%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWV905-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 19:23:12 EDT 2022
% Result : Unsatisfiable 12.89s 13.13s
% Output : CNFRefutation 12.93s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(c_fequal(V_x,T_a),V_x)),
input ).
fof(cls_ATP__Linkup_Oequal__imp__fequal_0_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(c_fequal(V_x,T_a),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
input ).
fof(clsarity_bool__HOL_Oord_0,plain,
( class_HOL_Oord(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__HOL_Oord]) ).
cnf(clsarity_bool__HOL_Ominus,axiom,
class_HOL_Ominus(tc_bool),
input ).
fof(clsarity_bool__HOL_Ominus_0,plain,
( class_HOL_Ominus(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__HOL_Ominus]) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
input ).
fof(clsarity_bool__Orderings_Obot_0,plain,
( class_Orderings_Obot(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Obot]) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Oorder]) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Olattice_0,plain,
( class_Lattices_Olattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Olattice]) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Opreorder]) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
input ).
fof(clsarity_bool__Finite__Set_Ofinite_Ofinite_0,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite]) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Obounded__lattice_0,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Obounded__lattice]) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Odistrib__lattice_0,plain,
( class_Lattices_Odistrib__lattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Odistrib__lattice]) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Olower__semilattice_0,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Olower__semilattice]) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Oupper__semilattice_0,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Oupper__semilattice]) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
input ).
fof(clsarity_bool__Complete__Lattice_Ocomplete__lattice_0,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Complete__Lattice_Ocomplete__lattice]) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat),
input ).
fof(clsarity_nat__HOL_Oord_0,plain,
( class_HOL_Oord(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__HOL_Oord]) ).
cnf(clsarity_nat__HOL_Ominus,axiom,
class_HOL_Ominus(tc_nat),
input ).
fof(clsarity_nat__HOL_Ominus_0,plain,
( class_HOL_Ominus(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__HOL_Ominus]) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
input ).
fof(clsarity_nat__Orderings_Obot_0,plain,
( class_Orderings_Obot(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Obot]) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Oorder]) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat),
input ).
fof(clsarity_nat__Lattices_Olattice_0,plain,
( class_Lattices_Olattice(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Lattices_Olattice]) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Olinorder_0,plain,
( class_Orderings_Olinorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Opreorder]) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
input ).
fof(clsarity_nat__Lattices_Odistrib__lattice_0,plain,
( class_Lattices_Odistrib__lattice(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Lattices_Odistrib__lattice]) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
input ).
fof(clsarity_nat__Lattices_Olower__semilattice_0,plain,
( class_Lattices_Olower__semilattice(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Lattices_Olower__semilattice]) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
input ).
fof(clsarity_nat__Lattices_Oupper__semilattice_0,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Lattices_Oupper__semilattice]) ).
cnf(cls_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),
input ).
fof(cls_doubleton__eq__iff_4_0,plain,
! [T_a,V_x,V_xa] :
( c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_doubleton__eq__iff_4]) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a),
input ).
fof(cls_insert__commute_0_0,plain,
! [T_a,V_A,V_x,V_y] :
( c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__commute_0]) ).
cnf(cls_insertCI_1,axiom,
hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)),
input ).
fof(cls_insertCI_1_0,plain,
! [T_a,V_B,V_x] :
( hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a))
| $false ),
inference(orientation,[status(thm)],[cls_insertCI_1]) ).
cnf(cls_insertI1_0,axiom,
hBOOL(c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a)),
input ).
fof(cls_insertI1_0_0,plain,
! [T_a,V_B,V_a] :
( hBOOL(c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a))
| $false ),
inference(orientation,[status(thm)],[cls_insertI1_0]) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a)),
input ).
fof(cls_insert__iff_1_0,plain,
! [T_a,V_A,V_x] :
( hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a))
| $false ),
inference(orientation,[status(thm)],[cls_insert__iff_1]) ).
cnf(cls_insert__not__empty_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_insert__not__empty_0_0,plain,
! [T_a,V_A,V_a] :
( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_insert__not__empty_0]) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a),
input ).
fof(cls_insert__absorb2_0_0,plain,
! [T_a,V_A,V_x] :
( c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__absorb2_0]) ).
cnf(cls_empty_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a),
input ).
fof(cls_empty_0_0,plain,
! [T_a,V_G] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_empty_0]) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
input ).
fof(cls_bot1E_0_0,plain,
! [T_a,V_x] :
( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_bot1E_0]) ).
cnf(cls_bot__empty__eq_0,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
input ).
fof(cls_bot__empty__eq_0_0,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)
| $false ),
inference(orientation,[status(thm)],[cls_bot__empty__eq_0]) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a),
input ).
fof(cls_empty__not__insert_0_0,plain,
! [T_a,V_A,V_a] :
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_empty__not__insert_0]) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),
input ).
fof(cls_emptyE_0_0,plain,
! [T_a,V_a] :
( ~ hBOOL(c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))
| $false ),
inference(orientation,[status(thm)],[cls_emptyE_0]) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),
input ).
fof(cls_empty__iff_0_0,plain,
! [T_a,V_c] :
( ~ hBOOL(c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))
| $false ),
inference(orientation,[status(thm)],[cls_empty__iff_0]) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),
input ).
fof(cls_ex__in__conv_0_0,plain,
! [T_a,V_x] :
( ~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))
| $false ),
inference(orientation,[status(thm)],[cls_ex__in__conv_0]) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)),
input ).
fof(cls_insert__code_1_0,plain,
! [T_a,V_A,V_x] :
( hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_insert__code_1]) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)),
input ).
fof(cls_singleton__iff_1_0,plain,
! [T_a,V_x] :
( hBOOL(c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a))
| $false ),
inference(orientation,[status(thm)],[cls_singleton__iff_1]) ).
cnf(cls_vimage__singleton__eq_1,axiom,
hBOOL(c_in(V_a,c_Set_Ovimage(V_f,c_Set_Oinsert(hAPP(V_f,V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_aa,T_a),T_aa)),
input ).
fof(cls_vimage__singleton__eq_1_0,plain,
! [T_a,T_aa,V_a,V_f] :
( hBOOL(c_in(V_a,c_Set_Ovimage(V_f,c_Set_Oinsert(hAPP(V_f,V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_aa,T_a),T_aa))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__singleton__eq_1]) ).
cnf(cls_finite__dom__body_0,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
input ).
fof(cls_finite__dom__body_0_0,plain,
( c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| $false ),
inference(orientation,[status(thm)],[cls_finite__dom__body_0]) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_insert__is__Un_0_0,plain,
! [T_a,V_A,V_a] :
( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_insert__is__Un_0]) ).
cnf(cls_insert__Diff__single_0,axiom,
c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,V_A,T_a),
input ).
fof(cls_insert__Diff__single_0_0,plain,
! [T_a,V_A,V_a] :
( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,V_A,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__Diff__single_0]) ).
cnf(cls_fold1__singleton_0,axiom,
c_Finite__Set_Ofold1(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a,
input ).
fof(cls_fold1__singleton_0_0,plain,
! [T_a,V_a,V_f] :
( c_Finite__Set_Ofold1(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a
| $false ),
inference(orientation,[status(thm)],[cls_fold1__singleton_0]) ).
cnf(cls_contents__eq_0,axiom,
c_Set_Ocontents(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_x,
input ).
fof(cls_contents__eq_0_0,plain,
! [T_a,V_x] :
( c_Set_Ocontents(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_contents__eq_0]) ).
cnf(cls_Diff__insert_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__insert_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__insert_0]) ).
cnf(cls_Diff__insert2_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__insert2_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__insert2_0]) ).
cnf(cls_Nitpick_OThe__psimp_0,axiom,
c_The(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_x,
input ).
fof(cls_Nitpick_OThe__psimp_0_0,plain,
! [T_a,V_x] :
( c_The(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_Nitpick_OThe__psimp_0]) ).
cnf(cls_fold1Set__sing_1,axiom,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),V_x)),
input ).
fof(cls_fold1Set__sing_1_0,plain,
! [T_a,V_f,V_x] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_fold1Set__sing_1]) ).
cnf(cls_UN__extend__simps_I1_J_0,axiom,
c_Set_Oinsert(V_a,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_UN__extend__simps_I1_J_0_0,plain,
! [T_a,T_b,V_B,V_a] :
( c_Set_Oinsert(V_a,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_UN__extend__simps_I1_J_0]) ).
cnf(cls_Nitpick_OEx1__def_2,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a))),
input ).
fof(cls_Nitpick_OEx1__def_2_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_Nitpick_OEx1__def_2]) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(c_fequal(V_a,T_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_singleton__conv2_0_0,plain,
! [T_a,V_a] :
( c_Collect(c_fequal(V_a,T_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_singleton__conv2_0]) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__Un_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__Un_0]) ).
cnf(cls_the_Osimps_0,axiom,
c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x,
input ).
fof(cls_the_Osimps_0_0,plain,
! [T_a,V_x] :
( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_the_Osimps_0]) ).
cnf(cls_the__sym__eq__trivial_0,axiom,
c_The(c_fequal(V_x,T_a),T_a) = V_x,
input ).
fof(cls_the__sym__eq__trivial_0_0,plain,
! [T_a,V_x] :
( c_The(c_fequal(V_x,T_a),T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_the__sym__eq__trivial_0]) ).
cnf(cls_UN__Un_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),V_M,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_b,tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_B,V_M,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_UN__Un_0_0,plain,
! [T_a,T_b,V_A,V_B,V_M] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),V_M,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_b,tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_B,V_M,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_UN__Un_0]) ).
cnf(cls_Diff__Int_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Int_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int_0]) ).
cnf(cls_Int__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool))),
input ).
fof(cls_Int__Diff_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Diff_0]) ).
cnf(cls_Diff__Un_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool))),
input ).
fof(cls_Diff__Un_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Un_0]) ).
cnf(cls_subset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_subset__refl_0_0,plain,
! [T_a,V_A] :
( c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_subset__refl_0]) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)),
input ).
fof(cls_equalityE_0_0,plain,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_equalityE_0]) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A,
input ).
fof(cls_Int__absorb_0_0,plain,
! [T_a,V_A] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Int__absorb_0]) ).
cnf(cls_Int__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),
input ).
fof(cls_Int__left__absorb_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)
| $false ),
inference(orientation,[status(thm)],[cls_Int__left__absorb_0]) ).
cnf(cls_Un__Int__distrib2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),V_A,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool))),
input ).
fof(cls_Un__Int__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),V_A,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__distrib2_0]) ).
cnf(cls_Un__Int__distrib_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool))),
input ).
fof(cls_Un__Int__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__distrib_0]) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__lower2_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__lower2_0]) ).
cnf(cls_Int__lower1_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__lower1_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__lower1_0]) ).
cnf(cls_UN__insert_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(V_a,V_A,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_UN__insert_0_0,plain,
! [T_a,T_b,V_A,V_B,V_a] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(V_a,V_A,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_UN__insert_0]) ).
cnf(cls_Un__Diff__Int_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Un__Diff__Int_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__Diff__Int_0]) ).
cnf(cls_Diff__Int2_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Int2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int2_0]) ).
cnf(cls_Diff__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),V_C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Int__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),V_C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int__distrib2_0]) ).
cnf(cls_Diff__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Int__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int__distrib_0]) ).
cnf(cls_UN__extend__simps_I3_J_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_UN__extend__simps_I3_J_0_0,plain,
! [T_a,T_b,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_UN__extend__simps_I3_J_0]) ).
cnf(cls_com_Osimps_I62_J_0,axiom,
c_Com_Ocom_OBODY(V_pname) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H),
input ).
fof(cls_com_Osimps_I62_J_0_0,plain,
! [V_fun_H,V_pname,V_pname_H,V_vname_H] :
( c_Com_Ocom_OBODY(V_pname) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I62_J_0]) ).
cnf(cls_com_Osimps_I63_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OBODY(V_pname),
input ).
fof(cls_com_Osimps_I63_J_0_0,plain,
! [V_fun_H,V_pname,V_pname_H,V_vname_H] :
( c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OBODY(V_pname)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I63_J_0]) ).
cnf(cls_Un__insert__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_Un__insert__left_0_0,plain,
! [T_a,V_B,V_C,V_a] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Un__insert__left_0]) ).
cnf(cls_Un__insert__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_Un__insert__right_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Un__insert__right_0]) ).
cnf(cls_insert__inter__insert_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_A,T_a)),c_Set_Oinsert(V_a,V_B,T_a)) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a),
input ).
fof(cls_insert__inter__insert_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_A,T_a)),c_Set_Oinsert(V_a,V_B,T_a)) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__inter__insert_0]) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_subset__insertI_0_0,plain,
! [T_a,V_B,V_a] :
( c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_subset__insertI_0]) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a),
input ).
fof(cls_image__insert_0_0,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_image__insert_0]) ).
cnf(cls_vimage__insert_0,axiom,
c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)),
input ).
fof(cls_vimage__insert_0_0,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__insert_0]) ).
cnf(cls_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a),
input ).
fof(cls_empty__is__image_1_0,plain,
! [T_a,T_b,V_f] :
( c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_empty__is__image_1]) ).
cnf(cls_fold__graph_OemptyI_0,axiom,
c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_z,T_a,T_b),
input ).
fof(cls_fold__graph_OemptyI_0_0,plain,
! [T_a,T_b,V_f,V_z] :
( c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_z,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_fold__graph_OemptyI_0]) ).
cnf(cls_image__empty_0,axiom,
c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__empty_0_0,plain,
! [T_a,T_b,V_f] :
( c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__empty_0]) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_empty__subsetI_0_0,plain,
! [T_a,V_A] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_empty__subsetI_0]) ).
cnf(cls_Int__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__empty__left_0_0,plain,
! [T_a,V_B] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__empty__left_0]) ).
cnf(cls_Int__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__empty__right_0_0,plain,
! [T_a,V_A] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__empty__right_0]) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_finite_OemptyI_0_0,plain,
! [T_a] :
( c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_finite_OemptyI_0]) ).
cnf(cls_Diff__empty_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Diff__empty_0_0,plain,
! [T_a,V_A] :
( c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Diff__empty_0]) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__cancel_0_0,plain,
! [T_a,V_A] :
( c_HOL_Ominus__class_Ominus(V_A,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__cancel_0]) ).
cnf(cls_Un__empty__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B,
input ).
fof(cls_Un__empty__left_0_0,plain,
! [T_a,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B
| $false ),
inference(orientation,[status(thm)],[cls_Un__empty__left_0]) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Un__empty__right_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__empty__right_0]) ).
cnf(cls_empty__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_empty__Diff_0_0,plain,
! [T_a,V_A] :
( c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_empty__Diff_0]) ).
cnf(cls_empty__fold1SetE_0,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_x)),
input ).
fof(cls_empty__fold1SetE_0_0,plain,
! [T_a,V_f,V_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_empty__fold1SetE_0]) ).
cnf(cls_subset__empty_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_subset__empty_1_0,plain,
! [T_a] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_subset__empty_1]) ).
cnf(cls_Un__empty_2,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__empty_2_0,plain,
! [T_a] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__empty_2]) ).
cnf(cls_vimage__empty_0,axiom,
c_Set_Ovimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_vimage__empty_0_0,plain,
! [T_a,T_b,V_f] :
( c_Set_Ovimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__empty_0]) ).
cnf(cls_UN__extend__simps_I2_J_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B,
input ).
fof(cls_UN__extend__simps_I2_J_0_0,plain,
! [T_a,T_b,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B
| $false ),
inference(orientation,[status(thm)],[cls_UN__extend__simps_I2_J_0]) ).
cnf(cls_Int__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)),
input ).
fof(cls_Int__left__commute_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C))
| $false ),
inference(orientation,[status(thm)],[cls_Int__left__commute_0]) ).
cnf(cls_Int__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)),
input ).
fof(cls_Int__assoc_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C))
| $false ),
inference(orientation,[status(thm)],[cls_Int__assoc_0]) ).
cnf(cls_map__add__assoc_0,axiom,
c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b),
input ).
fof(cls_map__add__assoc_0_0,plain,
! [T_a,T_b,V_m1,V_m2,V_m3] :
( c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_map__add__assoc_0]) ).
cnf(cls_not__None__eq_1,axiom,
c_Option_Ooption_OSome(V_xa,T_a) != c_Option_Ooption_ONone(T_a),
input ).
fof(cls_not__None__eq_1_0,plain,
! [T_a,V_xa] :
( c_Option_Ooption_OSome(V_xa,T_a) != c_Option_Ooption_ONone(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__None__eq_1]) ).
cnf(cls_option_Osimps_I3_J_0,axiom,
c_Option_Ooption_OSome(V_a_H,T_a) != c_Option_Ooption_ONone(T_a),
input ).
fof(cls_option_Osimps_I3_J_0_0,plain,
! [T_a,V_a_H] :
( c_Option_Ooption_OSome(V_a_H,T_a) != c_Option_Ooption_ONone(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I3_J_0]) ).
cnf(cls_image__Int__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_b,T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_b,T_a)),c_Set_Oimage(V_f,V_B,T_b,T_a)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__Int__subset_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_lessequals(c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_b,T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_b,T_a)),c_Set_Oimage(V_f,V_B,T_b,T_a)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__Int__subset_0]) ).
cnf(cls_dom__map__add_0,axiom,
c_Map_Odom(c_Map_Omap__add(V_m,V_n,T_a,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(V_n,T_a,T_b),c_Map_Odom(V_m,T_a,T_b),tc_fun(T_a,tc_bool)),
input ).
fof(cls_dom__map__add_0_0,plain,
! [T_a,T_b,V_m,V_n] :
( c_Map_Odom(c_Map_Omap__add(V_m,V_n,T_a,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(V_n,T_a,T_b),c_Map_Odom(V_m,T_a,T_b),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_dom__map__add_0]) ).
cnf(cls_map__le__refl_0,axiom,
c_Map_Omap__le(V_f,V_f,T_a,T_b),
input ).
fof(cls_map__le__refl_0_0,plain,
! [T_a,T_b,V_f] :
( c_Map_Omap__le(V_f,V_f,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_map__le__refl_0]) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(V_P,T_a) = V_P,
input ).
fof(cls_Collect__def_0_0,plain,
! [T_a,V_P] :
( c_Collect(V_P,T_a) = V_P
| $false ),
inference(orientation,[status(thm)],[cls_Collect__def_0]) ).
cnf(cls_image__vimage__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a),V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__vimage__subset_0_0,plain,
! [T_a,T_b,V_A,V_f] :
( c_lessequals(c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a),V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__vimage__subset_0]) ).
cnf(cls_vimage__Diff_0,axiom,
c_Set_Ovimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)),
input ).
fof(cls_vimage__Diff_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Ovimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__Diff_0]) ).
cnf(cls_fold1__def_0,axiom,
c_Finite__Set_Ofold1(V_f,V_A,T_a) = c_The(c_Finite__Set_Ofold1Set(V_f,V_A,T_a),T_a),
input ).
fof(cls_fold1__def_0_0,plain,
! [T_a,V_A,V_f] :
( c_Finite__Set_Ofold1(V_f,V_A,T_a) = c_The(c_Finite__Set_Ofold1Set(V_f,V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_fold1__def_0]) ).
cnf(cls_Int__Un__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool))),V_A) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__Un__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool))),V_A) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Un__distrib2_0]) ).
cnf(cls_Int__Un__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__Un__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Un__distrib_0]) ).
cnf(cls_Un__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Un__absorb_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__absorb_0]) ).
cnf(cls_INT__extend__simps_I4_J_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_INT__extend__simps_I4_J_0_0,plain,
! [T_a,T_b,V_A,V_B] :
( c_HOL_Ominus__class_Ominus(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_INT__extend__simps_I4_J_0]) ).
cnf(cls_Diff__idemp_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__idemp_0_0,plain,
! [T_a,V_A,V_B] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__idemp_0]) ).
cnf(cls_not__Some__eq_1,axiom,
c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_y,T_a),
input ).
fof(cls_not__Some__eq_1_0,plain,
! [T_a,V_y] :
( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_y,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__Some__eq_1]) ).
cnf(cls_option_Osimps_I2_J_0,axiom,
c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a),
input ).
fof(cls_option_Osimps_I2_J_0_0,plain,
! [T_a,V_a_H] :
( c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I2_J_0]) ).
cnf(cls_image__diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__diff__subset_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__diff__subset_0]) ).
cnf(cls_Un__left__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__left__commute_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__left__commute_0]) ).
cnf(cls_Un__assoc_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__assoc_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__assoc_0]) ).
cnf(cls_Un__upper2_0,axiom,
c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__upper2_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__upper2_0]) ).
cnf(cls_Un__upper1_0,axiom,
c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__upper1_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__upper1_0]) ).
cnf(cls_Int__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A),
input ).
fof(cls_Int__commute_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A)
| $false ),
inference(orientation,[status(thm)],[cls_Int__commute_0]) ).
cnf(cls_Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__subset_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__subset_0]) ).
cnf(cls_Un__Int__crazy_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)))),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool))),
input ).
fof(cls_Un__Int__crazy_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)))),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__crazy_0]) ).
cnf(cls_vimage__Int_0,axiom,
c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)),
input ).
fof(cls_vimage__Int_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__Int_0]) ).
cnf(cls_map__le__map__add_0,axiom,
c_Map_Omap__le(V_f,c_Map_Omap__add(V_g,V_f,T_a,T_b),T_a,T_b),
input ).
fof(cls_map__le__map__add_0_0,plain,
! [T_a,T_b,V_f,V_g] :
( c_Map_Omap__le(V_f,c_Map_Omap__add(V_g,V_f,T_a,T_b),T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_map__le__map__add_0]) ).
cnf(cls_vimage__Un_0,axiom,
c_Set_Ovimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)),
input ).
fof(cls_vimage__Un_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Ovimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__Un_0]) ).
cnf(cls_Diff__disjoint_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__disjoint_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__disjoint_0]) ).
cnf(cls_Un__left__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__left__absorb_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__left__absorb_0]) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__commute_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__commute_0]) ).
cnf(cls_Un__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__Diff_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Diff_0]) ).
cnf(cls_Un__Diff__cancel_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__Diff__cancel_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Diff__cancel_0]) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__Diff__cancel2_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Diff__cancel2_0]) ).
fof(def_lhs_atom1,axiom,
! [V_B,V_A,T_a] :
( lhs_atom1(V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_0,plain,
! [T_a,V_A,V_B] :
( lhs_atom1(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff__cancel2_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [V_B,V_A,T_a] :
( lhs_atom2(V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_1,plain,
! [T_a,V_A,V_B] :
( lhs_atom2(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff__cancel_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom3(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_2,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom3(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff_0_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [V_B,V_A,T_a] :
( lhs_atom4(V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_3,plain,
! [T_a,V_A,V_B] :
( lhs_atom4(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__commute_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [V_B,V_A,T_a] :
( lhs_atom5(V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_4,plain,
! [T_a,V_A,V_B] :
( lhs_atom5(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__absorb_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_B,V_A,T_a] :
( lhs_atom6(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_5,plain,
! [T_a,V_A,V_B] :
( lhs_atom6(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__disjoint_0_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom7(V_f,V_B,V_A,T_b,T_a)
<=> c_Set_Ovimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_6,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom7(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Un_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_g,V_f,T_b,T_a] :
( lhs_atom8(V_g,V_f,T_b,T_a)
<=> c_Map_Omap__le(V_f,c_Map_Omap__add(V_g,V_f,T_a,T_b),T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_7,plain,
! [T_a,T_b,V_f,V_g] :
( lhs_atom8(V_g,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__le__map__add_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom9(V_f,V_B,V_A,T_b,T_a)
<=> c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_8,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom9(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Int_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom10(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)))),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_9,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom10(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__crazy_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [V_B,V_A,T_a] :
( lhs_atom11(V_B,V_A,T_a)
<=> c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_10,plain,
! [T_a,V_A,V_B] :
( lhs_atom11(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__subset_0_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [V_B,V_A,T_a] :
( lhs_atom12(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A) ),
inference(definition,[],[]) ).
fof(to_be_clausified_11,plain,
! [T_a,V_A,V_B] :
( lhs_atom12(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__commute_0_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_B,V_A,T_a] :
( lhs_atom13(V_B,V_A,T_a)
<=> c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_12,plain,
! [T_a,V_A,V_B] :
( lhs_atom13(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper1_0_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_B,V_A,T_a] :
( lhs_atom14(V_B,V_A,T_a)
<=> c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_13,plain,
! [T_a,V_A,V_B] :
( lhs_atom14(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper2_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom15(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_14,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom15(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__assoc_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom16(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_15,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom16(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__commute_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom17(V_f,V_B,V_A,T_b,T_a)
<=> c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_16,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom17(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__diff__subset_0_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [V_a_H,T_a] :
( lhs_atom18(V_a_H,T_a)
<=> c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_17,plain,
! [T_a,V_a_H] :
( lhs_atom18(V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I2_J_0_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_y,T_a] :
( lhs_atom19(V_y,T_a)
<=> c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_y,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_18,plain,
! [T_a,V_y] :
( lhs_atom19(V_y,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Some__eq_1_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V_B,V_A,T_a] :
( lhs_atom20(V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_19,plain,
! [T_a,V_A,V_B] :
( lhs_atom20(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__idemp_0_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom21(V_B,V_A,T_b,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],[]) ).
fof(to_be_clausified_20,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom21(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_INT__extend__simps_I4_J_0_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [V_A,T_a] :
( lhs_atom22(V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],[]) ).
fof(to_be_clausified_21,plain,
! [T_a,V_A] :
( lhs_atom22(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__absorb_0_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom23(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_22,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom23(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Un__distrib_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom24(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool))),V_A) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_23,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom24(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Un__distrib2_0_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [V_f,V_A,T_a] :
( lhs_atom25(V_f,V_A,T_a)
<=> c_Finite__Set_Ofold1(V_f,V_A,T_a) = c_The(c_Finite__Set_Ofold1Set(V_f,V_A,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_24,plain,
! [T_a,V_A,V_f] :
( lhs_atom25(V_f,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold1__def_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom26(V_f,V_B,V_A,T_b,T_a)
<=> c_Set_Ovimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_25,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom26(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Diff_0_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [V_f,V_A,T_b,T_a] :
( lhs_atom27(V_f,V_A,T_b,T_a)
<=> c_lessequals(c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a),V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_26,plain,
! [T_a,T_b,V_A,V_f] :
( lhs_atom27(V_f,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__vimage__subset_0_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [V_P,T_a] :
( lhs_atom28(V_P,T_a)
<=> c_Collect(V_P,T_a) = V_P ),
inference(definition,[],[]) ).
fof(to_be_clausified_27,plain,
! [T_a,V_P] :
( lhs_atom28(V_P,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Collect__def_0_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [V_f,T_b,T_a] :
( lhs_atom29(V_f,T_b,T_a)
<=> c_Map_Omap__le(V_f,V_f,T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_28,plain,
! [T_a,T_b,V_f] :
( lhs_atom29(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__le__refl_0_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [V_n,V_m,T_b,T_a] :
( lhs_atom30(V_n,V_m,T_b,T_a)
<=> c_Map_Odom(c_Map_Omap__add(V_m,V_n,T_a,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(V_n,T_a,T_b),c_Map_Odom(V_m,T_a,T_b),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_29,plain,
! [T_a,T_b,V_m,V_n] :
( lhs_atom30(V_n,V_m,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__map__add_0_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom31(V_f,V_B,V_A,T_b,T_a)
<=> c_lessequals(c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_b,T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_b,T_a)),c_Set_Oimage(V_f,V_B,T_b,T_a)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_30,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom31(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__Int__subset_0_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [V_a_H,T_a] :
( lhs_atom32(V_a_H,T_a)
<=> c_Option_Ooption_OSome(V_a_H,T_a) != c_Option_Ooption_ONone(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_31,plain,
! [T_a,V_a_H] :
( lhs_atom32(V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I3_J_0_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [V_xa,T_a] :
( lhs_atom33(V_xa,T_a)
<=> c_Option_Ooption_OSome(V_xa,T_a) != c_Option_Ooption_ONone(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_32,plain,
! [T_a,V_xa] :
( lhs_atom33(V_xa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__None__eq_1_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [V_m3,V_m2,V_m1,T_b,T_a] :
( lhs_atom34(V_m3,V_m2,V_m1,T_b,T_a)
<=> c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_33,plain,
! [T_a,T_b,V_m1,V_m2,V_m3] :
( lhs_atom34(V_m3,V_m2,V_m1,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__add__assoc_0_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom35(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_34,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom35(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__assoc_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom36(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_35,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom36(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__left__commute_0_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom37(V_B,V_A,T_b,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B ),
inference(definition,[],[]) ).
fof(to_be_clausified_36,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom37(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__extend__simps_I2_J_0_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [V_f,T_b,T_a] :
( lhs_atom38(V_f,T_b,T_a)
<=> c_Set_Ovimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_37,plain,
! [T_a,T_b,V_f] :
( lhs_atom38(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__empty_0_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [T_a] :
( lhs_atom39(T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_38,plain,
! [T_a] :
( lhs_atom39(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty_2_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [T_a] :
( lhs_atom40(T_a)
<=> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_39,plain,
! [T_a] :
( lhs_atom40(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__empty_1_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [V_x,V_f,T_a] :
( lhs_atom41(V_x,V_f,T_a)
<=> ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_40,plain,
! [T_a,V_f,V_x] :
( lhs_atom41(V_x,V_f,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__fold1SetE_0_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [V_A,T_a] :
( lhs_atom42(V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_41,plain,
! [T_a,V_A] :
( lhs_atom42(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__Diff_0_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [V_A,T_a] :
( lhs_atom43(V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],[]) ).
fof(to_be_clausified_42,plain,
! [T_a,V_A] :
( lhs_atom43(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty__right_0_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [V_B,T_a] :
( lhs_atom44(V_B,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B ),
inference(definition,[],[]) ).
fof(to_be_clausified_43,plain,
! [T_a,V_B] :
( lhs_atom44(V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty__left_0_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [V_A,T_a] :
( lhs_atom45(V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_44,plain,
! [T_a,V_A] :
( lhs_atom45(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__cancel_0_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [V_A,T_a] :
( lhs_atom46(V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],[]) ).
fof(to_be_clausified_45,plain,
! [T_a,V_A] :
( lhs_atom46(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__empty_0_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [T_a] :
( lhs_atom47(T_a)
<=> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_46,plain,
! [T_a] :
( lhs_atom47(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_finite_OemptyI_0_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [V_A,T_a] :
( lhs_atom48(V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_47,plain,
! [T_a,V_A] :
( lhs_atom48(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__empty__right_0_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [V_B,T_a] :
( lhs_atom49(V_B,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_48,plain,
! [T_a,V_B] :
( lhs_atom49(V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__empty__left_0_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
! [V_A,T_a] :
( lhs_atom50(V_A,T_a)
<=> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_49,plain,
! [T_a,V_A] :
( lhs_atom50(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__subsetI_0_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [V_f,T_b,T_a] :
( lhs_atom51(V_f,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_50,plain,
! [T_a,T_b,V_f] :
( lhs_atom51(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__empty_0_0,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
! [V_z,V_f,T_b,T_a] :
( lhs_atom52(V_z,V_f,T_b,T_a)
<=> c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_z,T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_51,plain,
! [T_a,T_b,V_f,V_z] :
( lhs_atom52(V_z,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold__graph_OemptyI_0_0,def_lhs_atom52]) ).
fof(to_be_clausified_52,plain,
! [T_a,T_b,V_f] :
( lhs_atom51(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__is__image_1_0,def_lhs_atom51]) ).
fof(def_lhs_atom53,axiom,
! [V_f,V_a,V_B,T_b,T_a] :
( lhs_atom53(V_f,V_a,V_B,T_b,T_a)
<=> c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_53,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( lhs_atom53(V_f,V_a,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__insert_0_0,def_lhs_atom53]) ).
fof(def_lhs_atom54,axiom,
! [V_f,V_a,V_B,T_b,T_a] :
( lhs_atom54(V_f,V_a,V_B,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_54,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( lhs_atom54(V_f,V_a,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__insert_0_0,def_lhs_atom54]) ).
fof(def_lhs_atom55,axiom,
! [V_a,V_B,T_a] :
( lhs_atom55(V_a,V_B,T_a)
<=> c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_55,plain,
! [T_a,V_B,V_a] :
( lhs_atom55(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__insertI_0_0,def_lhs_atom55]) ).
fof(def_lhs_atom56,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom56(V_a,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_A,T_a)),c_Set_Oinsert(V_a,V_B,T_a)) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_56,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom56(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__inter__insert_0_0,def_lhs_atom56]) ).
fof(def_lhs_atom57,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom57(V_a,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_57,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom57(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__right_0_0,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
! [V_a,V_C,V_B,T_a] :
( lhs_atom58(V_a,V_C,V_B,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_58,plain,
! [T_a,V_B,V_C,V_a] :
( lhs_atom58(V_a,V_C,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__left_0_0,def_lhs_atom58]) ).
fof(def_lhs_atom59,axiom,
! [V_vname_H,V_pname_H,V_pname,V_fun_H] :
( lhs_atom59(V_vname_H,V_pname_H,V_pname,V_fun_H)
<=> c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OBODY(V_pname) ),
inference(definition,[],[]) ).
fof(to_be_clausified_59,plain,
! [V_fun_H,V_pname,V_pname_H,V_vname_H] :
( lhs_atom59(V_vname_H,V_pname_H,V_pname,V_fun_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I63_J_0_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
! [V_vname_H,V_pname_H,V_pname,V_fun_H] :
( lhs_atom60(V_vname_H,V_pname_H,V_pname,V_fun_H)
<=> c_Com_Ocom_OBODY(V_pname) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_60,plain,
! [V_fun_H,V_pname,V_pname_H,V_vname_H] :
( lhs_atom60(V_vname_H,V_pname_H,V_pname,V_fun_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I62_J_0_0,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom61(V_B,V_A,T_b,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],[]) ).
fof(to_be_clausified_61,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom61(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__extend__simps_I3_J_0_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom62(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_62,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom62(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int__distrib_0_0,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom63(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),V_C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_63,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom63(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int__distrib2_0_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom64(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_64,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom64(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int2_0_0,def_lhs_atom64]) ).
fof(def_lhs_atom65,axiom,
! [V_B,V_A,T_a] :
( lhs_atom65(V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],[]) ).
fof(to_be_clausified_65,plain,
! [T_a,V_A,V_B] :
( lhs_atom65(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff__Int_0_0,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
! [V_a,V_B,V_A,T_b,T_a] :
( lhs_atom66(V_a,V_B,V_A,T_b,T_a)
<=> c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(V_a,V_A,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_66,plain,
! [T_a,T_b,V_A,V_B,V_a] :
( lhs_atom66(V_a,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__insert_0_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
! [V_B,V_A,T_a] :
( lhs_atom67(V_B,V_A,T_a)
<=> c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_67,plain,
! [T_a,V_A,V_B] :
( lhs_atom67(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__lower1_0_0,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
! [V_B,V_A,T_a] :
( lhs_atom68(V_B,V_A,T_a)
<=> c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_68,plain,
! [T_a,V_A,V_B] :
( lhs_atom68(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__lower2_0_0,def_lhs_atom68]) ).
fof(def_lhs_atom69,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom69(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_69,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom69(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__distrib_0_0,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom70(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),V_A,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_70,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom70(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__distrib2_0_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
! [V_B,V_A,T_a] :
( lhs_atom71(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) ),
inference(definition,[],[]) ).
fof(to_be_clausified_71,plain,
! [T_a,V_A,V_B] :
( lhs_atom71(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__left__absorb_0_0,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
! [V_A,T_a] :
( lhs_atom72(V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ),
inference(definition,[],[]) ).
fof(to_be_clausified_72,plain,
! [T_a,V_A] :
( lhs_atom72(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__absorb_0_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
! [V_x,T_a] :
( lhs_atom73(V_x,T_a)
<=> c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_73,plain,
! [T_a,V_x] :
( lhs_atom73(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_equalityE_0_0,def_lhs_atom73]) ).
