ITP001 Axioms: ITP016+5.ax
%------------------------------------------------------------------------------
% File : ITP016+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 : arithmetic+2.ax [Gau20]
% : HL4016+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 446 ( 35 unt; 0 def)
% Number of atoms : 2057 ( 358 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1647 ( 36 ~; 53 |; 201 &)
% ( 176 <=>;1181 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 67 ( 67 usr; 34 con; 0-4 aty)
% Number of variables : 1065 (1019 !; 46 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Earithmetic_2E_2A,axiom,
mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2E_2B,axiom,
mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2E_2D,axiom,
mem(c_2Earithmetic_2E_2D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2E_3C_3D,axiom,
mem(c_2Earithmetic_2E_3C_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
fof(mem_c_2Earithmetic_2E_3E,axiom,
mem(c_2Earithmetic_2E_3E,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
fof(mem_c_2Earithmetic_2E_3E_3D,axiom,
mem(c_2Earithmetic_2E_3E_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
fof(mem_c_2Earithmetic_2EABS__DIFF,axiom,
mem(c_2Earithmetic_2EABS__DIFF,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2EBIT1,axiom,
mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2EBIT2,axiom,
mem(c_2Earithmetic_2EBIT2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2EDIV,axiom,
mem(c_2Earithmetic_2EDIV,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2EDIV2,axiom,
mem(c_2Earithmetic_2EDIV2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2EDIVMOD,axiom,
mem(c_2Earithmetic_2EDIVMOD,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2EEVEN,axiom,
mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool)) ).
fof(mem_c_2Earithmetic_2EEXP,axiom,
mem(c_2Earithmetic_2EEXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2EFACT,axiom,
mem(c_2Earithmetic_2EFACT,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2EFUNPOW,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Earithmetic_2EFUNPOW(A_27a),arr(arr(A_27a,A_27a),arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))) ) ).
fof(mem_c_2Earithmetic_2EMAX,axiom,
mem(c_2Earithmetic_2EMAX,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2EMIN,axiom,
mem(c_2Earithmetic_2EMIN,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2EMOD,axiom,
mem(c_2Earithmetic_2EMOD,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2EMODEQ,axiom,
mem(c_2Earithmetic_2EMODEQ,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))) ).
fof(mem_c_2Earithmetic_2ENRC,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Earithmetic_2ENRC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Enum_2Enum,arr(A_27a,arr(A_27a,bool))))) ) ).
fof(mem_c_2Earithmetic_2ENUMERAL,axiom,
mem(c_2Earithmetic_2ENUMERAL,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2EODD,axiom,
mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool)) ).
fof(mem_c_2Earithmetic_2EZERO,axiom,
mem(c_2Earithmetic_2EZERO,ty_2Enum_2Enum) ).
fof(mem_c_2Earithmetic_2Efindq,axiom,
mem(c_2Earithmetic_2Efindq,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2Enat__elim____magic,axiom,
mem(c_2Earithmetic_2Enat__elim____magic,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2Enum__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Earithmetic_2Enum__CASE(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,A_27a),A_27a)))) ) ).
fof(ax_thm_2Earithmetic_2EADD,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0n) = V0n )
& ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V1m)),V2n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)) ) ) ) ).
fof(ax_thm_2Earithmetic_2ENUMERAL__DEF,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ap(c_2Earithmetic_2ENUMERAL,V0x) = V0x ) ).
fof(ax_thm_2Earithmetic_2EALT__ZERO,axiom,
c_2Earithmetic_2EZERO = c_2Enum_2E0 ).
fof(ax_thm_2Earithmetic_2EBIT1,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Earithmetic_2EBIT1,V0n) = ap(ap(c_2Earithmetic_2E_2B,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Enum_2ESUC,c_2Enum_2E0))) ) ).
fof(ax_thm_2Earithmetic_2EBIT2,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Earithmetic_2EBIT2,V0n) = ap(ap(c_2Earithmetic_2E_2B,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0)))) ) ).
fof(ax_thm_2Earithmetic_2Enat__elim____magic,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Earithmetic_2Enat__elim____magic,V0n) = V0n ) ).
fof(ax_thm_2Earithmetic_2ESUB,axiom,
( ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V0m) = c_2Enum_2E0 )
& ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V1m)),V2n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1m),V2n)),c_2Enum_2E0),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2D,V1m),V2n))) ) ) ) ).
fof(ax_thm_2Earithmetic_2EMULT,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0n) = c_2Enum_2E0 )
& ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V1m)),V2n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1m),V2n)),V2n) ) ) ) ).
fof(ax_thm_2Earithmetic_2EEXP,axiom,
( ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,V0m),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) )
& ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,V1m),ap(c_2Enum_2ESUC,V2n)) = ap(ap(c_2Earithmetic_2E_2A,V1m),ap(ap(c_2Earithmetic_2EEXP,V1m),V2n)) ) ) ) ).
fof(ax_thm_2Earithmetic_2EGREATER__DEF,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) ) ) ) ).
fof(ax_thm_2Earithmetic_2ELESS__OR__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
| V0m = V1n ) ) ) ) ).
fof(ax_thm_2Earithmetic_2EGREATER__OR__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),V1n))
<=> ( p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n))
| V0m = V1n ) ) ) ) ).
fof(ax_thm_2Earithmetic_2EEVEN,axiom,
( ( p(ap(c_2Earithmetic_2EEVEN,c_2Enum_2E0))
<=> $true )
& ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,ap(c_2Enum_2ESUC,V0n)))
<=> ~ p(ap(c_2Earithmetic_2EEVEN,V0n)) ) ) ) ).
fof(ax_thm_2Earithmetic_2EODD,axiom,
( ( p(ap(c_2Earithmetic_2EODD,c_2Enum_2E0))
<=> $false )
& ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EODD,ap(c_2Enum_2ESUC,V0n)))
<=> ~ p(ap(c_2Earithmetic_2EODD,V0n)) ) ) ) ).
fof(ax_thm_2Earithmetic_2Enum__case__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0v] :
( mem(V0v,A_27a)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),c_2Enum_2E0),V0v),V1f) = V0v ) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3v] :
( mem(V3v,A_27a)
=> ! [V4f] :
( mem(V4f,arr(ty_2Enum_2Enum,A_27a))
=> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),ap(c_2Enum_2ESUC,V2n)),V3v),V4f) = ap(V4f,V2n) ) ) ) ) ) ).
fof(ax_thm_2Earithmetic_2EFUNPOW,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0f] :
( mem(V0f,arr(A_27a,A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),c_2Enum_2E0),V1x) = V1x ) )
& ! [V2f] :
( mem(V2f,arr(A_27a,A_27a))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4x] :
( mem(V4x,A_27a)
=> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V2f),ap(c_2Enum_2ESUC,V3n)),V4x) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V2f),V3n),ap(V2f,V4x)) ) ) ) ) ) ).
fof(ax_thm_2Earithmetic_2ENRC,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),c_2Enum_2E0),V1x),V2y))
<=> V1x = V2y ) ) ) )
& ! [V3R] :
( mem(V3R,arr(A_27a,arr(A_27a,bool)))
=> ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6y] :
( mem(V6y,A_27a)
=> ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V3R),ap(c_2Enum_2ESUC,V4n)),V5x),V6y))
<=> ? [V7z] :
( mem(V7z,A_27a)
& p(ap(ap(V3R,V5x),V7z))
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V3R),V4n),V7z),V6y)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EONE,axiom,
ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,c_2Enum_2E0) ).
fof(conj_thm_2Earithmetic_2ETWO,axiom,
ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).
fof(conj_thm_2Earithmetic_2ENORM__0,axiom,
ap(c_2Earithmetic_2ENUMERAL,c_2Earithmetic_2EZERO) = c_2Enum_2E0 ).
fof(conj_thm_2Earithmetic_2Enum__case__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,A_27a)
=> ! [V1g] :
( mem(V1g,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V2n),V0f),V1g) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),V0f),ap(V1g,ap(c_2Eprim__rec_2EPRE,V2n))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUC__NOT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> c_2Enum_2E0 != ap(c_2Enum_2ESUC,V0n) ) ).
fof(conj_thm_2Earithmetic_2EADD__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m ) ).
