b2))),ap(ap(ap(c_2Eint__bitwise_2Ebits__bitwise(A_27a,A_27b,A_27c),V5f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),c_2Elist_2ENIL(A_27b)),V4r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),V6bs2),V3r2))) ) ) ) ) )
& ! [V10r2] :
( mem(V10r2,A_27c)
=> ! [V11r1] :
( mem(V11r1,A_27b)
=> ! [V12f] :
( mem(V12f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V13bs1] :
( mem(V13bs1,ty_2Elist_2Elist(A_27b))
=> ! [V14b1] :
( mem(V14b1,A_27b)
=> ap(ap(ap(c_2Eint__bitwise_2Ebits__bitwise(A_27a,A_27b,A_27c),V12f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V14b1),V13bs1)),V11r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),c_2Elist_2ENIL(A_27c)),V10r2)) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a)),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(A_27a),A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a)),f2688(A_27b,A_27c,A_27a,V14b1,V12f,V10r2))),ap(ap(ap(c_2Eint__bitwise_2Ebits__bitwise(A_27a,A_27b,A_27c),V12f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),V13bs1),V11r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),c_2Elist_2ENIL(A_27c)),V10r2))) ) ) ) ) )
& ! [V17r2] :
( mem(V17r2,A_27c)
=> ! [V18r1] :
( mem(V18r1,A_27b)
=> ! [V19f] :
( mem(V19f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V20bs2] :
( mem(V20bs2,ty_2Elist_2Elist(A_27c))
=> ! [V21bs1] :
( mem(V21bs1,ty_2Elist_2Elist(A_27b))
=> ! [V22b2] :
( mem(V22b2,A_27c)
=> ! [V23b1] :
( mem(V23b1,A_27b)
=> ap(ap(ap(c_2Eint__bitwise_2Ebits__bitwise(A_27a,A_27b,A_27c),V19f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V23b1),V21bs1)),V18r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),ap(ap(c_2Elist_2ECONS(A_27c),V22b2),V20bs2)),V17r2)) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a)),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(A_27a),A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),A_27a)),f2690(A_27b,A_27c,A_27a,V23b1,V19f,V22b2))),ap(ap(ap(c_2Eint__bitwise_2Ebits__bitwise(A_27a,A_27b,A_27c),V19f),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),A_27b),V21bs1),V18r1)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),A_27c),V20bs2),V17r2))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Eint__bitwise_2Eint__bitwise__def,axiom,
! [V0f] :
( mem(V0f,arr(bool,arr(bool,bool)))
=> ! [V1i] :
( mem(V1i,ty_2Einteger_2Eint)
=> ! [V2j] :
( mem(V2j,ty_2Einteger_2Eint)
=> ap(ap(ap(c_2Eint__bitwise_2Eint__bitwise,V0f),V1i),V2j) = ap(c_2Eint__bitwise_2Eint__of__bits,ap(ap(ap(c_2Eint__bitwise_2Ebits__bitwise(bool,bool,bool),V0f),ap(c_2Eint__bitwise_2Ebits__of__int,V1i)),ap(c_2Eint__bitwise_2Ebits__of__int,V2j))) ) ) ) ).
fof(ax_thm_2Eint__bitwise_2Eint__and__def,axiom,
c_2Eint__bitwise_2Eint__and = ap(c_2Eint__bitwise_2Eint__bitwise,c_2Ebool_2E_2F_5C) ).
fof(ax_thm_2Eint__bitwise_2Eint__or__def,axiom,
c_2Eint__bitwise_2Eint__or = ap(c_2Eint__bitwise_2Eint__bitwise,c_2Ebool_2E_5C_2F) ).
fof(ax_thm_2Eint__bitwise_2Eint__xor__def,axiom,
c_2Eint__bitwise_2Eint__xor = ap(c_2Eint__bitwise_2Eint__bitwise,f2171) ).
fof(lameq_f2691,axiom,
! [V1y] : ap(f2691,V1y) = ap(c_2Ebool_2E_7E,V1y) ).
fof(conj_thm_2Eint__bitwise_2Eint__not,axiom,
c_2Eint__bitwise_2Eint__not = ap(ap(c_2Eint__bitwise_2Eint__bitwise,k(bool,f2691)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) ).
fof(lameq_f2692,axiom,
! [V2bs] :
( mem(V2bs,ty_2Elist_2Elist(bool))
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V3r] : ap(f2692(V2bs,V0n),V3r) = ap(c_2Eint__bitwise_2Eint__of__bits,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(bool),bool),ap(ap(c_2Elist_2EAPPEND(bool),ap(ap(c_2Elist_2EGENLIST(bool),ap(c_2Ecombin_2EK(bool,ty_2Enum_2Enum),c_2Ebool_2EF)),V0n)),V2bs)),V3r)) ) ) ).
fof(lameq_f2693,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V2bs] : ap(f2693(V0n),V2bs) = f2692(V2bs,V0n) ) ).