fof(def_lhs_atom74,axiom,
! [V_A,T_a] :
( lhs_atom74(V_A,T_a)
<=> c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_74,plain,
! [T_a,V_A] :
( lhs_atom74(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__refl_0_0,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom75(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_75,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom75(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Un_0_0,def_lhs_atom75]) ).
fof(def_lhs_atom76,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom76(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_76,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom76(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Diff_0_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom77(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_77,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom77(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int_0_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
! [V_M,V_B,V_A,T_b,T_a] :
( lhs_atom78(V_M,V_B,V_A,T_b,T_a)
<=> c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),V_M,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_b,tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_B,V_M,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_78,plain,
! [T_a,T_b,V_A,V_B,V_M] :
( lhs_atom78(V_M,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__Un_0_0,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
! [V_x,T_a] :
( lhs_atom79(V_x,T_a)
<=> c_The(c_fequal(V_x,T_a),T_a) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_79,plain,
! [T_a,V_x] :
( lhs_atom79(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_the__sym__eq__trivial_0_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
! [V_x,T_a] :
( lhs_atom80(V_x,T_a)
<=> c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_80,plain,
! [T_a,V_x] :
( lhs_atom80(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_the_Osimps_0_0,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom81(V_f,V_B,V_A,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_81,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom81(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__Un_0_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
! [V_a,T_a] :
( lhs_atom82(V_a,T_a)
<=> c_Collect(c_fequal(V_a,T_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_82,plain,
! [T_a,V_a] :
( lhs_atom82(V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_singleton__conv2_0_0,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
! [V_x,T_a] :
( lhs_atom83(V_x,T_a)
<=> hBOOL(hAPP(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_83,plain,
! [T_a,V_x] :
( lhs_atom83(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nitpick_OEx1__def_2_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
! [V_a,V_B,T_b,T_a] :
( lhs_atom84(V_a,V_B,T_b,T_a)
<=> c_Set_Oinsert(V_a,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_84,plain,
! [T_a,T_b,V_B,V_a] :
( lhs_atom84(V_a,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__extend__simps_I1_J_0_0,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
! [V_x,V_f,T_a] :
( lhs_atom85(V_x,V_f,T_a)
<=> hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_85,plain,
! [T_a,V_f,V_x] :
( lhs_atom85(V_x,V_f,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold1Set__sing_1_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
! [V_x,T_a] :
( lhs_atom86(V_x,T_a)
<=> c_The(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_86,plain,
! [T_a,V_x] :
( lhs_atom86(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nitpick_OThe__psimp_0_0,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom87(V_a,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_87,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom87(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__insert2_0_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom88(V_a,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_88,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom88(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__insert_0_0,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
! [V_x,T_a] :
( lhs_atom89(V_x,T_a)
<=> c_Set_Ocontents(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_89,plain,
! [T_a,V_x] :
( lhs_atom89(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_contents__eq_0_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
! [V_f,V_a,T_a] :
( lhs_atom90(V_f,V_a,T_a)
<=> c_Finite__Set_Ofold1(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a ),
inference(definition,[],[]) ).
fof(to_be_clausified_90,plain,
! [T_a,V_a,V_f] :
( lhs_atom90(V_f,V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold1__singleton_0_0,def_lhs_atom90]) ).
fof(def_lhs_atom91,axiom,
! [V_a,V_A,T_a] :
( lhs_atom91(V_a,V_A,T_a)
<=> c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,V_A,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_91,plain,
! [T_a,V_A,V_a] :
( lhs_atom91(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__Diff__single_0_0,def_lhs_atom91]) ).
fof(def_lhs_atom92,axiom,
! [V_a,V_A,T_a] :
( lhs_atom92(V_a,V_A,T_a)
<=> c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_92,plain,
! [T_a,V_A,V_a] :
( lhs_atom92(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__is__Un_0_0,def_lhs_atom92]) ).
fof(def_lhs_atom93,axiom,
( lhs_atom93
<=> c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) ),
inference(definition,[],[]) ).
fof(to_be_clausified_93,plain,
( lhs_atom93
| $false ),
inference(fold_definition,[status(thm)],[cls_finite__dom__body_0_0,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
! [V_f,V_a,T_aa,T_a] :
( lhs_atom94(V_f,V_a,T_aa,T_a)
<=> hBOOL(c_in(V_a,c_Set_Ovimage(V_f,c_Set_Oinsert(hAPP(V_f,V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_aa,T_a),T_aa)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_94,plain,
! [T_a,T_aa,V_a,V_f] :
( lhs_atom94(V_f,V_a,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__singleton__eq_1_0,def_lhs_atom94]) ).
fof(def_lhs_atom95,axiom,
! [V_x,T_a] :
( lhs_atom95(V_x,T_a)
<=> hBOOL(c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_95,plain,
! [T_a,V_x] :
( lhs_atom95(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_singleton__iff_1_0,def_lhs_atom95]) ).
fof(def_lhs_atom96,axiom,
! [V_x,V_A,T_a] :
( lhs_atom96(V_x,V_A,T_a)
<=> hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_96,plain,
! [T_a,V_A,V_x] :
( lhs_atom96(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__code_1_0,def_lhs_atom96]) ).
fof(def_lhs_atom97,axiom,
! [V_x,T_a] :
( lhs_atom97(V_x,T_a)
<=> ~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_97,plain,
! [T_a,V_x] :
( lhs_atom97(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ex__in__conv_0_0,def_lhs_atom97]) ).
fof(def_lhs_atom98,axiom,
! [V_c,T_a] :
( lhs_atom98(V_c,T_a)
<=> ~ hBOOL(c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_98,plain,
! [T_a,V_c] :
( lhs_atom98(V_c,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__iff_0_0,def_lhs_atom98]) ).
fof(def_lhs_atom99,axiom,
! [V_a,T_a] :
( lhs_atom99(V_a,T_a)
<=> ~ hBOOL(c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_99,plain,
! [T_a,V_a] :
( lhs_atom99(V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_emptyE_0_0,def_lhs_atom99]) ).
fof(def_lhs_atom100,axiom,
! [V_a,V_A,T_a] :
( lhs_atom100(V_a,V_A,T_a)
<=> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_100,plain,
! [T_a,V_A,V_a] :
( lhs_atom100(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__not__insert_0_0,def_lhs_atom100]) ).
fof(def_lhs_atom101,axiom,
( lhs_atom101
<=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_101,plain,
( lhs_atom101
| $false ),
inference(fold_definition,[status(thm)],[cls_bot__empty__eq_0_0,def_lhs_atom101]) ).
fof(def_lhs_atom102,axiom,
! [V_x,T_a] :
( lhs_atom102(V_x,T_a)
<=> ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_102,plain,
! [T_a,V_x] :
( lhs_atom102(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_bot1E_0_0,def_lhs_atom102]) ).
fof(def_lhs_atom103,axiom,
! [V_G,T_a] :
( lhs_atom103(V_G,T_a)
<=> c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_103,plain,
! [T_a,V_G] :
( lhs_atom103(V_G,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty_0_0,def_lhs_atom103]) ).
fof(def_lhs_atom104,axiom,
! [V_x,V_A,T_a] :
( lhs_atom104(V_x,V_A,T_a)
<=> c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_104,plain,
! [T_a,V_A,V_x] :
( lhs_atom104(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__absorb2_0_0,def_lhs_atom104]) ).
fof(def_lhs_atom105,axiom,
! [V_a,V_A,T_a] :
( lhs_atom105(V_a,V_A,T_a)
<=> c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_105,plain,
! [T_a,V_A,V_a] :
( lhs_atom105(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__not__empty_0_0,def_lhs_atom105]) ).
fof(def_lhs_atom106,axiom,
! [V_x,V_A,T_a] :
( lhs_atom106(V_x,V_A,T_a)
<=> hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_106,plain,
! [T_a,V_A,V_x] :
( lhs_atom106(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__iff_1_0,def_lhs_atom106]) ).
fof(def_lhs_atom107,axiom,
! [V_a,V_B,T_a] :
( lhs_atom107(V_a,V_B,T_a)
<=> hBOOL(c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_107,plain,
! [T_a,V_B,V_a] :
( lhs_atom107(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertI1_0_0,def_lhs_atom107]) ).
fof(def_lhs_atom108,axiom,
! [V_x,V_B,T_a] :
( lhs_atom108(V_x,V_B,T_a)
<=> hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_108,plain,
! [T_a,V_B,V_x] :
( lhs_atom108(V_x,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertCI_1_0,def_lhs_atom108]) ).
fof(def_lhs_atom109,axiom,
! [V_y,V_x,V_A,T_a] :
( lhs_atom109(V_y,V_x,V_A,T_a)
<=> c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_109,plain,
! [T_a,V_A,V_x,V_y] :
( lhs_atom109(V_y,V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__commute_0_0,def_lhs_atom109]) ).
fof(def_lhs_atom110,axiom,
! [V_xa,V_x,T_a] :
( lhs_atom110(V_xa,V_x,T_a)
<=> c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_110,plain,
! [T_a,V_x,V_xa] :
( lhs_atom110(V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_doubleton__eq__iff_4_0,def_lhs_atom110]) ).
fof(def_lhs_atom111,axiom,
( lhs_atom111
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_111,plain,
( lhs_atom111
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Oupper__semilattice_0,def_lhs_atom111]) ).
fof(def_lhs_atom112,axiom,
( lhs_atom112
<=> class_Lattices_Olower__semilattice(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_112,plain,
( lhs_atom112
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Olower__semilattice_0,def_lhs_atom112]) ).
fof(def_lhs_atom113,axiom,
( lhs_atom113
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_113,plain,
( lhs_atom113
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Odistrib__lattice_0,def_lhs_atom113]) ).
fof(def_lhs_atom114,axiom,
( lhs_atom114
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_114,plain,
( lhs_atom114
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom114]) ).
fof(def_lhs_atom115,axiom,
( lhs_atom115
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_115,plain,
( lhs_atom115
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom115]) ).
fof(def_lhs_atom116,axiom,
( lhs_atom116
<=> class_Lattices_Olattice(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_116,plain,
( lhs_atom116
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Olattice_0,def_lhs_atom116]) ).
fof(def_lhs_atom117,axiom,
( lhs_atom117
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_117,plain,
( lhs_atom117
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom117]) ).
fof(def_lhs_atom118,axiom,
( lhs_atom118
<=> class_Orderings_Obot(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_118,plain,
( lhs_atom118
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Obot_0,def_lhs_atom118]) ).
fof(def_lhs_atom119,axiom,
( lhs_atom119
<=> class_HOL_Ominus(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_119,plain,
( lhs_atom119
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__HOL_Ominus_0,def_lhs_atom119]) ).
fof(def_lhs_atom120,axiom,
( lhs_atom120
<=> class_HOL_Oord(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_120,plain,
( lhs_atom120
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__HOL_Oord_0,def_lhs_atom120]) ).
fof(def_lhs_atom121,axiom,
( lhs_atom121
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_121,plain,
( lhs_atom121
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Complete__Lattice_Ocomplete__lattice_0,def_lhs_atom121]) ).
fof(def_lhs_atom122,axiom,
( lhs_atom122
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_122,plain,
( lhs_atom122
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Oupper__semilattice_0,def_lhs_atom122]) ).
fof(def_lhs_atom123,axiom,
( lhs_atom123
<=> class_Lattices_Olower__semilattice(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_123,plain,
( lhs_atom123
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Olower__semilattice_0,def_lhs_atom123]) ).
fof(def_lhs_atom124,axiom,
( lhs_atom124
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_124,plain,
( lhs_atom124
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Odistrib__lattice_0,def_lhs_atom124]) ).
fof(def_lhs_atom125,axiom,
( lhs_atom125
<=> class_Lattices_Obounded__lattice(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_125,plain,
( lhs_atom125
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Obounded__lattice_0,def_lhs_atom125]) ).
fof(def_lhs_atom126,axiom,
( lhs_atom126
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_126,plain,
( lhs_atom126
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite_0,def_lhs_atom126]) ).
fof(def_lhs_atom127,axiom,
( lhs_atom127
<=> class_Orderings_Opreorder(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_127,plain,
( lhs_atom127
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom127]) ).
fof(def_lhs_atom128,axiom,
( lhs_atom128
<=> class_Lattices_Olattice(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_128,plain,
( lhs_atom128
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Olattice_0,def_lhs_atom128]) ).
fof(def_lhs_atom129,axiom,
( lhs_atom129
<=> class_Orderings_Oorder(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_129,plain,
( lhs_atom129
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom129]) ).
fof(def_lhs_atom130,axiom,
( lhs_atom130
<=> class_Orderings_Obot(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_130,plain,
( lhs_atom130
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Obot_0,def_lhs_atom130]) ).
fof(def_lhs_atom131,axiom,
( lhs_atom131
<=> class_HOL_Ominus(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_131,plain,
( lhs_atom131
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__HOL_Ominus_0,def_lhs_atom131]) ).
fof(def_lhs_atom132,axiom,
( lhs_atom132
<=> class_HOL_Oord(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_132,plain,
( lhs_atom132
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__HOL_Oord_0,def_lhs_atom132]) ).
fof(def_lhs_atom133,axiom,
! [V_x,T_a] :
( lhs_atom133(V_x,T_a)
<=> hBOOL(hAPP(c_fequal(V_x,T_a),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_133,plain,
! [T_a,V_x] :
( lhs_atom133(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom133]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X5,X1,X2,X6,X3] :
( lhs_atom81(X5,X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_1,axiom,
! [X24,X1,X2,X6,X3] :
( lhs_atom78(X24,X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_2,axiom,
! [X19,X1,X2,X6,X3] :
( lhs_atom66(X19,X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_3,axiom,
! [X5,X19,X1,X6,X3] :
( lhs_atom54(X5,X19,X1,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_4,axiom,
! [X5,X19,X1,X6,X3] :
( lhs_atom53(X5,X19,X1,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_5,axiom,
! [X14,X15,X16,X6,X3] :
( lhs_atom34(X14,X15,X16,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_6,axiom,
! [X5,X1,X2,X6,X3] :
( lhs_atom31(X5,X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_7,axiom,
! [X5,X1,X2,X6,X3] :
( lhs_atom26(X5,X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_8,axiom,
! [X5,X1,X2,X6,X3] :
( lhs_atom17(X5,X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_9,axiom,
! [X5,X1,X2,X6,X3] :
( lhs_atom9(X5,X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_10,axiom,
! [X5,X1,X2,X6,X3] :
( lhs_atom7(X5,X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_11,axiom,
! [X9,X17,X2,X3] :
( lhs_atom109(X9,X17,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_12,axiom,
! [X5,X19,X25,X3] :
( lhs_atom94(X5,X19,X25,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_13,axiom,
! [X19,X1,X2,X3] :
( lhs_atom88(X19,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_14,axiom,
! [X19,X1,X2,X3] :
( lhs_atom87(X19,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_15,axiom,
! [X19,X1,X6,X3] :
( lhs_atom84(X19,X1,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_16,axiom,
! [X4,X1,X2,X3] :
( lhs_atom77(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_17,axiom,
! [X4,X1,X2,X3] :
( lhs_atom76(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_18,axiom,
! [X4,X1,X2,X3] :
( lhs_atom75(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_19,axiom,
! [X4,X1,X2,X3] :
( lhs_atom70(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_20,axiom,
! [X4,X1,X2,X3] :
( lhs_atom69(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_21,axiom,
! [X4,X1,X2,X3] :
( lhs_atom64(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_22,axiom,
! [X4,X1,X2,X3] :
( lhs_atom63(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_23,axiom,
! [X4,X1,X2,X3] :
( lhs_atom62(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_24,axiom,
! [X1,X2,X6,X3] :
( lhs_atom61(X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_25,axiom,
! [X20,X21,X22,X23] :
( lhs_atom60(X20,X21,X22,X23)
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_26,axiom,
! [X20,X21,X22,X23] :
( lhs_atom59(X20,X21,X22,X23)
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_27,axiom,
! [X19,X4,X1,X3] :
( lhs_atom58(X19,X4,X1,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_28,axiom,
! [X19,X1,X2,X3] :
( lhs_atom57(X19,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_29,axiom,
! [X19,X1,X2,X3] :
( lhs_atom56(X19,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_30,axiom,
! [X18,X5,X6,X3] :
( lhs_atom52(X18,X5,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_31,axiom,
! [X1,X2,X6,X3] :
( lhs_atom37(X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_32,axiom,
! [X4,X1,X2,X3] :
( lhs_atom36(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_33,axiom,
! [X4,X1,X2,X3] :
( lhs_atom35(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_34,axiom,
! [X11,X12,X6,X3] :
( lhs_atom30(X11,X12,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_35,axiom,
! [X5,X2,X6,X3] :
( lhs_atom27(X5,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_36,axiom,
! [X4,X1,X2,X3] :
( lhs_atom24(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_37,axiom,
! [X4,X1,X2,X3] :
( lhs_atom23(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_38,axiom,
! [X1,X2,X6,X3] :
( lhs_atom21(X1,X2,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_39,axiom,
! [X4,X1,X2,X3] :
( lhs_atom16(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_40,axiom,
! [X4,X1,X2,X3] :
( lhs_atom15(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_41,axiom,
! [X4,X1,X2,X3] :
( lhs_atom10(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_42,axiom,
! [X7,X5,X6,X3] :
( lhs_atom8(X7,X5,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_43,axiom,
! [X4,X1,X2,X3] :
( lhs_atom3(X4,X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_44,axiom,
! [X13,X17,X3] :
( lhs_atom110(X13,X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_45,axiom,
! [X17,X1,X3] :
( lhs_atom108(X17,X1,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_46,axiom,
! [X19,X1,X3] :
( lhs_atom107(X19,X1,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_47,axiom,
! [X17,X2,X3] :
( lhs_atom106(X17,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_48,axiom,
! [X19,X2,X3] :
( lhs_atom105(X19,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_49,axiom,
! [X17,X2,X3] :
( lhs_atom104(X17,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_50,axiom,
! [X19,X2,X3] :
( lhs_atom100(X19,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_51,axiom,
! [X17,X2,X3] :
( lhs_atom96(X17,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_52,axiom,
! [X19,X2,X3] :
( lhs_atom92(X19,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_53,axiom,
! [X19,X2,X3] :
( lhs_atom91(X19,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_54,axiom,
! [X5,X19,X3] :
( lhs_atom90(X5,X19,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_55,axiom,
! [X17,X5,X3] :
( lhs_atom85(X17,X5,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_56,axiom,
! [X1,X2,X3] :
( lhs_atom71(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_57,axiom,
! [X1,X2,X3] :
( lhs_atom68(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_58,axiom,
! [X1,X2,X3] :
( lhs_atom67(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_59,axiom,
! [X1,X2,X3] :
( lhs_atom65(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_60,axiom,
! [X19,X1,X3] :
( lhs_atom55(X19,X1,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_61,axiom,
! [X5,X6,X3] :
( lhs_atom51(X5,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_62,axiom,
! [X5,X6,X3] :
( lhs_atom51(X5,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_63,axiom,
! [X17,X5,X3] :
( lhs_atom41(X17,X5,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_64,axiom,
! [X5,X6,X3] :
( lhs_atom38(X5,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_65,axiom,
! [X5,X6,X3] :
( lhs_atom29(X5,X6,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_66,axiom,
! [X5,X2,X3] :
( lhs_atom25(X5,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_67,axiom,
! [X1,X2,X3] :
( lhs_atom20(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_68,axiom,
! [X1,X2,X3] :
( lhs_atom14(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_69,axiom,
! [X1,X2,X3] :
( lhs_atom13(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_70,axiom,
! [X1,X2,X3] :
( lhs_atom12(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_71,axiom,
! [X1,X2,X3] :
( lhs_atom11(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_72,axiom,
! [X1,X2,X3] :
( lhs_atom6(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_73,axiom,
! [X1,X2,X3] :
( lhs_atom5(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_74,axiom,
! [X1,X2,X3] :
( lhs_atom4(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_75,axiom,
! [X1,X2,X3] :
( lhs_atom2(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_76,axiom,
! [X1,X2,X3] :
( lhs_atom1(X1,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_77,axiom,
! [X17,X3] :
( lhs_atom133(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_133) ).
fof(c_0_78,axiom,
! [X27,X3] :
( lhs_atom103(X27,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_79,axiom,
! [X17,X3] :
( lhs_atom102(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_80,axiom,
! [X19,X3] :
( lhs_atom99(X19,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_81,axiom,
! [X26,X3] :
( lhs_atom98(X26,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_82,axiom,
! [X17,X3] :
( lhs_atom97(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_83,axiom,
! [X17,X3] :
( lhs_atom95(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_84,axiom,
! [X17,X3] :
( lhs_atom89(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_85,axiom,
! [X17,X3] :
( lhs_atom86(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_86,axiom,
! [X17,X3] :
( lhs_atom83(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_87,axiom,
! [X19,X3] :
( lhs_atom82(X19,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_88,axiom,
! [X17,X3] :
( lhs_atom80(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_89,axiom,
! [X17,X3] :
( lhs_atom79(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_90,axiom,
! [X2,X3] :
( lhs_atom74(X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_91,axiom,
! [X17,X3] :
( lhs_atom73(X17,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_92,axiom,
! [X2,X3] :
( lhs_atom72(X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_93,axiom,
! [X2,X3] :
( lhs_atom50(X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_94,axiom,
! [X1,X3] :
( lhs_atom49(X1,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_95,axiom,
! [X2,X3] :
( lhs_atom48(X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_96,axiom,
! [X2,X3] :
( lhs_atom46(X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_97,axiom,
! [X2,X3] :
( lhs_atom45(X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_98,axiom,
! [X1,X3] :
( lhs_atom44(X1,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_99,axiom,
! [X2,X3] :
( lhs_atom43(X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_100,axiom,
! [X2,X3] :
( lhs_atom42(X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_101,axiom,
! [X13,X3] :
( lhs_atom33(X13,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_102,axiom,
! [X8,X3] :
( lhs_atom32(X8,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_103,axiom,
! [X10,X3] :
( lhs_atom28(X10,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_104,axiom,
! [X2,X3] :
( lhs_atom22(X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_105,axiom,
! [X9,X3] :
( lhs_atom19(X9,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_106,axiom,
! [X8,X3] :
( lhs_atom18(X8,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_107,axiom,
! [X3] :
( lhs_atom47(X3)
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_108,axiom,
! [X3] :
( lhs_atom40(X3)
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_109,axiom,
! [X3] :
( lhs_atom39(X3)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_110,axiom,
( lhs_atom132
| ~ $true ),
file('<stdin>',to_be_clausified_132) ).
fof(c_0_111,axiom,
( lhs_atom131
| ~ $true ),
file('<stdin>',to_be_clausified_131) ).
fof(c_0_112,axiom,
( lhs_atom130
| ~ $true ),
file('<stdin>',to_be_clausified_130) ).
fof(c_0_113,axiom,
( lhs_atom129
| ~ $true ),
file('<stdin>',to_be_clausified_129) ).
fof(c_0_114,axiom,
( lhs_atom128
| ~ $true ),
file('<stdin>',to_be_clausified_128) ).
fof(c_0_115,axiom,
( lhs_atom127
| ~ $true ),
file('<stdin>',to_be_clausified_127) ).
fof(c_0_116,axiom,
( lhs_atom126
| ~ $true ),
file('<stdin>',to_be_clausified_126) ).
fof(c_0_117,axiom,
( lhs_atom125
| ~ $true ),
file('<stdin>',to_be_clausified_125) ).
fof(c_0_118,axiom,
( lhs_atom124
| ~ $true ),
file('<stdin>',to_be_clausified_124) ).
fof(c_0_119,axiom,
( lhs_atom123
| ~ $true ),
file('<stdin>',to_be_clausified_123) ).
fof(c_0_120,axiom,
( lhs_atom122
| ~ $true ),
file('<stdin>',to_be_clausified_122) ).
fof(c_0_121,axiom,
( lhs_atom121
| ~ $true ),
file('<stdin>',to_be_clausified_121) ).
fof(c_0_122,axiom,
( lhs_atom120
| ~ $true ),
file('<stdin>',to_be_clausified_120) ).
fof(c_0_123,axiom,
( lhs_atom119
| ~ $true ),
file('<stdin>',to_be_clausified_119) ).
fof(c_0_124,axiom,
( lhs_atom118
| ~ $true ),
file('<stdin>',to_be_clausified_118) ).
fof(c_0_125,axiom,
( lhs_atom117
| ~ $true ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_126,axiom,
( lhs_atom116
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_127,axiom,
( lhs_atom115
| ~ $true ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_128,axiom,
( lhs_atom114
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_129,axiom,
( lhs_atom113
| ~ $true ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_130,axiom,
( lhs_atom112
| ~ $true ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_131,axiom,
( lhs_atom111
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_132,axiom,
( lhs_atom101
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_133,axiom,
( lhs_atom93
| ~ $true ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_134,plain,
! [X5,X1,X2,X6,X3] : lhs_atom81(X5,X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_135,plain,
! [X24,X1,X2,X6,X3] : lhs_atom78(X24,X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_136,plain,
! [X19,X1,X2,X6,X3] : lhs_atom66(X19,X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_137,plain,
! [X5,X19,X1,X6,X3] : lhs_atom54(X5,X19,X1,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_138,plain,
! [X5,X19,X1,X6,X3] : lhs_atom53(X5,X19,X1,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_139,plain,
! [X14,X15,X16,X6,X3] : lhs_atom34(X14,X15,X16,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_140,plain,
! [X5,X1,X2,X6,X3] : lhs_atom31(X5,X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_141,plain,
! [X5,X1,X2,X6,X3] : lhs_atom26(X5,X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_142,plain,
! [X5,X1,X2,X6,X3] : lhs_atom17(X5,X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_143,plain,
! [X5,X1,X2,X6,X3] : lhs_atom9(X5,X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_144,plain,
! [X5,X1,X2,X6,X3] : lhs_atom7(X5,X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_145,plain,
! [X9,X17,X2,X3] : lhs_atom109(X9,X17,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_146,plain,
! [X5,X19,X25,X3] : lhs_atom94(X5,X19,X25,X3),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_147,plain,
! [X19,X1,X2,X3] : lhs_atom88(X19,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_148,plain,
! [X19,X1,X2,X3] : lhs_atom87(X19,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_149,plain,
! [X19,X1,X6,X3] : lhs_atom84(X19,X1,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_150,plain,
! [X4,X1,X2,X3] : lhs_atom77(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_151,plain,
! [X4,X1,X2,X3] : lhs_atom76(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_152,plain,
! [X4,X1,X2,X3] : lhs_atom75(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_153,plain,
! [X4,X1,X2,X3] : lhs_atom70(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_154,plain,
! [X4,X1,X2,X3] : lhs_atom69(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_155,plain,
! [X4,X1,X2,X3] : lhs_atom64(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_156,plain,
! [X4,X1,X2,X3] : lhs_atom63(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_157,plain,
! [X4,X1,X2,X3] : lhs_atom62(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_158,plain,
! [X1,X2,X6,X3] : lhs_atom61(X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_159,plain,
! [X20,X21,X22,X23] : lhs_atom60(X20,X21,X22,X23),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_160,plain,
! [X20,X21,X22,X23] : lhs_atom59(X20,X21,X22,X23),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_161,plain,
! [X19,X4,X1,X3] : lhs_atom58(X19,X4,X1,X3),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_162,plain,
! [X19,X1,X2,X3] : lhs_atom57(X19,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_163,plain,
! [X19,X1,X2,X3] : lhs_atom56(X19,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_164,plain,
! [X18,X5,X6,X3] : lhs_atom52(X18,X5,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_165,plain,
! [X1,X2,X6,X3] : lhs_atom37(X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_166,plain,
! [X4,X1,X2,X3] : lhs_atom36(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_167,plain,
! [X4,X1,X2,X3] : lhs_atom35(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_168,plain,
! [X11,X12,X6,X3] : lhs_atom30(X11,X12,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_169,plain,
! [X5,X2,X6,X3] : lhs_atom27(X5,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_170,plain,
! [X4,X1,X2,X3] : lhs_atom24(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_171,plain,
! [X4,X1,X2,X3] : lhs_atom23(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_172,plain,
! [X1,X2,X6,X3] : lhs_atom21(X1,X2,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_173,plain,
! [X4,X1,X2,X3] : lhs_atom16(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_174,plain,
! [X4,X1,X2,X3] : lhs_atom15(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_175,plain,
! [X4,X1,X2,X3] : lhs_atom10(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_176,plain,
! [X7,X5,X6,X3] : lhs_atom8(X7,X5,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_177,plain,
! [X4,X1,X2,X3] : lhs_atom3(X4,X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_178,plain,
! [X13,X17,X3] : lhs_atom110(X13,X17,X3),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_179,plain,
! [X17,X1,X3] : lhs_atom108(X17,X1,X3),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_180,plain,
! [X19,X1,X3] : lhs_atom107(X19,X1,X3),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_181,plain,
! [X17,X2,X3] : lhs_atom106(X17,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_182,plain,
! [X19,X2,X3] : lhs_atom105(X19,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_183,plain,
! [X17,X2,X3] : lhs_atom104(X17,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_184,plain,
! [X19,X2,X3] : lhs_atom100(X19,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_185,plain,
! [X17,X2,X3] : lhs_atom96(X17,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_186,plain,
! [X19,X2,X3] : lhs_atom92(X19,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_187,plain,
! [X19,X2,X3] : lhs_atom91(X19,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_188,plain,
! [X5,X19,X3] : lhs_atom90(X5,X19,X3),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_189,plain,
! [X17,X5,X3] : lhs_atom85(X17,X5,X3),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_190,plain,
! [X1,X2,X3] : lhs_atom71(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_191,plain,
! [X1,X2,X3] : lhs_atom68(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_192,plain,
! [X1,X2,X3] : lhs_atom67(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_193,plain,
! [X1,X2,X3] : lhs_atom65(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_194,plain,
! [X19,X1,X3] : lhs_atom55(X19,X1,X3),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_195,plain,
! [X5,X6,X3] : lhs_atom51(X5,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_196,plain,
! [X5,X6,X3] : lhs_atom51(X5,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_197,plain,
! [X17,X5,X3] : lhs_atom41(X17,X5,X3),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_198,plain,
! [X5,X6,X3] : lhs_atom38(X5,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_199,plain,
! [X5,X6,X3] : lhs_atom29(X5,X6,X3),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_200,plain,
! [X5,X2,X3] : lhs_atom25(X5,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_201,plain,
! [X1,X2,X3] : lhs_atom20(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_202,plain,
! [X1,X2,X3] : lhs_atom14(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_203,plain,
! [X1,X2,X3] : lhs_atom13(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_204,plain,
! [X1,X2,X3] : lhs_atom12(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_205,plain,
! [X1,X2,X3] : lhs_atom11(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_206,plain,
! [X1,X2,X3] : lhs_atom6(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_207,plain,
! [X1,X2,X3] : lhs_atom5(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_208,plain,
! [X1,X2,X3] : lhs_atom4(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_209,plain,
! [X1,X2,X3] : lhs_atom2(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_210,plain,
! [X1,X2,X3] : lhs_atom1(X1,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_211,plain,
! [X17,X3] : lhs_atom133(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_212,plain,
! [X27,X3] : lhs_atom103(X27,X3),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_213,plain,
! [X17,X3] : lhs_atom102(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_214,plain,
! [X19,X3] : lhs_atom99(X19,X3),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_215,plain,
! [X26,X3] : lhs_atom98(X26,X3),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_216,plain,
! [X17,X3] : lhs_atom97(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_217,plain,
! [X17,X3] : lhs_atom95(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_218,plain,
! [X17,X3] : lhs_atom89(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_219,plain,
! [X17,X3] : lhs_atom86(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_220,plain,
! [X17,X3] : lhs_atom83(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_221,plain,
! [X19,X3] : lhs_atom82(X19,X3),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_222,plain,
! [X17,X3] : lhs_atom80(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_223,plain,
! [X17,X3] : lhs_atom79(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_224,plain,
! [X2,X3] : lhs_atom74(X2,X3),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_225,plain,
! [X17,X3] : lhs_atom73(X17,X3),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_226,plain,
! [X2,X3] : lhs_atom72(X2,X3),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_227,plain,
! [X2,X3] : lhs_atom50(X2,X3),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_228,plain,
! [X1,X3] : lhs_atom49(X1,X3),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_229,plain,
! [X2,X3] : lhs_atom48(X2,X3),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_230,plain,
! [X2,X3] : lhs_atom46(X2,X3),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_231,plain,
! [X2,X3] : lhs_atom45(X2,X3),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_232,plain,
! [X1,X3] : lhs_atom44(X1,X3),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_233,plain,
! [X2,X3] : lhs_atom43(X2,X3),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_234,plain,
! [X2,X3] : lhs_atom42(X2,X3),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_235,plain,
! [X13,X3] : lhs_atom33(X13,X3),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_236,plain,
! [X8,X3] : lhs_atom32(X8,X3),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_237,plain,
! [X10,X3] : lhs_atom28(X10,X3),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_238,plain,
! [X2,X3] : lhs_atom22(X2,X3),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_239,plain,
! [X9,X3] : lhs_atom19(X9,X3),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_240,plain,
! [X8,X3] : lhs_atom18(X8,X3),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_241,plain,
! [X3] : lhs_atom47(X3),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_242,plain,
! [X3] : lhs_atom40(X3),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_243,plain,
! [X3] : lhs_atom39(X3),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_244,plain,
lhs_atom132,
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_245,plain,
lhs_atom131,
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_246,plain,
lhs_atom130,
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_247,plain,
lhs_atom129,
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_248,plain,
lhs_atom128,
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_249,plain,
lhs_atom127,
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_250,plain,
lhs_atom126,
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_251,plain,
lhs_atom125,
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_252,plain,
lhs_atom124,
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_253,plain,
lhs_atom123,
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_254,plain,
lhs_atom122,
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_255,plain,
lhs_atom121,
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_256,plain,
lhs_atom120,
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_257,plain,
lhs_atom119,
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_258,plain,
lhs_atom118,
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_259,plain,
lhs_atom117,
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_260,plain,
lhs_atom116,
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_261,plain,
lhs_atom115,
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_262,plain,
lhs_atom114,
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_263,plain,
lhs_atom113,
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_264,plain,
lhs_atom112,
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_265,plain,
lhs_atom111,
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_266,plain,
lhs_atom101,
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_267,plain,
lhs_atom93,
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_268,plain,
! [X7,X8,X9,X10,X11] : lhs_atom81(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_134]) ).
fof(c_0_269,plain,
! [X25,X26,X27,X28,X29] : lhs_atom78(X25,X26,X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_135]) ).
fof(c_0_270,plain,
! [X20,X21,X22,X23,X24] : lhs_atom66(X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_136]) ).
fof(c_0_271,plain,
! [X20,X21,X22,X23,X24] : lhs_atom54(X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_137]) ).
fof(c_0_272,plain,
! [X20,X21,X22,X23,X24] : lhs_atom53(X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_138]) ).
fof(c_0_273,plain,
! [X17,X18,X19,X20,X21] : lhs_atom34(X17,X18,X19,X20,X21),
inference(variable_rename,[status(thm)],[c_0_139]) ).
fof(c_0_274,plain,
! [X7,X8,X9,X10,X11] : lhs_atom31(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_140]) ).
fof(c_0_275,plain,
! [X7,X8,X9,X10,X11] : lhs_atom26(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_141]) ).
fof(c_0_276,plain,
! [X7,X8,X9,X10,X11] : lhs_atom17(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_142]) ).
fof(c_0_277,plain,
! [X7,X8,X9,X10,X11] : lhs_atom9(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_143]) ).
fof(c_0_278,plain,
! [X7,X8,X9,X10,X11] : lhs_atom7(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_144]) ).