fof(conj_thm_2Earithmetic_2EADD__SUC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__CLAUSES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0m) = V0m
& ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m
& ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))
& ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__SYM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__COMM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__ASSOC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p) ) ) ) ).
fof(conj_thm_2Earithmetic_2Enum__CASES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ( V0m = c_2Enum_2E0
| ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& V0m = ap(c_2Enum_2ESUC,V1n) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__ZERO__LT__ZERO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( V0n != c_2Enum_2E0
<=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
<=> V0n = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__OR__EQ__ALT,axiom,
c_2Earithmetic_2E_3C_3D = ap(c_2Erelation_2ERTC(ty_2Enum_2Enum),f159) ).
fof(conj_thm_2Earithmetic_2ELESS__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m))
=> ? [V2p] :
( mem(V2p,ty_2Enum_2Enum)
& ap(ap(c_2Earithmetic_2E_2B,V2p),V1n) = V0m ) ) ) ) ).
fof(conj_thm_2Earithmetic_2Etransitive__LESS,axiom,
p(ap(c_2Erelation_2Etransitive(ty_2Enum_2Enum),c_2Eprim__rec_2E_3C)) ).
fof(conj_thm_2Earithmetic_2ELESS__TRANS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__ANTISYM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ~ ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MONO__REV,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n)))
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MONO__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__MONO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__LESS__SUC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ~ ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Enum_2ESUC,V0m))) ) ) ) ).
fof(conj_thm_2Earithmetic_2Etransitive__measure,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Eprim__rec_2Emeasure(A_27a),V0f))) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__OR,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EOR__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n))
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enum_2ESUC,V1m))) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__IMP__LESS__SUC,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enum_2ESUC,V1m))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EZERO__LESS__EQ,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V0n)) ) ).
fof(conj_thm_2Earithmetic_2ELESS__SUC__EQ__COR,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
& ap(c_2Enum_2ESUC,V0m) != V1n )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__NOT__SUC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
& V1n != ap(c_2Enum_2ESUC,V0m) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__0__CASES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ( c_2Enum_2E0 = V0m
| p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__CASES__IMP,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
& V0m != V1n )
=> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__CASES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__INV__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = V0m
=> V1n = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__ADD__EXISTS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m))
=> ? [V2p] :
( mem(V2p,ty_2Enum_2Enum)
& ap(ap(c_2Earithmetic_2E_2B,V2p),V1n) = V0m ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__STRONG__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m))
=> ? [V2p] :
( mem(V2p,ty_2Enum_2Enum)
& ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V2p)),V1n) = V0m ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__SUC__REFL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(c_2Enum_2ESUC,V0m))) ) ).
fof(conj_thm_2Earithmetic_2ELESS__ADD__NONZERO,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( V1n != c_2Enum_2E0
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__SUC__LESS__EQ__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ~ p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),c_2Enum_2E0)) ) ).
fof(conj_thm_2Earithmetic_2ENOT__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__LESS__EQUAL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__ANTISYM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ~ ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0))
<=> V0n = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V0m) = c_2Enum_2E0
& ap(ap(c_2Earithmetic_2E_2D,V0m),c_2Enum_2E0) = V0m ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__MONO__EQ,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m)) = ap(ap(c_2Earithmetic_2E_2D,V0n),V1m) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__EQ__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2D,V0m),V1n) = c_2Enum_2E0
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD1,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(c_2Enum_2ESUC,V0m) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Earithmetic_2ESUC__SUB1,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0m ) ).
fof(conj_thm_2Earithmetic_2EPRE__SUB1,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(c_2Eprim__rec_2EPRE,V0m) = ap(ap(c_2Earithmetic_2E_2D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Earithmetic_2EMULT__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0) = c_2Enum_2E0 ) ).
fof(conj_thm_2Earithmetic_2EMULT__SUC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__LEFT__1,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) = V0m ) ).
fof(conj_thm_2Earithmetic_2EMULT__RIGHT__1,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0m ) ).
fof(conj_thm_2Earithmetic_2EMULT__CLAUSES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0m) = c_2Enum_2E0
& ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0) = c_2Enum_2E0
& ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) = V0m
& ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0m
& ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n)
& ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__SYM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),V0m) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__COMM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),V0m) ) ) ).
fof(conj_thm_2Earithmetic_2ERIGHT__ADD__DISTRIB,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELEFT__ADD__DISTRIB,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__ASSOC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V2p) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m))
=> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V1n) = V0m ) ) ) ).
fof(conj_thm_2Earithmetic_2EPRE__SUB,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Eprim__rec_2EPRE,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eprim__rec_2EPRE,V0m)),V1n) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__EQ__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = c_2Enum_2E0
<=> ( V0m = c_2Enum_2E0
& V1n = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__EQ__1,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
<=> ( ( V0m = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
& V1n = c_2Enum_2E0 )
| ( V0m = c_2Enum_2E0
& V1n = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__INV__0__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = V0m
<=> V1n = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Earithmetic_2EPRE__SUC__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
=> ( V0m = ap(c_2Eprim__rec_2EPRE,V1n)
<=> ap(c_2Enum_2ESUC,V0m) = V1n ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EINV__PRE__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) )
=> ( ap(c_2Eprim__rec_2EPRE,V0m) = ap(c_2Eprim__rec_2EPRE,V1n)
<=> V0m = V1n ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__SUC__NOT,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
=> ~ p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Enum_2ESUC,V0m))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__EQ__SUB,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p))
=> ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = V2p
<=> V0m = ap(ap(c_2Earithmetic_2E_2D,V2p),V1n) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MONO__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MONO__ADD__INV,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MONO__ADD__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELT__ADD__RCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELT__ADD__LCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2B,V2p),V1n)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEQ__MONO__ADD__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)
<=> V0m = V1n ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__MONO__ADD__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__TRANS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) )
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__LESS__TRANS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__LESS__EQ__TRANS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__LESS__EQ__MONO,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ! [V3q] :
( mem(V3q,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V3q)) )
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V2p),V3q))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__REFL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V0m)) ) ).
fof(conj_thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MONO__MULT,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MONO__MULT2,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ! [V3j] :
( mem(V3j,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2i))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V3j)) )
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V2i),V3j))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ERIGHT__SUB__DISTRIB,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELEFT__SUB__DISTRIB,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__ADD__1,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m))
=> ? [V2p] :
( mem(V2p,ty_2Enum_2Enum)
& V0m = ap(ap(c_2Earithmetic_2E_2B,V1n),ap(ap(c_2Earithmetic_2E_2B,V2p),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__ADD,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,V2n),ap(ap(c_2Earithmetic_2E_2B,V0p),V1q)) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V2n),V0p)),ap(ap(c_2Earithmetic_2EEXP,V2n),V1q)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__ODD__EQ__EVEN,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V0n)) != ap(ap(c_2Earithmetic_2E_2B,V1m),V1m) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQUAL__ANTISYM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) )
=> V0n = V1m ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__ADD__SUC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)))) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__OR__EQ__ADD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m))
| ? [V2p] :
( mem(V2p,ty_2Enum_2Enum)
& V0n = ap(ap(c_2Earithmetic_2E_2B,V2p),V1m) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EWOP,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ( ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& p(ap(V0P,V1n)) )
=> ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& p(ap(V0P,V2n))
& ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3m),V2n))
=> ~ p(ap(V0P,V3m)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ECOMPLETE__INDUCTION,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V1n))
=> p(ap(V0P,V2m)) ) )
=> p(ap(V0P,V1n)) ) )
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> p(ap(V0P,V3n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EFORALL__NUM__THM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(V0P,V1n)) )
<=> ( p(ap(V0P,c_2Enum_2E0))
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(V0P,V2n))
=> p(ap(V0P,ap(c_2Enum_2ESUC,V2n))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_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_2Earithmetic_2ESUB__PLUS,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ! [V2c] :
( mem(V2c,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)),V2c) ) ) ) ).
