ITP001 Axioms: ITP039+5.ax
%------------------------------------------------------------------------------
% File : ITP039+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 : defCNF+2.ax [Gau20]
% : HL4039+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 31 ( 10 avg)
% Number of connectives : 139 ( 0 ~; 0 |; 25 &)
% ( 23 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-2 aty)
% Number of variables : 89 ( 86 !; 3 ?)
% SPC : FOF_SAT_RFO_NEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2EdefCNF_2EDEF,axiom,
mem(c_2EdefCNF_2EDEF,arr(arr(ty_2Enum_2Enum,bool),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))),bool)))) ).
fof(mem_c_2EdefCNF_2EOK,axiom,
mem(c_2EdefCNF_2EOK,arr(ty_2Enum_2Enum,arr(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),bool))) ).
fof(mem_c_2EdefCNF_2EOKDEF,axiom,
mem(c_2EdefCNF_2EOKDEF,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))),bool))) ).
fof(mem_c_2EdefCNF_2EUNIQUE,axiom,
mem(c_2EdefCNF_2EUNIQUE,arr(arr(ty_2Enum_2Enum,bool),arr(ty_2Enum_2Enum,arr(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),bool)))) ).
fof(conj_thm_2EdefCNF_2EUNIQUE__ind,axiom,
! [V0P] :
( mem(V0P,arr(arr(ty_2Enum_2Enum,bool),arr(ty_2Enum_2Enum,arr(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),bool))))
=> ( ( ! [V1v] :
( mem(V1v,arr(ty_2Enum_2Enum,bool))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3conn] :
( mem(V3conn,arr(bool,arr(bool,bool)))
=> ! [V4i] :
( mem(V4i,ty_2Enum_2Enum)
=> ! [V5j] :
( mem(V5j,ty_2Enum_2Enum)
=> p(ap(ap(ap(V0P,V1v),V2n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V3conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V4i)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V5j))))) ) ) ) ) )
& ! [V6v] :
( mem(V6v,arr(ty_2Enum_2Enum,bool))
=> ! [V7n] :
( mem(V7n,ty_2Enum_2Enum)
=> ! [V8conn] :
( mem(V8conn,arr(bool,arr(bool,bool)))
=> ! [V9i] :
( mem(V9i,ty_2Enum_2Enum)
=> ! [V10b] :
( mem(V10b,bool)
=> p(ap(ap(ap(V0P,V6v),V7n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V8conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V9i)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V10b))))) ) ) ) ) )
& ! [V11v] :
( mem(V11v,arr(ty_2Enum_2Enum,bool))
=> ! [V12n] :
( mem(V12n,ty_2Enum_2Enum)
=> ! [V13conn] :
( mem(V13conn,arr(bool,arr(bool,bool)))
=> ! [V14a] :
( mem(V14a,bool)
=> ! [V15j] :
( mem(V15j,ty_2Enum_2Enum)
=> p(ap(ap(ap(V0P,V11v),V12n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V13conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V14a)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V15j))))) ) ) ) ) )
& ! [V16v] :
( mem(V16v,arr(ty_2Enum_2Enum,bool))
=> ! [V17n] :
( mem(V17n,ty_2Enum_2Enum)
=> ! [V18conn] :
( mem(V18conn,arr(bool,arr(bool,bool)))
=> ! [V19a] :
( mem(V19a,bool)
=> ! [V20b] :
( mem(V20b,bool)
=> p(ap(ap(ap(V0P,V16v),V17n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V18conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V19a)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V20b))))) ) ) ) ) ) )
=> ! [V21v] :
( mem(V21v,arr(ty_2Enum_2Enum,bool))
=> ! [V22v1] :
( mem(V22v1,ty_2Enum_2Enum)
=> ! [V23v2] :
( mem(V23v2,arr(bool,arr(bool,bool)))
=> ! [V24v3] :
( mem(V24v3,ty_2Esum_2Esum(ty_2Enum_2Enum,bool))
=> ! [V25v4] :
( mem(V25v4,ty_2Esum_2Esum(ty_2Enum_2Enum,bool))
=> p(ap(ap(ap(V0P,V21v),V22v1),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V23v2),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),V24v3),V25v4)))) ) ) ) ) ) ) ) ).