fof(c_0_279,plain,
! [X18,X19,X20,X21] : lhs_atom109(X18,X19,X20,X21),
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_280,plain,
! [X26,X27,X28,X29] : lhs_atom94(X26,X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_146]) ).
fof(c_0_281,plain,
! [X20,X21,X22,X23] : lhs_atom88(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_147]) ).
fof(c_0_282,plain,
! [X20,X21,X22,X23] : lhs_atom87(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_283,plain,
! [X20,X21,X22,X23] : lhs_atom84(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_149]) ).
fof(c_0_284,plain,
! [X5,X6,X7,X8] : lhs_atom77(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_150]) ).
fof(c_0_285,plain,
! [X5,X6,X7,X8] : lhs_atom76(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_151]) ).
fof(c_0_286,plain,
! [X5,X6,X7,X8] : lhs_atom75(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_287,plain,
! [X5,X6,X7,X8] : lhs_atom70(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_153]) ).
fof(c_0_288,plain,
! [X5,X6,X7,X8] : lhs_atom69(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_154]) ).
fof(c_0_289,plain,
! [X5,X6,X7,X8] : lhs_atom64(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_155]) ).
fof(c_0_290,plain,
! [X5,X6,X7,X8] : lhs_atom63(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_156]) ).
fof(c_0_291,plain,
! [X5,X6,X7,X8] : lhs_atom62(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_157]) ).
fof(c_0_292,plain,
! [X7,X8,X9,X10] : lhs_atom61(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_158]) ).
fof(c_0_293,plain,
! [X24,X25,X26,X27] : lhs_atom60(X24,X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_159]) ).
fof(c_0_294,plain,
! [X24,X25,X26,X27] : lhs_atom59(X24,X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_295,plain,
! [X20,X21,X22,X23] : lhs_atom58(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_161]) ).
fof(c_0_296,plain,
! [X20,X21,X22,X23] : lhs_atom57(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_162]) ).
fof(c_0_297,plain,
! [X20,X21,X22,X23] : lhs_atom56(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_163]) ).
fof(c_0_298,plain,
! [X19,X20,X21,X22] : lhs_atom52(X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_164]) ).
fof(c_0_299,plain,
! [X7,X8,X9,X10] : lhs_atom37(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_300,plain,
! [X5,X6,X7,X8] : lhs_atom36(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_301,plain,
! [X5,X6,X7,X8] : lhs_atom35(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_302,plain,
! [X13,X14,X15,X16] : lhs_atom30(X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_303,plain,
! [X7,X8,X9,X10] : lhs_atom27(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_304,plain,
! [X5,X6,X7,X8] : lhs_atom24(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_305,plain,
! [X5,X6,X7,X8] : lhs_atom23(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_306,plain,
! [X7,X8,X9,X10] : lhs_atom21(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_307,plain,
! [X5,X6,X7,X8] : lhs_atom16(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_308,plain,
! [X5,X6,X7,X8] : lhs_atom15(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_309,plain,
! [X5,X6,X7,X8] : lhs_atom10(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_310,plain,
! [X8,X9,X10,X11] : lhs_atom8(X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_311,plain,
! [X5,X6,X7,X8] : lhs_atom3(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_312,plain,
! [X18,X19,X20] : lhs_atom110(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_313,plain,
! [X18,X19,X20] : lhs_atom108(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_314,plain,
! [X20,X21,X22] : lhs_atom107(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_315,plain,
! [X18,X19,X20] : lhs_atom106(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_316,plain,
! [X20,X21,X22] : lhs_atom105(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_317,plain,
! [X18,X19,X20] : lhs_atom104(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_318,plain,
! [X20,X21,X22] : lhs_atom100(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_319,plain,
! [X18,X19,X20] : lhs_atom96(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_185]) ).
fof(c_0_320,plain,
! [X20,X21,X22] : lhs_atom92(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_321,plain,
! [X20,X21,X22] : lhs_atom91(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_322,plain,
! [X20,X21,X22] : lhs_atom90(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_323,plain,
! [X18,X19,X20] : lhs_atom85(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_324,plain,
! [X4,X5,X6] : lhs_atom71(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_325,plain,
! [X4,X5,X6] : lhs_atom68(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_326,plain,
! [X4,X5,X6] : lhs_atom67(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_327,plain,
! [X4,X5,X6] : lhs_atom65(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_328,plain,
! [X20,X21,X22] : lhs_atom55(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_329,plain,
! [X7,X8,X9] : lhs_atom51(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_330,plain,
! [X7,X8,X9] : lhs_atom51(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_331,plain,
! [X18,X19,X20] : lhs_atom41(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_332,plain,
! [X7,X8,X9] : lhs_atom38(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_333,plain,
! [X7,X8,X9] : lhs_atom29(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_334,plain,
! [X6,X7,X8] : lhs_atom25(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_335,plain,
! [X4,X5,X6] : lhs_atom20(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_336,plain,
! [X4,X5,X6] : lhs_atom14(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_337,plain,
! [X4,X5,X6] : lhs_atom13(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_338,plain,
! [X4,X5,X6] : lhs_atom12(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_339,plain,
! [X4,X5,X6] : lhs_atom11(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_340,plain,
! [X4,X5,X6] : lhs_atom6(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_341,plain,
! [X4,X5,X6] : lhs_atom5(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_342,plain,
! [X4,X5,X6] : lhs_atom4(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_343,plain,
! [X4,X5,X6] : lhs_atom2(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_344,plain,
! [X4,X5,X6] : lhs_atom1(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_345,plain,
! [X18,X19] : lhs_atom133(X18,X19),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_346,plain,
! [X28,X29] : lhs_atom103(X28,X29),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_347,plain,
! [X18,X19] : lhs_atom102(X18,X19),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_348,plain,
! [X20,X21] : lhs_atom99(X20,X21),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_349,plain,
! [X27,X28] : lhs_atom98(X27,X28),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_350,plain,
! [X18,X19] : lhs_atom97(X18,X19),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_351,plain,
! [X18,X19] : lhs_atom95(X18,X19),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_352,plain,
! [X18,X19] : lhs_atom89(X18,X19),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_353,plain,
! [X18,X19] : lhs_atom86(X18,X19),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_354,plain,
! [X18,X19] : lhs_atom83(X18,X19),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_355,plain,
! [X20,X21] : lhs_atom82(X20,X21),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_356,plain,
! [X18,X19] : lhs_atom80(X18,X19),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_357,plain,
! [X18,X19] : lhs_atom79(X18,X19),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_358,plain,
! [X4,X5] : lhs_atom74(X4,X5),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_359,plain,
! [X18,X19] : lhs_atom73(X18,X19),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_360,plain,
! [X4,X5] : lhs_atom72(X4,X5),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_361,plain,
! [X4,X5] : lhs_atom50(X4,X5),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_362,plain,
! [X4,X5] : lhs_atom49(X4,X5),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_363,plain,
! [X4,X5] : lhs_atom48(X4,X5),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_364,plain,
! [X4,X5] : lhs_atom46(X4,X5),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_365,plain,
! [X4,X5] : lhs_atom45(X4,X5),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_366,plain,
! [X4,X5] : lhs_atom44(X4,X5),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_367,plain,
! [X4,X5] : lhs_atom43(X4,X5),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_368,plain,
! [X4,X5] : lhs_atom42(X4,X5),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_369,plain,
! [X14,X15] : lhs_atom33(X14,X15),
inference(variable_rename,[status(thm)],[c_0_235]) ).
fof(c_0_370,plain,
! [X9,X10] : lhs_atom32(X9,X10),
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_371,plain,
! [X11,X12] : lhs_atom28(X11,X12),
inference(variable_rename,[status(thm)],[c_0_237]) ).
fof(c_0_372,plain,
! [X4,X5] : lhs_atom22(X4,X5),
inference(variable_rename,[status(thm)],[c_0_238]) ).
fof(c_0_373,plain,
! [X10,X11] : lhs_atom19(X10,X11),
inference(variable_rename,[status(thm)],[c_0_239]) ).
fof(c_0_374,plain,
! [X9,X10] : lhs_atom18(X9,X10),
inference(variable_rename,[status(thm)],[c_0_240]) ).
fof(c_0_375,plain,
! [X4] : lhs_atom47(X4),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_376,plain,
! [X4] : lhs_atom40(X4),
inference(variable_rename,[status(thm)],[c_0_242]) ).
fof(c_0_377,plain,
! [X4] : lhs_atom39(X4),
inference(variable_rename,[status(thm)],[c_0_243]) ).
fof(c_0_378,plain,
lhs_atom132,
c_0_244 ).
fof(c_0_379,plain,
lhs_atom131,
c_0_245 ).
fof(c_0_380,plain,
lhs_atom130,
c_0_246 ).
fof(c_0_381,plain,
lhs_atom129,
c_0_247 ).
fof(c_0_382,plain,
lhs_atom128,
c_0_248 ).
fof(c_0_383,plain,
lhs_atom127,
c_0_249 ).
fof(c_0_384,plain,
lhs_atom126,
c_0_250 ).
fof(c_0_385,plain,
lhs_atom125,
c_0_251 ).
fof(c_0_386,plain,
lhs_atom124,
c_0_252 ).
fof(c_0_387,plain,
lhs_atom123,
c_0_253 ).
fof(c_0_388,plain,
lhs_atom122,
c_0_254 ).
fof(c_0_389,plain,
lhs_atom121,
c_0_255 ).
fof(c_0_390,plain,
lhs_atom120,
c_0_256 ).
fof(c_0_391,plain,
lhs_atom119,
c_0_257 ).
fof(c_0_392,plain,
lhs_atom118,
c_0_258 ).
fof(c_0_393,plain,
lhs_atom117,
c_0_259 ).
fof(c_0_394,plain,
lhs_atom116,
c_0_260 ).
fof(c_0_395,plain,
lhs_atom115,
c_0_261 ).
fof(c_0_396,plain,
lhs_atom114,
c_0_262 ).
fof(c_0_397,plain,
lhs_atom113,
c_0_263 ).
fof(c_0_398,plain,
lhs_atom112,
c_0_264 ).
fof(c_0_399,plain,
lhs_atom111,
c_0_265 ).
fof(c_0_400,plain,
lhs_atom101,
c_0_266 ).
fof(c_0_401,plain,
lhs_atom93,
c_0_267 ).
cnf(c_0_402,plain,
lhs_atom81(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_403,plain,
lhs_atom78(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_404,plain,
lhs_atom66(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_405,plain,
lhs_atom54(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_406,plain,
lhs_atom53(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_407,plain,
lhs_atom34(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_408,plain,
lhs_atom31(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_409,plain,
lhs_atom26(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_410,plain,
lhs_atom17(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_411,plain,
lhs_atom9(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_412,plain,
lhs_atom7(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_413,plain,
lhs_atom109(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_414,plain,
lhs_atom94(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_415,plain,
lhs_atom88(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_416,plain,
lhs_atom87(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_417,plain,
lhs_atom84(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_418,plain,
lhs_atom77(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_419,plain,
lhs_atom76(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_420,plain,
lhs_atom75(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_421,plain,
lhs_atom70(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_422,plain,
lhs_atom69(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_423,plain,
lhs_atom64(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_424,plain,
lhs_atom63(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_425,plain,
lhs_atom62(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_426,plain,
lhs_atom61(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_427,plain,
lhs_atom60(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_428,plain,
lhs_atom59(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_429,plain,
lhs_atom58(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_430,plain,
lhs_atom57(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_431,plain,
lhs_atom56(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_432,plain,
lhs_atom52(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_433,plain,
lhs_atom37(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_434,plain,
lhs_atom36(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_435,plain,
lhs_atom35(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_436,plain,
lhs_atom30(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_437,plain,
lhs_atom27(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_438,plain,
lhs_atom24(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_439,plain,
lhs_atom23(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_440,plain,
lhs_atom21(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_441,plain,
lhs_atom16(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_442,plain,
lhs_atom15(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_443,plain,
lhs_atom10(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_444,plain,
lhs_atom8(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_445,plain,
lhs_atom3(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_446,plain,
lhs_atom110(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_447,plain,
lhs_atom108(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_448,plain,
lhs_atom107(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_449,plain,
lhs_atom106(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_450,plain,
lhs_atom105(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_451,plain,
lhs_atom104(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_452,plain,
lhs_atom100(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_453,plain,
lhs_atom96(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_454,plain,
lhs_atom92(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_455,plain,
lhs_atom91(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_456,plain,
lhs_atom90(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_457,plain,
lhs_atom85(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_458,plain,
lhs_atom71(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_459,plain,
lhs_atom68(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_460,plain,
lhs_atom67(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_461,plain,
lhs_atom65(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_462,plain,
lhs_atom55(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_463,plain,
lhs_atom51(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_464,plain,
lhs_atom51(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_465,plain,
lhs_atom41(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_466,plain,
lhs_atom38(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_467,plain,
lhs_atom29(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_468,plain,
lhs_atom25(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_469,plain,
lhs_atom20(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_470,plain,
lhs_atom14(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_471,plain,
lhs_atom13(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_472,plain,
lhs_atom12(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_473,plain,
lhs_atom11(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_474,plain,
lhs_atom6(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_475,plain,
lhs_atom5(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_476,plain,
lhs_atom4(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_477,plain,
lhs_atom2(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_478,plain,
lhs_atom1(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_479,plain,
lhs_atom133(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_480,plain,
lhs_atom103(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_481,plain,
lhs_atom102(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_482,plain,
lhs_atom99(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_483,plain,
lhs_atom98(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_484,plain,
lhs_atom97(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_485,plain,
lhs_atom95(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_486,plain,
lhs_atom89(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_487,plain,
lhs_atom86(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_488,plain,
lhs_atom83(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_489,plain,
lhs_atom82(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_490,plain,
lhs_atom80(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_491,plain,
lhs_atom79(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_492,plain,
lhs_atom74(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_493,plain,
lhs_atom73(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_494,plain,
lhs_atom72(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_495,plain,
lhs_atom50(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_496,plain,
lhs_atom49(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_497,plain,
lhs_atom48(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_498,plain,
lhs_atom46(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_499,plain,
lhs_atom45(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_500,plain,
lhs_atom44(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_501,plain,
lhs_atom43(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_502,plain,
lhs_atom42(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_503,plain,
lhs_atom33(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_504,plain,
lhs_atom32(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_505,plain,
lhs_atom28(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_506,plain,
lhs_atom22(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_507,plain,
lhs_atom19(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_508,plain,
lhs_atom18(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_509,plain,
lhs_atom47(X1),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_510,plain,
lhs_atom40(X1),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_511,plain,
lhs_atom39(X1),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_512,plain,
lhs_atom132,
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_513,plain,
lhs_atom131,
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_514,plain,
lhs_atom130,
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_515,plain,
lhs_atom129,
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_516,plain,
lhs_atom128,
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_517,plain,
lhs_atom127,
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_518,plain,
lhs_atom126,
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_519,plain,
lhs_atom125,
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_520,plain,
lhs_atom124,
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_521,plain,
lhs_atom123,
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_522,plain,
lhs_atom122,
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_523,plain,
lhs_atom121,
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_524,plain,
lhs_atom120,
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_525,plain,
lhs_atom119,
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_526,plain,
lhs_atom118,
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_527,plain,
lhs_atom117,
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_528,plain,
lhs_atom116,
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_529,plain,
lhs_atom115,
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_530,plain,
lhs_atom114,
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_531,plain,
lhs_atom113,
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_532,plain,
lhs_atom112,
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_533,plain,
lhs_atom111,
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_534,plain,
lhs_atom101,
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_535,plain,
lhs_atom93,
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_536,plain,
lhs_atom81(X1,X2,X3,X4,X5),
c_0_402,
[final] ).
cnf(c_0_537,plain,
lhs_atom78(X1,X2,X3,X4,X5),
c_0_403,
[final] ).
cnf(c_0_538,plain,
lhs_atom66(X1,X2,X3,X4,X5),
c_0_404,
[final] ).
cnf(c_0_539,plain,
lhs_atom54(X1,X2,X3,X4,X5),
c_0_405,
[final] ).
cnf(c_0_540,plain,
lhs_atom53(X1,X2,X3,X4,X5),
c_0_406,
[final] ).
cnf(c_0_541,plain,
lhs_atom34(X1,X2,X3,X4,X5),
c_0_407,
[final] ).
cnf(c_0_542,plain,
lhs_atom31(X1,X2,X3,X4,X5),
c_0_408,
[final] ).
cnf(c_0_543,plain,
lhs_atom26(X1,X2,X3,X4,X5),
c_0_409,
[final] ).
cnf(c_0_544,plain,
lhs_atom17(X1,X2,X3,X4,X5),
c_0_410,
[final] ).
cnf(c_0_545,plain,
lhs_atom9(X1,X2,X3,X4,X5),
c_0_411,
[final] ).
cnf(c_0_546,plain,
lhs_atom7(X1,X2,X3,X4,X5),
c_0_412,
[final] ).
cnf(c_0_547,plain,
lhs_atom109(X1,X2,X3,X4),
c_0_413,
[final] ).
cnf(c_0_548,plain,
lhs_atom94(X1,X2,X3,X4),
c_0_414,
[final] ).
cnf(c_0_549,plain,
lhs_atom88(X1,X2,X3,X4),
c_0_415,
[final] ).
cnf(c_0_550,plain,
lhs_atom87(X1,X2,X3,X4),
c_0_416,
[final] ).
cnf(c_0_551,plain,
lhs_atom84(X1,X2,X3,X4),
c_0_417,
[final] ).
cnf(c_0_552,plain,
lhs_atom77(X1,X2,X3,X4),
c_0_418,
[final] ).
cnf(c_0_553,plain,
lhs_atom76(X1,X2,X3,X4),
c_0_419,
[final] ).
cnf(c_0_554,plain,
lhs_atom75(X1,X2,X3,X4),
c_0_420,
[final] ).
cnf(c_0_555,plain,
lhs_atom70(X1,X2,X3,X4),
c_0_421,
[final] ).
cnf(c_0_556,plain,
lhs_atom69(X1,X2,X3,X4),
c_0_422,
[final] ).
cnf(c_0_557,plain,
lhs_atom64(X1,X2,X3,X4),
c_0_423,
[final] ).
cnf(c_0_558,plain,
lhs_atom63(X1,X2,X3,X4),
c_0_424,
[final] ).
cnf(c_0_559,plain,
lhs_atom62(X1,X2,X3,X4),
c_0_425,
[final] ).
cnf(c_0_560,plain,
lhs_atom61(X1,X2,X3,X4),
c_0_426,
[final] ).
cnf(c_0_561,plain,
lhs_atom60(X1,X2,X3,X4),
c_0_427,
[final] ).
cnf(c_0_562,plain,
lhs_atom59(X1,X2,X3,X4),
c_0_428,
[final] ).
cnf(c_0_563,plain,
lhs_atom58(X1,X2,X3,X4),
c_0_429,
[final] ).
cnf(c_0_564,plain,
lhs_atom57(X1,X2,X3,X4),
c_0_430,
[final] ).
cnf(c_0_565,plain,
lhs_atom56(X1,X2,X3,X4),
c_0_431,
[final] ).
cnf(c_0_566,plain,
lhs_atom52(X1,X2,X3,X4),
c_0_432,
[final] ).
cnf(c_0_567,plain,
lhs_atom37(X1,X2,X3,X4),
c_0_433,
[final] ).
cnf(c_0_568,plain,
lhs_atom36(X1,X2,X3,X4),
c_0_434,
[final] ).
cnf(c_0_569,plain,
lhs_atom35(X1,X2,X3,X4),
c_0_435,
[final] ).
cnf(c_0_570,plain,
lhs_atom30(X1,X2,X3,X4),
c_0_436,
[final] ).
cnf(c_0_571,plain,
lhs_atom27(X1,X2,X3,X4),
c_0_437,
[final] ).
cnf(c_0_572,plain,
lhs_atom24(X1,X2,X3,X4),
c_0_438,
[final] ).
cnf(c_0_573,plain,
lhs_atom23(X1,X2,X3,X4),
c_0_439,
[final] ).
cnf(c_0_574,plain,
lhs_atom21(X1,X2,X3,X4),
c_0_440,
[final] ).
cnf(c_0_575,plain,
lhs_atom16(X1,X2,X3,X4),
c_0_441,
[final] ).
cnf(c_0_576,plain,
lhs_atom15(X1,X2,X3,X4),
c_0_442,
[final] ).
cnf(c_0_577,plain,
lhs_atom10(X1,X2,X3,X4),
c_0_443,
[final] ).
cnf(c_0_578,plain,
lhs_atom8(X1,X2,X3,X4),
c_0_444,
[final] ).
cnf(c_0_579,plain,
lhs_atom3(X1,X2,X3,X4),
c_0_445,
[final] ).
cnf(c_0_580,plain,
lhs_atom110(X1,X2,X3),
c_0_446,
[final] ).
cnf(c_0_581,plain,
lhs_atom108(X1,X2,X3),
c_0_447,
[final] ).
cnf(c_0_582,plain,
lhs_atom107(X1,X2,X3),
c_0_448,
[final] ).
cnf(c_0_583,plain,
lhs_atom106(X1,X2,X3),
c_0_449,
[final] ).
cnf(c_0_584,plain,
lhs_atom105(X1,X2,X3),
c_0_450,
[final] ).
cnf(c_0_585,plain,
lhs_atom104(X1,X2,X3),
c_0_451,
[final] ).
cnf(c_0_586,plain,
lhs_atom100(X1,X2,X3),
c_0_452,
[final] ).
cnf(c_0_587,plain,
lhs_atom96(X1,X2,X3),
c_0_453,
[final] ).
cnf(c_0_588,plain,
lhs_atom92(X1,X2,X3),
c_0_454,
[final] ).
cnf(c_0_589,plain,
lhs_atom91(X1,X2,X3),
c_0_455,
[final] ).
cnf(c_0_590,plain,
lhs_atom90(X1,X2,X3),
c_0_456,
[final] ).
cnf(c_0_591,plain,
lhs_atom85(X1,X2,X3),
c_0_457,
[final] ).
cnf(c_0_592,plain,
lhs_atom71(X1,X2,X3),
c_0_458,
[final] ).
cnf(c_0_593,plain,
lhs_atom68(X1,X2,X3),
c_0_459,
[final] ).
cnf(c_0_594,plain,
lhs_atom67(X1,X2,X3),
c_0_460,
[final] ).
cnf(c_0_595,plain,
lhs_atom65(X1,X2,X3),
c_0_461,
[final] ).
cnf(c_0_596,plain,
lhs_atom55(X1,X2,X3),
c_0_462,
[final] ).
cnf(c_0_597,plain,
lhs_atom51(X1,X2,X3),
c_0_463,
[final] ).
cnf(c_0_598,plain,
lhs_atom51(X1,X2,X3),
c_0_464,
[final] ).
cnf(c_0_599,plain,
lhs_atom41(X1,X2,X3),
c_0_465,
[final] ).
cnf(c_0_600,plain,
lhs_atom38(X1,X2,X3),
c_0_466,
[final] ).
cnf(c_0_601,plain,
lhs_atom29(X1,X2,X3),
c_0_467,
[final] ).
cnf(c_0_602,plain,
lhs_atom25(X1,X2,X3),
c_0_468,
[final] ).
cnf(c_0_603,plain,
lhs_atom20(X1,X2,X3),
c_0_469,
[final] ).
cnf(c_0_604,plain,
lhs_atom14(X1,X2,X3),
c_0_470,
[final] ).
cnf(c_0_605,plain,
lhs_atom13(X1,X2,X3),
c_0_471,
[final] ).
cnf(c_0_606,plain,
lhs_atom12(X1,X2,X3),
c_0_472,
[final] ).
cnf(c_0_607,plain,
lhs_atom11(X1,X2,X3),
c_0_473,
[final] ).
cnf(c_0_608,plain,
lhs_atom6(X1,X2,X3),
c_0_474,
[final] ).
cnf(c_0_609,plain,
lhs_atom5(X1,X2,X3),
c_0_475,
[final] ).
cnf(c_0_610,plain,
lhs_atom4(X1,X2,X3),
c_0_476,
[final] ).
cnf(c_0_611,plain,
lhs_atom2(X1,X2,X3),
c_0_477,
[final] ).
cnf(c_0_612,plain,
lhs_atom1(X1,X2,X3),
c_0_478,
[final] ).
cnf(c_0_613,plain,
lhs_atom133(X1,X2),
c_0_479,
[final] ).
cnf(c_0_614,plain,
lhs_atom103(X1,X2),
c_0_480,
[final] ).
cnf(c_0_615,plain,
lhs_atom102(X1,X2),
c_0_481,
[final] ).
cnf(c_0_616,plain,
lhs_atom99(X1,X2),
c_0_482,
[final] ).
cnf(c_0_617,plain,
lhs_atom98(X1,X2),
c_0_483,
[final] ).
cnf(c_0_618,plain,
lhs_atom97(X1,X2),
c_0_484,
[final] ).
cnf(c_0_619,plain,
lhs_atom95(X1,X2),
c_0_485,
[final] ).
cnf(c_0_620,plain,
lhs_atom89(X1,X2),
c_0_486,
[final] ).
cnf(c_0_621,plain,
lhs_atom86(X1,X2),
c_0_487,
[final] ).
cnf(c_0_622,plain,
lhs_atom83(X1,X2),
c_0_488,
[final] ).
cnf(c_0_623,plain,
lhs_atom82(X1,X2),
c_0_489,
[final] ).
cnf(c_0_624,plain,
lhs_atom80(X1,X2),
c_0_490,
[final] ).
cnf(c_0_625,plain,
lhs_atom79(X1,X2),
c_0_491,
[final] ).
cnf(c_0_626,plain,
lhs_atom74(X1,X2),
c_0_492,
[final] ).
cnf(c_0_627,plain,
lhs_atom73(X1,X2),
c_0_493,
[final] ).
cnf(c_0_628,plain,
lhs_atom72(X1,X2),
c_0_494,
[final] ).
cnf(c_0_629,plain,
lhs_atom50(X1,X2),
c_0_495,
[final] ).
cnf(c_0_630,plain,
lhs_atom49(X1,X2),
c_0_496,
[final] ).
cnf(c_0_631,plain,
lhs_atom48(X1,X2),
c_0_497,
[final] ).
cnf(c_0_632,plain,
lhs_atom46(X1,X2),
c_0_498,
[final] ).
cnf(c_0_633,plain,
lhs_atom45(X1,X2),
c_0_499,
[final] ).
cnf(c_0_634,plain,
lhs_atom44(X1,X2),
c_0_500,
[final] ).
cnf(c_0_635,plain,
lhs_atom43(X1,X2),
c_0_501,
[final] ).
cnf(c_0_636,plain,
lhs_atom42(X1,X2),
c_0_502,
[final] ).
cnf(c_0_637,plain,
lhs_atom33(X1,X2),
c_0_503,
[final] ).
cnf(c_0_638,plain,
lhs_atom32(X1,X2),
c_0_504,
[final] ).
cnf(c_0_639,plain,
lhs_atom28(X1,X2),
c_0_505,
[final] ).
cnf(c_0_640,plain,
lhs_atom22(X1,X2),
c_0_506,
[final] ).
cnf(c_0_641,plain,
lhs_atom19(X1,X2),
c_0_507,
[final] ).
cnf(c_0_642,plain,
lhs_atom18(X1,X2),
c_0_508,
[final] ).
cnf(c_0_643,plain,
lhs_atom47(X1),
c_0_509,
[final] ).
cnf(c_0_644,plain,
lhs_atom40(X1),
c_0_510,
[final] ).
cnf(c_0_645,plain,
lhs_atom39(X1),
c_0_511,
[final] ).
cnf(c_0_646,plain,
lhs_atom132,
c_0_512,
[final] ).
cnf(c_0_647,plain,
lhs_atom131,
c_0_513,
[final] ).
cnf(c_0_648,plain,
lhs_atom130,
c_0_514,
[final] ).
cnf(c_0_649,plain,
lhs_atom129,
c_0_515,
[final] ).
cnf(c_0_650,plain,
lhs_atom128,
c_0_516,
[final] ).
cnf(c_0_651,plain,
lhs_atom127,
c_0_517,
[final] ).
cnf(c_0_652,plain,
lhs_atom126,
c_0_518,
[final] ).
cnf(c_0_653,plain,
lhs_atom125,
c_0_519,
[final] ).
cnf(c_0_654,plain,
lhs_atom124,
c_0_520,
[final] ).
cnf(c_0_655,plain,
lhs_atom123,
c_0_521,
[final] ).
cnf(c_0_656,plain,
lhs_atom122,
c_0_522,
[final] ).
cnf(c_0_657,plain,
lhs_atom121,
c_0_523,
[final] ).
cnf(c_0_658,plain,
lhs_atom120,
c_0_524,
[final] ).
cnf(c_0_659,plain,
lhs_atom119,
c_0_525,
[final] ).
cnf(c_0_660,plain,
lhs_atom118,
c_0_526,
[final] ).
cnf(c_0_661,plain,
lhs_atom117,
c_0_527,
[final] ).
cnf(c_0_662,plain,
lhs_atom116,
c_0_528,
[final] ).
cnf(c_0_663,plain,
lhs_atom115,
c_0_529,
[final] ).
cnf(c_0_664,plain,
lhs_atom114,
c_0_530,
[final] ).
cnf(c_0_665,plain,
lhs_atom113,
c_0_531,
[final] ).
cnf(c_0_666,plain,
lhs_atom112,
c_0_532,
[final] ).
cnf(c_0_667,plain,
lhs_atom111,
c_0_533,
[final] ).
cnf(c_0_668,plain,
lhs_atom101,
c_0_534,
[final] ).
cnf(c_0_669,plain,
lhs_atom93,
c_0_535,
[final] ).
% End CNF derivation
cnf(c_0_536_0,axiom,
c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X3,X4,X5),c_Set_Oimage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_536,def_lhs_atom81]) ).
cnf(c_0_537_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,X4,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_537,def_lhs_atom78]) ).
cnf(c_0_538_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X1,X3,X4),X2,X4,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X2,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X2,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_538,def_lhs_atom66]) ).
cnf(c_0_539_0,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_539,def_lhs_atom54]) ).
cnf(c_0_540_0,axiom,
c_Set_Ovimage(X1,c_Set_Oinsert(X2,X3,X4),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_540,def_lhs_atom53]) ).
cnf(c_0_541_0,axiom,
c_Map_Omap__add(X3,c_Map_Omap__add(X2,X1,X5,X4),X5,X4) = c_Map_Omap__add(c_Map_Omap__add(X3,X2,X5,X4),X1,X5,X4),
inference(unfold_definition,[status(thm)],[c_0_541,def_lhs_atom34]) ).
cnf(c_0_542_0,axiom,
c_lessequals(c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2),X4,X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X4,X5)),c_Set_Oimage(X1,X2,X4,X5)),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_542,def_lhs_atom31]) ).
cnf(c_0_543_0,axiom,
c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X5,X4) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X3,X5,X4),c_Set_Ovimage(X1,X2,X5,X4),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_543,def_lhs_atom26]) ).
cnf(c_0_544_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X3,X4,X5),c_Set_Oimage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_544,def_lhs_atom17]) ).
cnf(c_0_545_0,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2),X5,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X4)),c_Set_Ovimage(X1,X2,X5,X4)),
inference(unfold_definition,[status(thm)],[c_0_545,def_lhs_atom9]) ).
cnf(c_0_546_0,axiom,
c_Set_Ovimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,X3,X5,X4),c_Set_Ovimage(X1,X2,X5,X4),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_546,def_lhs_atom7]) ).
cnf(c_0_547_0,axiom,
c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4) = c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_547,def_lhs_atom109]) ).
cnf(c_0_548_0,axiom,
hBOOL(c_in(X2,c_Set_Ovimage(X1,c_Set_Oinsert(hAPP(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X3,X4),X3)),
inference(unfold_definition,[status(thm)],[c_0_548,def_lhs_atom94]) ).
cnf(c_0_549_0,axiom,
c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X1,X2,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_549,def_lhs_atom88]) ).
cnf(c_0_550_0,axiom,
c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X1,X2,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_550,def_lhs_atom87]) ).
cnf(c_0_551_0,axiom,
c_Set_Oinsert(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,tc_fun(X4,tc_bool)),X4) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_551,def_lhs_atom84]) ).
cnf(c_0_552_0,axiom,
c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_552,def_lhs_atom77]) ).
cnf(c_0_553_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2),X1,tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_553,def_lhs_atom76]) ).
cnf(c_0_554_0,axiom,
c_HOL_Ominus__class_Ominus(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_554,def_lhs_atom75]) ).
cnf(c_0_555_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1),X3,tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_555,def_lhs_atom70]) ).
cnf(c_0_556_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1),tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_556,def_lhs_atom69]) ).
cnf(c_0_557_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1),X2,tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_557,def_lhs_atom64]) ).
cnf(c_0_558_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool))),X1) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_558,def_lhs_atom63]) ).
cnf(c_0_559_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X2),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_559,def_lhs_atom62]) ).
cnf(c_0_560_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X2,
inference(unfold_definition,[status(thm)],[c_0_560,def_lhs_atom61]) ).
cnf(c_0_561_0,axiom,
c_Com_Ocom_OBODY(X3) != c_Com_Ocom_OCall(X1,X2,X4),
inference(unfold_definition,[status(thm)],[c_0_561,def_lhs_atom60]) ).
cnf(c_0_562_0,axiom,
c_Com_Ocom_OCall(X1,X2,X4) != c_Com_Ocom_OBODY(X3),
inference(unfold_definition,[status(thm)],[c_0_562,def_lhs_atom59]) ).
cnf(c_0_563_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X3,X4),X2,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_563,def_lhs_atom58]) ).
cnf(c_0_564_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X3,c_Set_Oinsert(X1,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_564,def_lhs_atom57]) ).
cnf(c_0_565_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_Set_Oinsert(X1,X3,X4)),c_Set_Oinsert(X1,X2,X4)) = c_Set_Oinsert(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2),X4),
inference(unfold_definition,[status(thm)],[c_0_565,def_lhs_atom56]) ).
cnf(c_0_566_0,axiom,
c_Finite__Set_Ofold__graph(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X1,X4,X3),
inference(unfold_definition,[status(thm)],[c_0_566,def_lhs_atom52]) ).
cnf(c_0_567_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_567,def_lhs_atom37]) ).
cnf(c_0_568_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_568,def_lhs_atom36]) ).
cnf(c_0_569_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_569,def_lhs_atom35]) ).
cnf(c_0_570_0,axiom,
c_Map_Odom(c_Map_Omap__add(X2,X1,X4,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(X1,X4,X3),c_Map_Odom(X2,X4,X3),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_570,def_lhs_atom30]) ).
cnf(c_0_571_0,axiom,
c_lessequals(c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4),X2,tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_571,def_lhs_atom27]) ).
cnf(c_0_572_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool))),X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_572,def_lhs_atom24]) ).
cnf(c_0_573_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_573,def_lhs_atom23]) ).
cnf(c_0_574_0,axiom,
c_HOL_Ominus__class_Ominus(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X2,
inference(unfold_definition,[status(thm)],[c_0_574,def_lhs_atom21]) ).
cnf(c_0_575_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_575,def_lhs_atom16]) ).
cnf(c_0_576_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_576,def_lhs_atom15]) ).
cnf(c_0_577_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1),tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)))),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_577,def_lhs_atom10]) ).
cnf(c_0_578_0,axiom,
c_Map_Omap__le(X2,c_Map_Omap__add(X1,X2,X4,X3),X4,X3),
inference(unfold_definition,[status(thm)],[c_0_578,def_lhs_atom8]) ).
cnf(c_0_579_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_579,def_lhs_atom3]) ).
cnf(c_0_580_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
inference(unfold_definition,[status(thm)],[c_0_580,def_lhs_atom110]) ).
cnf(c_0_581_0,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
inference(unfold_definition,[status(thm)],[c_0_581,def_lhs_atom108]) ).