fof(conj_thm_2Earithmetic_2EINV__PRE__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eprim__rec_2EPRE,V0m)),ap(c_2Eprim__rec_2EPRE,V1n)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EINV__PRE__LESS__EQ,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Eprim__rec_2EPRE,V1m)),ap(c_2Eprim__rec_2EPRE,V0n)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EPRE__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Eprim__rec_2EPRE,V0m)),ap(c_2Eprim__rec_2EPRE,V1n))) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LESS__EQ,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)),V0n)) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__EQ__EQ__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2D,V0m),V1n) = V0m
<=> ( V0m = c_2Enum_2E0
| V1n = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LESS__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2D,V0n),V1m))) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LESS__OR,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(ap(c_2Earithmetic_2E_2D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__SUB__ADD__LESS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2i),ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2i),V1m)),V0n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ETIMES2,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n) = ap(ap(c_2Earithmetic_2E_2B,V0n),V0n) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MULT__MONO,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V0m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V1i)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1i)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__MONO__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V0m) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V1i)
<=> V0m = V1i ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__SUC__EQ,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,V2n),ap(c_2Enum_2ESUC,V0p)) = ap(ap(c_2Earithmetic_2E_2A,V1m),ap(c_2Enum_2ESUC,V0p))
<=> V2n = V1m ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__EXP__MONO,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1q)),V0p)) = ap(ap(c_2Earithmetic_2E_2A,V3m),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1q)),V0p))
<=> V2n = V3m ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEQ__ADD__LCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)
<=> V1n = V2p ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEQ__ADD__RCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)
<=> V0m = V1n ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEQ__MULT__LCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)
<=> ( V0m = c_2Enum_2E0
| V1n = V2p ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEQ__MULT__RCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,V1n),V0m) = ap(ap(c_2Earithmetic_2E_2A,V2p),V0m)
<=> ( V0m = c_2Enum_2E0
| V1n = V2p ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__SUB,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1c] :
( mem(V1c,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0a),V1c)),V1c) = V0a ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__ADD__SUB,axiom,
! [V0c] :
( mem(V0c,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0c),V1b))
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V2a),V1b)),V0c) = ap(ap(c_2Earithmetic_2E_2B,V2a),ap(ap(c_2Earithmetic_2E_2D,V1b),V0c)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__EQUAL__0,axiom,
! [V0c] :
( mem(V0c,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,V0c),V0c) = c_2Enum_2E0 ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__SUB__LESS,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a))
=> ! [V2c] :
( mem(V2c,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)),V2c))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__SUC__LESS__EQ,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),V1m))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__SUB,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1c] :
( mem(V1c,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1c),V0b))
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,V2a),ap(ap(c_2Earithmetic_2E_2D,V0b),V1c)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V2a),V1c)),V0b) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__IMP__LESS__ADD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m))
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(ap(c_2Earithmetic_2E_2B,V1m),V2p))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LESS__EQ__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1p] :
( mem(V1p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1p))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V1p),V0m)),V2n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1p),ap(ap(c_2Earithmetic_2E_2B,V0m),V2n))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LESS__SUC,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0p),V1m)),ap(c_2Enum_2ESUC,V0p))) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__CANCEL,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0p))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V0p)) )
=> ( ap(ap(c_2Earithmetic_2E_2D,V0p),V1n) = ap(ap(c_2Earithmetic_2E_2D,V0p),V2m)
<=> V1n = V2m ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ECANCEL__SUB,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0p),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V0p),V2m)) )
=> ( ap(ap(c_2Earithmetic_2E_2D,V1n),V0p) = ap(ap(c_2Earithmetic_2E_2D,V2m),V0p)
<=> V1n = V2m ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__EXP__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1n)),V0m) != c_2Enum_2E0 ) ) ).
fof(conj_thm_2Earithmetic_2EZERO__LESS__EXP,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1n)),V0m))) ) ) ).
fof(conj_thm_2Earithmetic_2EODD__OR__EVEN,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ? [V1m] :
( mem(V1m,ty_2Enum_2Enum)
& ( V0n = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0))),V1m)
| V0n = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0))),V1m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EXP__SUC__MONO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V1m))),V0n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V1m))),ap(c_2Enum_2ESUC,V0n)))) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__LESS__CASES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( V0m = V1n
| p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
| p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EGREATER__EQ,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V0n),V1m))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__CASES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQUAL__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
=> ? [V2p] :
( mem(V2p,ty_2Enum_2Enum)
& V1n = ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__EXISTS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
<=> ? [V2p] :
( mem(V2p,ty_2Enum_2Enum)
& V1n = ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__EQ__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = c_2Enum_2E0
<=> ( V0m = c_2Enum_2E0
| V1n = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__EQ__1,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,V0x),V1y) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
<=> ( V0x = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
& V1y = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__EQ__ID,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = V1n
<=> ( V0m = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| V1n = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MULT2,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EZERO__LESS__MULT,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EZERO__LESS__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
| p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) ) ) ) ) ).
fof(ax_thm_2Earithmetic_2EFACT,axiom,
( ap(c_2Earithmetic_2EFACT,c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
& ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Earithmetic_2EFACT,ap(c_2Enum_2ESUC,V0n)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0n)),ap(c_2Earithmetic_2EFACT,V0n)) ) ) ).
fof(conj_thm_2Earithmetic_2EFACT__LESS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2EFACT,V0n))) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__ODD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,V0n))
<=> ~ p(ap(c_2Earithmetic_2EODD,V0n)) ) ) ).
fof(conj_thm_2Earithmetic_2EODD__EVEN,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EODD,V0n))
<=> ~ p(ap(c_2Earithmetic_2EEVEN,V0n)) ) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__OR__ODD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,V0n))
| p(ap(c_2Earithmetic_2EODD,V0n)) ) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__AND__ODD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ~ ( p(ap(c_2Earithmetic_2EEVEN,V0n))
& p(ap(c_2Earithmetic_2EODD,V0n)) ) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))
<=> ( p(ap(c_2Earithmetic_2EEVEN,V0m))
<=> p(ap(c_2Earithmetic_2EEVEN,V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__MULT,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))
<=> ( p(ap(c_2Earithmetic_2EEVEN,V0m))
| p(ap(c_2Earithmetic_2EEVEN,V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EODD__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))
<=> ~ ( p(ap(c_2Earithmetic_2EODD,V0m))
<=> p(ap(c_2Earithmetic_2EODD,V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EODD__MULT,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))
<=> ( p(ap(c_2Earithmetic_2EODD,V0m))
& p(ap(c_2Earithmetic_2EODD,V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__DOUBLE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) ) ).
fof(conj_thm_2Earithmetic_2EODD__DOUBLE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> p(ap(c_2Earithmetic_2EODD,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)))) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__ODD__EXISTS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( ( p(ap(c_2Earithmetic_2EEVEN,V0n))
=> ? [V1m] :
( mem(V1m,ty_2Enum_2Enum)
& V0n = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m) ) )
& ( p(ap(c_2Earithmetic_2EODD,V0n))
=> ? [V2m] :
( mem(V2m,ty_2Enum_2Enum)
& V0n = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2m)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__EXISTS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,V0n))
<=> ? [V1m] :
( mem(V1m,ty_2Enum_2Enum)
& V0n = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m) ) ) ) ).
fof(conj_thm_2Earithmetic_2EODD__EXISTS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EODD,V0n))
<=> ? [V1m] :
( mem(V1m,ty_2Enum_2Enum)
& V0n = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__EXP__IFF,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2EEXP,V1m),V0n)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& p(ap(c_2Earithmetic_2EEVEN,V1m)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__EXP,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
& p(ap(c_2Earithmetic_2EEVEN,V0m)) )
=> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2EEXP,V0m),V1n))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EODD__EXP__IFF,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2EEXP,V1m),V0n)))
<=> ( V0n = c_2Enum_2E0
| p(ap(c_2Earithmetic_2EODD,V1m)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EODD__EXP,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
& p(ap(c_2Earithmetic_2EODD,V0m)) )
=> p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2EEXP,V0m),V1n))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEQ__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( V0m = V1n
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE__ADD__LCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE__ADD__RCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1n),V0m)),ap(ap(c_2Earithmetic_2E_2B,V2p),V0m)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__LEQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__NUM__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( V0m != V1n
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__GREATER,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__GREATER__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),V1n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUC__ONE__ADD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Enum_2ESUC,V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) ) ).
