ITP001 Axioms: ITP073+5.ax
%------------------------------------------------------------------------------
% File : ITP073+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 : quotient_sum+2.ax [Gau20]
% : HL4073+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 16 ( 0 unt; 0 def)
% Number of atoms : 252 ( 4 equ)
% Maximal formula atoms : 31 ( 15 avg)
% Number of connectives : 236 ( 0 ~; 0 |; 7 &)
% ( 8 <=>; 221 =>; 0 <=; 0 <~>)
% Maximal formula depth : 55 ( 25 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-4 aty)
% Number of variables : 187 ( 187 !; 0 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Equotient__sum_2E_2B_2B_2B,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27b,bool)),arr(ty_2Esum_2Esum(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),bool))))) ) ) ).
fof(conj_thm_2Equotient__sum_2ESUM__REL__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27b,bool)),arr(ty_2Esum_2Esum(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),bool)))))
=> ( ( ! [V1R1] :
( mem(V1R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V2R2] :
( mem(V2R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V3a1] :
( mem(V3a1,A_27a)
=> ! [V4a2] :
( mem(V4a2,A_27a)
=> p(ap(ap(ap(ap(V0P,V1R1),V2R2),ap(c_2Esum_2EINL(A_27a,A_27b),V3a1)),ap(c_2Esum_2EINL(A_27a,A_27b),V4a2))) ) ) ) )
& ! [V5R1] :
( mem(V5R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V6R2] :
( mem(V6R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V7b1] :
( mem(V7b1,A_27b)
=> ! [V8b2] :
( mem(V8b2,A_27b)
=> p(ap(ap(ap(ap(V0P,V5R1),V6R2),ap(c_2Esum_2EINR(A_27a,A_27b),V7b1)),ap(c_2Esum_2EINR(A_27a,A_27b),V8b2))) ) ) ) )
& ! [V9R1] :
( mem(V9R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V10R2] :
( mem(V10R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V11a1] :
( mem(V11a1,A_27a)
=> ! [V12b2] :
( mem(V12b2,A_27b)
=> p(ap(ap(ap(ap(V0P,V9R1),V10R2),ap(c_2Esum_2EINL(A_27a,A_27b),V11a1)),ap(c_2Esum_2EINR(A_27a,A_27b),V12b2))) ) ) ) )
& ! [V13R1] :
( mem(V13R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V14R2] :
( mem(V14R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V15b1] :
( mem(V15b1,A_27b)
=> ! [V16a2] :
( mem(V16a2,A_27a)
=> p(ap(ap(ap(ap(V0P,V13R1),V14R2),ap(c_2Esum_2EINR(A_27a,A_27b),V15b1)),ap(c_2Esum_2EINL(A_27a,A_27b),V16a2))) ) ) ) ) )
=> ! [V17v] :
( mem(V17v,arr(A_27a,arr(A_27a,bool)))
=> ! [V18v1] :
( mem(V18v1,arr(A_27b,arr(A_27b,bool)))
=> ! [V19v2] :
( mem(V19v2,ty_2Esum_2Esum(A_27a,A_27b))
=> ! [V20v3] :
( mem(V20v3,ty_2Esum_2Esum(A_27a,A_27b))
=> p(ap(ap(ap(ap(V0P,V17v),V18v1),V19v2),V20v3)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2ESUM__REL__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2a1] :
( mem(V2a1,A_27a)
=> ! [V3a2] :
( mem(V3a2,A_27a)
=> ! [V4b1] :
( mem(V4b1,A_27b)
=> ! [V5b2] :
( mem(V5b2,A_27b)
=> ( ( p(ap(ap(ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V1R2),ap(c_2Esum_2EINL(A_27a,A_27b),V2a1)),ap(c_2Esum_2EINL(A_27a,A_27b),V3a2)))
<=> p(ap(ap(V0R1,V2a1),V3a2)) )
& ( p(ap(ap(ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V1R2),ap(c_2Esum_2EINR(A_27a,A_27b),V4b1)),ap(c_2Esum_2EINR(A_27a,A_27b),V5b2)))
<=> p(ap(ap(V1R2,V4b1),V5b2)) )
& ( p(ap(ap(ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V1R2),ap(c_2Esum_2EINL(A_27a,A_27b),V2a1)),ap(c_2Esum_2EINR(A_27a,A_27b),V5b2)))
<=> $false )
& ( p(ap(ap(ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V1R2),ap(c_2Esum_2EINR(A_27a,A_27b),V4b1)),ap(c_2Esum_2EINL(A_27a,A_27b),V3a2)))
<=> $false ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2ESUM__REL__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),c_2Emin_2E_3D(A_27a)),c_2Emin_2E_3D(A_27b)) = c_2Emin_2E_3D(ty_2Esum_2Esum(A_27a,A_27b)) ) ) ).