cnf(c_0_582_0,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
inference(unfold_definition,[status(thm)],[c_0_582,def_lhs_atom107]) ).
cnf(c_0_583_0,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
inference(unfold_definition,[status(thm)],[c_0_583,def_lhs_atom106]) ).
cnf(c_0_584_0,axiom,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_584,def_lhs_atom105]) ).
cnf(c_0_585_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_585,def_lhs_atom104]) ).
cnf(c_0_586_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oinsert(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_586,def_lhs_atom100]) ).
cnf(c_0_587_0,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_587,def_lhs_atom96]) ).
cnf(c_0_588_0,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_588,def_lhs_atom92]) ).
cnf(c_0_589_0,axiom,
c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_589,def_lhs_atom91]) ).
cnf(c_0_590_0,axiom,
c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_590,def_lhs_atom90]) ).
cnf(c_0_591_0,axiom,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_591,def_lhs_atom85]) ).
cnf(c_0_592_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1),
inference(unfold_definition,[status(thm)],[c_0_592,def_lhs_atom71]) ).
cnf(c_0_593_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1),X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_593,def_lhs_atom68]) ).
cnf(c_0_594_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1),X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_594,def_lhs_atom67]) ).
cnf(c_0_595_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1),tc_fun(X3,tc_bool)) = X2,
inference(unfold_definition,[status(thm)],[c_0_595,def_lhs_atom65]) ).
cnf(c_0_596_0,axiom,
c_lessequals(X2,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_596,def_lhs_atom55]) ).
cnf(c_0_597_0,axiom,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_597,def_lhs_atom51]) ).
cnf(c_0_598_0,axiom,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_598,def_lhs_atom51]) ).
cnf(c_0_599_0,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_599,def_lhs_atom41]) ).
cnf(c_0_600_0,axiom,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_600,def_lhs_atom38]) ).
cnf(c_0_601_0,axiom,
c_Map_Omap__le(X1,X1,X3,X2),
inference(unfold_definition,[status(thm)],[c_0_601,def_lhs_atom29]) ).
cnf(c_0_602_0,axiom,
c_Finite__Set_Ofold1(X1,X2,X3) = c_The(c_Finite__Set_Ofold1Set(X1,X2,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_602,def_lhs_atom25]) ).
cnf(c_0_603_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_603,def_lhs_atom20]) ).
cnf(c_0_604_0,axiom,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_604,def_lhs_atom14]) ).
cnf(c_0_605_0,axiom,
c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_605,def_lhs_atom13]) ).
cnf(c_0_606_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2),
inference(unfold_definition,[status(thm)],[c_0_606,def_lhs_atom12]) ).
cnf(c_0_607_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_607,def_lhs_atom11]) ).
cnf(c_0_608_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_608,def_lhs_atom6]) ).
cnf(c_0_609_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_609,def_lhs_atom5]) ).
cnf(c_0_610_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_610,def_lhs_atom4]) ).
cnf(c_0_611_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_611,def_lhs_atom2]) ).
cnf(c_0_612_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_612,def_lhs_atom1]) ).
cnf(c_0_613_0,axiom,
hBOOL(hAPP(c_fequal(X1,X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_613,def_lhs_atom133]) ).
cnf(c_0_614_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_614,def_lhs_atom103]) ).
cnf(c_0_615_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1)),
inference(unfold_definition,[status(thm)],[c_0_615,def_lhs_atom102]) ).
cnf(c_0_616_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(unfold_definition,[status(thm)],[c_0_616,def_lhs_atom99]) ).
cnf(c_0_617_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(unfold_definition,[status(thm)],[c_0_617,def_lhs_atom98]) ).
cnf(c_0_618_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(unfold_definition,[status(thm)],[c_0_618,def_lhs_atom97]) ).
cnf(c_0_619_0,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)),
inference(unfold_definition,[status(thm)],[c_0_619,def_lhs_atom95]) ).
cnf(c_0_620_0,axiom,
c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_620,def_lhs_atom89]) ).
cnf(c_0_621_0,axiom,
c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_621,def_lhs_atom86]) ).
cnf(c_0_622_0,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))),
inference(unfold_definition,[status(thm)],[c_0_622,def_lhs_atom83]) ).
cnf(c_0_623_0,axiom,
c_Collect(c_fequal(X1,X2),X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_623,def_lhs_atom82]) ).
cnf(c_0_624_0,axiom,
c_Option_Othe(c_Option_Ooption_OSome(X1,X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_624,def_lhs_atom80]) ).
cnf(c_0_625_0,axiom,
c_The(c_fequal(X1,X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_625,def_lhs_atom79]) ).
cnf(c_0_626_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_626,def_lhs_atom74]) ).
cnf(c_0_627_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_627,def_lhs_atom73]) ).
cnf(c_0_628_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_628,def_lhs_atom72]) ).
cnf(c_0_629_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_629,def_lhs_atom50]) ).
cnf(c_0_630_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_630,def_lhs_atom49]) ).
cnf(c_0_631_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_631,def_lhs_atom48]) ).
cnf(c_0_632_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_632,def_lhs_atom46]) ).
cnf(c_0_633_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_633,def_lhs_atom45]) ).
cnf(c_0_634_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_634,def_lhs_atom44]) ).
cnf(c_0_635_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_635,def_lhs_atom43]) ).
cnf(c_0_636_0,axiom,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_636,def_lhs_atom42]) ).
cnf(c_0_637_0,axiom,
c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_ONone(X2),
inference(unfold_definition,[status(thm)],[c_0_637,def_lhs_atom33]) ).
cnf(c_0_638_0,axiom,
c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_ONone(X2),
inference(unfold_definition,[status(thm)],[c_0_638,def_lhs_atom32]) ).
cnf(c_0_639_0,axiom,
c_Collect(X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_639,def_lhs_atom28]) ).
cnf(c_0_640_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_640,def_lhs_atom22]) ).
cnf(c_0_641_0,axiom,
c_Option_Ooption_ONone(X2) != c_Option_Ooption_OSome(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_641,def_lhs_atom19]) ).
cnf(c_0_642_0,axiom,
c_Option_Ooption_ONone(X2) != c_Option_Ooption_OSome(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_642,def_lhs_atom18]) ).
cnf(c_0_643_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(unfold_definition,[status(thm)],[c_0_643,def_lhs_atom47]) ).
cnf(c_0_644_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_644,def_lhs_atom40]) ).
cnf(c_0_645_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_645,def_lhs_atom39]) ).
cnf(c_0_646_0,axiom,
class_HOL_Oord(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_646,def_lhs_atom132]) ).
cnf(c_0_647_0,axiom,
class_HOL_Ominus(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_647,def_lhs_atom131]) ).
cnf(c_0_648_0,axiom,
class_Orderings_Obot(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_648,def_lhs_atom130]) ).
cnf(c_0_649_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_649,def_lhs_atom129]) ).
cnf(c_0_650_0,axiom,
class_Lattices_Olattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_650,def_lhs_atom128]) ).
cnf(c_0_651_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_651,def_lhs_atom127]) ).
cnf(c_0_652_0,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_652,def_lhs_atom126]) ).
cnf(c_0_653_0,axiom,
class_Lattices_Obounded__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_653,def_lhs_atom125]) ).
cnf(c_0_654_0,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_654,def_lhs_atom124]) ).
cnf(c_0_655_0,axiom,
class_Lattices_Olower__semilattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_655,def_lhs_atom123]) ).
cnf(c_0_656_0,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_656,def_lhs_atom122]) ).
cnf(c_0_657_0,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_657,def_lhs_atom121]) ).
cnf(c_0_658_0,axiom,
class_HOL_Oord(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_658,def_lhs_atom120]) ).
cnf(c_0_659_0,axiom,
class_HOL_Ominus(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_659,def_lhs_atom119]) ).
cnf(c_0_660_0,axiom,
class_Orderings_Obot(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_660,def_lhs_atom118]) ).
cnf(c_0_661_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_661,def_lhs_atom117]) ).
cnf(c_0_662_0,axiom,
class_Lattices_Olattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_662,def_lhs_atom116]) ).
cnf(c_0_663_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_663,def_lhs_atom115]) ).
cnf(c_0_664_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_664,def_lhs_atom114]) ).
cnf(c_0_665_0,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_665,def_lhs_atom113]) ).
cnf(c_0_666_0,axiom,
class_Lattices_Olower__semilattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_666,def_lhs_atom112]) ).
cnf(c_0_667_0,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_667,def_lhs_atom111]) ).
cnf(c_0_668_0,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
inference(unfold_definition,[status(thm)],[c_0_668,def_lhs_atom101]) ).
cnf(c_0_669_0,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
inference(unfold_definition,[status(thm)],[c_0_669,def_lhs_atom93]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X33,X34,X35,X36,X37,X38,X18,X6,X39,X40,X3] :
( hAPP(X40,c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X37,X6),X18)
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OInf__binary_0) ).
fof(c_0_1_002,axiom,
! [X33,X34,X35,X36,X37,X38,X18,X6,X39,X40,X3] :
( hAPP(X39,c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X34,X6),X18)
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OSup__binary_0) ).
fof(c_0_2_003,axiom,
! [X10,X33,X34,X35,X36,X37,X38,X39,X40,X7,X3] :
( hBOOL(hAPP(hAPP(X35,hAPP(X40,X7)),X10))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OInf__lower_0) ).
fof(c_0_3_004,axiom,
! [X10,X33,X34,X35,X36,X37,X38,X39,X40,X7,X3] :
( hBOOL(hAPP(hAPP(X35,X10),hAPP(X39,X7)))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OSup__upper_0) ).
fof(c_0_4_005,axiom,
! [X33,X34,X35,X36,X37,X38,X6,X39,X40,X3] :
( hAPP(X40,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OInf__singleton_0) ).
fof(c_0_5_006,axiom,
! [X33,X34,X35,X36,X37,X38,X6,X39,X40,X3] :
( hAPP(X39,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OSup__singleton_0) ).
fof(c_0_6_007,axiom,
! [X33,X34,X35,X36,X37,X38,X6,X39,X40,X7,X3] :
( hAPP(X40,c_Set_Oinsert(X6,X7,X3)) = hAPP(hAPP(X37,X6),hAPP(X40,X7))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OInf__insert_0) ).
fof(c_0_7_008,axiom,
! [X33,X34,X35,X36,X37,X38,X6,X39,X40,X7,X3] :
( hAPP(X39,c_Set_Oinsert(X6,X7,X3)) = hAPP(hAPP(X34,X6),hAPP(X39,X7))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OSup__insert_0) ).
fof(c_0_8_009,axiom,
! [X33,X34,X35,X36,X37,X38,X39,X40,X3] :
( hAPP(X40,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X33
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OInf__empty_0) ).
fof(c_0_9_010,axiom,
! [X33,X34,X35,X36,X37,X38,X39,X40,X3] :
( hAPP(X39,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X38
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
file('<stdin>',cls_complete__lattice_OSup__empty_0) ).
fof(c_0_10_011,axiom,
! [X10,X25,X18,X6,X7,X3] :
( c_Finite__Set_Ofold__graph(X25,X6,c_Set_Oinsert(X18,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),X10,X3,X3)
| hBOOL(c_in(X18,X7,X3))
| ~ hBOOL(c_in(X6,X7,X3))
| ~ c_Finite__Set_Ofold__graph(X25,X18,X7,X10,X3,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold__graph__permute__diff_0) ).
fof(c_0_11_012,axiom,
! [X41,X12,X10,X26,X7,X20,X3] :
( c_Finite__Set_Ofold__graph(X26,X41,X7,hAPP(hAPP(X26,X10),X12),X3,X20)
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofold__graph(X26,X41,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X12,X3,X20) ),
file('<stdin>',cls_Diff1__fold__graph_0) ).
fof(c_0_12_013,axiom,
! [X41,X12,X25,X18,X7,X3] :
( c_Finite__Set_Ofold__graph(X25,X41,c_Set_Oinsert(X18,X7,X3),hAPP(hAPP(X25,X41),X12),X3,X3)
| hBOOL(c_in(X18,X7,X3))
| ~ c_Finite__Set_Ofold__graph(X25,X18,X7,X12,X3,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold__graph__insert__swap_0) ).
fof(c_0_13_014,axiom,
! [X41,X12,X10,X26,X7,X20,X3] :
( c_Finite__Set_Ofold__graph(X26,X41,c_Set_Oinsert(X10,X7,X3),hAPP(hAPP(X26,X10),X12),X3,X20)
| ~ c_Finite__Set_Ofold__graph(X26,X41,X7,X12,X3,X20)
| hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_fold__graph_OinsertI_0) ).
fof(c_0_14_015,axiom,
! [X10,X26,X6,X7,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26,c_Set_Oinsert(X6,X7,X3),X3),X10))
| hBOOL(c_in(X6,X7,X3))
| ~ c_Finite__Set_Ofold__graph(X26,X6,X7,X10,X3,X3) ),
file('<stdin>',cls_fold1Set_Ointros_0) ).
fof(c_0_15_016,axiom,
! [X41,X10,X26,X20,X3] :
( X10 = X41
| ~ c_Finite__Set_Ofold__graph(X26,X41,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X10,X3,X20) ),
file('<stdin>',cls_empty__fold__graphE_0) ).
fof(c_0_16_017,axiom,
! [X41,X10,X26,X7,X20,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofold__graph(X26,X41,X7,X10,X3,X20) ),
file('<stdin>',cls_fold__graph__imp__finite_0) ).
fof(c_0_17_018,axiom,
! [X24,X27,X17,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Com_Ocom_OBODY(X24),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Com_Ocom_OBODY(X24),X27,X3),X15,tc_Hoare__Mirabelle_Otriple(X3)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Option_Othe(hAPP(c_Com_Obody,X24),tc_Com_Ocom),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_BodyN_0) ).
fof(c_0_18_019,axiom,
! [X22,X27,X17] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,X22,X27,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,X22,X27,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X22),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
file('<stdin>',cls_MGF__complete_0) ).
fof(c_0_19_020,axiom,
! [X24,X27,X17,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Com_Ocom_OBODY(X24),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Option_Othe(hAPP(c_Com_Obody,X24),tc_Com_Ocom),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_weak__Body_0) ).
fof(c_0_20_021,axiom,
! [X26,X18,X6,X20,X3] :
( hAPP(X26,X6) = X18
| ~ hBOOL(c_in(X6,c_Set_Ovimage(X26,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X3,X20),X3)) ),
file('<stdin>',cls_vimage__singleton__eq_0) ).
fof(c_0_21_022,axiom,
! [X57,X46,X26,X20,X3] :
( c_Map_Omap__le(c_Map_Omap__add(X26,X46,X3,X20),X57,X3,X20)
| ~ c_Map_Omap__le(X26,c_Map_Omap__add(X26,X46,X3,X20),X3,X20)
| ~ c_Map_Omap__le(X46,X57,X3,X20)
| ~ c_Map_Omap__le(X26,X57,X3,X20) ),
file('<stdin>',cls_map__add__le__mapI_0) ).
fof(c_0_22_023,axiom,
! [X26,X6,X11,X20,X3] :
( hBOOL(c_in(hAPP(X26,X6),X11,X20))
| ~ hBOOL(c_in(X6,c_Set_Ovimage(X26,X11,X3,X20),X3)) ),
file('<stdin>',cls_vimageE_0) ).
fof(c_0_23_024,axiom,
! [X26,X6,X7,X20,X3] :
( hBOOL(c_in(hAPP(X26,X6),X7,X20))
| ~ hBOOL(c_in(X6,c_Set_Ovimage(X26,X7,X3,X20),X3)) ),
file('<stdin>',cls_vimageD_0) ).
fof(c_0_24_025,axiom,
! [X26,X18,X6,X3] :
( X6 = X18
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X18)) ),
file('<stdin>',cls_fold1Set__sing_0) ).
fof(c_0_25_026,axiom,
! [X10,X26,X7,X20,X3] :
( hBOOL(hAPP(X7,hAPP(X26,X10)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X26,X7,X3,X20),X10)) ),
file('<stdin>',cls_vimage__code_0) ).
fof(c_0_26_027,axiom,
! [X46,X26,X20,X3] :
( c_Map_Omap__add(X26,X46,X3,X20) = c_Map_Omap__add(X46,X26,X3,X20)
| ~ c_Map_Omap__le(X26,c_Map_Omap__add(X26,X46,X3,X20),X3,X20) ),
file('<stdin>',cls_map__le__iff__map__add__commute_0) ).
fof(c_0_27_028,axiom,
! [X10,X18,X11,X7,X20,X3] :
( hBOOL(c_in(X18,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X20,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X18,hAPP(X11,X10),X3))
| ~ hBOOL(c_in(X10,X7,X20)) ),
file('<stdin>',cls_UN__iff_2) ).
fof(c_0_28_029,axiom,
! [X18,X6,X11,X7,X20,X3] :
( hBOOL(c_in(X18,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),X20))
| ~ hBOOL(c_in(X18,hAPP(X11,X6),X20))
| ~ hBOOL(c_in(X6,X7,X3)) ),
file('<stdin>',cls_UN__I_0) ).
fof(c_0_29_030,axiom,
! [X46,X26,X20,X3] :
( c_Map_Omap__add(X26,X46,X3,X20) != c_Map_Omap__add(X46,X26,X3,X20)
| c_Map_Omap__le(X26,c_Map_Omap__add(X26,X46,X3,X20),X3,X20) ),
file('<stdin>',cls_map__le__iff__map__add__commute_1) ).
fof(c_0_30_031,axiom,
! [X24,X15] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X24)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X24)),X15,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Option_Othe(hAPP(c_Com_Obody,X24),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
file('<stdin>',cls_MGT__BodyN_0) ).
fof(c_0_31_032,axiom,
! [X10,X18,X11,X7,X20,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),X18))
| ~ hBOOL(hAPP(hAPP(X11,X10),X18))
| ~ hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_SUP1__iff_2) ).
fof(c_0_32_033,axiom,
! [X18,X6,X11,X7,X20,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),X18))
| ~ hBOOL(hAPP(hAPP(X11,X6),X18))
| ~ hBOOL(c_in(X6,X7,X3)) ),
file('<stdin>',cls_SUP1__I_0) ).
fof(c_0_33_034,axiom,
! [X57,X46,X26,X20,X3] :
( c_Map_Omap__le(X46,X57,X3,X20)
| ~ c_Map_Omap__le(c_Map_Omap__add(X26,X46,X3,X20),X57,X3,X20) ),
file('<stdin>',cls_map__add__le__mapE_0) ).
fof(c_0_34_035,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_diff__single__insert_0) ).
fof(c_0_35_036,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_3) ).
fof(c_0_36_037,axiom,
! [X26,X6,X11,X20,X3] :
( hBOOL(c_in(X6,c_Set_Ovimage(X26,X11,X3,X20),X3))
| ~ hBOOL(c_in(hAPP(X26,X6),X11,X20)) ),
file('<stdin>',cls_vimage__eq_1) ).
fof(c_0_37_038,axiom,
! [X26,X6,X7,X20,X3] :
( hBOOL(c_in(X6,c_Set_Ovimage(X26,X7,X20,X3),X20))
| ~ hBOOL(c_in(hAPP(X26,X6),X7,X3)) ),
file('<stdin>',cls_vimageI2_0) ).
fof(c_0_38_039,axiom,
! [X26,X6,X11,X20,X3] :
( hBOOL(c_in(X6,c_Set_Ovimage(X26,X11,X20,X3),X20))
| ~ hBOOL(c_in(hAPP(X26,X6),X11,X3)) ),
file('<stdin>',cls_vimageI_0) ).
fof(c_0_39_040,axiom,
! [X10,X17,X7,X3] :
( hBOOL(c_in(X10,X7,X3))
| ~ hBOOL(c_in(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Collect(X17,X3)),X3)) ),
file('<stdin>',cls_Int__Collect_0) ).
fof(c_0_40_041,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_4) ).
fof(c_0_41_042,axiom,
! [X10,X26,X7,X61,X3] :
( ~ hBOOL(c_in(X10,X7,X61))
| hBOOL(c_in(hAPP(X26,X10),c_Set_Oimage(X26,X7,X61,X3),X3)) ),
file('<stdin>',cls_rev__image__eqI_0) ).
fof(c_0_42_043,axiom,
! [X10,X26,X7,X20,X3] :
( ~ hBOOL(c_in(X10,X7,X20))
| hBOOL(c_in(hAPP(X26,X10),c_Set_Oimage(X26,X7,X20,X3),X3)) ),
file('<stdin>',cls_image__iff_2) ).
fof(c_0_43_044,axiom,
! [X10,X26,X7,X20,X3] :
( hBOOL(c_in(hAPP(X26,X10),c_Set_Oimage(X26,X7,X20,X3),X3))
| ~ hBOOL(c_in(X10,X7,X20)) ),
file('<stdin>',cls_image__eqI_0) ).
fof(c_0_44_045,axiom,
! [X10,X26,X7,X20,X3] :
( hBOOL(c_in(hAPP(X26,X10),c_Set_Oimage(X26,X7,X3,X20),X20))
| ~ hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_imageI_0) ).
fof(c_0_45_046,axiom,
! [X59,X60,X20,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X60,X3,X20)),c_Map_Odom(X59,X3,X20)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Map_Omap__add(X60,X59,X3,X20) = c_Map_Omap__add(X59,X60,X3,X20) ),
file('<stdin>',cls_map__add__comm_0) ).
fof(c_0_46_047,axiom,
! [X10,X17,X7,X3] :
( hBOOL(hAPP(X17,X10))
| ~ hBOOL(c_in(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Collect(X17,X3)),X3)) ),
file('<stdin>',cls_Int__Collect_1) ).
fof(c_0_47_048,axiom,
! [X10,X63,X11,X7,X20,X3] :
( c_lessequals(hAPP(X7,X10),X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X63,X20))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X63,X7,X20,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_UN__subset__iff_0) ).
fof(c_0_48_049,axiom,
! [X10,X26,X11,X7,X20,X3] :
( hBOOL(c_in(hAPP(X26,X10),X11,X3))
| ~ hBOOL(c_in(X10,X7,X20))
| ~ c_lessequals(c_Set_Oimage(X26,X7,X20,X3),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_image__subset__iff_0) ).
fof(c_0_49_050,axiom,
! [X26,X11,X7,X20,X3] :
( c_lessequals(c_Set_Ovimage(X26,X7,X20,X3),c_Set_Ovimage(X26,X11,X20,X3),tc_fun(X20,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_vimage__mono_0) ).
fof(c_0_50_051,axiom,
! [X26,X11,X7,X20,X3] :
( c_lessequals(c_Set_Oimage(X26,X7,X3,X20),c_Set_Oimage(X26,X11,X3,X20),tc_fun(X20,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_image__mono_0) ).
fof(c_0_51_052,axiom,
! [X10,X26,X7,X20,X3] :
( ~ c_lessequals(X10,X7,tc_fun(X20,tc_bool))
| c_lessequals(c_Set_Oimage(X26,X10,X20,X3),c_Set_Oimage(X26,X7,X20,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__image__iff_2) ).
fof(c_0_52_053,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3)) ),
file('<stdin>',cls_IntE_1) ).
fof(c_0_53_054,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X7,X3))
| ~ hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3)) ),
file('<stdin>',cls_IntE_0) ).
fof(c_0_54_055,axiom,
! [X10,X26,X7,X20,X3] :
( hBOOL(hAPP(c_Set_Ovimage(X26,X7,X3,X20),X10))
| ~ hBOOL(hAPP(X7,hAPP(X26,X10))) ),
file('<stdin>',cls_vimage__code_1) ).
fof(c_0_55_056,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_0) ).
fof(c_0_56_057,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3)),c_Lattices_Oupper__semilattice__class_Osup(X10,X41,X3)),X3) ),
file('<stdin>',cls_distrib__sup__le_0) ).
fof(c_0_57_058,axiom,
! [X42,X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X42,tc_fun(X3,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool)))
| c_lessequals(X42,X7,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_0) ).
fof(c_0_58_059,axiom,
! [X10,X11,X7,X20,X3] :
( c_Finite__Set_Ofinite(hAPP(X11,X10),X20)
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),X20)
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_finite__UN_0) ).
fof(c_0_59_060,axiom,
! [X48,X63,X7,X20,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X48),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X63,X7,X3,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X63,X7,X3,tc_fun(X20,tc_bool))
| ~ hBOOL(c_in(X48,X63,X3)) ),
file('<stdin>',cls_UN__absorb_0) ).
fof(c_0_60_061,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3))
| ~ hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
file('<stdin>',cls_Int__iff_2) ).
fof(c_0_61_062,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3))
| ~ hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
file('<stdin>',cls_IntI_0) ).
fof(c_0_62_063,axiom,
! [X28,X29,X30,X20,X3] :
( hAPP(c_Map_Omap__add(X30,X29,X3,X20),X28) = hAPP(X29,X28)
| ~ hBOOL(c_in(X28,c_Map_Odom(X29,X3,X20),X3)) ),
file('<stdin>',cls_map__add__dom__app__simps_I1_J_0) ).
fof(c_0_63_064,axiom,
! [X64,X59,X60,X20,X3] :
( c_Map_Omap__le(X60,X64,X3,X20)
| ~ c_Map_Omap__le(X59,X64,X3,X20)
| ~ c_Map_Omap__le(X60,X59,X3,X20) ),
file('<stdin>',cls_map__le__trans_0) ).
fof(c_0_64_065,axiom,
! [X10,X17,X7,X3] :
( hBOOL(c_in(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Collect(X17,X3)),X3))
| ~ hBOOL(hAPP(X17,X10))
| ~ hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_Int__Collect_2) ).
fof(c_0_65_066,axiom,
! [X10,X26,X7,X20,X3] :
( c_Set_Oinsert(hAPP(X26,X10),c_Set_Oimage(X26,X7,X3,X20),X20) = c_Set_Oimage(X26,X7,X3,X20)
| ~ hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_insert__image_0) ).
fof(c_0_66_067,axiom,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X10)) ),
file('<stdin>',cls_inf1E_1) ).
fof(c_0_67_068,axiom,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(X7,X10))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X10)) ),
file('<stdin>',cls_inf1E_0) ).
fof(c_0_68_069,axiom,
! [X25,X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X11 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X11,X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3)
| c_Finite__Set_Ofold1(X25,c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X3) = hAPP(hAPP(X25,c_Finite__Set_Ofold1(X25,X7,X3)),c_Finite__Set_Ofold1(X25,X11,X3)) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold1__Un_0) ).
fof(c_0_69_070,axiom,
! [X12,X10,X3] :
( X12 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| ~ hBOOL(hAPP(c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X12)) ),
file('<stdin>',cls_Nitpick_OEx1__def_3) ).
fof(c_0_70_071,axiom,
! [X26,X11,X7,X20,X3] :
( c_Finite__Set_Ofinite(X11,X20)
| ~ c_lessequals(X11,c_Set_Oimage(X26,X7,X3,X20),tc_fun(X20,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_finite__surj_0) ).
fof(c_0_71_072,axiom,
! [X10,X31,X32,X20,X3] :
( hAPP(X32,X10) = hAPP(X31,X10)
| ~ hBOOL(c_in(X10,c_Map_Odom(X32,X3,X20),X3))
| ~ c_Map_Omap__le(X32,X31,X3,X20) ),
file('<stdin>',cls_map__le__def_0) ).
fof(c_0_72_073,axiom,
! [X22,X15] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X22),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X22)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X15))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('<stdin>',cls_MGF__lemma1_1) ).
fof(c_0_73_074,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X41),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3)),X3) ),
file('<stdin>',cls_distrib__inf__le_0) ).
fof(c_0_74_075,axiom,
! [X45,X42,X11,X7,X3] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X42),X45),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X45,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__mono_0) ).
fof(c_0_75_076,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X11,X3))
| hBOOL(c_in(X22,X7,X3))
| ~ hBOOL(c_in(X22,c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_UnE_0) ).
fof(c_0_76_077,axiom,
! [X10,X47,X28,X48,X20,X3] :
( hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) != c_Option_Ooption_OSome(X10,X3)
| hAPP(X28,X48) = c_Option_Ooption_OSome(X10,X3)
| hAPP(X47,X48) = c_Option_Ooption_OSome(X10,X3) ),
file('<stdin>',cls_map__add__SomeD_1) ).
fof(c_0_77_078,axiom,
! [X6,X42,X11,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X6,X11,X3)),X42) = c_Set_Oinsert(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X11),X42),X3)
| ~ hBOOL(c_in(X6,X42,X3)) ),
file('<stdin>',cls_Int__insert__left_0) ).
fof(c_0_78_079,axiom,
! [X10,X47,X28,X48,X20,X3] :
( hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) != c_Option_Ooption_OSome(X10,X3)
| hAPP(X47,X48) = c_Option_Ooption_ONone(X3)
| hAPP(X47,X48) = c_Option_Ooption_OSome(X10,X3) ),
file('<stdin>',cls_map__add__SomeD_0) ).
fof(c_0_79_080,axiom,
! [X28,X29,X30,X20,X3] :
( hAPP(c_Map_Omap__add(X30,X29,X3,X20),X28) = hAPP(X30,X28)
| hBOOL(c_in(X28,c_Map_Odom(X29,X3,X20),X3)) ),
file('<stdin>',cls_map__add__dom__app__simps_I3_J_0) ).
fof(c_0_80_081,axiom,
! [X28,X29,X30,X20,X3] :
( hAPP(c_Map_Omap__add(X30,X29,X3,X20),X28) = hAPP(X29,X28)
| hBOOL(c_in(X28,c_Map_Odom(X30,X3,X20),X3)) ),
file('<stdin>',cls_map__add__dom__app__simps_I2_J_0) ).
fof(c_0_81_082,axiom,
! [X18,X6,X3] :
( X18 = X6
| ~ hBOOL(c_in(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
file('<stdin>',cls_singletonE_0) ).
fof(c_0_82_083,axiom,
! [X21,X22,X18,X6,X3] :
( c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X18 = X22
| X18 = X21 ),
file('<stdin>',cls_doubleton__eq__iff_3) ).
fof(c_0_83_084,axiom,
! [X21,X22,X18,X6,X3] :
( c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X6 = X21
| X18 = X21 ),
file('<stdin>',cls_doubleton__eq__iff_2) ).
fof(c_0_84_085,axiom,
! [X21,X22,X18,X6,X3] :
( c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X18 = X22
| X6 = X22 ),
file('<stdin>',cls_doubleton__eq__iff_1) ).
fof(c_0_85_086,axiom,
! [X21,X22,X18,X6,X3] :
( c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X6 = X21
| X6 = X22 ),
file('<stdin>',cls_doubleton__eq__iff_0) ).
fof(c_0_86_087,axiom,
! [X22,X11,X7,X3] :
( ~ hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_DiffE_1) ).
fof(c_0_87_088,axiom,
! [X47,X28,X48,X20,X3] :
( hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) != c_Option_Ooption_ONone(X3)
| hAPP(X28,X48) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__add__None_1) ).
fof(c_0_88_089,axiom,
! [X47,X28,X48,X20,X3] :
( hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) != c_Option_Ooption_ONone(X3)
| hAPP(X47,X48) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__add__None_0) ).
fof(c_0_89_090,axiom,
! [X6,X11,X7,X20,X3] :
( c_lessequals(hAPP(X11,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool))
| ~ hBOOL(c_in(X6,X7,X3)) ),
file('<stdin>',cls_UN__upper_0) ).
fof(c_0_90_091,axiom,
! [X6,X7,X3] :
( c_Set_Oinsert(X6,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X7
| ~ hBOOL(c_in(X6,X7,X3)) ),
file('<stdin>',cls_insert__Diff_0) ).
fof(c_0_91_092,axiom,
! [X46,X26,X20,X3] :
( X26 = X46
| ~ c_Map_Omap__le(X46,X26,X3,X20)
| ~ c_Map_Omap__le(X26,X46,X3,X20) ),
file('<stdin>',cls_map__le__antisym_0) ).
fof(c_0_92_093,axiom,
! [X42,X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X42,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool)))
| ~ c_lessequals(X42,X7,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_1) ).
fof(c_0_93_094,axiom,
! [X49,X50,X51,X52,X53,X54,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X52,X54,X50,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X51,X53,X49,X3)
| X52 = X51 ),
file('<stdin>',cls_triple_Oinject_0) ).
fof(c_0_94_095,axiom,
! [X49,X50,X51,X52,X53,X54,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X52,X54,X50,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X51,X53,X49,X3)
| X54 = X53 ),
file('<stdin>',cls_triple_Oinject_1) ).
fof(c_0_95_096,axiom,
! [X49,X50,X51,X52,X53,X54,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X52,X54,X50,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X51,X53,X49,X3)
| X50 = X49 ),
file('<stdin>',cls_triple_Oinject_2) ).
fof(c_0_96_097,axiom,
! [X13,X14,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,X13,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_hoare__derivs_Oinsert_0) ).
fof(c_0_97_098,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X7,X3))
| ~ hBOOL(c_in(X22,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_DiffE_0) ).
fof(c_0_98_099,axiom,
! [X6,X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Set_Oinsert(X6,X11,X3)) = c_Set_Oinsert(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3)
| ~ hBOOL(c_in(X6,X7,X3)) ),
file('<stdin>',cls_Int__insert__right_0) ).
fof(c_0_99_100,axiom,
! [X6,X11,X7,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X6,X11,X3),tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Diff__insert_0) ).
fof(c_0_100_101,axiom,
! [X69,X56,X7,X20,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| c_lessequals(hAPP(X56,X69),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X56,X3,X20),X20)
| ~ hBOOL(c_in(X69,X7,X3)) ),
file('<stdin>',cls_le__SUPI_0) ).
fof(c_0_101_102,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
file('<stdin>',cls_Diff__iff_2) ).
fof(c_0_102_103,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
file('<stdin>',cls_DiffI_0) ).
fof(c_0_103_104,axiom,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X10))
| ~ hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(X7,X10)) ),
file('<stdin>',cls_inf1I_0) ).
fof(c_0_104_105,axiom,
! [X10,X11,X7,X20,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X20,tc_fun(X3,tc_bool))
| hAPP(X11,X10) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X20)) ),
file('<stdin>',cls_UNION__empty__conv_I1_J_0) ).
fof(c_0_105_106,axiom,
! [X10,X11,X7,X20,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X20,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hAPP(X11,X10) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X20)) ),
file('<stdin>',cls_UNION__empty__conv_I2_J_0) ).
fof(c_0_106_107,axiom,
! [X46,X26,X20,X3] :
( c_lessequals(c_Map_Odom(X26,X3,X20),c_Map_Odom(X46,X3,X20),tc_fun(X3,tc_bool))
| ~ c_Map_Omap__le(X26,X46,X3,X20) ),
file('<stdin>',cls_map__le__implies__dom__le_0) ).
fof(c_0_107_108,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(X42,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_1) ).
fof(c_0_108_109,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(X42,X7,tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_0) ).
fof(c_0_109_110,axiom,
! [X6,X11,X7,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X6,X11,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Diff__insert_1) ).
fof(c_0_110_111,axiom,
! [X22,X15] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X22),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X22)
| hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X15),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('<stdin>',cls_MGF__lemma1_0) ).
fof(c_0_111_112,axiom,
! [X45,X42,X11,X7,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X42,X45,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Diff__mono_0) ).
fof(c_0_112_113,axiom,
! [X45,X42,X11,X7,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X42,X45,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X45,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__mono_0) ).
fof(c_0_113_114,axiom,
! [X18,X6,X7,X3] :
( hBOOL(c_in(X6,X7,X3))
| X6 = X18
| ~ hBOOL(c_in(X6,c_Set_Oinsert(X18,X7,X3),X3)) ),
file('<stdin>',cls_insertE_0) ).
fof(c_0_114_115,axiom,
! [X10,X11,X7,X3] :
( ~ hBOOL(c_in(X10,X11,X3))
| ~ hBOOL(c_in(X10,X7,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_disjoint__iff__not__equal_0) ).