fof(conj_thm_2Earithmetic_2ESUC__ADD__SYM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V1n)),V0m) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__SUC__ADD__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ~ p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))),V0m)) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__LESS__EQ__SUC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2p)),V0m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2p)),V1n))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE__MULT__LCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)))
<=> ( V0m = c_2Enum_2E0
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE__MULT__RCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)))
<=> ( V1n = c_2Enum_2E0
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELT__MULT__LCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
& p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELT__MULT__RCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELT__MULT__CANCEL__LBARE,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1n)) ) )
& ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1n)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V0m))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
& V1n = c_2Enum_2E0 ) )
& ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
& V0m = c_2Enum_2E0 ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))
<=> ( V0m = c_2Enum_2E0
| p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) ) )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m)))
<=> ( V0m = c_2Enum_2E0
| p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE__MULT__CANCEL__RBARE,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V0m))
<=> ( V0m = c_2Enum_2E0
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n))
<=> ( V1n = c_2Enum_2E0
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)),V0m),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__ADD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)),V2p),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__SUB,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)),V0m),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__SUB,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__SUC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)),ap(c_2Enum_2ESUC,c_2Enum_2E0)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0m)),V1n)) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),c_2Enum_2E0)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2p)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__GREATER__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))
<=> p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__GREATER__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))
<=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))
| p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),V2p)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__GREATER,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3E,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n))
& p(ap(ap(c_2Earithmetic_2E_3E,V0m),c_2Enum_2E0)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__GREATER,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))
<=> p(ap(ap(c_2Earithmetic_2E_3E,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( V0m = ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)
<=> ( ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = V1n
| ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),c_2Enum_2E0))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2D,V0m),V1n) = V2p
<=> ( V0m = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)
| ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),c_2Enum_2E0)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0))
<=> V0n = c_2Enum_2E0 ) )
& ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),ap(c_2Enum_2ESUC,V2n)))
<=> ( V1m = ap(c_2Enum_2ESUC,V2n)
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDA,axiom,
! [V0k] :
( mem(V0k,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
=> ? [V2r] :
( mem(V2r,ty_2Enum_2Enum)
& ? [V3q] :
( mem(V3q,ty_2Enum_2Enum)
& V0k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V1n)),V2r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V2r),V1n)) ) ) ) ) ) ).
fof(ax_thm_2Earithmetic_2EDIVISION,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [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),V0n)),V0n)),ap(ap(c_2Earithmetic_2EMOD,V1k),V0n))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)),V0n)) ) ) ) ) ).
fof(ax_thm_2Earithmetic_2EDIV2__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Earithmetic_2EDIV2,V0n) = ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Earithmetic_2EMOD__ONE,axiom,
! [V0k] :
( mem(V0k,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,V0k),ap(c_2Enum_2ESUC,c_2Enum_2E0)) = c_2Enum_2E0 ) ).
fof(conj_thm_2Earithmetic_2EMOD__1,axiom,
! [V0k] :
( mem(V0k,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,V0k),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = c_2Enum_2E0 ) ).
fof(conj_thm_2Earithmetic_2EDIV__LESS__EQ,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EDIV,V1k),V0n)),V1k)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__UNIQUE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> ! [V2q] :
( mem(V2q,ty_2Enum_2Enum)
=> ( ? [V3r] :
( mem(V3r,ty_2Enum_2Enum)
& V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2q),V0n)),V3r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V3r),V0n)) )
=> ap(ap(c_2Earithmetic_2EDIV,V1k),V0n) = V2q ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__UNIQUE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> ! [V2r] :
( mem(V2r,ty_2Enum_2Enum)
=> ( ? [V3q] :
( mem(V3q,ty_2Enum_2Enum)
& V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V0n)),V2r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V2r),V0n)) )
=> ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = V2r ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__MULT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1r] :
( mem(V1r,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1r),V0n))
=> ! [V2q] :
( mem(V2q,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2q),V0n)),V1r)),V0n) = V2q ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__MOD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1k),V0n))
=> ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = V1k ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__EQ__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,V1k),V0n)),V0n) = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Earithmetic_2EZERO__MOD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(c_2Earithmetic_2EMOD,c_2Enum_2E0),V0n) = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Earithmetic_2EZERO__DIV,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(c_2Earithmetic_2EDIV,c_2Enum_2E0),V0n) = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__MULT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1r] :
( mem(V1r,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1r),V0n))
=> ! [V2q] :
( mem(V2q,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2q),V0n)),V1r)),V0n) = V1r ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__TIMES,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ! [V2r] :
( mem(V2r,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1q),V0n)),V2r)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2r),V0n) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__TIMES__SUB,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ! [V2r] :
( mem(V2r,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1q))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V2r),V0n)) )
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,V1q),V0n)),V2r)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,V0n),V2r)),V0n) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__PLUS,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,V1j),V0n)),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_2Earithmetic_2EMOD__MOD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__DIV__EQ__ZERO,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,V0r),V1n) = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__DIV,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2A,V1q),V0n)),V0n) = V1q ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__DIV__ADD__DIV,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)
=> ! [V2r] :
( mem(V2r,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1x),V0n)),V2r)),V0n) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(ap(c_2Earithmetic_2EDIV,V2r),V0n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__DIV__RWT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( ap(ap(c_2Earithmetic_2EMOD,V1m),V0n) = c_2Enum_2E0
| ap(ap(c_2Earithmetic_2EMOD,V2p),V0n) = c_2Enum_2E0 )
=> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,V1m),V2p)),V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EDIV,V1m),V0n)),ap(ap(c_2Earithmetic_2EDIV,V2p),V0n)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__MULT__MOD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) )
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EMOD,V2x),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m))),V1n) = ap(ap(c_2Earithmetic_2EMOD,V2x),V1n) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__ONE,axiom,
! [V0q] :
( mem(V0q,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EDIV,V0q),ap(c_2Enum_2ESUC,c_2Enum_2E0)) = V0q ) ).
fof(conj_thm_2Earithmetic_2EDIV__1,axiom,
! [V0q] :
( mem(V0q,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EDIV,V0q),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0q ) ).
