ITP001 Axioms: ITP055+5.ax
%------------------------------------------------------------------------------
% File : ITP055+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 : sum_num+2.ax [Gau20]
% : HL4055+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 24 ( 2 unt; 0 def)
% Number of atoms : 156 ( 35 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 136 ( 4 ~; 2 |; 25 &)
% ( 6 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 22 ( 22 usr; 15 con; 0-2 aty)
% Number of variables : 89 ( 87 !; 2 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Esum__num_2EGSUM,axiom,
mem(c_2Esum__num_2EGSUM,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))) ).
fof(mem_c_2Esum__num_2ESUM,axiom,
mem(c_2Esum__num_2ESUM,arr(ty_2Enum_2Enum,arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))) ).
fof(conj_thm_2Esum__num_2EGSUM__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)))
=> ( ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> p(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1n),c_2Enum_2E0)),V2f)) ) )
& ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4m] :
( mem(V4m,ty_2Enum_2Enum)
=> ! [V5f] :
( mem(V5f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( p(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V3n),V4m)),V5f))
=> p(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V3n),ap(c_2Enum_2ESUC,V4m))),V5f)) ) ) ) ) )
=> ! [V6v] :
( mem(V6v,ty_2Enum_2Enum)
=> ! [V7v1] :
( mem(V7v1,ty_2Enum_2Enum)
=> ! [V8v2] :
( mem(V8v2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> p(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V6v),V7v1)),V8v2)) ) ) ) ) ) ).
fof(conj_thm_2Esum__num_2EGSUM__def,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0n),c_2Enum_2E0)),V1f) = c_2Enum_2E0 ) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ! [V4f] :
( mem(V4f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2n),ap(c_2Enum_2ESUC,V3m))),V4f) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2n),V3m)),V4f)),ap(V4f,ap(ap(c_2Earithmetic_2E_2B,V2n),V3m))) ) ) ) ) ).
fof(conj_thm_2Esum__num_2EGSUM__def__compute,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0n),c_2Enum_2E0)),V1f) = c_2Enum_2E0 ) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ! [V4f] :
( mem(V4f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3m)))),V4f) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2n),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V4f)),ap(V4f,ap(ap(c_2Earithmetic_2E_2B,V2n),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) ) ) )
& ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ! [V6m] :
( mem(V6m,ty_2Enum_2Enum)
=> ! [V7f] :
( mem(V7f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V5n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6m)))),V7f) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V5n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6m)))),V7f)),ap(V7f,ap(ap(c_2Earithmetic_2E_2B,V5n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6m))))) ) ) ) ) ).
fof(conj_thm_2Esum__num_2EGSUM__1,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1f) = ap(V1f,V0m) ) ) ).
fof(conj_thm_2Esum__num_2EGSUM__ADD,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3f] :
( mem(V3f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n))),V3f) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),V1m)),V3f)),ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2B,V0p),V1m)),V2n)),V3f)) ) ) ) ) ).
fof(conj_thm_2Esum__num_2EGSUM__ZERO,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0p),V3m))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3m),ap(ap(c_2Earithmetic_2E_2B,V0p),V1n))) )
=> ap(V2f,V3m) = c_2Enum_2E0 ) )
<=> ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),V1n)),V2f) = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Esum__num_2EGSUM__MONO,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3f] :
( mem(V3f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))
& ap(V3f,ap(ap(c_2Earithmetic_2E_2B,V0p),V2n)) != c_2Enum_2E0 )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),V1m)),V3f)),ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),ap(c_2Enum_2ESUC,V2n))),V3f))) ) ) ) ) ) ).
fof(conj_thm_2Esum__num_2EGSUM__LESS,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3f] :
( mem(V3f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ? [V4q] :
( mem(V4q,ty_2Enum_2Enum)
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1m),V0p)),V4q))
& p(ap(ap(c_2Eprim__rec_2E_3C,V4q),ap(ap(c_2Earithmetic_2E_2B,V2n),V0p)))
& ap(V3f,V4q) != c_2Enum_2E0 )
<=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),V1m)),V3f)),ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),V2n)),V3f))) ) ) ) ) ) ).