fof(c_0_115_116,axiom,
! [X6,X42,X11,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X6,X11,X3)),X42) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X11),X42)
| hBOOL(c_in(X6,X42,X3)) ),
file('<stdin>',cls_Int__insert__left_1) ).
fof(c_0_116_117,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(X42,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X7,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__greatest_0) ).
fof(c_0_117_118,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(X42,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X7,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_2) ).
fof(c_0_118_119,axiom,
! [X21,X22,X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X18,X21,X3)
| ~ c_lessequals(X6,X18,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_atLeastatMost__subset__iff_1) ).
fof(c_0_119_120,axiom,
! [X21,X22,X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X22,X6,X3)
| ~ c_lessequals(X6,X18,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_atLeastatMost__subset__iff_0) ).
fof(c_0_120_121,axiom,
! [X18,X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3) ),
file('<stdin>',cls_Sup__binary_0) ).
fof(c_0_121_122,axiom,
! [X18,X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18) ),
file('<stdin>',cls_Inf__binary_0) ).
fof(c_0_122_123,axiom,
! [X13,X14,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,X13,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_derivs__insertD_0) ).
fof(c_0_123_124,axiom,
! [X10,X47,X28,X48,X20,X3] :
( hAPP(X28,X48) != c_Option_Ooption_OSome(X10,X3)
| hAPP(X47,X48) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) = c_Option_Ooption_OSome(X10,X3) ),
file('<stdin>',cls_map__add__Some__iff_3) ).
fof(c_0_124_125,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Diff__subset__conv_1) ).
fof(c_0_125_126,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Diff__subset__conv_0) ).
fof(c_0_126_127,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
file('<stdin>',cls_UnCI_1) ).
fof(c_0_127_128,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X22,X11,X3)) ),
file('<stdin>',cls_UnCI_0) ).
fof(c_0_128_129,axiom,
! [X10,X7,X3] :
( X7 = c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__singletonD_0) ).
fof(c_0_129_130,axiom,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(X11,X10))
| hBOOL(hAPP(X7,X10))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X10)) ),
file('<stdin>',cls_sup1E_0) ).
fof(c_0_130_131,axiom,
! [X47,X28,X48,X20,X3] :
( hAPP(X28,X48) != c_Option_Ooption_ONone(X3)
| hAPP(X47,X48) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__add__None_2) ).
fof(c_0_131_132,axiom,
! [X70,X47,X28,X48,X20,X3] :
( hAPP(X47,X48) != c_Option_Ooption_OSome(X70,X3)
| hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) = c_Option_Ooption_OSome(X70,X3) ),
file('<stdin>',cls_map__add__find__right_0) ).
fof(c_0_132_133,axiom,
! [X10,X47,X28,X48,X20,X3] :
( hAPP(X47,X48) != c_Option_Ooption_OSome(X10,X3)
| hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) = c_Option_Ooption_OSome(X10,X3) ),
file('<stdin>',cls_map__add__Some__iff_2) ).
fof(c_0_133_134,axiom,
! [X16,X10,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X16,X3)
| ~ hBOOL(c_in(X16,X7,X3))
| ~ c_lessequals(X10,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X7,X3),X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_below__fold1__iff_0) ).
fof(c_0_134_135,axiom,
! [X28,X6,X20,X3] :
( hAPP(X28,X6) != c_Option_Ooption_ONone(X20)
| ~ hBOOL(c_in(X6,c_Map_Odom(X28,X3,X20),X3)) ),
file('<stdin>',cls_domIff_0) ).
fof(c_0_135_136,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X10,X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3)),c_Lattices_Oupper__semilattice__class_Osup(X41,X10,X3)) ),
file('<stdin>',cls_sup__inf__distrib2_0) ).
fof(c_0_136_137,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3)),c_Lattices_Oupper__semilattice__class_Osup(X10,X41,X3)) ),
file('<stdin>',cls_sup__inf__distrib1_0) ).
fof(c_0_137_138,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3)),X10) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X41),X10),X3) ),
file('<stdin>',cls_inf__sup__distrib2_0) ).
fof(c_0_138_139,axiom,
! [X57,X58,X20,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X57,X58,X3,X20),X20)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
file('<stdin>',cls_finite__imageI_0) ).
fof(c_0_139_140,axiom,
! [X10,X7,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X7,X3),c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X7
| hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_Diff__insert__absorb_0) ).
fof(c_0_140_141,axiom,
! [X6,X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Set_Oinsert(X6,X11,X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11)
| hBOOL(c_in(X6,X7,X3)) ),
file('<stdin>',cls_Int__insert__right_1) ).
fof(c_0_141_142,axiom,
! [X10,X26,X7,X20,X3] :
( hAPP(X26,X10) != c_Option_Ooption_ONone(X3)
| c_HOL_Ominus__class_Ominus(c_Map_Odom(X26,X20,X3),c_Set_Oinsert(X10,X7,X20),tc_fun(X20,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X26,X20,X3),X7,tc_fun(X20,tc_bool)) ),
file('<stdin>',cls_dom__minus_0) ).
fof(c_0_142_143,axiom,
! [X10,X11,X7,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X10,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| hBOOL(c_in(X10,X11,X3)) ),
file('<stdin>',cls_insert__Diff__if_1) ).
fof(c_0_143_144,axiom,
! [X18,X6,X7,X3] :
( hBOOL(c_in(X6,c_Set_Oinsert(X18,X7,X3),X3))
| ~ hBOOL(c_in(X6,X7,X3)) ),
file('<stdin>',cls_insert__iff_2) ).
fof(c_0_144_145,axiom,
! [X18,X6,X11,X3] :
( hBOOL(c_in(X6,c_Set_Oinsert(X18,X11,X3),X3))
| ~ hBOOL(c_in(X6,X11,X3)) ),
file('<stdin>',cls_insertCI_0) ).
fof(c_0_145_146,axiom,
! [X10,X25,X7,X3] :
( c_Finite__Set_Ofold1(X25,c_Set_Oinsert(X10,X7,X3),X3) = hAPP(hAPP(X25,X10),c_Finite__Set_Ofold1(X25,X7,X3))
| hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofinite(X7,X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold1__insert_0) ).
fof(c_0_146_147,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X11,X3)) ),
file('<stdin>',cls_insert__subset_2) ).
fof(c_0_147_148,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_1) ).
fof(c_0_148_149,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_subset__insert_0) ).
fof(c_0_149_150,axiom,
! [X42,X11,X7,X3] :
( c_HOL_Ominus__class_Ominus(X11,c_HOL_Ominus__class_Ominus(X42,X7,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X7
| ~ c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_double__diff_0) ).
fof(c_0_150_151,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__least_0) ).
fof(c_0_151_152,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_2) ).
fof(c_0_152_153,axiom,
! [X21,X22,X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,X3)
| ~ c_lessequals(X22,X6,X3) ),
file('<stdin>',cls_atLeastatMost__subset__iff_3) ).
fof(c_0_153_154,axiom,
! [X26,X7,X20,X3] :
( c_Set_Oimage(X26,X7,X20,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) ),
file('<stdin>',cls_image__is__empty_0) ).
fof(c_0_154_155,axiom,
! [X26,X7,X20,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X26,X7,X20,X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) ),
file('<stdin>',cls_empty__is__image_0) ).
fof(c_0_155_156,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(X7,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_0) ).
fof(c_0_156_157,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_1) ).
fof(c_0_157_158,axiom,
! [X10,X11,X7,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X11,X3)) ),
file('<stdin>',cls_insert__Diff1_0) ).
fof(c_0_158_159,axiom,
! [X46,X26,X20] :
( ~ class_Lattices_Olattice(X20)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X20)),X26),X46),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X20),hAPP(X26,v_x)),hAPP(X46,v_x)) ),
file('<stdin>',cls_inf__fun__eq_0) ).
fof(c_0_159_160,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X41),X3) ),
file('<stdin>',cls_inf__sup__distrib1_0) ).
fof(c_0_160_161,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12)),X41) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41)) ),
file('<stdin>',cls_inf__sup__aci_I2_J_0) ).
fof(c_0_161_162,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12)),X41) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41)) ),
file('<stdin>',cls_inf__assoc_0) ).
fof(c_0_162_163,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_subset__insert__iff_2) ).
fof(c_0_163_164,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_subset__insert_1) ).
fof(c_0_164_165,axiom,
! [X12,X10,X7,X3] :
( hBOOL(hAPP(X7,X10))
| X12 = X10
| ~ hBOOL(hAPP(c_Set_Oinsert(X12,X7,X3),X10)) ),
file('<stdin>',cls_insert__code_0) ).
fof(c_0_165_166,axiom,
! [X6,X45,X42,X3] :
( c_lessequals(c_Set_Oinsert(X6,X42,X3),c_Set_Oinsert(X6,X45,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X45,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__mono_0) ).
fof(c_0_166_167,axiom,
! [X14,X11,X7,X3] :
( hBOOL(c_in(X14,X11,X3))
| ~ hBOOL(c_in(X14,X7,X3))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__iff_0) ).
fof(c_0_167_168,axiom,
! [X10,X11,X7,X3] :
( hBOOL(c_in(X10,X11,X3))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_set__rev__mp_0) ).
fof(c_0_168_169,axiom,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subsetD_0) ).
fof(c_0_169_170,axiom,
! [X10,X11,X7,X3] :
( hBOOL(c_in(X10,X11,X3))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_set__mp_0) ).
fof(c_0_170_171,axiom,
! [X10,X11,X7,X3] :
( hBOOL(c_in(X10,X11,X3))
| ~ c_lessequals(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__subset_0) ).
fof(c_0_171_172,axiom,
! [X10,X11,X7,X3] :
( c_Set_Oinsert(X10,X7,X3) != c_Set_Oinsert(X10,X11,X3)
| hBOOL(c_in(X10,X11,X3))
| hBOOL(c_in(X10,X7,X3))
| X7 = X11 ),
file('<stdin>',cls_insert__ident_0) ).
fof(c_0_172_173,axiom,
! [X10,X17,X3] :
( ~ hBOOL(hAPP(X17,X10))
| ~ hBOOL(c_in(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_bex__empty_0) ).
fof(c_0_173_174,axiom,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X11,X10)) ),
file('<stdin>',cls_sup1CI_0) ).
fof(c_0_174_175,axiom,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X7,X10)) ),
file('<stdin>',cls_sup1CI_1) ).
fof(c_0_175_176,axiom,
! [X22] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X22),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X22)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('<stdin>',cls_MGF_0) ).
fof(c_0_176_177,axiom,
! [X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X7,X3),X6,X3)
| ~ hBOOL(c_in(X6,X7,X3))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_fold1__belowI_0) ).
fof(c_0_177_178,axiom,
! [X28,X18,X6,X20,X3] :
( hAPP(X28,X6) != c_Option_Ooption_OSome(X18,X3)
| hBOOL(c_in(X6,c_Map_Odom(X28,X20,X3),X20)) ),
file('<stdin>',cls_domI_0) ).
fof(c_0_178_179,axiom,
! [X10,X17,X3] :
( hBOOL(hAPP(X17,X10))
| ~ hBOOL(c_in(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_ball__empty_0) ).
fof(c_0_179_180,axiom,
! [X10,X11,X7,X3] :
( c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__subset_1) ).
fof(c_0_180_181,axiom,
! [X21,X22,X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X3),tc_fun(X3,tc_bool))
| c_lessequals(X6,X18,X3) ),
file('<stdin>',cls_atLeastatMost__subset__iff_2) ).
fof(c_0_181_182,axiom,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,c_HOL_Ominus__class_Ominus(X11,X7,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X11
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Diff__partition_0) ).
fof(c_0_182_183,axiom,
! [X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)) = X7 ),
file('<stdin>',cls_Diff__triv_0) ).
fof(c_0_183_184,axiom,
! [X28,X6,X20,X3] :
( hBOOL(c_in(X6,c_Map_Odom(X28,X3,X20),X3))
| hAPP(X28,X6) = c_Option_Ooption_ONone(X20) ),
file('<stdin>',cls_domIff_1) ).
fof(c_0_184_185,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3)
| ~ c_lessequals(X12,X41,X3)
| ~ c_lessequals(X10,X41,X3) ),
file('<stdin>',cls_le__sup__iff_2) ).
fof(c_0_185_186,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X10,X3)
| ~ c_lessequals(X41,X10,X3)
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_sup__least_0) ).
fof(c_0_186_187,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X10,X3)
| ~ c_lessequals(X18,X10,X3)
| ~ c_lessequals(X6,X10,X3) ),
file('<stdin>',cls_le__supI_0) ).
fof(c_0_187_188,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3)
| ~ c_lessequals(X10,X41,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_inf__greatest_0) ).
fof(c_0_188_189,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3)
| ~ c_lessequals(X10,X41,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__inf__iff_2) ).
fof(c_0_189_190,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X3)
| ~ c_lessequals(X10,X18,X3)
| ~ c_lessequals(X10,X6,X3) ),
file('<stdin>',cls_le__infI_0) ).
fof(c_0_190_191,axiom,
! [X18,X6,X3] :
( c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X6 = X18 ),
file('<stdin>',cls_singleton__inject_0) ).
fof(c_0_191_192,axiom,
! [X25,X22,X18,X6,X3] :
( hAPP(hAPP(X25,hAPP(hAPP(X25,X6),X18)),X22) = hAPP(hAPP(X25,X6),hAPP(hAPP(X25,X18),X22))
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).
fof(c_0_192_193,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I6_J_0) ).
fof(c_0_193_194,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X41,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I7_J_0) ).
fof(c_0_194_195,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X41,X3),X3) ),
file('<stdin>',cls_sup__left__commute_0) ).
fof(c_0_195_196,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X3) ),
file('<stdin>',cls_sup__assoc_0) ).
fof(c_0_196_197,axiom,
! [X13,X14,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,X13,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_derivs__insertD_1) ).
fof(c_0_197_198,axiom,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X58),X15),X3)
| ~ c_Finite__Set_Ofinite(X15,X3) ),
file('<stdin>',cls_finite__Int_1) ).
fof(c_0_198_199,axiom,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X58),X15),X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
file('<stdin>',cls_finite__Int_0) ).
fof(c_0_199_200,axiom,
! [X42,X11,X7,X3] :
( c_lessequals(X7,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__trans_0) ).
fof(c_0_200_201,axiom,
! [X43,X12,X44,X10,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X10,X12,X3) != c_HOL_Ominus__class_Ominus(X44,X43,X3)
| c_lessequals(X43,X44,X3)
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_le__eqI_0) ).
fof(c_0_201_202,axiom,
! [X43,X12,X44,X10,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X10,X12,X3) != c_HOL_Ominus__class_Ominus(X44,X43,X3)
| c_lessequals(X12,X10,X3)
| ~ c_lessequals(X43,X44,X3) ),
file('<stdin>',cls_le__eqI_1) ).
fof(c_0_202_203,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X12,X41,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3) ),
file('<stdin>',cls_le__sup__iff_1) ).
fof(c_0_203_204,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,X41,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3) ),
file('<stdin>',cls_le__sup__iff_0) ).
fof(c_0_204_205,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X18,X10,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X10,X3) ),
file('<stdin>',cls_le__supE_1) ).
fof(c_0_205_206,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,X10,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X10,X3) ),
file('<stdin>',cls_le__supE_0) ).
fof(c_0_206_207,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X41)) ),
file('<stdin>',cls_inf__sup__aci_I3_J_0) ).
fof(c_0_207_208,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X41)) ),
file('<stdin>',cls_inf__left__commute_0) ).
fof(c_0_208_209,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X6,X3)
| ~ c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X3) ),
file('<stdin>',cls_le__infE_0) ).
fof(c_0_209_210,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X18,X3)
| ~ c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X3) ),
file('<stdin>',cls_le__infE_1) ).
fof(c_0_210_211,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X12,X3)
| ~ c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3) ),
file('<stdin>',cls_le__inf__iff_0) ).
fof(c_0_211_212,axiom,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X41,X3)
| ~ c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3) ),
file('<stdin>',cls_le__inf__iff_1) ).
fof(c_0_212_213,axiom,
! [X18,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X18,X11,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insertI2_0) ).
fof(c_0_213_214,axiom,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X11,X3) ),
file('<stdin>',cls_finite__Diff2_0) ).
fof(c_0_214_215,axiom,
! [X12,X10,X7,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X12,X7,X3),X10))
| ~ hBOOL(hAPP(X7,X10)) ),
file('<stdin>',cls_insert__code_2) ).
fof(c_0_215_216,axiom,
! [X55,X56,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X56,X3),c_Finite__Set_Olinorder__class_OMax(X55,X3),X3)
| ~ c_Finite__Set_Ofinite(X55,X3)
| X56 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X56,X55,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Max__mono_0) ).
fof(c_0_216_217,axiom,
! [X55,X56,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X55,X3),c_Finite__Set_Olinorder__class_OMin(X56,X3),X3)
| ~ c_Finite__Set_Ofinite(X55,X3)
| X56 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X56,X55,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Min__antimono_0) ).
fof(c_0_217_218,axiom,
! [X6,X17,X3] :
( hBOOL(hAPP(X17,X6))
| ~ hBOOL(c_in(X6,c_Collect(X17,X3),X3)) ),
file('<stdin>',cls_CollectD_0) ).
fof(c_0_218_219,axiom,
! [X10,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X7,X3),X10,X3)
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_Min__le_0) ).
fof(c_0_219_220,axiom,
! [X10,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X10,c_Finite__Set_Olinorder__class_OMax(X7,X3),X3)
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_Max__ge_0) ).
fof(c_0_220_221,axiom,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(X58,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X58,X15,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Un_0) ).
fof(c_0_221_222,axiom,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(X15,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X58,X15,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Un_1) ).
fof(c_0_222_223,axiom,
! [X11,X7,X20] :
( ~ class_HOL_Ominus(X20)
| hAPP(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(t_a,X20)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X7,v_x),hAPP(X11,v_x),X20) ),
file('<stdin>',cls_fun__diff__def_0) ).
fof(c_0_223_224,axiom,
! [X46,X26,X20] :
( ~ class_Lattices_Olattice(X20)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X26,X46,tc_fun(t_a,X20)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X26,v_x),hAPP(X46,v_x),X20) ),
file('<stdin>',cls_sup__fun__eq_0) ).
fof(c_0_224_225,axiom,
! [X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) = X11
| ~ c_lessequals(X11,X7,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__absorb1_0) ).
fof(c_0_225_226,axiom,
! [X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) = X7
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__absorb2_0) ).
fof(c_0_226_227,axiom,
! [X10,X7,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X7,X3),X10,X3)
| ~ hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_Inf__lower_0) ).
fof(c_0_227_228,axiom,
! [X10,X7,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(X10,c_Complete__Lattice_OSup__class_OSup(X7,X3),X3)
| ~ hBOOL(c_in(X10,X7,X3)) ),
file('<stdin>',cls_Sup__upper_0) ).
fof(c_0_228_229,axiom,
! [X16,X10,X25,X20,X3] :
( c_Set_Oinsert(X10,X16,X20) != c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))
| hBOOL(c_in(X10,X16,X20))
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ononempty__iff_2) ).
fof(c_0_229_230,axiom,
! [X12,X10,X26,X20,X3] :
( hAPP(X26,X10) != c_Option_Ooption_OSome(X12,X3)
| c_Set_Oinsert(X10,c_Map_Odom(X26,X20,X3),X20) = c_Map_Odom(X26,X20,X3) ),
file('<stdin>',cls_insert__dom_0) ).
fof(c_0_230_231,axiom,
! [X25,X22,X18,X6,X3] :
( hAPP(hAPP(X25,X6),hAPP(hAPP(X25,X18),X22)) = hAPP(hAPP(X25,X18),hAPP(hAPP(X25,X6),X22))
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Omult__left__commute_0) ).
fof(c_0_231_232,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X3)
| ~ c_lessequals(X10,X18,X3) ),
file('<stdin>',cls_le__supI2_0) ).
fof(c_0_232_233,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X3)
| ~ c_lessequals(X10,X6,X3) ),
file('<stdin>',cls_le__supI1_0) ).
fof(c_0_233_234,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X10,X3)
| ~ c_lessequals(X6,X10,X3) ),
file('<stdin>',cls_le__infI1_0) ).
fof(c_0_234_235,axiom,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X10,X3)
| ~ c_lessequals(X18,X10,X3) ),
file('<stdin>',cls_le__infI2_0) ).
fof(c_0_235_236,axiom,
! [X11,X7,X3] :
( X7 = X11
| ~ c_lessequals(X11,X7,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_equalityI_0) ).
fof(c_0_236_237,axiom,
! [X11,X7,X3] :
( X7 = X11
| ~ c_lessequals(X11,X7,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_set__eq__subset_2) ).
fof(c_0_237_238,axiom,
! [X10,X46,X26,X20,X3] :
( ~ class_HOL_Oord(X20)
| c_lessequals(hAPP(X26,X10),hAPP(X46,X10),X20)
| ~ c_lessequals(X26,X46,tc_fun(X3,X20)) ),
file('<stdin>',cls_le__funD_0) ).
fof(c_0_238_239,axiom,
! [X16,X10,X3] :
( c_Set_Oinsert(X10,X16,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X16,X3)) ),
file('<stdin>',cls_comm__monoid__add_Ononempty__iff_2) ).
fof(c_0_239_240,axiom,
! [X41,X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X41,X10,X3)
| ~ c_lessequals(X41,X12,X3)
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_240_241,axiom,
! [X41,X12,X10,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X10,X41,X3)
| ~ c_lessequals(X12,X41,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_241_242,axiom,
! [X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
file('<stdin>',cls_Sup__singleton_0) ).
fof(c_0_242_243,axiom,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
file('<stdin>',cls_Min__singleton_0) ).
fof(c_0_243_244,axiom,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
file('<stdin>',cls_Max__singleton_0) ).
fof(c_0_244_245,axiom,
! [X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
file('<stdin>',cls_Inf__singleton_0) ).
fof(c_0_245_246,axiom,
! [X7,X3] :
( X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__empty_0) ).
fof(c_0_246_247,axiom,
! [X6,X7,X3] :
( c_Set_Oinsert(X6,X7,X3) = X7
| ~ hBOOL(c_in(X6,X7,X3)) ),
file('<stdin>',cls_insert__absorb_0) ).
fof(c_0_247_248,axiom,
! [X13,X23,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,X23,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X23,X13,X3) ),
file('<stdin>',cls_cut_0) ).
fof(c_0_248_249,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) ),
file('<stdin>',cls_sup__left__idem_0) ).
fof(c_0_249_250,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) ),
file('<stdin>',cls_inf__sup__aci_I8_J_0) ).
fof(c_0_250_251,axiom,
! [X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3)
| ~ c_lessequals(X6,X18,X3) ),
file('<stdin>',cls_atLeastatMost__empty__iff2_0) ).
fof(c_0_251_252,axiom,
! [X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X18,X3) ),
file('<stdin>',cls_atLeastatMost__empty__iff_0) ).
fof(c_0_252_253,axiom,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X7,X3),X7,X3))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_Min__in_0) ).
fof(c_0_253_254,axiom,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X7,X3),X7,X3))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_Max__in_0) ).
fof(c_0_254_255,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) ),
file('<stdin>',cls_inf__sup__aci_I4_J_0) ).
fof(c_0_255_256,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) ),
file('<stdin>',cls_inf__left__idem_0) ).
fof(c_0_256_257,axiom,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofinite(X11,X3) ),
file('<stdin>',cls_finite__Diff2_1) ).
fof(c_0_257_258,axiom,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X58,X15,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X15,X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
file('<stdin>',cls_finite__Un_2) ).
fof(c_0_258_259,axiom,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X58,X15,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X15,X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
file('<stdin>',cls_finite__UnI_0) ).
fof(c_0_259_260,axiom,
! [X6,X17,X3] :
( hBOOL(c_in(X6,c_Collect(X17,X3),X3))
| ~ hBOOL(hAPP(X17,X6)) ),
file('<stdin>',cls_CollectI_0) ).
fof(c_0_260_261,axiom,
! [X6,X7,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,X7,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X7,X3),X3) ),
file('<stdin>',cls_Sup__insert_0) ).
fof(c_0_261_262,axiom,
! [X6,X7,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X6,X7,X3),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),c_Complete__Lattice_OInf__class_OInf(X7,X3)) ),
file('<stdin>',cls_Inf__insert_0) ).
fof(c_0_262_263,axiom,
! [X10,X19,X3] :
( hBOOL(hAPP(X19,X10))
| ~ hBOOL(c_in(X10,X19,X3)) ),
file('<stdin>',cls_mem__def_0) ).
fof(c_0_263_264,axiom,
! [X6,X7,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X6,X7,X3),X3) ),
file('<stdin>',cls_finite__insert_0) ).
fof(c_0_264_265,axiom,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) != X11
| c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__Un__eq_1) ).
fof(c_0_265_266,axiom,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) = X11
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__absorb1_0) ).
fof(c_0_266_267,axiom,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) = X7
| ~ c_lessequals(X11,X7,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__absorb2_0) ).
fof(c_0_267_268,axiom,
! [X10,X27,X17,X3] :
( hBOOL(hAPP(X27,X10))
| ~ hBOOL(hAPP(X17,X10))
| ~ c_lessequals(X17,X27,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_predicate1D_0) ).
fof(c_0_268_269,axiom,
! [X10,X27,X17,X3] :
( hBOOL(hAPP(X27,X10))
| ~ c_lessequals(X17,X27,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X17,X10)) ),
file('<stdin>',cls_rev__predicate1D_0) ).
fof(c_0_269_270,axiom,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X11 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_1) ).
fof(c_0_270_271,axiom,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_0) ).
fof(c_0_271_272,axiom,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_finite__Diff_0) ).
fof(c_0_272_273,axiom,
! [X6,X2,X17] :
( c_Com_OWT(c_Com_Ocom_OBODY(X17))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X2,X17,X6)) ),
file('<stdin>',cls_WTs__elim__cases_I8_J_0) ).
fof(c_0_273_274,axiom,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X12,X10,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_274_275,axiom,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X12,X10,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_275_276,axiom,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X10,X12,X3)
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_276_277,axiom,
! [X43,X44,X10,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X10,X10,X3) != c_HOL_Ominus__class_Ominus(X44,X43,X3)
| X44 = X43 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_277_278,axiom,
! [X12,X16,X10,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X16,X12,X3) != c_HOL_Ominus__class_Ominus(X10,X10,X3)
| X16 = X12 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_278_279,axiom,
! [X65,X66,X8,X9,X67,X68] :
( c_Com_Ocom_OCall(X66,X9,X68) != c_Com_Ocom_OCall(X65,X8,X67)
| X68 = X67 ),
file('<stdin>',cls_com_Osimps_I7_J_2) ).
fof(c_0_279_280,axiom,
! [X65,X66,X8,X9,X67,X68] :
( c_Com_Ocom_OCall(X66,X9,X68) != c_Com_Ocom_OCall(X65,X8,X67)
| X9 = X8 ),
file('<stdin>',cls_com_Osimps_I7_J_1) ).
fof(c_0_280_281,axiom,
! [X65,X66,X8,X9,X67,X68] :
( c_Com_Ocom_OCall(X66,X9,X68) != c_Com_Ocom_OCall(X65,X8,X67)
| X66 = X65 ),
file('<stdin>',cls_com_Osimps_I7_J_0) ).
fof(c_0_281_282,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
file('<stdin>',cls_inf__sup__ord_I3_J_0) ).
fof(c_0_282_283,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
file('<stdin>',cls_inf__sup__ord_I4_J_0) ).
fof(c_0_283_284,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
file('<stdin>',cls_sup__ge2_0) ).
fof(c_0_284_285,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
file('<stdin>',cls_sup__ge1_0) ).
fof(c_0_285_286,axiom,
! [X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X6,X6,X3) = c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_atLeastAtMost__singleton_0) ).
fof(c_0_286_287,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3)) = X10 ),
file('<stdin>',cls_inf__sup__absorb_0) ).
fof(c_0_287_288,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X3) = X10 ),
file('<stdin>',cls_sup__inf__absorb_0) ).
fof(c_0_288_289,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X10,X3) ),
file('<stdin>',cls_inf__sup__ord_I1_J_0) ).
fof(c_0_289_290,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X12,X3) ),
file('<stdin>',cls_inf__sup__ord_I2_J_0) ).
fof(c_0_290_291,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X12,X3) ),
file('<stdin>',cls_inf__le2_0) ).
fof(c_0_291_292,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X10,X3) ),
file('<stdin>',cls_inf__le1_0) ).
fof(c_0_292_293,axiom,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofinite(X11,X3)
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_finite__subset_0) ).
fof(c_0_293_294,axiom,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X11,X3) ),
file('<stdin>',cls_rev__finite__subset_0) ).
fof(c_0_294_295,axiom,
! [X10,X19,X3] :
( hBOOL(c_in(X10,X19,X3))
| ~ hBOOL(hAPP(X19,X10)) ),
file('<stdin>',cls_mem__def_1) ).
fof(c_0_295_296,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) != X12
| c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__iff__sup_1) ).
fof(c_0_296_297,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = X10
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_sup__absorb1_0) ).
fof(c_0_297_298,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = X12
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__iff__sup_0) ).
fof(c_0_298_299,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) = X12
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_inf__absorb2_0) ).
fof(c_0_299_300,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) = X10
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__iff__inf_0) ).
fof(c_0_300_301,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) != X10
| c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__iff__inf_1) ).
fof(c_0_301_302,axiom,
! [X6,X7,X3] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X6,X7,X3),X3)
| ~ c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_finite__insert_1) ).
fof(c_0_302_303,axiom,
! [X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3)
| c_lessequals(X6,X18,X3) ),
file('<stdin>',cls_atLeastatMost__empty__iff2_1) ).
fof(c_0_303_304,axiom,
! [X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(X6,X18,X3) ),
file('<stdin>',cls_atLeastatMost__empty__iff_1) ).
fof(c_0_304_305,axiom,
! [X13,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__valids(X15,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,X13,X3) ),
file('<stdin>',cls_hoare__sound_0) ).
fof(c_0_305_306,axiom,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(c_fequal(X2,X3),X1)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_306_307,axiom,
! [X24,X6,X2] :
( c_Com_OWT(c_Com_Ocom_OCall(X2,X24,X6))
| ~ c_Com_OWT(c_Com_Ocom_OBODY(X24)) ),
file('<stdin>',cls_WT_OCall_0) ).
fof(c_0_307_308,axiom,
! [X12,X10,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X12,X10,X3)
| c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_308_309,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3) ),
file('<stdin>',cls_sup__commute_0) ).
fof(c_0_309_310,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3) ),
file('<stdin>',cls_inf__sup__aci_I5_J_0) ).
fof(c_0_310_311,axiom,
! [X10,X17,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X17,X3)
| ~ hBOOL(hAPP(X17,X10)) ),
file('<stdin>',cls_empty__Collect__eq_0) ).
fof(c_0_311_312,axiom,
! [X10,X17,X3] :
( c_Collect(X17,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X17,X10)) ),
file('<stdin>',cls_Collect__empty__eq_0) ).
fof(c_0_312_313,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X10) ),
file('<stdin>',cls_inf__sup__aci_I1_J_0) ).
fof(c_0_313_314,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X10) ),
file('<stdin>',cls_inf__commute_0) ).
fof(c_0_314_315,axiom,
! [X11,X7,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X7,X11,X3) != c_Orderings_Obot__class_Obot(X3)
| X7 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq1_0) ).
fof(c_0_315_316,axiom,
! [X11,X7,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X7,X11,X3) != c_Orderings_Obot__class_Obot(X3)
| X11 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq2_0) ).
fof(c_0_316_317,axiom,
! [X25,X18,X6,X3] :
( hAPP(hAPP(X25,X6),X18) = hAPP(hAPP(X25,X18),X6)
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Omult__commute_0) ).
fof(c_0_317_318,axiom,
! [X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_Sup__empty_0) ).
fof(c_0_318_319,axiom,
! [X10,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Orderings_Obot__class_Obot(X3)),X10) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_inf__bot__left_0) ).
fof(c_0_319_320,axiom,
! [X20] :
( ~ class_Orderings_Obot(X20)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X20)),v_x) = c_Orderings_Obot__class_Obot(X20) ),
file('<stdin>',cls_bot__fun__eq_0) ).
fof(c_0_320_321,axiom,
! [X10,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),c_Orderings_Obot__class_Obot(X3)) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_inf__bot__right_0) ).
fof(c_0_321_322,axiom,
! [X10,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X10,X3) = X10 ),
file('<stdin>',cls_sup__bot__left_0) ).
fof(c_0_322_323,axiom,
! [X10,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Orderings_Obot__class_Obot(X3),X3) = X10 ),
file('<stdin>',cls_sup__bot__right_0) ).
fof(c_0_323_324,axiom,
! [X10,X3] :
( ~ class_Orderings_Obot(X3)
| c_lessequals(c_Orderings_Obot__class_Obot(X3),X10,X3) ),
file('<stdin>',cls_bot__least_0) ).
fof(c_0_324_325,axiom,
! [X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X10,X3) = X10 ),
file('<stdin>',cls_sup__idem_0) ).
fof(c_0_325_326,axiom,
! [X10,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X10,X10,X3) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_326_327,axiom,
! [X10,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X10,X10,X3) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_327_328,axiom,
! [X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X10) = X10 ),
file('<stdin>',cls_inf__idem_0) ).
fof(c_0_328_329,axiom,
! [X62,X6,X3] :
( c_Option_Ooption_OSome(X6,X3) != c_Option_Ooption_OSome(X62,X3)
| X6 = X62 ),
file('<stdin>',cls_option_Oinject_0) ).
fof(c_0_329_330,axiom,
! [X24,X18] :
( hAPP(c_Com_Obody,X24) != c_Option_Ooption_OSome(X18,tc_Com_Ocom)
| ~ c_Com_OWT__bodies
| c_Com_OWT(X18) ),
file('<stdin>',cls_WT__bodiesD_0) ).
fof(c_0_330_331,axiom,
! [X5,X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X5,X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4)
| ~ class_Finite__Set_Ofinite_Ofinite(X5) ),
file('<stdin>',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_331_332,axiom,
! [X5,X4] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X5,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
file('<stdin>',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_332_333,axiom,
! [X5,X4] :
( class_Lattices_Oupper__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(c_0_333_334,axiom,
! [X5,X4] :
( class_Lattices_Olower__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Olower__semilattice) ).
fof(c_0_334_335,axiom,
! [X5,X4] :
( class_Lattices_Odistrib__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Odistrib__lattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(c_0_335_336,axiom,
! [X5,X4] :
( class_Lattices_Obounded__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Obounded__lattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Obounded__lattice) ).
fof(c_0_336_337,axiom,
! [X5,X4] :
( class_Orderings_Opreorder(tc_fun(X5,X4))
| ~ class_Orderings_Opreorder(X4) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_337_338,axiom,
! [X5,X4] :
( class_Lattices_Olattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Olattice) ).
fof(c_0_338_339,axiom,
! [X5,X4] :
( class_Orderings_Oorder(tc_fun(X5,X4))
| ~ class_Orderings_Oorder(X4) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_339_340,axiom,
! [X5,X4] :
( class_Orderings_Obot(tc_fun(X5,X4))
| ~ class_Orderings_Obot(X4) ),
file('<stdin>',clsarity_fun__Orderings_Obot) ).
fof(c_0_340_341,axiom,
! [X5,X4] :
( class_HOL_Ominus(tc_fun(X5,X4))
| ~ class_HOL_Ominus(X4) ),
file('<stdin>',clsarity_fun__HOL_Ominus) ).
fof(c_0_341_342,axiom,
! [X5,X4] :
( class_HOL_Oord(tc_fun(X5,X4))
| ~ class_HOL_Oord(X4) ),
file('<stdin>',clsarity_fun__HOL_Oord) ).