fof(ax_thm_2Eint__bitwise_2Eint__shift__left__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Einteger_2Eint)
=> ap(ap(c_2Eint__bitwise_2Eint__shift__left,V0n),V1i) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(bool),bool),ty_2Einteger_2Eint),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(bool),bool,ty_2Einteger_2Eint),f2693(V0n))),ap(c_2Eint__bitwise_2Ebits__of__int,V1i)) ) ) ).
fof(lameq_f2694,axiom,
! [V2bs] :
( mem(V2bs,ty_2Elist_2Elist(bool))
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V3r] : ap(f2694(V2bs,V0n),V3r) = ap(c_2Eint__bitwise_2Eint__of__bits,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(bool),bool),ap(ap(c_2Elist_2EDROP(bool),V0n),V2bs)),V3r)) ) ) ).
fof(lameq_f2695,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V2bs] : ap(f2695(V0n),V2bs) = f2694(V2bs,V0n) ) ).
fof(ax_thm_2Eint__bitwise_2Eint__shift__right__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Einteger_2Eint)
=> ap(ap(c_2Eint__bitwise_2Eint__shift__right,V0n),V1i) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(bool),bool),ty_2Einteger_2Eint),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(bool),bool,ty_2Einteger_2Eint),f2695(V0n))),ap(c_2Eint__bitwise_2Ebits__of__int,V1i)) ) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__bit__int__of__bits,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Epair_2Eprod(ty_2Elist_2Elist(bool),bool))
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V0n),ap(c_2Eint__bitwise_2Eint__of__bits,V1b)))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(bool),ap(c_2Epair_2EFST(ty_2Elist_2Elist(bool),bool),V1b)))),ap(ap(c_2Elist_2EEL(bool),V0n),ap(c_2Epair_2EFST(ty_2Elist_2Elist(bool),bool),V1b))),ap(c_2Epair_2ESND(ty_2Elist_2Elist(bool),bool),V1b))) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__of__bits__bits__of__int,axiom,
! [V0i] :
( mem(V0i,ty_2Einteger_2Eint)
=> ap(c_2Eint__bitwise_2Eint__of__bits,ap(c_2Eint__bitwise_2Ebits__of__int,V0i)) = V0i ) ).
fof(conj_thm_2Eint__bitwise_2Eint__bit__bitwise,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(bool,arr(bool,bool)))
=> ! [V2i] :
( mem(V2i,ty_2Einteger_2Eint)
=> ! [V3j] :
( mem(V3j,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V0n),ap(ap(ap(c_2Eint__bitwise_2Eint__bitwise,V1f),V2i),V3j)))
<=> p(ap(ap(V1f,ap(ap(c_2Eint__bitwise_2Eint__bit,V0n),V2i)),ap(ap(c_2Eint__bitwise_2Eint__bit,V0n),V3j))) ) ) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__bit__and,axiom,
! [V0j] :
( mem(V0j,ty_2Einteger_2Eint)
=> ! [V1i] :
( mem(V1i,ty_2Einteger_2Eint)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),ap(ap(c_2Eint__bitwise_2Eint__and,V1i),V0j)))
<=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),V1i))
& p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),V0j)) ) ) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__bit__or,axiom,
! [V0j] :
( mem(V0j,ty_2Einteger_2Eint)
=> ! [V1i] :
( mem(V1i,ty_2Einteger_2Eint)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),ap(ap(c_2Eint__bitwise_2Eint__or,V1i),V0j)))
<=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),V1i))
| p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),V0j)) ) ) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__bit__xor,axiom,
! [V0j] :
( mem(V0j,ty_2Einteger_2Eint)
=> ! [V1i] :
( mem(V1i,ty_2Einteger_2Eint)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),ap(ap(c_2Eint__bitwise_2Eint__xor,V1i),V0j)))
<=> ~ ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),V1i))
<=> p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),V0j)) ) ) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__bit__equiv,axiom,
! [V0i] :
( mem(V0i,ty_2Einteger_2Eint)
=> ! [V1j] :
( mem(V1j,ty_2Einteger_2Eint)
=> ( V0i = V1j
<=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),V0i))
<=> p(ap(ap(c_2Eint__bitwise_2Eint__bit,V2n),V1j)) ) ) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__bit__shift__left,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2i] :
( mem(V2i,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V0b),ap(ap(c_2Eint__bitwise_2Eint__shift__left,V1n),V2i)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0b))
& p(ap(ap(c_2Eint__bitwise_2Eint__bit,ap(ap(c_2Earithmetic_2E_2D,V0b),V1n)),V2i)) ) ) ) ) ) ).
fof(conj_thm_2Eint__bitwise_2Eint__bit__shift__right,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2i] :
( mem(V2i,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Eint__bitwise_2Eint__bit,V0b),ap(ap(c_2Eint__bitwise_2Eint__shift__right,V1n),V2i)))
<=> p(ap(ap(c_2Eint__bitwise_2Eint__bit,ap(ap(c_2Earithmetic_2E_2B,V0b),V1n)),V2i)) ) ) ) ) ).
%------------------------------------------------------------------------------