fof(conj_thm_2Earithmetic_2EDIVMOD__ID,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ( ap(ap(c_2Earithmetic_2EDIV,V0n),V0n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
& ap(ap(c_2Earithmetic_2EMOD,V0n),V0n) = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__DIV__DIV__MULT,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) )
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EDIV,V2x),V0m)),V1n) = ap(ap(c_2Earithmetic_2EDIV,V2x),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUC__PRE,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))
<=> ap(c_2Enum_2ESUC,ap(c_2Eprim__rec_2EPRE,V0m)) = V0m ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__LESS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1d] :
( mem(V1d,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1d)) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V0n),V1d)),V0n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V0m),V1n)),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__MODULUS,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),V0n)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1x),V0n) ) ) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3x] :
( mem(V3x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n))
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2n),V3x)),V2n) = ap(ap(c_2Earithmetic_2EMOD,V3x),V2n) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__MODULUS__LEFT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),V0n)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1x),V0n) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__MODULUS__RIGHT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V0n),V1x)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1x),V0n) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__P,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1p] :
( mem(V1p,ty_2Enum_2Enum)
=> ! [V2q] :
( mem(V2q,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2q))
=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,V1p),V2q)))
<=> ? [V3k] :
( mem(V3k,ty_2Enum_2Enum)
& ? [V4r] :
( mem(V4r,ty_2Enum_2Enum)
& V1p = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3k),V2q)),V4r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2q))
& p(ap(V0P,V3k)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__P__UNIV,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n))
=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,V1m),V2n)))
<=> ! [V3q] :
( mem(V3q,ty_2Enum_2Enum)
=> ! [V4r] :
( mem(V4r,ty_2Enum_2Enum)
=> ( ( V1m = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V2n)),V4r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2n)) )
=> p(ap(V0P,V3q)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__P,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1p] :
( mem(V1p,ty_2Enum_2Enum)
=> ! [V2q] :
( mem(V2q,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2q))
=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2EMOD,V1p),V2q)))
<=> ? [V3k] :
( mem(V3k,ty_2Enum_2Enum)
& ? [V4r] :
( mem(V4r,ty_2Enum_2Enum)
& V1p = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3k),V2q)),V4r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2q))
& p(ap(V0P,V4r)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__P__UNIV,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n))
=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2EMOD,V1m),V2n)))
<=> ! [V3q] :
( mem(V3q,ty_2Enum_2Enum)
=> ! [V4r] :
( mem(V4r,ty_2Enum_2Enum)
=> ( ( V1m = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V2n)),V4r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2n)) )
=> p(ap(V0P,V4r)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__TIMES2,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_2A,ap(ap(c_2Earithmetic_2EMOD,V1j),V0n)),ap(ap(c_2Earithmetic_2EMOD,V2k),V0n))),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,V1j),V2k)),V0n) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__COMMON__FACTOR,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1p] :
( mem(V1p,ty_2Enum_2Enum)
=> ! [V2q] :
( mem(V2q,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2q)) )
=> ap(ap(c_2Earithmetic_2E_2A,V0n),ap(ap(c_2Earithmetic_2EMOD,V1p),V2q)) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,V0n),V1p)),ap(ap(c_2Earithmetic_2E_2A,V0n),V2q)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EX__MOD__Y__EQ__X,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1y))
=> ( ap(ap(c_2Earithmetic_2EMOD,V0x),V1y) = V0x
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1y)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__LE__MONOTONE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),V2y)) )
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EDIV,V1x),V0n)),ap(ap(c_2Earithmetic_2EDIV,V2y),V0n))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE__LT1,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),V1y))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2E_2B,V1y),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EX__LE__DIV,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2z] :
( mem(V2z,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z))
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(ap(c_2Earithmetic_2EDIV,V1y),V2z)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0x),V2z)),V1y)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EX__LT__DIV,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2z] :
( mem(V2z,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2EDIV,V1y),V2z)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2z)),V1y)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__LT__X,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2z] :
( mem(V2z,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V1y),V2z)),V0x))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V1y),ap(ap(c_2Earithmetic_2E_2A,V0x),V2z))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__LE__X,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2z] :
( mem(V2z,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z))
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EDIV,V1y),V2z)),V0x))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V1y),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2z))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__EQ__X,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2z] :
( mem(V2z,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z))
=> ( ap(ap(c_2Earithmetic_2EDIV,V1y),V2z) = V0x
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0x),V2z)),V1y))
& p(ap(ap(c_2Eprim__rec_2E_3C,V1y),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0x)),V2z))) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__MOD__MOD__DIV,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2k] :
( mem(V2k,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2k)) )
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,V0m),V1n)),V2k) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EMOD,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V2k))),V1n) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__EQ__DIV,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2z] :
( mem(V2z,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x))
=> ( ap(ap(c_2Earithmetic_2E_2A,V0x),V1y) = V2z
<=> ( V1y = ap(ap(c_2Earithmetic_2EDIV,V2z),V0x)
& ap(ap(c_2Earithmetic_2EMOD,V2z),V0x) = c_2Enum_2E0 ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2z] :
( mem(V2z,ty_2Enum_2Enum)
=> ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0x))),V1y) = ap(c_2Earithmetic_2ENUMERAL,V2z)
<=> ( V1y = ap(ap(c_2Earithmetic_2EDIV,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0x)))
& ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0x))) = c_2Enum_2E0 ) )
& ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0x))),V1y) = ap(c_2Earithmetic_2ENUMERAL,V2z)
<=> ( V1y = ap(ap(c_2Earithmetic_2EDIV,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0x)))
& ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0x))) = c_2Enum_2E0 ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__EQ__0__DIVISOR,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ( ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = c_2Enum_2E0
<=> ? [V2d] :
( mem(V2d,ty_2Enum_2Enum)
& V1k = ap(ap(c_2Earithmetic_2E_2A,V2d),V0n) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__SUC,axiom,
! [V0y] :
( mem(V0y,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0y))
& ap(c_2Enum_2ESUC,V1x) != ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EDIV,V1x),V0y))),V0y) )
=> ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V1x)),V0y) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMOD,V1x),V0y)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__SUC__IFF,axiom,
! [V0y] :
( mem(V0y,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0y))
=> ( ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V1x)),V0y) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMOD,V1x),V0y))
<=> ap(c_2Enum_2ESUC,V1x) != ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EDIV,V1x),V0y))),V0y) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EONE__MOD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n))
=> ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ).
fof(conj_thm_2Earithmetic_2EONE__MOD__IFF,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__LESS__EQ,axiom,
! [V0y] :
( mem(V0y,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0y))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMOD,V1x),V0y)),V1x)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__LIFT__PLUS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V1k),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2EMOD,V2x),V0n)))) )
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2x),V1k)),V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V2x),V0n)),V1k) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__LIFT__PLUS__IFF,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2k] :
( mem(V2k,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ( ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),V2k)),V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),V2k)
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V2k),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2Enum__case__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v_27] :
( mem(V0v_27,A_27a)
=> ! [V1f_27] :
( mem(V1f_27,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2M] :
( mem(V2M,ty_2Enum_2Enum)
=> ! [V3M_27] :
( mem(V3M_27,ty_2Enum_2Enum)
=> ! [V4v] :
( mem(V4v,A_27a)
=> ! [V5f] :
( mem(V5f,arr(ty_2Enum_2Enum,A_27a))
=> ( ( V2M = V3M_27
& ( V3M_27 = c_2Enum_2E0
=> V4v = V0v_27 )
& ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ( V3M_27 = ap(c_2Enum_2ESUC,V6n)
=> ap(V5f,V6n) = ap(V1f_27,V6n) ) ) )
=> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V2M),V4v),V5f) = ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V3M_27),V0v_27),V1f_27) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUC__ELIM__THM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V1n)),V1n)) )
<=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n))
=> p(ap(ap(V0P,V2n),ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUC__ELIM__NUMERALS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,A_27a)))
=> ! [V1g] :
( mem(V1g,arr(ty_2Enum_2Enum,A_27a))
=> ( ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(V1g,ap(c_2Enum_2ESUC,V2n)) = ap(ap(V0f,V2n),ap(c_2Enum_2ESUC,V2n)) )
<=> ( ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ap(V1g,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))) = ap(ap(V0f,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))) )
& ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ap(V1g,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))) = ap(ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__ELIM__THM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1a),V2b)))
<=> ! [V3d] :
( mem(V3d,ty_2Enum_2Enum)
=> ( ( V2b = ap(ap(c_2Earithmetic_2E_2B,V1a),V3d)
=> p(ap(V0P,c_2Enum_2E0)) )
& ( V1a = ap(ap(c_2Earithmetic_2E_2B,V2b),V3d)
=> p(ap(V0P,V3d)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EPRE__ELIM__THM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(V0P,ap(c_2Eprim__rec_2EPRE,V1n)))
<=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( ( V1n = c_2Enum_2E0
=> p(ap(V0P,c_2Enum_2E0)) )
& ( V1n = ap(c_2Enum_2ESUC,V2m)
=> p(ap(V0P,V2m)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__INCREASES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) )
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__ALWAYS__BIG__ENOUGH,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ? [V2m] :
( mem(V2m,ty_2Enum_2Enum)
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(ap(c_2Earithmetic_2EEXP,V0b),V2m))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__EQ__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EEXP,V0n),V1m) = c_2Enum_2E0
<=> ( V0n = c_2Enum_2E0
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1m)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EZERO__LT__EXP,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,V0x),V1y)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x))
| V1y = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__1,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
& ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0n ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__EQ__1,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EEXP,V0n),V1m) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
<=> ( V0n = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| V1m = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__BASE__LE__MONO,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0b),V2m)),ap(ap(c_2Earithmetic_2EEXP,V0b),V1n)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V1n)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__BASE__LT__MONO,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V0b),V2m)),ap(ap(c_2Earithmetic_2EEXP,V0b),V1n)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V1n)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__BASE__INJECTIVE,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EEXP,V0b),V1n) = ap(ap(c_2Earithmetic_2EEXP,V0b),V2m)
<=> V1n = V2m ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__IMP,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2b))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) )
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V2b),V1m)),ap(ap(c_2Earithmetic_2EEXP,V2b),V0n))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__SUC__IMP,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2b)),V0m)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2b)),V1n))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__BASE__LE__IFF,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0b),V1m)),ap(ap(c_2Earithmetic_2EEXP,V0b),V2n)))
<=> ( ( V0b = c_2Enum_2E0
& V2n = c_2Enum_2E0 )
| ( V0b = c_2Enum_2E0
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1m)) )
| V0b = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EX__LE__X__EXP,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(ap(c_2Earithmetic_2EEXP,V1x),V0n))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EX__LT__EXP__X,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b))
=> p(ap(ap(c_2Eprim__rec_2E_3C,V1x),ap(ap(c_2Earithmetic_2EEXP,V0b),V1x))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EZERO__EXP,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),V0x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0x),c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0) ) ).