fof(c_0_342_343,axiom,
! [X24] :
( c_Com_OWT(c_Com_Ocom_OBODY(X24))
| hAPP(c_Com_Obody,X24) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
file('<stdin>',cls_WT_OBody_0) ).
fof(c_0_343_344,axiom,
! [X7,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X7,X3) ),
file('<stdin>',cls_finite_0) ).
fof(c_0_344_345,axiom,
! [X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
file('<stdin>',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_345_346,axiom,
! [X8,X9] :
( c_Com_Ocom_OBODY(X9) != c_Com_Ocom_OBODY(X8)
| X9 = X8 ),
file('<stdin>',cls_com_Osimps_I6_J_0) ).
fof(c_0_346_347,axiom,
! [X16,X10] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| X10 = X16 ),
file('<stdin>',cls_state__not__singleton__def_1) ).
fof(c_0_347_348,plain,
! [X33,X34,X35,X36,X37,X38,X18,X6,X39,X40,X3] :
( hAPP(X40,c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X37,X6),X18)
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_348_349,plain,
! [X33,X34,X35,X36,X37,X38,X18,X6,X39,X40,X3] :
( hAPP(X39,c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X34,X6),X18)
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_349_350,plain,
! [X10,X33,X34,X35,X36,X37,X38,X39,X40,X7,X3] :
( hBOOL(hAPP(hAPP(X35,hAPP(X40,X7)),X10))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_350_351,plain,
! [X10,X33,X34,X35,X36,X37,X38,X39,X40,X7,X3] :
( hBOOL(hAPP(hAPP(X35,X10),hAPP(X39,X7)))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_351_352,plain,
! [X33,X34,X35,X36,X37,X38,X6,X39,X40,X3] :
( hAPP(X40,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_352_353,plain,
! [X33,X34,X35,X36,X37,X38,X6,X39,X40,X3] :
( hAPP(X39,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_353_354,plain,
! [X33,X34,X35,X36,X37,X38,X6,X39,X40,X7,X3] :
( hAPP(X40,c_Set_Oinsert(X6,X7,X3)) = hAPP(hAPP(X37,X6),hAPP(X40,X7))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_354_355,plain,
! [X33,X34,X35,X36,X37,X38,X6,X39,X40,X7,X3] :
( hAPP(X39,c_Set_Oinsert(X6,X7,X3)) = hAPP(hAPP(X34,X6),hAPP(X39,X7))
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_355_356,plain,
! [X33,X34,X35,X36,X37,X38,X39,X40,X3] :
( hAPP(X40,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X33
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_356_357,plain,
! [X33,X34,X35,X36,X37,X38,X39,X40,X3] :
( hAPP(X39,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X38
| ~ c_Complete__Lattice_Ocomplete__lattice(X40,X39,X35,X36,X37,X34,X38,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_357_358,plain,
! [X10,X25,X18,X6,X7,X3] :
( c_Finite__Set_Ofold__graph(X25,X6,c_Set_Oinsert(X18,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),X10,X3,X3)
| hBOOL(c_in(X18,X7,X3))
| ~ hBOOL(c_in(X6,X7,X3))
| ~ c_Finite__Set_Ofold__graph(X25,X18,X7,X10,X3,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_358_359,plain,
! [X41,X12,X10,X26,X7,X20,X3] :
( c_Finite__Set_Ofold__graph(X26,X41,X7,hAPP(hAPP(X26,X10),X12),X3,X20)
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofold__graph(X26,X41,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X12,X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_359_360,plain,
! [X41,X12,X25,X18,X7,X3] :
( c_Finite__Set_Ofold__graph(X25,X41,c_Set_Oinsert(X18,X7,X3),hAPP(hAPP(X25,X41),X12),X3,X3)
| hBOOL(c_in(X18,X7,X3))
| ~ c_Finite__Set_Ofold__graph(X25,X18,X7,X12,X3,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_360_361,plain,
! [X41,X12,X10,X26,X7,X20,X3] :
( c_Finite__Set_Ofold__graph(X26,X41,c_Set_Oinsert(X10,X7,X3),hAPP(hAPP(X26,X10),X12),X3,X20)
| ~ c_Finite__Set_Ofold__graph(X26,X41,X7,X12,X3,X20)
| hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_361_362,plain,
! [X10,X26,X6,X7,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26,c_Set_Oinsert(X6,X7,X3),X3),X10))
| hBOOL(c_in(X6,X7,X3))
| ~ c_Finite__Set_Ofold__graph(X26,X6,X7,X10,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_362_363,plain,
! [X41,X10,X26,X20,X3] :
( X10 = X41
| ~ c_Finite__Set_Ofold__graph(X26,X41,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X10,X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_363_364,plain,
! [X41,X10,X26,X7,X20,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofold__graph(X26,X41,X7,X10,X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_364_365,plain,
! [X24,X27,X17,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Com_Ocom_OBODY(X24),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Com_Ocom_OBODY(X24),X27,X3),X15,tc_Hoare__Mirabelle_Otriple(X3)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Option_Othe(hAPP(c_Com_Obody,X24),tc_Com_Ocom),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_365_366,plain,
! [X22,X27,X17] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,X22,X27,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,X22,X27,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X22),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_366_367,plain,
! [X24,X27,X17,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Com_Ocom_OBODY(X24),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X17,c_Option_Othe(hAPP(c_Com_Obody,X24),tc_Com_Ocom),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_367_368,plain,
! [X26,X18,X6,X20,X3] :
( hAPP(X26,X6) = X18
| ~ hBOOL(c_in(X6,c_Set_Ovimage(X26,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X3,X20),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_368_369,plain,
! [X57,X46,X26,X20,X3] :
( c_Map_Omap__le(c_Map_Omap__add(X26,X46,X3,X20),X57,X3,X20)
| ~ c_Map_Omap__le(X26,c_Map_Omap__add(X26,X46,X3,X20),X3,X20)
| ~ c_Map_Omap__le(X46,X57,X3,X20)
| ~ c_Map_Omap__le(X26,X57,X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_369_370,plain,
! [X26,X6,X11,X20,X3] :
( hBOOL(c_in(hAPP(X26,X6),X11,X20))
| ~ hBOOL(c_in(X6,c_Set_Ovimage(X26,X11,X3,X20),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_370_371,plain,
! [X26,X6,X7,X20,X3] :
( hBOOL(c_in(hAPP(X26,X6),X7,X20))
| ~ hBOOL(c_in(X6,c_Set_Ovimage(X26,X7,X3,X20),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_371_372,plain,
! [X26,X18,X6,X3] :
( X6 = X18
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_372_373,plain,
! [X10,X26,X7,X20,X3] :
( hBOOL(hAPP(X7,hAPP(X26,X10)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X26,X7,X3,X20),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_373_374,plain,
! [X46,X26,X20,X3] :
( c_Map_Omap__add(X26,X46,X3,X20) = c_Map_Omap__add(X46,X26,X3,X20)
| ~ c_Map_Omap__le(X26,c_Map_Omap__add(X26,X46,X3,X20),X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_374_375,plain,
! [X10,X18,X11,X7,X20,X3] :
( hBOOL(c_in(X18,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X20,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X18,hAPP(X11,X10),X3))
| ~ hBOOL(c_in(X10,X7,X20)) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_375_376,plain,
! [X18,X6,X11,X7,X20,X3] :
( hBOOL(c_in(X18,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),X20))
| ~ hBOOL(c_in(X18,hAPP(X11,X6),X20))
| ~ hBOOL(c_in(X6,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_376_377,axiom,
! [X46,X26,X20,X3] :
( c_Map_Omap__add(X26,X46,X3,X20) != c_Map_Omap__add(X46,X26,X3,X20)
| c_Map_Omap__le(X26,c_Map_Omap__add(X26,X46,X3,X20),X3,X20) ),
c_0_29 ).
fof(c_0_377_378,plain,
! [X24,X15] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X24)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X24)),X15,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Option_Othe(hAPP(c_Com_Obody,X24),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_378_379,plain,
! [X10,X18,X11,X7,X20,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),X18))
| ~ hBOOL(hAPP(hAPP(X11,X10),X18))
| ~ hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_379_380,plain,
! [X18,X6,X11,X7,X20,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),X18))
| ~ hBOOL(hAPP(hAPP(X11,X6),X18))
| ~ hBOOL(c_in(X6,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_380_381,plain,
! [X57,X46,X26,X20,X3] :
( c_Map_Omap__le(X46,X57,X3,X20)
| ~ c_Map_Omap__le(c_Map_Omap__add(X26,X46,X3,X20),X57,X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_381_382,plain,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_382_383,plain,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_383_384,plain,
! [X26,X6,X11,X20,X3] :
( hBOOL(c_in(X6,c_Set_Ovimage(X26,X11,X3,X20),X3))
| ~ hBOOL(c_in(hAPP(X26,X6),X11,X20)) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_384_385,plain,
! [X26,X6,X7,X20,X3] :
( hBOOL(c_in(X6,c_Set_Ovimage(X26,X7,X20,X3),X20))
| ~ hBOOL(c_in(hAPP(X26,X6),X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_385_386,plain,
! [X26,X6,X11,X20,X3] :
( hBOOL(c_in(X6,c_Set_Ovimage(X26,X11,X20,X3),X20))
| ~ hBOOL(c_in(hAPP(X26,X6),X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_386_387,plain,
! [X10,X17,X7,X3] :
( hBOOL(c_in(X10,X7,X3))
| ~ hBOOL(c_in(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Collect(X17,X3)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_387_388,plain,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_388_389,plain,
! [X10,X26,X7,X61,X3] :
( ~ hBOOL(c_in(X10,X7,X61))
| hBOOL(c_in(hAPP(X26,X10),c_Set_Oimage(X26,X7,X61,X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_389_390,plain,
! [X10,X26,X7,X20,X3] :
( ~ hBOOL(c_in(X10,X7,X20))
| hBOOL(c_in(hAPP(X26,X10),c_Set_Oimage(X26,X7,X20,X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_390_391,plain,
! [X10,X26,X7,X20,X3] :
( hBOOL(c_in(hAPP(X26,X10),c_Set_Oimage(X26,X7,X20,X3),X3))
| ~ hBOOL(c_in(X10,X7,X20)) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_391_392,plain,
! [X10,X26,X7,X20,X3] :
( hBOOL(c_in(hAPP(X26,X10),c_Set_Oimage(X26,X7,X3,X20),X20))
| ~ hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_392_393,axiom,
! [X59,X60,X20,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X60,X3,X20)),c_Map_Odom(X59,X3,X20)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Map_Omap__add(X60,X59,X3,X20) = c_Map_Omap__add(X59,X60,X3,X20) ),
c_0_45 ).
fof(c_0_393_394,plain,
! [X10,X17,X7,X3] :
( hBOOL(hAPP(X17,X10))
| ~ hBOOL(c_in(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Collect(X17,X3)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_394_395,plain,
! [X10,X63,X11,X7,X20,X3] :
( c_lessequals(hAPP(X7,X10),X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X63,X20))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X63,X7,X20,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_395_396,plain,
! [X10,X26,X11,X7,X20,X3] :
( hBOOL(c_in(hAPP(X26,X10),X11,X3))
| ~ hBOOL(c_in(X10,X7,X20))
| ~ c_lessequals(c_Set_Oimage(X26,X7,X20,X3),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_396_397,plain,
! [X26,X11,X7,X20,X3] :
( c_lessequals(c_Set_Ovimage(X26,X7,X20,X3),c_Set_Ovimage(X26,X11,X20,X3),tc_fun(X20,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_397_398,plain,
! [X26,X11,X7,X20,X3] :
( c_lessequals(c_Set_Oimage(X26,X7,X3,X20),c_Set_Oimage(X26,X11,X3,X20),tc_fun(X20,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_398_399,plain,
! [X10,X26,X7,X20,X3] :
( ~ c_lessequals(X10,X7,tc_fun(X20,tc_bool))
| c_lessequals(c_Set_Oimage(X26,X10,X20,X3),c_Set_Oimage(X26,X7,X20,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_399_400,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_400_401,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X7,X3))
| ~ hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_401_402,plain,
! [X10,X26,X7,X20,X3] :
( hBOOL(hAPP(c_Set_Ovimage(X26,X7,X3,X20),X10))
| ~ hBOOL(hAPP(X7,hAPP(X26,X10))) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_402_403,plain,
! [X10,X11,X7,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_403_404,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3)),c_Lattices_Oupper__semilattice__class_Osup(X10,X41,X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_404_405,axiom,
! [X42,X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X42,tc_fun(X3,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool)))
| c_lessequals(X42,X7,tc_fun(X3,tc_bool)) ),
c_0_57 ).
fof(c_0_405_406,plain,
! [X10,X11,X7,X20,X3] :
( c_Finite__Set_Ofinite(hAPP(X11,X10),X20)
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),X20)
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_406_407,plain,
! [X48,X63,X7,X20,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X7,X48),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X63,X7,X3,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X63,X7,X3,tc_fun(X20,tc_bool))
| ~ hBOOL(c_in(X48,X63,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_407_408,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3))
| ~ hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_408_409,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3))
| ~ hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_409_410,plain,
! [X28,X29,X30,X20,X3] :
( hAPP(c_Map_Omap__add(X30,X29,X3,X20),X28) = hAPP(X29,X28)
| ~ hBOOL(c_in(X28,c_Map_Odom(X29,X3,X20),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_410_411,plain,
! [X64,X59,X60,X20,X3] :
( c_Map_Omap__le(X60,X64,X3,X20)
| ~ c_Map_Omap__le(X59,X64,X3,X20)
| ~ c_Map_Omap__le(X60,X59,X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_411_412,plain,
! [X10,X17,X7,X3] :
( hBOOL(c_in(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Collect(X17,X3)),X3))
| ~ hBOOL(hAPP(X17,X10))
| ~ hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_412_413,plain,
! [X10,X26,X7,X20,X3] :
( c_Set_Oinsert(hAPP(X26,X10),c_Set_Oimage(X26,X7,X3,X20),X20) = c_Set_Oimage(X26,X7,X3,X20)
| ~ hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_413_414,plain,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_414_415,plain,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(X7,X10))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_415_416,plain,
! [X25,X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X11 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X11,X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3)
| c_Finite__Set_Ofold1(X25,c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X3) = hAPP(hAPP(X25,c_Finite__Set_Ofold1(X25,X7,X3)),c_Finite__Set_Ofold1(X25,X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_416_417,plain,
! [X12,X10,X3] :
( X12 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| ~ hBOOL(hAPP(c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_417_418,plain,
! [X26,X11,X7,X20,X3] :
( c_Finite__Set_Ofinite(X11,X20)
| ~ c_lessequals(X11,c_Set_Oimage(X26,X7,X3,X20),tc_fun(X20,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_418_419,plain,
! [X10,X31,X32,X20,X3] :
( hAPP(X32,X10) = hAPP(X31,X10)
| ~ hBOOL(c_in(X10,c_Map_Odom(X32,X3,X20),X3))
| ~ c_Map_Omap__le(X32,X31,X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_419_420,plain,
! [X22,X15] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X22),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X22)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X15))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_420_421,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X41),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_421_422,plain,
! [X45,X42,X11,X7,X3] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X42),X45),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X45,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_422_423,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X11,X3))
| hBOOL(c_in(X22,X7,X3))
| ~ hBOOL(c_in(X22,c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_423_424,axiom,
! [X10,X47,X28,X48,X20,X3] :
( hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) != c_Option_Ooption_OSome(X10,X3)
| hAPP(X28,X48) = c_Option_Ooption_OSome(X10,X3)
| hAPP(X47,X48) = c_Option_Ooption_OSome(X10,X3) ),
c_0_76 ).
fof(c_0_424_425,plain,
! [X6,X42,X11,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X6,X11,X3)),X42) = c_Set_Oinsert(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X11),X42),X3)
| ~ hBOOL(c_in(X6,X42,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_425_426,axiom,
! [X10,X47,X28,X48,X20,X3] :
( hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) != c_Option_Ooption_OSome(X10,X3)
| hAPP(X47,X48) = c_Option_Ooption_ONone(X3)
| hAPP(X47,X48) = c_Option_Ooption_OSome(X10,X3) ),
c_0_78 ).
fof(c_0_426_427,axiom,
! [X28,X29,X30,X20,X3] :
( hAPP(c_Map_Omap__add(X30,X29,X3,X20),X28) = hAPP(X30,X28)
| hBOOL(c_in(X28,c_Map_Odom(X29,X3,X20),X3)) ),
c_0_79 ).
fof(c_0_427_428,axiom,
! [X28,X29,X30,X20,X3] :
( hAPP(c_Map_Omap__add(X30,X29,X3,X20),X28) = hAPP(X29,X28)
| hBOOL(c_in(X28,c_Map_Odom(X30,X3,X20),X3)) ),
c_0_80 ).
fof(c_0_428_429,plain,
! [X18,X6,X3] :
( X18 = X6
| ~ hBOOL(c_in(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_429_430,axiom,
! [X21,X22,X18,X6,X3] :
( c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X18 = X22
| X18 = X21 ),
c_0_82 ).
fof(c_0_430_431,axiom,
! [X21,X22,X18,X6,X3] :
( c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X6 = X21
| X18 = X21 ),
c_0_83 ).
fof(c_0_431_432,axiom,
! [X21,X22,X18,X6,X3] :
( c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X18 = X22
| X6 = X22 ),
c_0_84 ).
fof(c_0_432_433,axiom,
! [X21,X22,X18,X6,X3] :
( c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X6 = X21
| X6 = X22 ),
c_0_85 ).
fof(c_0_433_434,plain,
! [X22,X11,X7,X3] :
( ~ hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_434_435,axiom,
! [X47,X28,X48,X20,X3] :
( hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) != c_Option_Ooption_ONone(X3)
| hAPP(X28,X48) = c_Option_Ooption_ONone(X3) ),
c_0_87 ).
fof(c_0_435_436,axiom,
! [X47,X28,X48,X20,X3] :
( hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) != c_Option_Ooption_ONone(X3)
| hAPP(X47,X48) = c_Option_Ooption_ONone(X3) ),
c_0_88 ).
fof(c_0_436_437,plain,
! [X6,X11,X7,X20,X3] :
( c_lessequals(hAPP(X11,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X3,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool))
| ~ hBOOL(c_in(X6,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_437_438,plain,
! [X6,X7,X3] :
( c_Set_Oinsert(X6,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X7
| ~ hBOOL(c_in(X6,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_438_439,plain,
! [X46,X26,X20,X3] :
( X26 = X46
| ~ c_Map_Omap__le(X46,X26,X3,X20)
| ~ c_Map_Omap__le(X26,X46,X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_439_440,plain,
! [X42,X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X42,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool)))
| ~ c_lessequals(X42,X7,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_440_441,axiom,
! [X49,X50,X51,X52,X53,X54,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X52,X54,X50,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X51,X53,X49,X3)
| X52 = X51 ),
c_0_93 ).
fof(c_0_441_442,axiom,
! [X49,X50,X51,X52,X53,X54,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X52,X54,X50,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X51,X53,X49,X3)
| X54 = X53 ),
c_0_94 ).
fof(c_0_442_443,axiom,
! [X49,X50,X51,X52,X53,X54,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X52,X54,X50,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X51,X53,X49,X3)
| X50 = X49 ),
c_0_95 ).
fof(c_0_443_444,plain,
! [X13,X14,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,X13,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_444_445,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X7,X3))
| ~ hBOOL(c_in(X22,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_445_446,plain,
! [X6,X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Set_Oinsert(X6,X11,X3)) = c_Set_Oinsert(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X3)
| ~ hBOOL(c_in(X6,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_446_447,plain,
! [X6,X11,X7,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X6,X11,X3),tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_447_448,plain,
! [X69,X56,X7,X20,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| c_lessequals(hAPP(X56,X69),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X56,X3,X20),X20)
| ~ hBOOL(c_in(X69,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_448_449,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_449_450,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_450_451,plain,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),X10))
| ~ hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(X7,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_451_452,plain,
! [X10,X11,X7,X20,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X20,tc_fun(X3,tc_bool))
| hAPP(X11,X10) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X20)) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_452_453,plain,
! [X10,X11,X7,X20,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X11,X20,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hAPP(X11,X10) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X20)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_453_454,plain,
! [X46,X26,X20,X3] :
( c_lessequals(c_Map_Odom(X26,X3,X20),c_Map_Odom(X46,X3,X20),tc_fun(X3,tc_bool))
| ~ c_Map_Omap__le(X26,X46,X3,X20) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_454_455,plain,
! [X42,X11,X7,X3] :
( c_lessequals(X42,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_455_456,plain,
! [X42,X11,X7,X3] :
( c_lessequals(X42,X7,tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_456_457,plain,
! [X6,X11,X7,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X6,X11,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_457_458,plain,
! [X22,X15] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X22),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X22)
| hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X15),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_458_459,plain,
! [X45,X42,X11,X7,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X42,X45,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_459_460,plain,
! [X45,X42,X11,X7,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X42,X45,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X45,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_460_461,plain,
! [X18,X6,X7,X3] :
( hBOOL(c_in(X6,X7,X3))
| X6 = X18
| ~ hBOOL(c_in(X6,c_Set_Oinsert(X18,X7,X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_461_462,plain,
! [X10,X11,X7,X3] :
( ~ hBOOL(c_in(X10,X11,X3))
| ~ hBOOL(c_in(X10,X7,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_462_463,axiom,
! [X6,X42,X11,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X6,X11,X3)),X42) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X11),X42)
| hBOOL(c_in(X6,X42,X3)) ),
c_0_115 ).
fof(c_0_463_464,plain,
! [X42,X11,X7,X3] :
( c_lessequals(X42,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X7,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_464_465,plain,
! [X42,X11,X7,X3] :
( c_lessequals(X42,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11),tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X7,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_465_466,plain,
! [X21,X22,X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X18,X21,X3)
| ~ c_lessequals(X6,X18,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_466_467,plain,
! [X21,X22,X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X22,X6,X3)
| ~ c_lessequals(X6,X18,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_467_468,plain,
! [X18,X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_468_469,plain,
! [X18,X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X6,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_469_470,plain,
! [X13,X14,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,X13,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_470_471,axiom,
! [X10,X47,X28,X48,X20,X3] :
( hAPP(X28,X48) != c_Option_Ooption_OSome(X10,X3)
| hAPP(X47,X48) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) = c_Option_Ooption_OSome(X10,X3) ),
c_0_123 ).
fof(c_0_471_472,plain,
! [X42,X11,X7,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_472_473,plain,
! [X42,X11,X7,X3] :
( c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_473_474,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X22,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_474_475,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X22,X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_475_476,plain,
! [X10,X7,X3] :
( X7 = c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_476_477,plain,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(X11,X10))
| hBOOL(hAPP(X7,X10))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_477_478,axiom,
! [X47,X28,X48,X20,X3] :
( hAPP(X28,X48) != c_Option_Ooption_ONone(X3)
| hAPP(X47,X48) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) = c_Option_Ooption_ONone(X3) ),
c_0_130 ).
fof(c_0_478_479,axiom,
! [X70,X47,X28,X48,X20,X3] :
( hAPP(X47,X48) != c_Option_Ooption_OSome(X70,X3)
| hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) = c_Option_Ooption_OSome(X70,X3) ),
c_0_131 ).
fof(c_0_479_480,axiom,
! [X10,X47,X28,X48,X20,X3] :
( hAPP(X47,X48) != c_Option_Ooption_OSome(X10,X3)
| hAPP(c_Map_Omap__add(X28,X47,X20,X3),X48) = c_Option_Ooption_OSome(X10,X3) ),
c_0_132 ).
fof(c_0_480_481,plain,
! [X16,X10,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X16,X3)
| ~ hBOOL(c_in(X16,X7,X3))
| ~ c_lessequals(X10,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X7,X3),X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_481_482,plain,
! [X28,X6,X20,X3] :
( hAPP(X28,X6) != c_Option_Ooption_ONone(X20)
| ~ hBOOL(c_in(X6,c_Map_Odom(X28,X3,X20),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_482_483,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X10,X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3)),c_Lattices_Oupper__semilattice__class_Osup(X41,X10,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_483_484,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3)),c_Lattices_Oupper__semilattice__class_Osup(X10,X41,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_484_485,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3)),X10) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X41),X10),X3) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_485_486,plain,
! [X57,X58,X20,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X57,X58,X3,X20),X20)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_486_487,axiom,
! [X10,X7,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X7,X3),c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X7
| hBOOL(c_in(X10,X7,X3)) ),
c_0_139 ).
fof(c_0_487_488,axiom,
! [X6,X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),c_Set_Oinsert(X6,X11,X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11)
| hBOOL(c_in(X6,X7,X3)) ),
c_0_140 ).
fof(c_0_488_489,axiom,
! [X10,X26,X7,X20,X3] :
( hAPP(X26,X10) != c_Option_Ooption_ONone(X3)
| c_HOL_Ominus__class_Ominus(c_Map_Odom(X26,X20,X3),c_Set_Oinsert(X10,X7,X20),tc_fun(X20,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X26,X20,X3),X7,tc_fun(X20,tc_bool)) ),
c_0_141 ).
fof(c_0_489_490,axiom,
! [X10,X11,X7,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X10,c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| hBOOL(c_in(X10,X11,X3)) ),
c_0_142 ).
fof(c_0_490_491,plain,
! [X18,X6,X7,X3] :
( hBOOL(c_in(X6,c_Set_Oinsert(X18,X7,X3),X3))
| ~ hBOOL(c_in(X6,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_491_492,plain,
! [X18,X6,X11,X3] :
( hBOOL(c_in(X6,c_Set_Oinsert(X18,X11,X3),X3))
| ~ hBOOL(c_in(X6,X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_492_493,plain,
! [X10,X25,X7,X3] :
( c_Finite__Set_Ofold1(X25,c_Set_Oinsert(X10,X7,X3),X3) = hAPP(hAPP(X25,X10),c_Finite__Set_Ofold1(X25,X7,X3))
| hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofinite(X7,X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_493_494,plain,
! [X10,X11,X7,X3] :
( c_lessequals(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_494_495,plain,
! [X10,X11,X7,X3] :
( c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_495_496,plain,
! [X10,X11,X7,X3] :
( c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_496_497,plain,
! [X42,X11,X7,X3] :
( c_HOL_Ominus__class_Ominus(X11,c_HOL_Ominus__class_Ominus(X42,X7,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X7
| ~ c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_497_498,plain,
! [X42,X11,X7,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_498_499,plain,
! [X42,X11,X7,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X42,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_499_500,plain,
! [X21,X22,X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,X3)
| ~ c_lessequals(X22,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_500_501,axiom,
! [X26,X7,X20,X3] :
( c_Set_Oimage(X26,X7,X20,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) ),
c_0_153 ).
fof(c_0_501_502,axiom,
! [X26,X7,X20,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X26,X7,X20,X3)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) ),
c_0_154 ).
fof(c_0_502_503,plain,
! [X42,X11,X7,X3] :
( c_lessequals(X7,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_503_504,plain,
! [X42,X11,X7,X3] :
( c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X42,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_504_505,plain,
! [X10,X11,X7,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_505_506,plain,
! [X46,X26,X20] :
( ~ class_Lattices_Olattice(X20)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X20)),X26),X46),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X20),hAPP(X26,v_x)),hAPP(X46,v_x)) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_506_507,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X41),X3) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_507_508,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12)),X41) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41)) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_508_509,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12)),X41) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41)) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_509_510,plain,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_510_511,plain,
! [X10,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X10,X11,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_511_512,plain,
! [X12,X10,X7,X3] :
( hBOOL(hAPP(X7,X10))
| X12 = X10
| ~ hBOOL(hAPP(c_Set_Oinsert(X12,X7,X3),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_512_513,plain,
! [X6,X45,X42,X3] :
( c_lessequals(c_Set_Oinsert(X6,X42,X3),c_Set_Oinsert(X6,X45,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X42,X45,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_513_514,plain,
! [X14,X11,X7,X3] :
( hBOOL(c_in(X14,X11,X3))
| ~ hBOOL(c_in(X14,X7,X3))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_514_515,plain,
! [X10,X11,X7,X3] :
( hBOOL(c_in(X10,X11,X3))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_515_516,plain,
! [X22,X11,X7,X3] :
( hBOOL(c_in(X22,X11,X3))
| ~ hBOOL(c_in(X22,X7,X3))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_516_517,plain,
! [X10,X11,X7,X3] :
( hBOOL(c_in(X10,X11,X3))
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_517_518,plain,
! [X10,X11,X7,X3] :
( hBOOL(c_in(X10,X11,X3))
| ~ c_lessequals(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_518_519,axiom,
! [X10,X11,X7,X3] :
( c_Set_Oinsert(X10,X7,X3) != c_Set_Oinsert(X10,X11,X3)
| hBOOL(c_in(X10,X11,X3))
| hBOOL(c_in(X10,X7,X3))
| X7 = X11 ),
c_0_171 ).
fof(c_0_519_520,plain,
! [X10,X17,X3] :
( ~ hBOOL(hAPP(X17,X10))
| ~ hBOOL(c_in(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_520_521,plain,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X11,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_521_522,plain,
! [X10,X11,X7,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X7,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_522_523,plain,
! [X22] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X22),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X22)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_523_524,plain,
! [X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X7,X3),X6,X3)
| ~ hBOOL(c_in(X6,X7,X3))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_524_525,axiom,
! [X28,X18,X6,X20,X3] :
( hAPP(X28,X6) != c_Option_Ooption_OSome(X18,X3)
| hBOOL(c_in(X6,c_Map_Odom(X28,X20,X3),X20)) ),
c_0_177 ).
fof(c_0_525_526,plain,
! [X10,X17,X3] :
( hBOOL(hAPP(X17,X10))
| ~ hBOOL(c_in(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_526_527,plain,
! [X10,X11,X7,X3] :
( c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X10,X7,X3),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_527_528,plain,
! [X21,X22,X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X3),tc_fun(X3,tc_bool))
| c_lessequals(X6,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_528_529,plain,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,c_HOL_Ominus__class_Ominus(X11,X7,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X11
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_529_530,axiom,
! [X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)) = X7 ),
c_0_182 ).
fof(c_0_530_531,axiom,
! [X28,X6,X20,X3] :
( hBOOL(c_in(X6,c_Map_Odom(X28,X3,X20),X3))
| hAPP(X28,X6) = c_Option_Ooption_ONone(X20) ),
c_0_183 ).
fof(c_0_531_532,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3)
| ~ c_lessequals(X12,X41,X3)
| ~ c_lessequals(X10,X41,X3) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_532_533,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X10,X3)
| ~ c_lessequals(X41,X10,X3)
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_533_534,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X10,X3)
| ~ c_lessequals(X18,X10,X3)
| ~ c_lessequals(X6,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_534_535,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3)
| ~ c_lessequals(X10,X41,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_535_536,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3)
| ~ c_lessequals(X10,X41,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_536_537,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X3)
| ~ c_lessequals(X10,X18,X3)
| ~ c_lessequals(X10,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_537_538,axiom,
! [X18,X6,X3] :
( c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X6 = X18 ),
c_0_190 ).
fof(c_0_538_539,plain,
! [X25,X22,X18,X6,X3] :
( hAPP(hAPP(X25,hAPP(hAPP(X25,X6),X18)),X22) = hAPP(hAPP(X25,X6),hAPP(hAPP(X25,X18),X22))
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_539_540,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_540_541,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X41,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_541_542,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X41,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_542_543,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X41,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_543_544,plain,
! [X13,X14,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,c_Set_Oinsert(X14,X13,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_544_545,plain,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X58),X15),X3)
| ~ c_Finite__Set_Ofinite(X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_545_546,plain,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X58),X15),X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_546_547,plain,
! [X42,X11,X7,X3] :
( c_lessequals(X7,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X42,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_547_548,plain,
! [X43,X12,X44,X10,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X10,X12,X3) != c_HOL_Ominus__class_Ominus(X44,X43,X3)
| c_lessequals(X43,X44,X3)
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_548_549,plain,
! [X43,X12,X44,X10,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X10,X12,X3) != c_HOL_Ominus__class_Ominus(X44,X43,X3)
| c_lessequals(X12,X10,X3)
| ~ c_lessequals(X43,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_549_550,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X12,X41,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_550_551,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,X41,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X41,X3) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_551_552,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X18,X10,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_552_553,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,X10,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_553_554,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X41)) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_554_555,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X41)) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_555_556,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X6,X3)
| ~ c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X3) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_556_557,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X18,X3)
| ~ c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X3) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_557_558,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X12,X3)
| ~ c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_558_559,plain,
! [X41,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X41,X3)
| ~ c_lessequals(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X41),X3) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_559_560,plain,
! [X18,X11,X7,X3] :
( c_lessequals(X7,c_Set_Oinsert(X18,X11,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_560_561,plain,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_561_562,plain,
! [X12,X10,X7,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X12,X7,X3),X10))
| ~ hBOOL(hAPP(X7,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_562_563,plain,
! [X55,X56,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X56,X3),c_Finite__Set_Olinorder__class_OMax(X55,X3),X3)
| ~ c_Finite__Set_Ofinite(X55,X3)
| X56 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X56,X55,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_563_564,plain,
! [X55,X56,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X55,X3),c_Finite__Set_Olinorder__class_OMin(X56,X3),X3)
| ~ c_Finite__Set_Ofinite(X55,X3)
| X56 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X56,X55,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_564_565,plain,
! [X6,X17,X3] :
( hBOOL(hAPP(X17,X6))
| ~ hBOOL(c_in(X6,c_Collect(X17,X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_565_566,plain,
! [X10,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X7,X3),X10,X3)
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_566_567,plain,
! [X10,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X10,c_Finite__Set_Olinorder__class_OMax(X7,X3),X3)
| ~ hBOOL(c_in(X10,X7,X3))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_567_568,plain,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(X58,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X58,X15,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_568_569,plain,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(X15,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X58,X15,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_569_570,plain,
! [X11,X7,X20] :
( ~ class_HOL_Ominus(X20)
| hAPP(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(t_a,X20)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X7,v_x),hAPP(X11,v_x),X20) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_570_571,plain,
! [X46,X26,X20] :
( ~ class_Lattices_Olattice(X20)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X26,X46,tc_fun(t_a,X20)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X26,v_x),hAPP(X46,v_x),X20) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_571_572,plain,
! [X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) = X11
| ~ c_lessequals(X11,X7,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_572_573,plain,
! [X11,X7,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X7),X11) = X7
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_573_574,plain,
! [X10,X7,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X7,X3),X10,X3)
| ~ hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_574_575,plain,
! [X10,X7,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(X10,c_Complete__Lattice_OSup__class_OSup(X7,X3),X3)
| ~ hBOOL(c_in(X10,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_575_576,plain,
! [X16,X10,X25,X20,X3] :
( c_Set_Oinsert(X10,X16,X20) != c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))
| hBOOL(c_in(X10,X16,X20))
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_576_577,axiom,
! [X12,X10,X26,X20,X3] :
( hAPP(X26,X10) != c_Option_Ooption_OSome(X12,X3)
| c_Set_Oinsert(X10,c_Map_Odom(X26,X20,X3),X20) = c_Map_Odom(X26,X20,X3) ),
c_0_229 ).
fof(c_0_577_578,plain,
! [X25,X22,X18,X6,X3] :
( hAPP(hAPP(X25,X6),hAPP(hAPP(X25,X18),X22)) = hAPP(hAPP(X25,X18),hAPP(hAPP(X25,X6),X22))
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_578_579,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X3)
| ~ c_lessequals(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_579_580,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X6,X18,X3),X3)
| ~ c_lessequals(X10,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_580_581,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X10,X3)
| ~ c_lessequals(X6,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_581_582,plain,
! [X10,X18,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),X18),X10,X3)
| ~ c_lessequals(X18,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_582_583,plain,
! [X11,X7,X3] :
( X7 = X11
| ~ c_lessequals(X11,X7,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_583_584,plain,
! [X11,X7,X3] :
( X7 = X11
| ~ c_lessequals(X11,X7,tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_584_585,plain,
! [X10,X46,X26,X20,X3] :
( ~ class_HOL_Oord(X20)
| c_lessequals(hAPP(X26,X10),hAPP(X46,X10),X20)
| ~ c_lessequals(X26,X46,tc_fun(X3,X20)) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_585_586,axiom,
! [X16,X10,X3] :
( c_Set_Oinsert(X10,X16,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X10,X16,X3)) ),
c_0_238 ).