fof(conj_thm_2Equotient__sum_2ESUM__EQUIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ( p(ap(c_2Equotient_2EEQUIV(A_27a),V0R1))
=> ( p(ap(c_2Equotient_2EEQUIV(A_27b),V1R2))
=> p(ap(c_2Equotient_2EEQUIV(ty_2Esum_2Esum(A_27a,A_27b)),ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V1R2))) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2ESUM__QUOTIENT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> p(ap(ap(ap(c_2Equotient_2EQUOTIENT(ty_2Esum_2Esum(A_27a,A_27b),ty_2Esum_2Esum(A_27c,A_27d)),ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V3R2)),ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V1abs1),V4abs2)),ap(ap(c_2Esum_2E_2B_2B(A_27c,A_27d,A_27a,A_27b),V2rep1),V5rep2))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2EINL__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6a] :
( mem(V6a,A_27c)
=> ap(c_2Esum_2EINL(A_27c,A_27d),V6a) = ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V1abs1),V4abs2),ap(c_2Esum_2EINL(A_27a,A_27b),ap(V2rep1,V6a))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2EINL__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6a1] :
( mem(V6a1,A_27a)
=> ! [V7a2] :
( mem(V7a2,A_27a)
=> ( p(ap(ap(V0R1,V6a1),V7a2))
=> p(ap(ap(ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V3R2),ap(c_2Esum_2EINL(A_27a,A_27b),V6a1)),ap(c_2Esum_2EINL(A_27a,A_27b),V7a2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2EINR__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6b] :
( mem(V6b,A_27d)
=> ap(c_2Esum_2EINR(A_27c,A_27d),V6b) = ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V1abs1),V4abs2),ap(c_2Esum_2EINR(A_27a,A_27b),ap(V5rep2,V6b))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2EINR__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6b1] :
( mem(V6b1,A_27b)
=> ! [V7b2] :
( mem(V7b2,A_27b)
=> ( p(ap(ap(V3R2,V6b1),V7b2))
=> p(ap(ap(ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V3R2),ap(c_2Esum_2EINR(A_27a,A_27b),V6b1)),ap(c_2Esum_2EINR(A_27a,A_27b),V7b2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2EISL__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6a] :
( mem(V6a,ty_2Esum_2Esum(A_27c,A_27d))
=> ( p(ap(c_2Esum_2EISL(A_27c,A_27d),V6a))
<=> p(ap(c_2Esum_2EISL(A_27a,A_27b),ap(ap(ap(c_2Esum_2E_2B_2B(A_27c,A_27d,A_27a,A_27b),V2rep1),V5rep2),V6a))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2EISL__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6a1] :
( mem(V6a1,ty_2Esum_2Esum(A_27a,A_27b))
=> ! [V7a2] :
( mem(V7a2,ty_2Esum_2Esum(A_27a,A_27b))
=> ( p(ap(ap(ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V3R2),V6a1),V7a2))
=> ( p(ap(c_2Esum_2EISL(A_27a,A_27b),V6a1))
<=> p(ap(c_2Esum_2EISL(A_27a,A_27b),V7a2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2EISR__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6a] :
( mem(V6a,ty_2Esum_2Esum(A_27c,A_27d))
=> ( p(ap(c_2Esum_2EISR(A_27c,A_27d),V6a))
<=> p(ap(c_2Esum_2EISR(A_27a,A_27b),ap(ap(ap(c_2Esum_2E_2B_2B(A_27c,A_27d,A_27a,A_27b),V2rep1),V5rep2),V6a))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2EISR__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6a1] :
( mem(V6a1,ty_2Esum_2Esum(A_27a,A_27b))
=> ! [V7a2] :
( mem(V7a2,ty_2Esum_2Esum(A_27a,A_27b))
=> ( p(ap(ap(ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27b),V0R1),V3R2),V6a1),V7a2))
=> ( p(ap(c_2Esum_2EISR(A_27a,A_27b),V6a1))
<=> p(ap(c_2Esum_2EISR(A_27a,A_27b),V7a2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2ESUM__MAP__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [A_27g] :