fof(conj_thm_2Earithmetic_2EX__LT__EXP__X__IFF,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2EEXP,V1b),V0x)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1b))
| V0x = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__EXP__LT__MONO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),ap(ap(c_2Earithmetic_2EEXP,V2b),V0n)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1a),V2b))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__EXP__LE__MONO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),ap(ap(c_2Earithmetic_2EEXP,V2b),V0n)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1a),V2b))
| V0n = c_2Enum_2E0 ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__EXP__INJECTIVE,axiom,
! [V0b1] :
( mem(V0b1,ty_2Enum_2Enum)
=> ! [V1b2] :
( mem(V1b2,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EEXP,V0b1),V2x) = ap(ap(c_2Earithmetic_2EEXP,V1b2),V2x)
<=> ( V2x = c_2Enum_2E0
| V0b1 = V1b2 ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__SUB,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1q),V0p)) )
=> ap(ap(c_2Earithmetic_2EEXP,V2n),ap(ap(c_2Earithmetic_2E_2D,V0p),V1q)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EEXP,V2n),V0p)),ap(ap(c_2Earithmetic_2EEXP,V2n),V1q)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__SUB__NUMERAL,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ( ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x)))),V0n) = ap(ap(c_2Earithmetic_2EEXP,V0n),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))
& ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1x)))),V0n) = ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__BASE__MULT,axiom,
! [V0z] :
( mem(V0z,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2E_2A,V1x),V2y)),V0z) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V1x),V0z)),ap(ap(c_2Earithmetic_2EEXP,V2y),V0z)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__EXP__MULT,axiom,
! [V0z] :
( mem(V0z,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,V1x),ap(ap(c_2Earithmetic_2E_2A,V2y),V0z)) = ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2EEXP,V1x),V2y)),V0z) ) ) ) ).
fof(ax_thm_2Earithmetic_2EMAX__DEF,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMAX,V0m),V1n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)),V1n),V0m) ) ) ).
fof(ax_thm_2Earithmetic_2EMIN__DEF,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMIN,V0m),V1n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)),V0m),V1n) ) ) ).
fof(conj_thm_2Earithmetic_2EMAX__COMM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMAX,V0m),V1n) = ap(ap(c_2Earithmetic_2EMAX,V1n),V0m) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__COMM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMIN,V0m),V1n) = ap(ap(c_2Earithmetic_2EMIN,V1n),V0m) ) ) ).
fof(conj_thm_2Earithmetic_2EMAX__ASSOC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMAX,V0m),ap(ap(c_2Earithmetic_2EMAX,V1n),V2p)) = ap(ap(c_2Earithmetic_2EMAX,ap(ap(c_2Earithmetic_2EMAX,V0m),V1n)),V2p) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__ASSOC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMIN,V0m),ap(ap(c_2Earithmetic_2EMIN,V1n),V2p)) = ap(ap(c_2Earithmetic_2EMIN,ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)),V2p) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__MAX__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EMIN,V0m),V1n) = ap(ap(c_2Earithmetic_2EMAX,V0m),V1n)
<=> V0m = V1n ) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__MAX__LT,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)),ap(ap(c_2Earithmetic_2EMAX,V0m),V1n)))
<=> V0m != V1n ) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__MAX__LE,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)),ap(ap(c_2Earithmetic_2EMAX,V0m),V1n))) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__MAX__PRED,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( p(ap(V0P,V1m))
& p(ap(V0P,V2n)) )
=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2EMIN,V1m),V2n)))
& p(ap(V0P,ap(ap(c_2Earithmetic_2EMAX,V1m),V2n))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__LT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)),V2p))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V2p))
| p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V2p)) ) )
& ( p(ap(ap(c_2Eprim__rec_2E_3C,V2p),ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V1m))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V0n)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMAX__LT,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V2p),ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V1m))
| p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V0n)) ) )
& ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)),V2p))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V2p))
& p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V2p)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__LE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)),V2p))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2p))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V2p)) ) )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V1m))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V0n)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMAX__LE,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V1m))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V0n)) ) )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)),V2p))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2p))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V2p)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EMIN,V0n),c_2Enum_2E0) = c_2Enum_2E0
& ap(ap(c_2Earithmetic_2EMIN,c_2Enum_2E0),V0n) = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Earithmetic_2EMAX__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EMAX,V0n),c_2Enum_2E0) = V0n
& ap(ap(c_2Earithmetic_2EMAX,c_2Enum_2E0),V0n) = V0n ) ) ).
fof(conj_thm_2Earithmetic_2EMAX__EQ__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EMAX,V0m),V1n) = c_2Enum_2E0
<=> ( V0m = c_2Enum_2E0
& V1n = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__EQ__0,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EMIN,V0m),V1n) = c_2Enum_2E0
<=> ( V0m = c_2Enum_2E0
| V1n = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMIN__IDEM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMIN,V0n),V0n) = V0n ) ).
fof(conj_thm_2Earithmetic_2EMAX__IDEM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMAX,V0n),V0n) = V0n ) ).
fof(conj_thm_2Earithmetic_2EEXISTS__GREATEST,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ( ( ? [V1x] :
( mem(V1x,ty_2Enum_2Enum)
& p(ap(V0P,V1x)) )
& ? [V2x] :
( mem(V2x,ty_2Enum_2Enum)
& ! [V3y] :
( mem(V3y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E,V3y),V2x))
=> ~ p(ap(V0P,V3y)) ) ) ) )
<=> ? [V4x] :
( mem(V4x,ty_2Enum_2Enum)
& p(ap(V0P,V4x))
& ! [V5y] :
( mem(V5y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E,V5y),V4x))
=> ~ p(ap(V0P,V5y)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXISTS__NUM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ( ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& p(ap(V0P,V1n)) )
<=> ( p(ap(V0P,c_2Enum_2E0))
| ? [V2m] :
( mem(V2m,ty_2Enum_2Enum)
& p(ap(V0P,ap(c_2Enum_2ESUC,V2m))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EFORALL__NUM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(V0P,V1n)) )
<=> ( p(ap(V0P,c_2Enum_2E0))
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> p(ap(V0P,ap(c_2Enum_2ESUC,V2n))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EBOUNDED__FORALL__THM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1c] :
( mem(V1c,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1c))
=> ( ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1c))
=> p(ap(V0P,V2n)) ) )
<=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
& ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
=> p(ap(V0P,V3n)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EBOUNDED__EXISTS__THM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1c] :
( mem(V1c,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1c))
=> ( ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1c))
& p(ap(V0P,V2n)) )
<=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
| ? [V3n] :
( mem(V3n,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
& p(ap(V0P,V3n)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2Etransitive__monotone,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R))
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> p(ap(ap(V0R,ap(V1f,V2n)),ap(V1f,ap(c_2Enum_2ESUC,V2n)))) ) )
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3m),V4n))
=> p(ap(ap(V0R,ap(V1f,V3m)),ap(V1f,V4n))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__TC,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))) )
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V3n))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V2m)),ap(V0f,V3n))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__ONE__ONE,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))) )
=> p(ap(c_2Ebool_2EONE__ONE(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f)) ) ) ).
fof(conj_thm_2Earithmetic_2EONE__ONE__INV__IMAGE__BOUNDED,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( p(ap(c_2Ebool_2EONE__ONE(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f))
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ? [V2a] :
( mem(V2a,ty_2Enum_2Enum)
& ! [V3x] :
( mem(V3x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V3x)),V1b))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V3x),V2a)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EONE__ONE__UNBOUNDED,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( p(ap(c_2Ebool_2EONE__ONE(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f))
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V1b),ap(V0f,V2n))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__UNBOUNDED,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))) )
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ? [V3n] :
( mem(V3n,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V2b),ap(V0f,V3n))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__STRICTLY__DECREASING,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ~ ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,ap(c_2Enum_2ESUC,V1n))),ap(V0f,V1n))) ) ) ).