fof(c_0_586_587,plain,
! [X41,X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X41,X10,X3)
| ~ c_lessequals(X41,X12,X3)
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_587_588,plain,
! [X41,X12,X10,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X10,X41,X3)
| ~ c_lessequals(X12,X41,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_588_589,plain,
! [X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_589_590,plain,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_590_591,plain,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_591_592,plain,
! [X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_592_593,plain,
! [X7,X3] :
( X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_593_594,plain,
! [X6,X7,X3] :
( c_Set_Oinsert(X6,X7,X3) = X7
| ~ hBOOL(c_in(X6,X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_594_595,plain,
! [X13,X23,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X15,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,X23,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X23,X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_595_596,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_596_597,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_597_598,plain,
! [X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3)
| ~ c_lessequals(X6,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_598_599,plain,
! [X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_599_600,plain,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X7,X3),X7,X3))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_600_601,plain,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X7,X3),X7,X3))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_601_602,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_602_603,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_603_604,plain,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofinite(X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_604_605,plain,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X58,X15,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X15,X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_605_606,plain,
! [X15,X58,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X58,X15,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X15,X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_606_607,plain,
! [X6,X17,X3] :
( hBOOL(c_in(X6,c_Collect(X17,X3),X3))
| ~ hBOOL(hAPP(X17,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_607_608,plain,
! [X6,X7,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,X7,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X7,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_608_609,plain,
! [X6,X7,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X6,X7,X3),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X6),c_Complete__Lattice_OInf__class_OInf(X7,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_609_610,plain,
! [X10,X19,X3] :
( hBOOL(hAPP(X19,X10))
| ~ hBOOL(c_in(X10,X19,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_610_611,plain,
! [X6,X7,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X6,X7,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_611_612,axiom,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) != X11
| c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
c_0_264 ).
fof(c_0_612_613,plain,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) = X11
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_613_614,plain,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) = X7
| ~ c_lessequals(X11,X7,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_614_615,plain,
! [X10,X27,X17,X3] :
( hBOOL(hAPP(X27,X10))
| ~ hBOOL(hAPP(X17,X10))
| ~ c_lessequals(X17,X27,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_615_616,plain,
! [X10,X27,X17,X3] :
( hBOOL(hAPP(X27,X10))
| ~ c_lessequals(X17,X27,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X17,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_616_617,axiom,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X11 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_269 ).
fof(c_0_617_618,axiom,
! [X11,X7,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X7,X11,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_270 ).
fof(c_0_618_619,plain,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X11,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_619_620,plain,
! [X6,X2,X17] :
( c_Com_OWT(c_Com_Ocom_OBODY(X17))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X2,X17,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_620_621,plain,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X12,X10,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_621_622,plain,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X12,X10,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_622_623,plain,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X10,X12,X3)
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_623_624,plain,
! [X43,X44,X10,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X10,X10,X3) != c_HOL_Ominus__class_Ominus(X44,X43,X3)
| X44 = X43 ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_624_625,plain,
! [X12,X16,X10,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X16,X12,X3) != c_HOL_Ominus__class_Ominus(X10,X10,X3)
| X16 = X12 ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_625_626,axiom,
! [X65,X66,X8,X9,X67,X68] :
( c_Com_Ocom_OCall(X66,X9,X68) != c_Com_Ocom_OCall(X65,X8,X67)
| X68 = X67 ),
c_0_278 ).
fof(c_0_626_627,axiom,
! [X65,X66,X8,X9,X67,X68] :
( c_Com_Ocom_OCall(X66,X9,X68) != c_Com_Ocom_OCall(X65,X8,X67)
| X9 = X8 ),
c_0_279 ).
fof(c_0_627_628,axiom,
! [X65,X66,X8,X9,X67,X68] :
( c_Com_Ocom_OCall(X66,X9,X68) != c_Com_Ocom_OCall(X65,X8,X67)
| X66 = X65 ),
c_0_280 ).
fof(c_0_628_629,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_629_630,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_630_631,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_631_632,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_632_633,plain,
! [X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X6,X6,X3) = c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_633_634,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3)) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_634_635,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X3) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_635_636,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_636_637,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_637_638,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_638_639,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_639_640,plain,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_Finite__Set_Ofinite(X11,X3)
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_640_641,plain,
! [X11,X7,X3] :
( c_Finite__Set_Ofinite(X7,X3)
| ~ c_lessequals(X7,X11,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_641_642,plain,
! [X10,X19,X3] :
( hBOOL(c_in(X10,X19,X3))
| ~ hBOOL(hAPP(X19,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_642_643,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) != X12
| c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_643_644,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = X10
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_644_645,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = X12
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_645_646,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) = X12
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_646_647,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) = X10
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_647_648,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) != X10
| c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_648_649,plain,
! [X6,X7,X3] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X6,X7,X3),X3)
| ~ c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_649_650,plain,
! [X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3)
| c_lessequals(X6,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_650_651,plain,
! [X18,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X6,X18,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(X6,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_651_652,plain,
! [X13,X15,X3] :
( c_Hoare__Mirabelle_Ohoare__valids(X15,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X15,X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_652_653,plain,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(c_fequal(X2,X3),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_653_654,plain,
! [X24,X6,X2] :
( c_Com_OWT(c_Com_Ocom_OCall(X2,X24,X6))
| ~ c_Com_OWT(c_Com_Ocom_OBODY(X24)) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_654_655,plain,
! [X12,X10,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X12,X10,X3)
| c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_655_656,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_656_657,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_657_658,plain,
! [X10,X17,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X17,X3)
| ~ hBOOL(hAPP(X17,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_658_659,plain,
! [X10,X17,X3] :
( c_Collect(X17,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X17,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_659_660,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X10) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_660_661,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X10) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_661_662,plain,
! [X11,X7,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X7,X11,X3) != c_Orderings_Obot__class_Obot(X3)
| X7 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_662_663,plain,
! [X11,X7,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X7,X11,X3) != c_Orderings_Obot__class_Obot(X3)
| X11 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_663_664,plain,
! [X25,X18,X6,X3] :
( hAPP(hAPP(X25,X6),X18) = hAPP(hAPP(X25,X18),X6)
| ~ c_OrderedGroup_Oab__semigroup__mult(X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_664_665,plain,
! [X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_665_666,plain,
! [X10,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Orderings_Obot__class_Obot(X3)),X10) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_666_667,plain,
! [X20] :
( ~ class_Orderings_Obot(X20)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X20)),v_x) = c_Orderings_Obot__class_Obot(X20) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_667_668,plain,
! [X10,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),c_Orderings_Obot__class_Obot(X3)) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_668_669,plain,
! [X10,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X10,X3) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_669_670,plain,
! [X10,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Orderings_Obot__class_Obot(X3),X3) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_670,plain,
! [X10,X3] :
( ~ class_Orderings_Obot(X3)
| c_lessequals(c_Orderings_Obot__class_Obot(X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_671,plain,
! [X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X10,X3) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_672,plain,
! [X10,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X10,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_673,plain,
! [X10,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X10,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_674,plain,
! [X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X10),X10) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_675,axiom,
! [X62,X6,X3] :
( c_Option_Ooption_OSome(X6,X3) != c_Option_Ooption_OSome(X62,X3)
| X6 = X62 ),
c_0_328 ).
fof(c_0_676,plain,
! [X24,X18] :
( hAPP(c_Com_Obody,X24) != c_Option_Ooption_OSome(X18,tc_Com_Ocom)
| ~ c_Com_OWT__bodies
| c_Com_OWT(X18) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_677,plain,
! [X5,X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X5,X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4)
| ~ class_Finite__Set_Ofinite_Ofinite(X5) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_678,plain,
! [X5,X4] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X5,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_679,plain,
! [X5,X4] :
( class_Lattices_Oupper__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_680,plain,
! [X5,X4] :
( class_Lattices_Olower__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_681,plain,
! [X5,X4] :
( class_Lattices_Odistrib__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_682,plain,
! [X5,X4] :
( class_Lattices_Obounded__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Obounded__lattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_683,plain,
! [X5,X4] :
( class_Orderings_Opreorder(tc_fun(X5,X4))
| ~ class_Orderings_Opreorder(X4) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_684,plain,
! [X5,X4] :
( class_Lattices_Olattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_685,plain,
! [X5,X4] :
( class_Orderings_Oorder(tc_fun(X5,X4))
| ~ class_Orderings_Oorder(X4) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_686,plain,
! [X5,X4] :
( class_Orderings_Obot(tc_fun(X5,X4))
| ~ class_Orderings_Obot(X4) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_687,plain,
! [X5,X4] :
( class_HOL_Ominus(tc_fun(X5,X4))
| ~ class_HOL_Ominus(X4) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_688,plain,
! [X5,X4] :
( class_HOL_Oord(tc_fun(X5,X4))
| ~ class_HOL_Oord(X4) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_689,axiom,
! [X24] :
( c_Com_OWT(c_Com_Ocom_OBODY(X24))
| hAPP(c_Com_Obody,X24) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
c_0_342 ).
fof(c_0_690,plain,
! [X7,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_691,plain,
! [X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_692,axiom,
! [X8,X9] :
( c_Com_Ocom_OBODY(X9) != c_Com_Ocom_OBODY(X8)
| X9 = X8 ),
c_0_345 ).
fof(c_0_693,axiom,
! [X16,X10] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| X10 = X16 ),
c_0_346 ).
fof(c_0_694,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
( hAPP(X50,c_Set_Oinsert(X48,c_Set_Oinsert(X47,c_Orderings_Obot__class_Obot(tc_fun(X51,tc_bool)),X51),X51)) = hAPP(hAPP(X45,X48),X47)
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X43,X44,X45,X42,X46,X41,X51) ),
inference(variable_rename,[status(thm)],[c_0_347]) ).
fof(c_0_695,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
( hAPP(X49,c_Set_Oinsert(X48,c_Set_Oinsert(X47,c_Orderings_Obot__class_Obot(tc_fun(X51,tc_bool)),X51),X51)) = hAPP(hAPP(X42,X48),X47)
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X43,X44,X45,X42,X46,X41,X51) ),
inference(variable_rename,[status(thm)],[c_0_348]) ).
fof(c_0_696,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
( hBOOL(hAPP(hAPP(X44,hAPP(X49,X50)),X41))
| ~ hBOOL(c_in(X41,X50,X51))
| ~ c_Complete__Lattice_Ocomplete__lattice(X49,X48,X44,X45,X46,X43,X47,X42,X51) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_349])])]) ).
fof(c_0_697,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
( hBOOL(hAPP(hAPP(X44,X41),hAPP(X48,X50)))
| ~ hBOOL(c_in(X41,X50,X51))
| ~ c_Complete__Lattice_Ocomplete__lattice(X49,X48,X44,X45,X46,X43,X47,X42,X51) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_350])])]) ).
fof(c_0_698,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49,X50] :
( hAPP(X49,c_Set_Oinsert(X47,c_Orderings_Obot__class_Obot(tc_fun(X50,tc_bool)),X50)) = X47
| ~ c_Complete__Lattice_Ocomplete__lattice(X49,X48,X43,X44,X45,X42,X46,X41,X50) ),
inference(variable_rename,[status(thm)],[c_0_351]) ).
fof(c_0_699,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49,X50] :
( hAPP(X48,c_Set_Oinsert(X47,c_Orderings_Obot__class_Obot(tc_fun(X50,tc_bool)),X50)) = X47
| ~ c_Complete__Lattice_Ocomplete__lattice(X49,X48,X43,X44,X45,X42,X46,X41,X50) ),
inference(variable_rename,[status(thm)],[c_0_352]) ).
fof(c_0_700,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
( hAPP(X49,c_Set_Oinsert(X47,X50,X51)) = hAPP(hAPP(X45,X47),hAPP(X49,X50))
| ~ c_Complete__Lattice_Ocomplete__lattice(X49,X48,X43,X44,X45,X42,X46,X41,X51) ),
inference(variable_rename,[status(thm)],[c_0_353]) ).
fof(c_0_701,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
( hAPP(X48,c_Set_Oinsert(X47,X50,X51)) = hAPP(hAPP(X42,X47),hAPP(X48,X50))
| ~ c_Complete__Lattice_Ocomplete__lattice(X49,X48,X43,X44,X45,X42,X46,X41,X51) ),
inference(variable_rename,[status(thm)],[c_0_354]) ).
fof(c_0_702,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49] :
( hAPP(X48,c_Orderings_Obot__class_Obot(tc_fun(X49,tc_bool))) = X41
| ~ c_Complete__Lattice_Ocomplete__lattice(X48,X47,X43,X44,X45,X42,X46,X41,X49) ),
inference(variable_rename,[status(thm)],[c_0_355]) ).
fof(c_0_703,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49] :
( hAPP(X47,c_Orderings_Obot__class_Obot(tc_fun(X49,tc_bool))) = X46
| ~ c_Complete__Lattice_Ocomplete__lattice(X48,X47,X43,X44,X45,X42,X46,X41,X49) ),
inference(variable_rename,[status(thm)],[c_0_356]) ).
fof(c_0_704,plain,
! [X26,X27,X28,X29,X30,X31] :
( c_Finite__Set_Ofold__graph(X27,X29,c_Set_Oinsert(X28,c_HOL_Ominus__class_Ominus(X30,c_Set_Oinsert(X29,c_Orderings_Obot__class_Obot(tc_fun(X31,tc_bool)),X31),tc_fun(X31,tc_bool)),X31),X26,X31,X31)
| hBOOL(c_in(X28,X30,X31))
| ~ hBOOL(c_in(X29,X30,X31))
| ~ c_Finite__Set_Ofold__graph(X27,X28,X30,X26,X31,X31)
| ~ c_OrderedGroup_Oab__semigroup__mult(X27,X31) ),
inference(variable_rename,[status(thm)],[c_0_357]) ).
fof(c_0_705,plain,
! [X42,X43,X44,X45,X46,X47,X48] :
( c_Finite__Set_Ofold__graph(X45,X42,X46,hAPP(hAPP(X45,X44),X43),X48,X47)
| ~ hBOOL(c_in(X44,X46,X48))
| ~ c_Finite__Set_Ofold__graph(X45,X42,c_HOL_Ominus__class_Ominus(X46,c_Set_Oinsert(X44,c_Orderings_Obot__class_Obot(tc_fun(X48,tc_bool)),X48),tc_fun(X48,tc_bool)),X43,X48,X47) ),
inference(variable_rename,[status(thm)],[c_0_358]) ).
fof(c_0_706,plain,
! [X42,X43,X44,X45,X46,X47] :
( c_Finite__Set_Ofold__graph(X44,X42,c_Set_Oinsert(X45,X46,X47),hAPP(hAPP(X44,X42),X43),X47,X47)
| hBOOL(c_in(X45,X46,X47))
| ~ c_Finite__Set_Ofold__graph(X44,X45,X46,X43,X47,X47)
| ~ c_OrderedGroup_Oab__semigroup__mult(X44,X47) ),
inference(variable_rename,[status(thm)],[c_0_359]) ).
fof(c_0_707,plain,
! [X42,X43,X44,X45,X46,X47,X48] :
( c_Finite__Set_Ofold__graph(X45,X42,c_Set_Oinsert(X44,X46,X48),hAPP(hAPP(X45,X44),X43),X48,X47)
| ~ c_Finite__Set_Ofold__graph(X45,X42,X46,X43,X48,X47)
| hBOOL(c_in(X44,X46,X48)) ),
inference(variable_rename,[status(thm)],[c_0_360]) ).
fof(c_0_708,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28,c_Set_Oinsert(X29,X30,X31),X31),X27))
| hBOOL(c_in(X29,X30,X31))
| ~ c_Finite__Set_Ofold__graph(X28,X29,X30,X27,X31,X31) ),
inference(variable_rename,[status(thm)],[c_0_361]) ).
fof(c_0_709,plain,
! [X42,X43,X44,X45,X46] :
( X43 = X42
| ~ c_Finite__Set_Ofold__graph(X44,X42,c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool)),X43,X46,X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_362])])]) ).
fof(c_0_710,plain,
! [X42,X43,X44,X45,X46,X47] :
( c_Finite__Set_Ofinite(X45,X47)
| ~ c_Finite__Set_Ofold__graph(X44,X42,X45,X43,X47,X46) ),
inference(variable_rename,[status(thm)],[c_0_363]) ).
fof(c_0_711,plain,
! [X28,X29,X30,X31,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X31,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,c_Com_Ocom_OBODY(X28),X29,X32),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X32),tc_bool)),tc_Hoare__Mirabelle_Otriple(X32)),X32)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,c_Com_Ocom_OBODY(X28),X29,X32),X31,tc_Hoare__Mirabelle_Otriple(X32)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,c_Option_Othe(hAPP(c_Com_Obody,X28),tc_Com_Ocom),X29,X32),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X32),tc_bool)),tc_Hoare__Mirabelle_Otriple(X32)),X32) ),
inference(variable_rename,[status(thm)],[c_0_364]) ).
fof(c_0_712,plain,
! [X28,X29,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,X28,X29,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,X28,X29,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X28),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(variable_rename,[status(thm)],[c_0_365]) ).
fof(c_0_713,plain,
! [X28,X29,X30,X31,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X31,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,c_Com_Ocom_OBODY(X28),X29,X32),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X32),tc_bool)),tc_Hoare__Mirabelle_Otriple(X32)),X32)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X31,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X30,c_Option_Othe(hAPP(c_Com_Obody,X28),tc_Com_Ocom),X29,X32),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X32),tc_bool)),tc_Hoare__Mirabelle_Otriple(X32)),X32) ),
inference(variable_rename,[status(thm)],[c_0_366]) ).
fof(c_0_714,plain,
! [X27,X28,X29,X30,X31] :
( hAPP(X27,X29) = X28
| ~ hBOOL(c_in(X29,c_Set_Ovimage(X27,c_Set_Oinsert(X28,c_Orderings_Obot__class_Obot(tc_fun(X30,tc_bool)),X30),X31,X30),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_367])])]) ).
fof(c_0_715,plain,
! [X58,X59,X60,X61,X62] :
( c_Map_Omap__le(c_Map_Omap__add(X60,X59,X62,X61),X58,X62,X61)
| ~ c_Map_Omap__le(X60,c_Map_Omap__add(X60,X59,X62,X61),X62,X61)
| ~ c_Map_Omap__le(X59,X58,X62,X61)
| ~ c_Map_Omap__le(X60,X58,X62,X61) ),
inference(variable_rename,[status(thm)],[c_0_368]) ).
fof(c_0_716,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(c_in(hAPP(X27,X28),X29,X30))
| ~ hBOOL(c_in(X28,c_Set_Ovimage(X27,X29,X31,X30),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_369])])]) ).
fof(c_0_717,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(c_in(hAPP(X27,X28),X29,X30))
| ~ hBOOL(c_in(X28,c_Set_Ovimage(X27,X29,X31,X30),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_370])])]) ).
fof(c_0_718,plain,
! [X27,X28,X29,X30] :
( X29 = X28
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X27,c_Set_Oinsert(X29,c_Orderings_Obot__class_Obot(tc_fun(X30,tc_bool)),X30),X30),X28)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_371])])]) ).
fof(c_0_719,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(hAPP(X29,hAPP(X28,X27)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X28,X29,X31,X30),X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_372])])]) ).
fof(c_0_720,plain,
! [X47,X48,X49,X50] :
( c_Map_Omap__add(X48,X47,X50,X49) = c_Map_Omap__add(X47,X48,X50,X49)
| ~ c_Map_Omap__le(X48,c_Map_Omap__add(X48,X47,X50,X49),X50,X49) ),
inference(variable_rename,[status(thm)],[c_0_373]) ).
fof(c_0_721,plain,
! [X21,X22,X23,X24,X25,X26] :
( hBOOL(c_in(X22,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24,X23,X25,tc_fun(X26,tc_bool)),X26))
| ~ hBOOL(c_in(X22,hAPP(X23,X21),X26))
| ~ hBOOL(c_in(X21,X24,X25)) ),
inference(variable_rename,[status(thm)],[c_0_374]) ).
fof(c_0_722,plain,
! [X21,X22,X23,X24,X25,X26] :
( hBOOL(c_in(X21,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24,X23,X26,tc_fun(X25,tc_bool)),X25))
| ~ hBOOL(c_in(X21,hAPP(X23,X22),X25))
| ~ hBOOL(c_in(X22,X24,X26)) ),
inference(variable_rename,[status(thm)],[c_0_375]) ).
fof(c_0_723,plain,
! [X47,X48,X49,X50] :
( c_Map_Omap__add(X48,X47,X50,X49) != c_Map_Omap__add(X47,X48,X50,X49)
| c_Map_Omap__le(X48,c_Map_Omap__add(X48,X47,X50,X49),X50,X49) ),
inference(variable_rename,[status(thm)],[c_0_376]) ).
fof(c_0_724,plain,
! [X25,X26] :
( c_Hoare__Mirabelle_Ohoare__derivs(X26,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X25)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X25)),X26,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Option_Othe(hAPP(c_Com_Obody,X25),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(variable_rename,[status(thm)],[c_0_377]) ).
fof(c_0_725,plain,
! [X21,X22,X23,X24,X25,X26] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24,X23,X26,tc_fun(X25,tc_bool)),X22))
| ~ hBOOL(hAPP(hAPP(X23,X21),X22))
| ~ hBOOL(c_in(X21,X24,X26)) ),
inference(variable_rename,[status(thm)],[c_0_378]) ).
fof(c_0_726,plain,
! [X21,X22,X23,X24,X25,X26] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24,X23,X26,tc_fun(X25,tc_bool)),X21))
| ~ hBOOL(hAPP(hAPP(X23,X22),X21))
| ~ hBOOL(c_in(X22,X24,X26)) ),
inference(variable_rename,[status(thm)],[c_0_379]) ).
fof(c_0_727,plain,
! [X58,X59,X60,X61,X62] :
( c_Map_Omap__le(X59,X58,X62,X61)
| ~ c_Map_Omap__le(c_Map_Omap__add(X60,X59,X62,X61),X58,X62,X61) ),
inference(variable_rename,[status(thm)],[c_0_380]) ).
fof(c_0_728,plain,
! [X12,X13,X14,X15] :
( c_lessequals(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool))
| ~ hBOOL(c_in(X12,X14,X15))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X14,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),tc_fun(X15,tc_bool)),X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_381]) ).
fof(c_0_729,plain,
! [X12,X13,X14,X15] :
( c_lessequals(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool))
| ~ hBOOL(c_in(X12,X14,X15))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X14,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),tc_fun(X15,tc_bool)),X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_382]) ).
fof(c_0_730,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(c_in(X28,c_Set_Ovimage(X27,X29,X31,X30),X31))
| ~ hBOOL(c_in(hAPP(X27,X28),X29,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_383])])]) ).
fof(c_0_731,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(c_in(X28,c_Set_Ovimage(X27,X29,X30,X31),X30))
| ~ hBOOL(c_in(hAPP(X27,X28),X29,X31)) ),
inference(variable_rename,[status(thm)],[c_0_384]) ).
fof(c_0_732,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(c_in(X28,c_Set_Ovimage(X27,X29,X30,X31),X30))
| ~ hBOOL(c_in(hAPP(X27,X28),X29,X31)) ),
inference(variable_rename,[status(thm)],[c_0_385]) ).
fof(c_0_733,plain,
! [X18,X19,X20,X21] :
( hBOOL(c_in(X18,X20,X21))
| ~ hBOOL(c_in(X18,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X21,tc_bool)),X20),c_Collect(X19,X21)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_386]) ).
fof(c_0_734,plain,
! [X12,X13,X14,X15] :
( c_lessequals(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,X13,tc_fun(X15,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X14,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),tc_fun(X15,tc_bool)),X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_387]) ).
fof(c_0_735,plain,
! [X62,X63,X64,X65,X66] :
( ~ hBOOL(c_in(X62,X64,X65))
| hBOOL(c_in(hAPP(X63,X62),c_Set_Oimage(X63,X64,X65,X66),X66)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_388])])]) ).
fof(c_0_736,plain,
! [X27,X28,X29,X30,X31] :
( ~ hBOOL(c_in(X27,X29,X30))
| hBOOL(c_in(hAPP(X28,X27),c_Set_Oimage(X28,X29,X30,X31),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_389])])]) ).
fof(c_0_737,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(c_in(hAPP(X28,X27),c_Set_Oimage(X28,X29,X30,X31),X31))
| ~ hBOOL(c_in(X27,X29,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_390])])]) ).
fof(c_0_738,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(c_in(hAPP(X28,X27),c_Set_Oimage(X28,X29,X31,X30),X30))
| ~ hBOOL(c_in(X27,X29,X31)) ),
inference(variable_rename,[status(thm)],[c_0_391]) ).
fof(c_0_739,plain,
! [X61,X62,X63,X64] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X64,tc_bool)),c_Map_Odom(X62,X64,X63)),c_Map_Odom(X61,X64,X63)) != c_Orderings_Obot__class_Obot(tc_fun(X64,tc_bool))
| c_Map_Omap__add(X62,X61,X64,X63) = c_Map_Omap__add(X61,X62,X64,X63) ),
inference(variable_rename,[status(thm)],[c_0_392]) ).
fof(c_0_740,plain,
! [X18,X19,X20,X21] :
( hBOOL(hAPP(X19,X18))
| ~ hBOOL(c_in(X18,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X21,tc_bool)),X20),c_Collect(X19,X21)),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_393])])]) ).
fof(c_0_741,plain,
! [X64,X65,X66,X67,X68,X69] :
( c_lessequals(hAPP(X67,X64),X66,tc_fun(X69,tc_bool))
| ~ hBOOL(c_in(X64,X65,X68))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X65,X67,X68,tc_fun(X69,tc_bool)),X66,tc_fun(X69,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_394]) ).
fof(c_0_742,plain,
! [X27,X28,X29,X30,X31,X32] :
( hBOOL(c_in(hAPP(X28,X27),X29,X32))
| ~ hBOOL(c_in(X27,X30,X31))
| ~ c_lessequals(c_Set_Oimage(X28,X30,X31,X32),X29,tc_fun(X32,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_395]) ).
fof(c_0_743,plain,
! [X27,X28,X29,X30,X31] :
( c_lessequals(c_Set_Ovimage(X27,X29,X30,X31),c_Set_Ovimage(X27,X28,X30,X31),tc_fun(X30,tc_bool))
| ~ c_lessequals(X29,X28,tc_fun(X31,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_396]) ).
fof(c_0_744,plain,
! [X27,X28,X29,X30,X31] :
( c_lessequals(c_Set_Oimage(X27,X29,X31,X30),c_Set_Oimage(X27,X28,X31,X30),tc_fun(X30,tc_bool))
| ~ c_lessequals(X29,X28,tc_fun(X31,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_397]) ).
fof(c_0_745,plain,
! [X27,X28,X29,X30,X31] :
( ~ c_lessequals(X27,X29,tc_fun(X30,tc_bool))
| c_lessequals(c_Set_Oimage(X28,X27,X30,X31),c_Set_Oimage(X28,X29,X30,X31),tc_fun(X31,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_398])])]) ).
fof(c_0_746,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,X24,X26))
| ~ hBOOL(c_in(X23,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X26,tc_bool)),X25),X24),X26)) ),
inference(variable_rename,[status(thm)],[c_0_399]) ).
fof(c_0_747,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,X25,X26))
| ~ hBOOL(c_in(X23,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X26,tc_bool)),X25),X24),X26)) ),
inference(variable_rename,[status(thm)],[c_0_400]) ).
fof(c_0_748,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(hAPP(c_Set_Ovimage(X28,X29,X31,X30),X27))
| ~ hBOOL(hAPP(X29,hAPP(X28,X27))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_401])])]) ).
fof(c_0_749,plain,
! [X12,X13,X14,X15] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X14,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),tc_fun(X15,tc_bool)),X13,tc_fun(X15,tc_bool))
| ~ hBOOL(c_in(X12,X14,X15))
| ~ c_lessequals(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_402]) ).
fof(c_0_750,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olattice(X45)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X44,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42),X45),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),c_Lattices_Oupper__semilattice__class_Osup(X44,X43,X45)),c_Lattices_Oupper__semilattice__class_Osup(X44,X42,X45)),X45) ),
inference(variable_rename,[status(thm)],[c_0_403]) ).
fof(c_0_751,plain,
! [X43,X44,X45,X46] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),X44),X43,tc_fun(X46,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),c_Lattices_Oupper__semilattice__class_Osup(X44,X43,tc_fun(X46,tc_bool)))
| c_lessequals(X43,X45,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_404]) ).
fof(c_0_752,plain,
! [X21,X22,X23,X24,X25] :
( c_Finite__Set_Ofinite(hAPP(X22,X21),X24)
| ~ hBOOL(c_in(X21,X23,X25))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23,X22,X25,tc_fun(X24,tc_bool)),X24)
| ~ c_Finite__Set_Ofinite(X23,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_405])])]) ).
fof(c_0_753,plain,
! [X64,X65,X66,X67,X68] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X66,X64),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X65,X66,X68,tc_fun(X67,tc_bool)),tc_fun(X67,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X65,X66,X68,tc_fun(X67,tc_bool))
| ~ hBOOL(c_in(X64,X65,X68)) ),
inference(variable_rename,[status(thm)],[c_0_406]) ).
fof(c_0_754,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X26,tc_bool)),X25),X24),X26))
| ~ hBOOL(c_in(X23,X24,X26))
| ~ hBOOL(c_in(X23,X25,X26)) ),
inference(variable_rename,[status(thm)],[c_0_407]) ).
fof(c_0_755,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X26,tc_bool)),X25),X24),X26))
| ~ hBOOL(c_in(X23,X24,X26))
| ~ hBOOL(c_in(X23,X25,X26)) ),
inference(variable_rename,[status(thm)],[c_0_408]) ).
fof(c_0_756,plain,
! [X31,X32,X33,X34,X35] :
( hAPP(c_Map_Omap__add(X33,X32,X35,X34),X31) = hAPP(X32,X31)
| ~ hBOOL(c_in(X31,c_Map_Odom(X32,X35,X34),X35)) ),
inference(variable_rename,[status(thm)],[c_0_409]) ).
fof(c_0_757,plain,
! [X65,X66,X67,X68,X69] :
( c_Map_Omap__le(X67,X65,X69,X68)
| ~ c_Map_Omap__le(X66,X65,X69,X68)
| ~ c_Map_Omap__le(X67,X66,X69,X68) ),
inference(variable_rename,[status(thm)],[c_0_410]) ).
fof(c_0_758,plain,
! [X18,X19,X20,X21] :
( hBOOL(c_in(X18,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X21,tc_bool)),X20),c_Collect(X19,X21)),X21))
| ~ hBOOL(hAPP(X19,X18))
| ~ hBOOL(c_in(X18,X20,X21)) ),
inference(variable_rename,[status(thm)],[c_0_411]) ).
fof(c_0_759,plain,
! [X27,X28,X29,X30,X31] :
( c_Set_Oinsert(hAPP(X28,X27),c_Set_Oimage(X28,X29,X31,X30),X30) = c_Set_Oimage(X28,X29,X31,X30)
| ~ hBOOL(c_in(X27,X29,X31)) ),
inference(variable_rename,[status(thm)],[c_0_412]) ).
fof(c_0_760,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(X13,X12))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X15,tc_bool)),X14),X13),X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_413])])]) ).
fof(c_0_761,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(X14,X12))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X15,tc_bool)),X14),X13),X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_414])])]) ).
fof(c_0_762,plain,
! [X26,X27,X28,X29] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X29,tc_bool)),X28),X27) != c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))
| X27 = c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))
| ~ c_Finite__Set_Ofinite(X27,X29)
| X28 = c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))
| ~ c_Finite__Set_Ofinite(X28,X29)
| ~ c_OrderedGroup_Oab__semigroup__mult(X26,X29)
| c_Finite__Set_Ofold1(X26,c_Lattices_Oupper__semilattice__class_Osup(X28,X27,tc_fun(X29,tc_bool)),X29) = hAPP(hAPP(X26,c_Finite__Set_Ofold1(X26,X28,X29)),c_Finite__Set_Ofold1(X26,X27,X29)) ),
inference(variable_rename,[status(thm)],[c_0_415]) ).
fof(c_0_763,plain,
! [X13,X14,X15] :
( X13 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),X15)
| ~ hBOOL(hAPP(c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),X13)) ),
inference(variable_rename,[status(thm)],[c_0_416]) ).
fof(c_0_764,plain,
! [X27,X28,X29,X30,X31] :
( c_Finite__Set_Ofinite(X28,X30)
| ~ c_lessequals(X28,c_Set_Oimage(X27,X29,X31,X30),tc_fun(X30,tc_bool))
| ~ c_Finite__Set_Ofinite(X29,X31) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_417])])]) ).
fof(c_0_765,plain,
! [X33,X34,X35,X36,X37] :
( hAPP(X35,X33) = hAPP(X34,X33)
| ~ hBOOL(c_in(X33,c_Map_Odom(X35,X37,X36),X37))
| ~ c_Map_Omap__le(X35,X34,X37,X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_418])])]) ).
fof(c_0_766,plain,
! [X23,X24] :
( c_Hoare__Mirabelle_Ohoare__derivs(X24,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X23)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X24,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X24))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(variable_rename,[status(thm)],[c_0_419]) ).
fof(c_0_767,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olattice(X45)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),X43),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),X42),X45),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),c_Lattices_Oupper__semilattice__class_Osup(X43,X42,X45)),X45) ),
inference(variable_rename,[status(thm)],[c_0_420]) ).
fof(c_0_768,plain,
! [X46,X47,X48,X49,X50] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X50,tc_bool)),X49),X48),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X50,tc_bool)),X47),X46),tc_fun(X50,tc_bool))
| ~ c_lessequals(X48,X46,tc_fun(X50,tc_bool))
| ~ c_lessequals(X49,X47,tc_fun(X50,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_421]) ).
fof(c_0_769,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,X24,X26))
| hBOOL(c_in(X23,X25,X26))
| ~ hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X25,X24,tc_fun(X26,tc_bool)),X26)) ),
inference(variable_rename,[status(thm)],[c_0_422]) ).
fof(c_0_770,plain,
! [X49,X50,X51,X52,X53,X54] :
( hAPP(c_Map_Omap__add(X51,X50,X53,X54),X52) != c_Option_Ooption_OSome(X49,X54)
| hAPP(X51,X52) = c_Option_Ooption_OSome(X49,X54)
| hAPP(X50,X52) = c_Option_Ooption_OSome(X49,X54) ),
inference(variable_rename,[status(thm)],[c_0_423]) ).
fof(c_0_771,plain,
! [X43,X44,X45,X46] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),c_Set_Oinsert(X43,X45,X46)),X44) = c_Set_Oinsert(X43,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),X44),X46)
| ~ hBOOL(c_in(X43,X44,X46)) ),
inference(variable_rename,[status(thm)],[c_0_424]) ).
fof(c_0_772,plain,
! [X49,X50,X51,X52,X53,X54] :
( hAPP(c_Map_Omap__add(X51,X50,X53,X54),X52) != c_Option_Ooption_OSome(X49,X54)
| hAPP(X50,X52) = c_Option_Ooption_ONone(X54)
| hAPP(X50,X52) = c_Option_Ooption_OSome(X49,X54) ),
inference(variable_rename,[status(thm)],[c_0_425]) ).