fof(conj_thm_2EdefCNF_2EUNIQUE__def,axiom,
! [V0v] :
( mem(V0v,arr(ty_2Enum_2Enum,bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2conn] :
( mem(V2conn,arr(bool,arr(bool,bool)))
=> ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ! [V4j] :
( mem(V4j,ty_2Enum_2Enum)
=> ! [V5b] :
( mem(V5b,bool)
=> ! [V6a] :
( mem(V6a,bool)
=> ( ( p(ap(ap(ap(c_2EdefCNF_2EUNIQUE,V0v),V1n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V2conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V3i)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V4j)))))
<=> ( p(ap(V0v,V1n))
<=> p(ap(ap(V2conn,ap(V0v,V3i)),ap(V0v,V4j))) ) )
& ( p(ap(ap(ap(c_2EdefCNF_2EUNIQUE,V0v),V1n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V2conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V3i)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V5b)))))
<=> ( p(ap(V0v,V1n))
<=> p(ap(ap(V2conn,ap(V0v,V3i)),V5b)) ) )
& ( p(ap(ap(ap(c_2EdefCNF_2EUNIQUE,V0v),V1n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V2conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V6a)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V4j)))))
<=> ( p(ap(V0v,V1n))
<=> p(ap(ap(V2conn,V6a),ap(V0v,V4j))) ) )
& ( p(ap(ap(ap(c_2EdefCNF_2EUNIQUE,V0v),V1n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V2conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V6a)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V5b)))))
<=> ( p(ap(V0v,V1n))
<=> p(ap(ap(V2conn,V6a),V5b)) ) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2EdefCNF_2EDEF__def,axiom,
( ! [V0v] :
( mem(V0v,arr(ty_2Enum_2Enum,bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2EdefCNF_2EDEF,V0v),V1n),c_2Elist_2ENIL(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))))))
<=> $true ) ) )
& ! [V2v] :
( mem(V2v,arr(ty_2Enum_2Enum,bool))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4x] :
( mem(V4x,ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))))
=> ! [V5xs] :
( mem(V5xs,ty_2Elist_2Elist(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))))
=> ( p(ap(ap(ap(c_2EdefCNF_2EDEF,V2v),V3n),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))),V4x),V5xs)))
<=> ( p(ap(ap(ap(c_2EdefCNF_2EUNIQUE,V2v),V3n),V4x))
& p(ap(ap(ap(c_2EdefCNF_2EDEF,V2v),ap(c_2Enum_2ESUC,V3n)),V5xs)) ) ) ) ) ) ) ) ).
fof(conj_thm_2EdefCNF_2EOK__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),bool)))
=> ( ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2conn] :
( mem(V2conn,arr(bool,arr(bool,bool)))
=> ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ! [V4j] :
( mem(V4j,ty_2Enum_2Enum)
=> p(ap(ap(V0P,V1n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V2conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V3i)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V4j))))) ) ) ) )
& ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ! [V6conn] :
( mem(V6conn,arr(bool,arr(bool,bool)))
=> ! [V7i] :
( mem(V7i,ty_2Enum_2Enum)
=> ! [V8b] :
( mem(V8b,bool)
=> p(ap(ap(V0P,V5n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V6conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V7i)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V8b))))) ) ) ) )
& ! [V9n] :
( mem(V9n,ty_2Enum_2Enum)
=> ! [V10conn] :
( mem(V10conn,arr(bool,arr(bool,bool)))
=> ! [V11a] :
( mem(V11a,bool)
=> ! [V12j] :
( mem(V12j,ty_2Enum_2Enum)
=> p(ap(ap(V0P,V9n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V10conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V11a)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V12j))))) ) ) ) )
& ! [V13n] :
( mem(V13n,ty_2Enum_2Enum)
=> ! [V14conn] :
( mem(V14conn,arr(bool,arr(bool,bool)))
=> ! [V15a] :
( mem(V15a,bool)
=> ! [V16b] :
( mem(V16b,bool)
=> p(ap(ap(V0P,V13n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V14conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V15a)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V16b))))) ) ) ) ) )
=> ! [V17v] :
( mem(V17v,ty_2Enum_2Enum)
=> ! [V18v1] :
( mem(V18v1,arr(bool,arr(bool,bool)))
=> ! [V19v2] :
( mem(V19v2,ty_2Esum_2Esum(ty_2Enum_2Enum,bool))
=> ! [V20v3] :
( mem(V20v3,ty_2Esum_2Esum(ty_2Enum_2Enum,bool))
=> p(ap(ap(V0P,V17v),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V18v1),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),V19v2),V20v3)))) ) ) ) ) ) ) ).