fof(ax_thm_2Earithmetic_2EABS__DIFF__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)),ap(ap(c_2Earithmetic_2E_2D,V1m),V0n)),ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__SYM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) = ap(ap(c_2Earithmetic_2EABS__DIFF,V1m),V0n) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__COMM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) = ap(ap(c_2Earithmetic_2EABS__DIFF,V1m),V0n) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__EQS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V0n) = c_2Enum_2E0 ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__EQ__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) = c_2Enum_2E0
<=> V0n = V1m ) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__ZERO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),c_2Enum_2E0) = V0n
& ap(ap(c_2Earithmetic_2EABS__DIFF,c_2Enum_2E0),V0n) = V0n ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__SUC,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EABS__DIFF,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m)) = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__SUC__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1z] :
( mem(V1z,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),ap(c_2Enum_2ESUC,V1z))),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1z)))) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__PLUS__LE,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1z] :
( mem(V1z,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),ap(ap(c_2Earithmetic_2E_2B,V2y),V1z))),ap(ap(c_2Earithmetic_2E_2B,V2y),ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1z)))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__LE__SUM,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1z] :
( mem(V1z,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1z)),ap(ap(c_2Earithmetic_2E_2B,V0x),V1z))) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__TRIANGLE__lem,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1y)),V1y))) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__TRIANGLE,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2z] :
( mem(V2z,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V2z)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1y)),ap(ap(c_2Earithmetic_2EABS__DIFF,V1y),V2z)))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__ADD__SAME,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EABS__DIFF,ap(ap(c_2Earithmetic_2E_2B,V0n),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1m),V2p)) = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE__SUB__RCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V1n),V0m)),ap(ap(c_2Earithmetic_2E_2D,V2p),V0m)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELT__SUB__RCANCEL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V1n),V0m)),ap(ap(c_2Earithmetic_2E_2D,V2p),V0m)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p))
& p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELE__SUB__LCANCEL,axiom,
! [V0z] :
( mem(V0z,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V2x),V1y)),ap(ap(c_2Earithmetic_2E_2D,V2x),V0z)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0z),V1y))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V2x),V1y)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELT__SUB__LCANCEL,axiom,
! [V0z] :
( mem(V0z,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V2x),V1y)),ap(ap(c_2Earithmetic_2E_2D,V2x),V0z)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0z),V1y))
& p(ap(ap(c_2Eprim__rec_2E_3C,V0z),V2x)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EABS__DIFF__SUMS,axiom,
! [V0n1] :
( mem(V0n1,ty_2Enum_2Enum)
=> ! [V1n2] :
( mem(V1n2,ty_2Enum_2Enum)
=> ! [V2m1] :
( mem(V2m1,ty_2Enum_2Enum)
=> ! [V3m2] :
( mem(V3m2,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,ap(ap(c_2Earithmetic_2E_2B,V0n1),V1n2)),ap(ap(c_2Earithmetic_2E_2B,V2m1),V3m2))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EABS__DIFF,V0n1),V2m1)),ap(ap(c_2Earithmetic_2EABS__DIFF,V1n2),V3m2)))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EFUNPOW__SUC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Enum_2ESUC,V1n)),V2x) = ap(V0f,ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),V1n),V2x)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EFUNPOW__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),c_2Enum_2E0),V1x) = V1x ) ) ) ).
fof(conj_thm_2Earithmetic_2EFUNPOW__ADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(ap(c_2Earithmetic_2E_2B,V2m),V3n)),V1x) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),V2m),ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),V3n),V1x)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EFUNPOW__1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) = ap(V0f,V1x) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENRC__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),c_2Enum_2E0),V1x),V2y))
<=> V1x = V2y ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENRC__1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x),V2y))
<=> p(ap(ap(V0R,V1x),V2y)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENRC__ADD__I,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ! [V5z] :
( mem(V5z,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1m),V3x),V4y))
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V2n),V4y),V5z)) )
=> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)),V3x),V5z)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENRC__ADD__E,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4z] :
( mem(V4z,A_27a)
=> ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)),V3x),V4z))
=> ? [V5y] :
( mem(V5y,A_27a)
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1m),V3x),V5y))
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V2n),V5y),V4z)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENRC__ADD__EQN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4z] :
( mem(V4z,A_27a)
=> ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)),V3x),V4z))
<=> ? [V5y] :
( mem(V5y,A_27a)
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1m),V3x),V5y))
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V2n),V5y),V4z)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENRC__SUC__RECURSE__LEFT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(c_2Enum_2ESUC,V1n)),V2x),V3y))
<=> ? [V4z] :
( mem(V4z,A_27a)
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1n),V2x),V4z))
& p(ap(ap(V0R,V4z),V3y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENRC__RTC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1n),V2x),V3y))
=> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V3y)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ERTC__NRC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))
=> ? [V3n] :
( mem(V3n,ty_2Enum_2Enum)
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V3n),V1x),V2y)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ERTC__eq__NRC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))
<=> ? [V3n] :
( mem(V3n,ty_2Enum_2Enum)
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V3n),V1x),V2y)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ETC__eq__NRC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))
<=> ? [V3n] :
( mem(V3n,ty_2Enum_2Enum)
& p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(c_2Enum_2ESUC,V3n)),V1x),V2y)) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQUAL__DIFF,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
=> ? [V2k] :
( mem(V2k,ty_2Enum_2Enum)
& V0m = ap(ap(c_2Earithmetic_2E_2D,V1n),V2k) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__2,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(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,V0n)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Earithmetic_2EEVEN__MOD2,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,V0x))
<=> ap(ap(c_2Earithmetic_2EMOD,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Earithmetic_2ESUC__MOD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ( ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V1a)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V2b)),V0n)
<=> ap(ap(c_2Earithmetic_2EMOD,V1a),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2b),V0n) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__MOD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ! [V3p] :
( mem(V3p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ( ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1a),V3p)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2b),V3p)),V0n)
<=> ap(ap(c_2Earithmetic_2EMOD,V1a),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2b),V0n) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__ELIM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n))
& p(ap(V0P,V1x))
& ! [V3y] :
( mem(V3y,ty_2Enum_2Enum)
=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2E_2B,V3y),V2n)))
=> p(ap(V0P,V3y)) ) ) )
=> p(ap(V0P,ap(ap(c_2Earithmetic_2EMOD,V1x),V2n))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDOUBLE__LT,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0p)),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))),V1q)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0p)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1q))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP2__LT,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0m)))
<=> 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))),ap(c_2Enum_2ESUC,V0m)))) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__MOD,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) )
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V1n) = ap(ap(c_2Earithmetic_2EMOD,V0m),V1n) ) ) ) ).
fof(conj_thm_2Earithmetic_2EONE__LT__MULT__IMP,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0p))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1q)) )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2A,V0p),V1q))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EONE__LT__MULT,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2A,V0x),V1y)))
<=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1y)) )
| ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1y))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EONE__LT__EXP,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EEXP,V0x),V1y)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1y)) ) ) ) ) ).
fof(lameq_f172,axiom,
! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] : ap(f172(V1m),V2n) = ap(ap(c_2Earithmetic_2E_2D,V1m),V2n) ) ).
fof(lameq_f173,axiom,
! [V1m] : ap(f173,V1m) = f172(V1m) ).
fof(lameq_f174,axiom,
! [V3f] :
( mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum))
=> ! [V5m] :
( mem(V5m,ty_2Enum_2Enum)
=> ! [V4a] :
( mem(V4a,ty_2Enum_2Enum)
=> ! [V7d] : ap(f174(V3f,V5m,V4a),V7d) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V5m),V7d)),V4a),ap(V3f,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V4a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V5m),V7d)))) ) ) ) ).
fof(lameq_f175,axiom,
! [V5m] :
( mem(V5m,ty_2Enum_2Enum)
=> ! [V3f] :
( mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum))
=> ! [V4a] :
( mem(V4a,ty_2Enum_2Enum)
=> ! [V6n] : ap(f175(V5m,V3f,V4a),V6n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6n),c_2Enum_2E0)),V4a),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f174(V3f,V5m,V4a)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V6n))) ) ) ) ).
fof(lameq_f176,axiom,
! [V3f] :
( mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum))
=> ! [V4a] :
( mem(V4a,ty_2Enum_2Enum)
=> ! [V5m] : ap(f176(V3f,V4a),V5m) = f175(V5m,V3f,V4a) ) ) ).