( ne(A_27g)
=> ! [A_27h] :
( ne(A_27h)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27e))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27e,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27e),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27f))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27f,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27f),V3R2),V4abs2),V5rep2))
=> ! [V6R3] :
( mem(V6R3,arr(A_27c,arr(A_27c,bool)))
=> ! [V7abs3] :
( mem(V7abs3,arr(A_27c,A_27g))
=> ! [V8rep3] :
( mem(V8rep3,arr(A_27g,A_27c))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27c,A_27g),V6R3),V7abs3),V8rep3))
=> ! [V9R4] :
( mem(V9R4,arr(A_27d,arr(A_27d,bool)))
=> ! [V10abs4] :
( mem(V10abs4,arr(A_27d,A_27h))
=> ! [V11rep4] :
( mem(V11rep4,arr(A_27h,A_27d))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27d,A_27h),V9R4),V10abs4),V11rep4))
=> ! [V12f] :
( mem(V12f,arr(A_27e,A_27f))
=> ! [V13g] :
( mem(V13g,arr(A_27g,A_27h))
=> ap(ap(c_2Esum_2E_2B_2B(A_27e,A_27g,A_27f,A_27h),V12f),V13g) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(ty_2Esum_2Esum(A_27e,A_27g),ty_2Esum_2Esum(A_27b,A_27d),ty_2Esum_2Esum(A_27a,A_27c),ty_2Esum_2Esum(A_27f,A_27h)),ap(ap(c_2Esum_2E_2B_2B(A_27e,A_27g,A_27a,A_27c),V2rep1),V8rep3)),ap(ap(c_2Esum_2E_2B_2B(A_27b,A_27d,A_27f,A_27h),V4abs2),V10abs4)),ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27c,A_27b,A_27d),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27f,A_27e,A_27b),V1abs1),V5rep2),V12f)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27h,A_27g,A_27d),V7abs3),V11rep4),V13g))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient__sum_2ESUM__MAP__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [A_27g] :
( ne(A_27g)
=> ! [A_27h] :
( ne(A_27h)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27e))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27e,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27e),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27f))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27f,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27f),V3R2),V4abs2),V5rep2))
=> ! [V6R3] :
( mem(V6R3,arr(A_27c,arr(A_27c,bool)))
=> ! [V7abs3] :
( mem(V7abs3,arr(A_27c,A_27g))
=> ! [V8rep3] :
( mem(V8rep3,arr(A_27g,A_27c))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27c,A_27g),V6R3),V7abs3),V8rep3))
=> ! [V9R4] :
( mem(V9R4,arr(A_27d,arr(A_27d,bool)))
=> ! [V10abs4] :
( mem(V10abs4,arr(A_27d,A_27h))
=> ! [V11rep4] :
( mem(V11rep4,arr(A_27h,A_27d))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27d,A_27h),V9R4),V10abs4),V11rep4))
=> ! [V12f1] :
( mem(V12f1,arr(A_27a,A_27b))
=> ! [V13f2] :
( mem(V13f2,arr(A_27a,A_27b))
=> ! [V14g1] :
( mem(V14g1,arr(A_27c,A_27d))
=> ! [V15g2] :
( mem(V15g2,arr(A_27c,A_27d))
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V12f1),V13f2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27c,A_27d),V6R3),V9R4),V14g1),V15g2)) )
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(ty_2Esum_2Esum(A_27a,A_27c),ty_2Esum_2Esum(A_27b,A_27d)),ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27a,A_27c),V0R1),V6R3)),ap(ap(c_2Equotient__sum_2E_2B_2B_2B(A_27b,A_27d),V3R2),V9R4)),ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27c,A_27b,A_27d),V12f1),V14g1)),ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27c,A_27b,A_27d),V13f2),V15g2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------