fof(conj_thm_2EdefCNF_2EOK__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1conn] :
( mem(V1conn,arr(bool,arr(bool,bool)))
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ! [V3j] :
( mem(V3j,ty_2Enum_2Enum)
=> ! [V4b] :
( mem(V4b,bool)
=> ! [V5a] :
( mem(V5a,bool)
=> ( ( p(ap(ap(c_2EdefCNF_2EOK,V0n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V1conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V2i)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V3j)))))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2i),V0n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3j),V0n)) ) )
& ( p(ap(ap(c_2EdefCNF_2EOK,V0n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V1conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V2i)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V4b)))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V2i),V0n)) )
& ( p(ap(ap(c_2EdefCNF_2EOK,V0n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V1conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V5a)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,bool),V3j)))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V3j),V0n)) )
& ( p(ap(ap(c_2EdefCNF_2EOK,V0n),ap(ap(c_2Epair_2E_2C(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))),V1conn),ap(ap(c_2Epair_2E_2C(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V5a)),ap(c_2Esum_2EINR(ty_2Enum_2Enum,bool),V4b)))))
<=> $true ) ) ) ) ) ) ) ) ).
fof(ax_thm_2EdefCNF_2EOKDEF__def,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2EdefCNF_2EOKDEF,V0n),c_2Elist_2ENIL(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))))))
<=> $true ) )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))))
=> ! [V3xs] :
( mem(V3xs,ty_2Elist_2Elist(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))))
=> ( p(ap(ap(c_2EdefCNF_2EOKDEF,V1n),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))),V2x),V3xs)))
<=> ( p(ap(ap(c_2EdefCNF_2EOK,V1n),V2x))
& p(ap(ap(c_2EdefCNF_2EOKDEF,ap(c_2Enum_2ESUC,V1n)),V3xs)) ) ) ) ) ) ) ).
fof(conj_thm_2EdefCNF_2EDEF__SNOC,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))))
=> ! [V3v] :
( mem(V3v,arr(ty_2Enum_2Enum,bool))
=> ( p(ap(ap(ap(c_2EdefCNF_2EDEF,V3v),V0n),ap(ap(c_2Elist_2ESNOC(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))),V1x),V2l)))
<=> ( p(ap(ap(ap(c_2EdefCNF_2EDEF,V3v),V0n),V2l))
& p(ap(ap(ap(c_2EdefCNF_2EUNIQUE,V3v),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))),V2l))),V1x)) ) ) ) ) ) ) ).
fof(conj_thm_2EdefCNF_2EOKDEF__SNOC,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool))))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))))
=> ( p(ap(ap(c_2EdefCNF_2EOKDEF,V0n),ap(ap(c_2Elist_2ESNOC(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))),V1x),V2l)))
<=> ( p(ap(ap(c_2EdefCNF_2EOKDEF,V0n),V2l))
& p(ap(ap(c_2EdefCNF_2EOK,ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))),V2l))),V1x)) ) ) ) ) ) ).
fof(conj_thm_2EdefCNF_2ECONSISTENCY,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))))
=> ( p(ap(ap(c_2EdefCNF_2EOKDEF,V0n),V1l))
=> ? [V2v] :
( mem(V2v,arr(ty_2Enum_2Enum,bool))
& p(ap(ap(ap(c_2EdefCNF_2EDEF,V2v),V0n),V1l)) ) ) ) ) ).
fof(conj_thm_2EdefCNF_2EBIGSTEP,axiom,
! [V0P] :
( mem(V0P,arr(arr(ty_2Enum_2Enum,bool),bool))
=> ! [V1Q] :
( mem(V1Q,bool)
=> ! [V2R] :
( mem(V2R,arr(arr(ty_2Enum_2Enum,bool),bool))
=> ( ! [V3v] :
( mem(V3v,arr(ty_2Enum_2Enum,bool))
=> ( p(ap(V0P,V3v))
=> ( p(V1Q)
<=> p(ap(V2R,V3v)) ) ) )
=> ( ( ? [V4v] :
( mem(V4v,arr(ty_2Enum_2Enum,bool))
& p(ap(V0P,V4v)) )
& p(V1Q) )
<=> ? [V5v] :
( mem(V5v,arr(ty_2Enum_2Enum,bool))
& p(ap(V0P,V5v))
& p(ap(V2R,V5v)) ) ) ) ) ) ) ).
fof(conj_thm_2EdefCNF_2EFINAL__DEF,axiom,
! [V0v] :
( mem(V0v,arr(ty_2Enum_2Enum,bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,bool)
=> ( ( p(ap(V0v,V1n))
<=> p(V2x) )
<=> ( ( p(ap(V0v,V1n))
<=> p(V2x) )
& p(ap(ap(ap(c_2EdefCNF_2EDEF,V0v),ap(c_2Enum_2ESUC,V1n)),c_2Elist_2ENIL(ty_2Epair_2Eprod(arr(bool,arr(bool,bool)),ty_2Epair_2Eprod(ty_2Esum_2Esum(ty_2Enum_2Enum,bool),ty_2Esum_2Esum(ty_2Enum_2Enum,bool)))))) ) ) ) ) ) ).
%------------------------------------------------------------------------------