fof(lameq_f177,axiom,
! [V3f] :
( mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum))
=> ! [V4a] : ap(f177(V3f),V4a) = ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Enum_2Enum),f176(V3f,V4a)) ) ).
fof(lameq_f178,axiom,
! [V3f] : ap(f178,V3f) = ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),f177(V3f)) ).
fof(ax_thm_2Earithmetic_2Efindq__def,axiom,
c_2Earithmetic_2Efindq = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum),ap(c_2Eprim__rec_2Emeasure(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),k(ty_2Enum_2Enum,ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Enum_2Enum),f173))))),f178) ).
fof(lameq_f179,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V3d] : ap(f179(V0a,V1m),V3d) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1m),V3d)),V0a),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V3d)))) ) ) ).
fof(conj_thm_2Earithmetic_2Efindq__thm,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),V0a),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f179(V0a,V1m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2n))) ) ) ) ).
fof(conj_thm_2Earithmetic_2Efindq__eq__0,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))) = c_2Enum_2E0
<=> V0a = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Earithmetic_2Efindq__divisor,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V2a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V0n)))),V0n)),ap(ap(c_2Earithmetic_2E_2A,V2a),V1m))) ) ) ) ) ).
fof(lameq_f180,axiom,
! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V0f] :
( mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V4q] : ap(f180(V1a,V2m,V3n,V0f),V4q) = ap(V0f,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2B,V1a),V4q)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2D,V2m),ap(ap(c_2Earithmetic_2E_2A,V3n),V4q))),V3n))) ) ) ) ) ).
fof(lameq_f181,axiom,
! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V0f] :
( mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V3n] : ap(f181(V2m,V1a,V0f),V3n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3n),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V2m),V3n)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1a),V2m)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f180(V1a,V2m,V3n,V0f)),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)))))) ) ) ) ).
fof(lameq_f182,axiom,
! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V0f] :
( mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V2m] : ap(f182(V1a,V0f),V2m) = f181(V2m,V1a,V0f) ) ) ).
fof(lameq_f183,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V1a] : ap(f183(V0f),V1a) = ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f182(V1a,V0f)) ) ).
fof(lameq_f184,axiom,
! [V0f] : ap(f184,V0f) = ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f183(V0f)) ).
fof(ax_thm_2Earithmetic_2EDIVMOD__DEF,axiom,
c_2Earithmetic_2EDIVMOD = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Eprim__rec_2Emeasure(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ecombin_2Eo(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))))),f184) ).
fof(lameq_f185,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3q] : ap(f185(V0a,V1m,V2n),V3q) = ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2B,V0a),V3q)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2D,V1m),ap(ap(c_2Earithmetic_2E_2A,V2n),V3q))),V2n))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIVMOD__THM,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V1m),V2n)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0a),V1m)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f185(V0a,V1m,V2n)),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n)))))) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMOD__SUB,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0n),V1q)),V2m)) )
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,V2m),ap(ap(c_2Earithmetic_2E_2A,V0n),V1q))),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2m),V0n) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIV__SUB,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1q] :
( mem(V1q,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0n),V1q)),V2m)) )
=> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V2m),ap(ap(c_2Earithmetic_2E_2A,V0n),V1q))),V0n) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EDIV,V2m),V0n)),V1q) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIVMOD__CORRECT,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
=> ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V2a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),V1n))) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2B,V2a),ap(ap(c_2Earithmetic_2EDIV,V0m),V1n))),ap(ap(c_2Earithmetic_2EMOD,V0m),V1n)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EDIVMOD__CALC,axiom,
( ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))
=> ap(ap(c_2Earithmetic_2EDIV,V0m),V1n) = ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),V1n)))) ) ) )
& ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3n))
=> ap(ap(c_2Earithmetic_2EMOD,V2m),V3n) = ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)))) ) ) ) ) ).
fof(ax_thm_2Earithmetic_2EMODEQ__DEF,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m1] :
( mem(V1m1,ty_2Enum_2Enum)
=> ! [V2m2] :
( mem(V2m2,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1m1),V2m2))
<=> ? [V3a] :
( mem(V3a,ty_2Enum_2Enum)
& ? [V4b] :
( mem(V4b,ty_2Enum_2Enum)
& ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3a),V0n)),V1m1) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V4b),V0n)),V2m2) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__0__CONG,axiom,
! [V0m1] :
( mem(V0m1,ty_2Enum_2Enum)
=> ! [V1m2] :
( mem(V1m2,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,c_2Enum_2E0),V0m1),V1m2))
<=> V0m1 = V1m2 ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m1] :
( mem(V1m1,ty_2Enum_2Enum)
=> ! [V2m2] :
( mem(V2m2,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1m1),V2m2))
<=> ap(ap(c_2Earithmetic_2EMOD,V1m1),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2m2),V0n) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__THM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m1] :
( mem(V1m1,ty_2Enum_2Enum)
=> ! [V2m2] :
( mem(V2m2,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1m1),V2m2))
<=> ( ( V0n = c_2Enum_2E0
& V1m1 = V2m2 )
| ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
& ap(ap(c_2Earithmetic_2EMOD,V1m1),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2m2),V0n) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__INTRO__CONG,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1e0] :
( mem(V1e0,ty_2Enum_2Enum)
=> ! [V2e1] :
( mem(V2e1,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1e0),V2e1))
=> ap(ap(c_2Earithmetic_2EMOD,V1e0),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2e1),V0n) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__PLUS__CONG,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x0] :
( mem(V1x0,ty_2Enum_2Enum)
=> ! [V2x1] :
( mem(V2x1,ty_2Enum_2Enum)
=> ! [V3y0] :
( mem(V3y0,ty_2Enum_2Enum)
=> ! [V4y1] :
( mem(V4y1,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x0),V2x1))
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V3y0),V4y1))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2E_2B,V1x0),V3y0)),ap(ap(c_2Earithmetic_2E_2B,V2x1),V4y1))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__MULT__CONG,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x0] :
( mem(V1x0,ty_2Enum_2Enum)
=> ! [V2x1] :
( mem(V2x1,ty_2Enum_2Enum)
=> ! [V3y0] :
( mem(V3y0,ty_2Enum_2Enum)
=> ! [V4y1] :
( mem(V4y1,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x0),V2x1))
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V3y0),V4y1))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2E_2A,V1x0),V3y0)),ap(ap(c_2Earithmetic_2E_2A,V2x1),V4y1))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__REFL,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V1x)) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__SUC__CONG,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(c_2Enum_2ESUC,V1x)),ap(c_2Enum_2ESUC,V2y))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__EXP__CONG,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ! [V3e] :
( mem(V3e,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2EEXP,V1x),V3e)),ap(ap(c_2Earithmetic_2EEXP,V2y),V3e))) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEXP__MOD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2e] :
( mem(V2e,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),V2e)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EEXP,V1x),V2e)),V0n) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__SYM,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y))
<=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V2y),V1x)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__TRANS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ! [V3z] :
( mem(V3z,ty_2Enum_2Enum)
=> ( ( p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y))
& p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V2y),V3z)) )
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V3z)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__NUMERAL,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m)))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m)))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m)))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))))) )
& ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m)))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__MOD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),V1x)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EMODEQ__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V0n),c_2Enum_2E0)) ) ) ).
fof(conj_thm_2Earithmetic_2Enum__case__eq,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1zc] :
( mem(V1zc,A_27a)
=> ! [V2sc] :
( mem(V2sc,arr(ty_2Enum_2Enum,A_27a))
=> ! [V3v] :
( mem(V3v,A_27a)
=> ( ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V0n),V1zc),V2sc) = V3v
<=> ( ( V0n = c_2Enum_2E0
& V1zc = V3v )
| ? [V4x] :
( mem(V4x,ty_2Enum_2Enum)
& V0n = ap(c_2Enum_2ESUC,V4x)
& ap(V2sc,V4x) = V3v ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2Edatatype__num,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0num] :
( mem(V0num,arr(ty_2Enum_2Enum,arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),A_27a)))
=> p(ap(c_2Ebool_2EDATATYPE(A_27a),ap(ap(V0num,c_2Enum_2E0),c_2Enum_2ESUC))) ) ) ).
%------------------------------------------------------------------------------