fof(conj_thm_2Esum__num_2EGSUM__EQUAL,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3f] :
( mem(V3f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),V1m)),V3f) = ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),V2n)),V3f)
<=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))
& ! [V4q] :
( mem(V4q,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0p),V1m)),V4q))
& p(ap(ap(c_2Eprim__rec_2E_3C,V4q),ap(ap(c_2Earithmetic_2E_2B,V0p),V2n))) )
=> ap(V3f,V4q) = c_2Enum_2E0 ) ) )
| ( p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1m))
& ! [V5q] :
( mem(V5q,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0p),V2n)),V5q))
& p(ap(ap(c_2Eprim__rec_2E_3C,V5q),ap(ap(c_2Earithmetic_2E_2B,V0p),V1m))) )
=> ap(V3f,V5q) = c_2Enum_2E0 ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Esum__num_2EGSUM__FUN__EQUAL,axiom,
! [V0p] :
( mem(V0p,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V3g] :
( mem(V3g,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ! [V4x] :
( mem(V4x,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0p),V4x))
& p(ap(ap(c_2Eprim__rec_2E_3C,V4x),ap(ap(c_2Earithmetic_2E_2B,V0p),V1n))) )
=> ap(V2f,V4x) = ap(V3g,V4x) ) )
=> ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),V1n)),V2f) = ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0p),V1n)),V3g) ) ) ) ) ) ).
fof(ax_thm_2Esum__num_2ESUM__def,axiom,
( ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2ESUM,c_2Enum_2E0),V0f) = c_2Enum_2E0 )
& ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2ESUM,ap(c_2Enum_2ESUC,V1m)),V2f) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Esum__num_2ESUM,V1m),V2f)),ap(V2f,V1m)) ) ) ) ).
fof(conj_thm_2Esum__num_2ESUM__def__compute,axiom,
( ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2ESUM,c_2Enum_2E0),V0f) = c_2Enum_2E0 )
& ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2ESUM,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),V2f) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Esum__num_2ESUM,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2f)),ap(V2f,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) )
& ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ! [V4f] :
( mem(V4f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2ESUM,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V3m))),V4f) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Esum__num_2ESUM,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3m))),V4f)),ap(V4f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3m)))) ) ) ) ).
fof(conj_thm_2Esum__num_2ESUM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2ESUM,V0m),V1f) = ap(ap(c_2Esum__num_2EGSUM,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V0m)),V1f) ) ) ).
fof(conj_thm_2Esum__num_2ESUM__1,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2ESUM,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0f) = ap(V0f,c_2Enum_2E0) ) ).
fof(conj_thm_2Esum__num_2ESUM__MONO,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
& ap(V2f,V1n) != c_2Enum_2E0 )
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Esum__num_2ESUM,V0m),V2f)),ap(ap(c_2Esum__num_2ESUM,ap(c_2Enum_2ESUC,V1n)),V2f))) ) ) ) ) ).
fof(conj_thm_2Esum__num_2ESUM__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ? [V3q] :
( mem(V3q,ty_2Enum_2Enum)
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V3q))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3q),V1n))
& ap(V2f,V3q) != c_2Enum_2E0 )
<=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Esum__num_2ESUM,V0m),V2f)),ap(ap(c_2Esum__num_2ESUM,V1n),V2f))) ) ) ) ) ).
fof(conj_thm_2Esum__num_2ESUM__EQUAL,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ap(ap(c_2Esum__num_2ESUM,V0m),V2f) = ap(ap(c_2Esum__num_2ESUM,V1n),V2f)
<=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
& ! [V3q] :
( mem(V3q,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V3q))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3q),V1n)) )
=> ap(V2f,V3q) = c_2Enum_2E0 ) ) )
| ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m))
& ! [V4q] :
( mem(V4q,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V4q))
& p(ap(ap(c_2Eprim__rec_2E_3C,V4q),V0m)) )
=> ap(V2f,V4q) = c_2Enum_2E0 ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Esum__num_2ESUM__FUN__EQUAL,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V2g] :
( mem(V2g,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ! [V3x] :
( mem(V3x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3x),V0n))
=> ap(V1f,V3x) = ap(V2g,V3x) ) )
=> ap(ap(c_2Esum__num_2ESUM,V0n),V1f) = ap(ap(c_2Esum__num_2ESUM,V0n),V2g) ) ) ) ) ).
fof(conj_thm_2Esum__num_2ESUM__ZERO,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V0n))
=> ap(V1f,V2m) = c_2Enum_2E0 ) )
<=> ap(ap(c_2Esum__num_2ESUM,V0n),V1f) = c_2Enum_2E0 ) ) ) ).
fof(lameq_f1099,axiom,
! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ! [V3n] : ap(f1099(V1f,V2x),V3n) = ap(ap(c_2Earithmetic_2E_2B,ap(V1f,V3n)),V2x) ) ) ).
fof(lameq_f1100,axiom,
! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V2x] : ap(f1100(V1f),V2x) = f1099(V1f,V2x) ) ).
fof(conj_thm_2Esum__num_2ESUM__FOLDL,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(ap(c_2Esum__num_2ESUM,V0n),V1f) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Enum_2Enum,ty_2Enum_2Enum),f1100(V1f)),c_2Enum_2E0),ap(c_2Erich__list_2ECOUNT__LIST,V0n)) ) ) ).
%------------------------------------------------------------------------------