fof(c_0_773,plain,
! [X31,X32,X33,X34,X35] :
( hAPP(c_Map_Omap__add(X33,X32,X35,X34),X31) = hAPP(X33,X31)
| hBOOL(c_in(X31,c_Map_Odom(X32,X35,X34),X35)) ),
inference(variable_rename,[status(thm)],[c_0_426]) ).
fof(c_0_774,plain,
! [X31,X32,X33,X34,X35] :
( hAPP(c_Map_Omap__add(X33,X32,X35,X34),X31) = hAPP(X32,X31)
| hBOOL(c_in(X31,c_Map_Odom(X33,X35,X34),X35)) ),
inference(variable_rename,[status(thm)],[c_0_427]) ).
fof(c_0_775,plain,
! [X19,X20,X21] :
( X19 = X20
| ~ hBOOL(c_in(X19,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_428])])]) ).
fof(c_0_776,plain,
! [X23,X24,X25,X26,X27] :
( c_Set_Oinsert(X26,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27) != c_Set_Oinsert(X24,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27)
| X25 = X24
| X25 = X23 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_429])])]) ).
fof(c_0_777,plain,
! [X23,X24,X25,X26,X27] :
( c_Set_Oinsert(X26,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27) != c_Set_Oinsert(X24,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27)
| X26 = X23
| X25 = X23 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_430])])]) ).
fof(c_0_778,plain,
! [X23,X24,X25,X26,X27] :
( c_Set_Oinsert(X26,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27) != c_Set_Oinsert(X24,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27)
| X25 = X24
| X26 = X24 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_431])])]) ).
fof(c_0_779,plain,
! [X23,X24,X25,X26,X27] :
( c_Set_Oinsert(X26,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27) != c_Set_Oinsert(X24,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27)
| X26 = X23
| X26 = X24 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_432])])]) ).
fof(c_0_780,plain,
! [X23,X24,X25,X26] :
( ~ hBOOL(c_in(X23,X24,X26))
| ~ hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X25,X24,tc_fun(X26,tc_bool)),X26)) ),
inference(variable_rename,[status(thm)],[c_0_433]) ).
fof(c_0_781,plain,
! [X49,X50,X51,X52,X53] :
( hAPP(c_Map_Omap__add(X50,X49,X52,X53),X51) != c_Option_Ooption_ONone(X53)
| hAPP(X50,X51) = c_Option_Ooption_ONone(X53) ),
inference(variable_rename,[status(thm)],[c_0_434]) ).
fof(c_0_782,plain,
! [X49,X50,X51,X52,X53] :
( hAPP(c_Map_Omap__add(X50,X49,X52,X53),X51) != c_Option_Ooption_ONone(X53)
| hAPP(X49,X51) = c_Option_Ooption_ONone(X53) ),
inference(variable_rename,[status(thm)],[c_0_435]) ).
fof(c_0_783,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(hAPP(X22,X21),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23,X22,X25,tc_fun(X24,tc_bool)),tc_fun(X24,tc_bool))
| ~ hBOOL(c_in(X21,X23,X25)) ),
inference(variable_rename,[status(thm)],[c_0_436]) ).
fof(c_0_784,plain,
! [X8,X9,X10] :
( c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X9,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),tc_fun(X10,tc_bool)),X10) = X9
| ~ hBOOL(c_in(X8,X9,X10)) ),
inference(variable_rename,[status(thm)],[c_0_437]) ).
fof(c_0_785,plain,
! [X47,X48,X49,X50] :
( X48 = X47
| ~ c_Map_Omap__le(X47,X48,X50,X49)
| ~ c_Map_Omap__le(X48,X47,X50,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_438])])]) ).
fof(c_0_786,plain,
! [X43,X44,X45,X46] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),X44),X43,tc_fun(X46,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),c_Lattices_Oupper__semilattice__class_Osup(X44,X43,tc_fun(X46,tc_bool)))
| ~ c_lessequals(X43,X45,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_439]) ).
fof(c_0_787,plain,
! [X55,X56,X57,X58,X59,X60,X61] :
( c_Hoare__Mirabelle_Otriple_Otriple(X58,X60,X56,X61) != c_Hoare__Mirabelle_Otriple_Otriple(X57,X59,X55,X61)
| X58 = X57 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_440])])]) ).
fof(c_0_788,plain,
! [X55,X56,X57,X58,X59,X60,X61] :
( c_Hoare__Mirabelle_Otriple_Otriple(X58,X60,X56,X61) != c_Hoare__Mirabelle_Otriple_Otriple(X57,X59,X55,X61)
| X60 = X59 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_441])])]) ).
fof(c_0_789,plain,
! [X55,X56,X57,X58,X59,X60,X61] :
( c_Hoare__Mirabelle_Otriple_Otriple(X58,X60,X56,X61) != c_Hoare__Mirabelle_Otriple_Otriple(X57,X59,X55,X61)
| X56 = X55 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_442])])]) ).
fof(c_0_790,plain,
! [X16,X17,X18,X19] :
( c_Hoare__Mirabelle_Ohoare__derivs(X18,c_Set_Oinsert(X17,X16,tc_Hoare__Mirabelle_Otriple(X19)),X19)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X18,X16,X19)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X19),tc_bool)),tc_Hoare__Mirabelle_Otriple(X19)),X19) ),
inference(variable_rename,[status(thm)],[c_0_443]) ).
fof(c_0_791,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,X25,X26))
| ~ hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X25,X24,tc_fun(X26,tc_bool)),X26)) ),
inference(variable_rename,[status(thm)],[c_0_444]) ).
fof(c_0_792,plain,
! [X12,X13,X14,X15] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X15,tc_bool)),X14),c_Set_Oinsert(X12,X13,X15)) = c_Set_Oinsert(X12,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X15,tc_bool)),X14),X13),X15)
| ~ hBOOL(c_in(X12,X14,X15)) ),
inference(variable_rename,[status(thm)],[c_0_445]) ).
fof(c_0_793,plain,
! [X12,X13,X14,X15] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool)),X15)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool)),X15) ),
inference(variable_rename,[status(thm)],[c_0_446]) ).
fof(c_0_794,plain,
! [X70,X71,X72,X73,X74] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X73)
| c_lessequals(hAPP(X71,X70),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X72,X71,X74,X73),X73)
| ~ hBOOL(c_in(X70,X72,X74)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_447])])]) ).
fof(c_0_795,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X25,X24,tc_fun(X26,tc_bool)),X26))
| hBOOL(c_in(X23,X24,X26))
| ~ hBOOL(c_in(X23,X25,X26)) ),
inference(variable_rename,[status(thm)],[c_0_448]) ).
fof(c_0_796,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X25,X24,tc_fun(X26,tc_bool)),X26))
| hBOOL(c_in(X23,X24,X26))
| ~ hBOOL(c_in(X23,X25,X26)) ),
inference(variable_rename,[status(thm)],[c_0_449]) ).
fof(c_0_797,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X15,tc_bool)),X14),X13),X12))
| ~ hBOOL(hAPP(X13,X12))
| ~ hBOOL(hAPP(X14,X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_450])])]) ).
fof(c_0_798,plain,
! [X21,X22,X23,X24,X25] :
( c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23,X22,X24,tc_fun(X25,tc_bool))
| hAPP(X22,X21) = c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool))
| ~ hBOOL(c_in(X21,X23,X24)) ),
inference(variable_rename,[status(thm)],[c_0_451]) ).
fof(c_0_799,plain,
! [X21,X22,X23,X24,X25] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23,X22,X24,tc_fun(X25,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool))
| hAPP(X22,X21) = c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool))
| ~ hBOOL(c_in(X21,X23,X24)) ),
inference(variable_rename,[status(thm)],[c_0_452]) ).
fof(c_0_800,plain,
! [X47,X48,X49,X50] :
( c_lessequals(c_Map_Odom(X48,X50,X49),c_Map_Odom(X47,X50,X49),tc_fun(X50,tc_bool))
| ~ c_Map_Omap__le(X48,X47,X50,X49) ),
inference(variable_rename,[status(thm)],[c_0_453]) ).
fof(c_0_801,plain,
! [X43,X44,X45,X46] :
( c_lessequals(X43,X44,tc_fun(X46,tc_bool))
| ~ c_lessequals(X43,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),X44),tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_454]) ).
fof(c_0_802,plain,
! [X43,X44,X45,X46] :
( c_lessequals(X43,X45,tc_fun(X46,tc_bool))
| ~ c_lessequals(X43,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),X44),tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_455]) ).
fof(c_0_803,plain,
! [X12,X13,X14,X15] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool)),X15)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool)),X15) ),
inference(variable_rename,[status(thm)],[c_0_456]) ).
fof(c_0_804,plain,
! [X23,X24] :
( c_Hoare__Mirabelle_Ohoare__derivs(X24,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X23)
| hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X24),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(variable_rename,[status(thm)],[c_0_457]) ).
fof(c_0_805,plain,
! [X46,X47,X48,X49,X50] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X49,X48,tc_fun(X50,tc_bool)),c_HOL_Ominus__class_Ominus(X47,X46,tc_fun(X50,tc_bool)),tc_fun(X50,tc_bool))
| ~ c_lessequals(X46,X48,tc_fun(X50,tc_bool))
| ~ c_lessequals(X49,X47,tc_fun(X50,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_458]) ).
fof(c_0_806,plain,
! [X46,X47,X48,X49,X50] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X49,X48,tc_fun(X50,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X47,X46,tc_fun(X50,tc_bool)),tc_fun(X50,tc_bool))
| ~ c_lessequals(X48,X46,tc_fun(X50,tc_bool))
| ~ c_lessequals(X49,X47,tc_fun(X50,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_459]) ).
fof(c_0_807,plain,
! [X19,X20,X21,X22] :
( hBOOL(c_in(X20,X21,X22))
| X20 = X19
| ~ hBOOL(c_in(X20,c_Set_Oinsert(X19,X21,X22),X22)) ),
inference(variable_rename,[status(thm)],[c_0_460]) ).
fof(c_0_808,plain,
! [X12,X13,X14,X15] :
( ~ hBOOL(c_in(X12,X13,X15))
| ~ hBOOL(c_in(X12,X14,X15))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X15,tc_bool)),X14),X13) != c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_461]) ).
fof(c_0_809,plain,
! [X43,X44,X45,X46] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),c_Set_Oinsert(X43,X45,X46)),X44) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),X44)
| hBOOL(c_in(X43,X44,X46)) ),
inference(variable_rename,[status(thm)],[c_0_462]) ).
fof(c_0_810,plain,
! [X43,X44,X45,X46] :
( c_lessequals(X43,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),X44),tc_fun(X46,tc_bool))
| ~ c_lessequals(X43,X44,tc_fun(X46,tc_bool))
| ~ c_lessequals(X43,X45,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_463]) ).
fof(c_0_811,plain,
! [X43,X44,X45,X46] :
( c_lessequals(X43,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X46,tc_bool)),X45),X44),tc_fun(X46,tc_bool))
| ~ c_lessequals(X43,X44,tc_fun(X46,tc_bool))
| ~ c_lessequals(X43,X45,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_464]) ).
fof(c_0_812,plain,
! [X23,X24,X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| c_lessequals(X25,X23,X27)
| ~ c_lessequals(X26,X25,X27)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X27),c_SetInterval_Oord__class_OatLeastAtMost(X24,X23,X27),tc_fun(X27,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_465]) ).
fof(c_0_813,plain,
! [X23,X24,X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| c_lessequals(X24,X26,X27)
| ~ c_lessequals(X26,X25,X27)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X27),c_SetInterval_Oord__class_OatLeastAtMost(X24,X23,X27),tc_fun(X27,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_466]) ).
fof(c_0_814,plain,
! [X19,X20,X21] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X21)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21),X21),X21) = c_Lattices_Oupper__semilattice__class_Osup(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_467]) ).
fof(c_0_815,plain,
! [X19,X20,X21] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X21)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21),X21),X21) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X21),X20),X19) ),
inference(variable_rename,[status(thm)],[c_0_468]) ).
fof(c_0_816,plain,
! [X16,X17,X18,X19] :
( c_Hoare__Mirabelle_Ohoare__derivs(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X19),tc_bool)),tc_Hoare__Mirabelle_Otriple(X19)),X19)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X18,c_Set_Oinsert(X17,X16,tc_Hoare__Mirabelle_Otriple(X19)),X19) ),
inference(variable_rename,[status(thm)],[c_0_469]) ).
fof(c_0_817,plain,
! [X49,X50,X51,X52,X53,X54] :
( hAPP(X51,X52) != c_Option_Ooption_OSome(X49,X54)
| hAPP(X50,X52) != c_Option_Ooption_ONone(X54)
| hAPP(c_Map_Omap__add(X51,X50,X53,X54),X52) = c_Option_Ooption_OSome(X49,X54) ),
inference(variable_rename,[status(thm)],[c_0_470]) ).
fof(c_0_818,plain,
! [X43,X44,X45,X46] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X45,X44,tc_fun(X46,tc_bool)),X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(X45,c_Lattices_Oupper__semilattice__class_Osup(X44,X43,tc_fun(X46,tc_bool)),tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_471]) ).
fof(c_0_819,plain,
! [X43,X44,X45,X46] :
( c_lessequals(X45,c_Lattices_Oupper__semilattice__class_Osup(X44,X43,tc_fun(X46,tc_bool)),tc_fun(X46,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X45,X44,tc_fun(X46,tc_bool)),X43,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_472]) ).
fof(c_0_820,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X25,X24,tc_fun(X26,tc_bool)),X26))
| ~ hBOOL(c_in(X23,X25,X26)) ),
inference(variable_rename,[status(thm)],[c_0_473]) ).
fof(c_0_821,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X25,X24,tc_fun(X26,tc_bool)),X26))
| ~ hBOOL(c_in(X23,X24,X26)) ),
inference(variable_rename,[status(thm)],[c_0_474]) ).
fof(c_0_822,plain,
! [X11,X12,X13] :
( X12 = c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13)
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_475]) ).
fof(c_0_823,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(X13,X12))
| hBOOL(hAPP(X14,X12))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool)),X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_476])])]) ).
fof(c_0_824,plain,
! [X49,X50,X51,X52,X53] :
( hAPP(X50,X51) != c_Option_Ooption_ONone(X53)
| hAPP(X49,X51) != c_Option_Ooption_ONone(X53)
| hAPP(c_Map_Omap__add(X50,X49,X52,X53),X51) = c_Option_Ooption_ONone(X53) ),
inference(variable_rename,[status(thm)],[c_0_477]) ).
fof(c_0_825,plain,
! [X71,X72,X73,X74,X75,X76] :
( hAPP(X72,X74) != c_Option_Ooption_OSome(X71,X76)
| hAPP(c_Map_Omap__add(X73,X72,X75,X76),X74) = c_Option_Ooption_OSome(X71,X76) ),
inference(variable_rename,[status(thm)],[c_0_478]) ).
fof(c_0_826,plain,
! [X49,X50,X51,X52,X53,X54] :
( hAPP(X50,X52) != c_Option_Ooption_OSome(X49,X54)
| hAPP(c_Map_Omap__add(X51,X50,X53,X54),X52) = c_Option_Ooption_OSome(X49,X54) ),
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_827,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Olower__semilattice(X20)
| c_lessequals(X18,X17,X20)
| ~ hBOOL(c_in(X17,X19,X20))
| ~ c_lessequals(X18,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X20),X19,X20),X20)
| X19 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))
| ~ c_Finite__Set_Ofinite(X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_480]) ).
fof(c_0_828,plain,
! [X29,X30,X31,X32] :
( hAPP(X29,X30) != c_Option_Ooption_ONone(X31)
| ~ hBOOL(c_in(X30,c_Map_Odom(X29,X32,X31),X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_481])])]) ).
fof(c_0_829,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Odistrib__lattice(X45)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42),X44,X45) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),c_Lattices_Oupper__semilattice__class_Osup(X43,X44,X45)),c_Lattices_Oupper__semilattice__class_Osup(X42,X44,X45)) ),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_830,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Odistrib__lattice(X45)
| c_Lattices_Oupper__semilattice__class_Osup(X44,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42),X45) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),c_Lattices_Oupper__semilattice__class_Osup(X44,X43,X45)),c_Lattices_Oupper__semilattice__class_Osup(X44,X42,X45)) ),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_831,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Odistrib__lattice(X45)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),c_Lattices_Oupper__semilattice__class_Osup(X43,X42,X45)),X44) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X44),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X42),X44),X45) ),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_832,plain,
! [X59,X60,X61,X62] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X59,X60,X62,X61),X61)
| ~ c_Finite__Set_Ofinite(X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_485]) ).
fof(c_0_833,plain,
! [X11,X12,X13] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X11,X12,X13),c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)) = X12
| hBOOL(c_in(X11,X12,X13)) ),
inference(variable_rename,[status(thm)],[c_0_486]) ).
fof(c_0_834,plain,
! [X12,X13,X14,X15] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X15,tc_bool)),X14),c_Set_Oinsert(X12,X13,X15)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X15,tc_bool)),X14),X13)
| hBOOL(c_in(X12,X14,X15)) ),
inference(variable_rename,[status(thm)],[c_0_487]) ).
fof(c_0_835,plain,
! [X27,X28,X29,X30,X31] :
( hAPP(X28,X27) != c_Option_Ooption_ONone(X31)
| c_HOL_Ominus__class_Ominus(c_Map_Odom(X28,X30,X31),c_Set_Oinsert(X27,X29,X30),tc_fun(X30,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X28,X30,X31),X29,tc_fun(X30,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_488]) ).
fof(c_0_836,plain,
! [X12,X13,X14,X15] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X12,X14,X15),X13,tc_fun(X15,tc_bool)) = c_Set_Oinsert(X12,c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool)),X15)
| hBOOL(c_in(X12,X13,X15)) ),
inference(variable_rename,[status(thm)],[c_0_489]) ).
fof(c_0_837,plain,
! [X19,X20,X21,X22] :
( hBOOL(c_in(X20,c_Set_Oinsert(X19,X21,X22),X22))
| ~ hBOOL(c_in(X20,X21,X22)) ),
inference(variable_rename,[status(thm)],[c_0_490]) ).
fof(c_0_838,plain,
! [X19,X20,X21,X22] :
( hBOOL(c_in(X20,c_Set_Oinsert(X19,X21,X22),X22))
| ~ hBOOL(c_in(X20,X21,X22)) ),
inference(variable_rename,[status(thm)],[c_0_491]) ).
fof(c_0_839,plain,
! [X26,X27,X28,X29] :
( c_Finite__Set_Ofold1(X27,c_Set_Oinsert(X26,X28,X29),X29) = hAPP(hAPP(X27,X26),c_Finite__Set_Ofold1(X27,X28,X29))
| hBOOL(c_in(X26,X28,X29))
| ~ c_Finite__Set_Ofinite(X28,X29)
| X28 = c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X27,X29) ),
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_840,plain,
! [X12,X13,X14,X15] :
( c_lessequals(c_Set_Oinsert(X12,X14,X15),X13,tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,X13,tc_fun(X15,tc_bool))
| ~ hBOOL(c_in(X12,X13,X15)) ),
inference(variable_rename,[status(thm)],[c_0_493]) ).
fof(c_0_841,plain,
! [X12,X13,X14,X15] :
( c_lessequals(X14,X13,tc_fun(X15,tc_bool))
| hBOOL(c_in(X12,X14,X15))
| ~ c_lessequals(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_842,plain,
! [X12,X13,X14,X15] :
( c_lessequals(X14,X13,tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool))
| hBOOL(c_in(X12,X14,X15)) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_843,plain,
! [X43,X44,X45,X46] :
( c_HOL_Ominus__class_Ominus(X44,c_HOL_Ominus__class_Ominus(X43,X45,tc_fun(X46,tc_bool)),tc_fun(X46,tc_bool)) = X45
| ~ c_lessequals(X44,X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(X45,X44,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_844,plain,
! [X43,X44,X45,X46] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X44,tc_fun(X46,tc_bool)),X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(X44,X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(X45,X43,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_845,plain,
! [X43,X44,X45,X46] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X44,tc_fun(X46,tc_bool)),X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(X44,X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(X45,X43,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_846,plain,
! [X23,X24,X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X27),c_SetInterval_Oord__class_OatLeastAtMost(X24,X23,X27),tc_fun(X27,tc_bool))
| ~ c_lessequals(X25,X23,X27)
| ~ c_lessequals(X24,X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_499]) ).
fof(c_0_847,plain,
! [X27,X28,X29,X30] :
( c_Set_Oimage(X27,X28,X29,X30) != c_Orderings_Obot__class_Obot(tc_fun(X30,tc_bool))
| X28 = c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_500])])]) ).
fof(c_0_848,plain,
! [X27,X28,X29,X30] :
( c_Orderings_Obot__class_Obot(tc_fun(X30,tc_bool)) != c_Set_Oimage(X27,X28,X29,X30)
| X28 = c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_501])])]) ).
fof(c_0_849,plain,
! [X43,X44,X45,X46] :
( c_lessequals(X45,X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X44,tc_fun(X46,tc_bool)),X43,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_502]) ).
fof(c_0_850,plain,
! [X43,X44,X45,X46] :
( c_lessequals(X44,X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X44,tc_fun(X46,tc_bool)),X43,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_851,plain,
! [X12,X13,X14,X15] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X12,X14,X15),X13,tc_fun(X15,tc_bool)) = c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool))
| ~ hBOOL(c_in(X12,X13,X15)) ),
inference(variable_rename,[status(thm)],[c_0_504]) ).
fof(c_0_852,plain,
! [X47,X48,X49] :
( ~ class_Lattices_Olattice(X49)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X49)),X48),X47),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X49),hAPP(X48,v_x)),hAPP(X47,v_x)) ),
inference(variable_rename,[status(thm)],[c_0_505]) ).
fof(c_0_853,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Odistrib__lattice(X45)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),c_Lattices_Oupper__semilattice__class_Osup(X43,X42,X45)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),X43),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),X42),X45) ),
inference(variable_rename,[status(thm)],[c_0_506]) ).
fof(c_0_854,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olattice(X45)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),X43)),X42) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42)) ),
inference(variable_rename,[status(thm)],[c_0_507]) ).
fof(c_0_855,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olower__semilattice(X45)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),X43)),X42) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42)) ),
inference(variable_rename,[status(thm)],[c_0_508]) ).
fof(c_0_856,plain,
! [X12,X13,X14,X15] :
( c_lessequals(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,X13,tc_fun(X15,tc_bool))
| hBOOL(c_in(X12,X14,X15)) ),
inference(variable_rename,[status(thm)],[c_0_509]) ).
fof(c_0_857,plain,
! [X12,X13,X14,X15] :
( c_lessequals(X14,c_Set_Oinsert(X12,X13,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,X13,tc_fun(X15,tc_bool))
| hBOOL(c_in(X12,X14,X15)) ),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_858,plain,
! [X13,X14,X15,X16] :
( hBOOL(hAPP(X15,X14))
| X13 = X14
| ~ hBOOL(hAPP(c_Set_Oinsert(X13,X15,X16),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_511])])]) ).
fof(c_0_859,plain,
! [X46,X47,X48,X49] :
( c_lessequals(c_Set_Oinsert(X46,X48,X49),c_Set_Oinsert(X46,X47,X49),tc_fun(X49,tc_bool))
| ~ c_lessequals(X48,X47,tc_fun(X49,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_512]) ).
fof(c_0_860,plain,
! [X15,X16,X17,X18] :
( hBOOL(c_in(X15,X16,X18))
| ~ hBOOL(c_in(X15,X17,X18))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_513]) ).
fof(c_0_861,plain,
! [X12,X13,X14,X15] :
( hBOOL(c_in(X12,X13,X15))
| ~ c_lessequals(X14,X13,tc_fun(X15,tc_bool))
| ~ hBOOL(c_in(X12,X14,X15)) ),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_862,plain,
! [X23,X24,X25,X26] :
( hBOOL(c_in(X23,X24,X26))
| ~ hBOOL(c_in(X23,X25,X26))
| ~ c_lessequals(X25,X24,tc_fun(X26,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_863,plain,
! [X12,X13,X14,X15] :
( hBOOL(c_in(X12,X13,X15))
| ~ hBOOL(c_in(X12,X14,X15))
| ~ c_lessequals(X14,X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_516]) ).
fof(c_0_864,plain,
! [X12,X13,X14,X15] :
( hBOOL(c_in(X12,X13,X15))
| ~ c_lessequals(c_Set_Oinsert(X12,X14,X15),X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_865,plain,
! [X12,X13,X14,X15] :
( c_Set_Oinsert(X12,X14,X15) != c_Set_Oinsert(X12,X13,X15)
| hBOOL(c_in(X12,X13,X15))
| hBOOL(c_in(X12,X14,X15))
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_518]) ).
fof(c_0_866,plain,
! [X18,X19,X20] :
( ~ hBOOL(hAPP(X19,X18))
| ~ hBOOL(c_in(X18,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_519])])]) ).
fof(c_0_867,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool)),X12))
| ~ hBOOL(hAPP(X13,X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_520])])]) ).
fof(c_0_868,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool)),X12))
| ~ hBOOL(hAPP(X14,X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_521])])]) ).
fof(c_0_869,plain,
! [X23] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X23)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(variable_rename,[status(thm)],[c_0_522]) ).
fof(c_0_870,plain,
! [X8,X9,X10] :
( ~ class_Lattices_Olower__semilattice(X10)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X10),X9,X10),X8,X10)
| ~ hBOOL(c_in(X8,X9,X10))
| ~ c_Finite__Set_Ofinite(X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_523]) ).
fof(c_0_871,plain,
! [X29,X30,X31,X32,X33] :
( hAPP(X29,X31) != c_Option_Ooption_OSome(X30,X33)
| hBOOL(c_in(X31,c_Map_Odom(X29,X32,X33),X32)) ),
inference(variable_rename,[status(thm)],[c_0_524]) ).
fof(c_0_872,plain,
! [X18,X19,X20] :
( hBOOL(hAPP(X19,X18))
| ~ hBOOL(c_in(X18,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_525])])]) ).
fof(c_0_873,plain,
! [X12,X13,X14,X15] :
( c_lessequals(X14,X13,tc_fun(X15,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X12,X14,X15),X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_526]) ).
fof(c_0_874,plain,
! [X23,X24,X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X27),c_SetInterval_Oord__class_OatLeastAtMost(X24,X23,X27),tc_fun(X27,tc_bool))
| c_lessequals(X26,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_527]) ).
fof(c_0_875,plain,
! [X12,X13,X14] :
( c_Lattices_Oupper__semilattice__class_Osup(X13,c_HOL_Ominus__class_Ominus(X12,X13,tc_fun(X14,tc_bool)),tc_fun(X14,tc_bool)) = X12
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_528]) ).
fof(c_0_876,plain,
! [X12,X13,X14] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12) != c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))
| c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X14,tc_bool)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_529]) ).
fof(c_0_877,plain,
! [X29,X30,X31,X32] :
( hBOOL(c_in(X30,c_Map_Odom(X29,X32,X31),X32))
| hAPP(X29,X30) = c_Option_Ooption_ONone(X31) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_530])])]) ).
fof(c_0_878,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Oupper__semilattice(X45)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X44,X43,X45),X42,X45)
| ~ c_lessequals(X43,X42,X45)
| ~ c_lessequals(X44,X42,X45) ),
inference(variable_rename,[status(thm)],[c_0_531]) ).
fof(c_0_879,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Oupper__semilattice(X45)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X43,X42,X45),X44,X45)
| ~ c_lessequals(X42,X44,X45)
| ~ c_lessequals(X43,X44,X45) ),
inference(variable_rename,[status(thm)],[c_0_532]) ).
fof(c_0_880,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X19,X22)
| ~ c_lessequals(X20,X19,X22)
| ~ c_lessequals(X21,X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_533]) ).
fof(c_0_881,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olower__semilattice(X45)
| c_lessequals(X44,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42),X45)
| ~ c_lessequals(X44,X42,X45)
| ~ c_lessequals(X44,X43,X45) ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_882,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olower__semilattice(X45)
| c_lessequals(X44,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42),X45)
| ~ c_lessequals(X44,X42,X45)
| ~ c_lessequals(X44,X43,X45) ),
inference(variable_rename,[status(thm)],[c_0_535]) ).
fof(c_0_883,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_lessequals(X19,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22),X21),X20),X22)
| ~ c_lessequals(X19,X20,X22)
| ~ c_lessequals(X19,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_884,plain,
! [X19,X20,X21] :
( c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21) != c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21)
| X20 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_537])])]) ).
fof(c_0_885,plain,
! [X26,X27,X28,X29,X30] :
( hAPP(hAPP(X26,hAPP(hAPP(X26,X29),X28)),X27) = hAPP(hAPP(X26,X29),hAPP(hAPP(X26,X28),X27))
| ~ c_OrderedGroup_Oab__semigroup__mult(X26,X30) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_538])])]) ).
fof(c_0_886,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olattice(X45)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X44,X43,X45),X42,X45) = c_Lattices_Oupper__semilattice__class_Osup(X44,c_Lattices_Oupper__semilattice__class_Osup(X43,X42,X45),X45) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_887,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olattice(X45)
| c_Lattices_Oupper__semilattice__class_Osup(X44,c_Lattices_Oupper__semilattice__class_Osup(X43,X42,X45),X45) = c_Lattices_Oupper__semilattice__class_Osup(X43,c_Lattices_Oupper__semilattice__class_Osup(X44,X42,X45),X45) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_888,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Oupper__semilattice(X45)
| c_Lattices_Oupper__semilattice__class_Osup(X44,c_Lattices_Oupper__semilattice__class_Osup(X43,X42,X45),X45) = c_Lattices_Oupper__semilattice__class_Osup(X43,c_Lattices_Oupper__semilattice__class_Osup(X44,X42,X45),X45) ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_889,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Oupper__semilattice(X45)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X44,X43,X45),X42,X45) = c_Lattices_Oupper__semilattice__class_Osup(X44,c_Lattices_Oupper__semilattice__class_Osup(X43,X42,X45),X45) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_890,plain,
! [X16,X17,X18,X19] :
( c_Hoare__Mirabelle_Ohoare__derivs(X18,X16,X19)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X18,c_Set_Oinsert(X17,X16,tc_Hoare__Mirabelle_Otriple(X19)),X19) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_891,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X61,tc_bool)),X60),X59),X61)
| ~ c_Finite__Set_Ofinite(X59,X61) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_892,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X61,tc_bool)),X60),X59),X61)
| ~ c_Finite__Set_Ofinite(X60,X61) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_893,plain,
! [X43,X44,X45,X46] :
( c_lessequals(X45,X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(X44,X43,tc_fun(X46,tc_bool))
| ~ c_lessequals(X45,X44,tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_894,plain,
! [X45,X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X49)
| c_HOL_Ominus__class_Ominus(X48,X46,X49) != c_HOL_Ominus__class_Ominus(X47,X45,X49)
| c_lessequals(X45,X47,X49)
| ~ c_lessequals(X46,X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_895,plain,
! [X45,X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X49)
| c_HOL_Ominus__class_Ominus(X48,X46,X49) != c_HOL_Ominus__class_Ominus(X47,X45,X49)
| c_lessequals(X46,X48,X49)
| ~ c_lessequals(X45,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_896,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Oupper__semilattice(X45)
| c_lessequals(X43,X42,X45)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X44,X43,X45),X42,X45) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_897,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Oupper__semilattice(X45)
| c_lessequals(X44,X42,X45)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X44,X43,X45),X42,X45) ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_898,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_lessequals(X20,X19,X22)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_899,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_lessequals(X21,X19,X22)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_900,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olattice(X45)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),X42)) ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_901,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olower__semilattice(X45)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X44),X42)) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_902,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_lessequals(X19,X21,X22)
| ~ c_lessequals(X19,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22),X21),X20),X22) ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_903,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_lessequals(X19,X20,X22)
| ~ c_lessequals(X19,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22),X21),X20),X22) ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_904,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olower__semilattice(X45)
| c_lessequals(X44,X43,X45)
| ~ c_lessequals(X44,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42),X45) ),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_905,plain,
! [X42,X43,X44,X45] :
( ~ class_Lattices_Olower__semilattice(X45)
| c_lessequals(X44,X42,X45)
| ~ c_lessequals(X44,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X45),X43),X42),X45) ),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_906,plain,
! [X19,X20,X21,X22] :
( c_lessequals(X21,c_Set_Oinsert(X19,X20,X22),tc_fun(X22,tc_bool))
| ~ c_lessequals(X21,X20,tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_907,plain,
! [X12,X13,X14] :
( c_Finite__Set_Ofinite(X13,X14)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X14,tc_bool)),X14)
| ~ c_Finite__Set_Ofinite(X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_560]) ).
fof(c_0_908,plain,
! [X13,X14,X15,X16] :
( hBOOL(hAPP(c_Set_Oinsert(X13,X15,X16),X14))
| ~ hBOOL(hAPP(X15,X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_561])])]) ).
fof(c_0_909,plain,
! [X57,X58,X59] :
( ~ class_Orderings_Olinorder(X59)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X58,X59),c_Finite__Set_Olinorder__class_OMax(X57,X59),X59)
| ~ c_Finite__Set_Ofinite(X57,X59)
| X58 = c_Orderings_Obot__class_Obot(tc_fun(X59,tc_bool))
| ~ c_lessequals(X58,X57,tc_fun(X59,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_910,plain,
! [X57,X58,X59] :
( ~ class_Orderings_Olinorder(X59)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X57,X59),c_Finite__Set_Olinorder__class_OMin(X58,X59),X59)
| ~ c_Finite__Set_Ofinite(X57,X59)
| X58 = c_Orderings_Obot__class_Obot(tc_fun(X59,tc_bool))
| ~ c_lessequals(X58,X57,tc_fun(X59,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_911,plain,
! [X18,X19,X20] :
( hBOOL(hAPP(X19,X18))
| ~ hBOOL(c_in(X18,c_Collect(X19,X20),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_564])])]) ).
fof(c_0_912,plain,
! [X11,X12,X13] :
( ~ class_Orderings_Olinorder(X13)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X12,X13),X11,X13)
| ~ hBOOL(c_in(X11,X12,X13))
| ~ c_Finite__Set_Ofinite(X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_913,plain,
! [X11,X12,X13] :
( ~ class_Orderings_Olinorder(X13)
| c_lessequals(X11,c_Finite__Set_Olinorder__class_OMax(X12,X13),X13)
| ~ hBOOL(c_in(X11,X12,X13))
| ~ c_Finite__Set_Ofinite(X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_914,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(X60,X61)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X60,X59,tc_fun(X61,tc_bool)),X61) ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_915,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(X59,X61)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X60,X59,tc_fun(X61,tc_bool)),X61) ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_916,plain,
! [X21,X22,X23] :
( ~ class_HOL_Ominus(X23)
| hAPP(c_HOL_Ominus__class_Ominus(X22,X21,tc_fun(t_a,X23)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X22,v_x),hAPP(X21,v_x),X23) ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_917,plain,
! [X47,X48,X49] :
( ~ class_Lattices_Olattice(X49)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X48,X47,tc_fun(t_a,X49)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X48,v_x),hAPP(X47,v_x),X49) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_918,plain,
! [X12,X13,X14] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12) = X12
| ~ c_lessequals(X12,X13,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_919,plain,
! [X12,X13,X14] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12) = X13
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_920,plain,
! [X11,X12,X13] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X13)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X12,X13),X11,X13)
| ~ hBOOL(c_in(X11,X12,X13)) ),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_921,plain,
! [X11,X12,X13] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X13)
| c_lessequals(X11,c_Complete__Lattice_OSup__class_OSup(X12,X13),X13)
| ~ hBOOL(c_in(X11,X12,X13)) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_922,plain,
! [X26,X27,X28,X29,X30] :
( c_Set_Oinsert(X27,X26,X29) != c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))
| hBOOL(c_in(X27,X26,X29))
| ~ c_OrderedGroup_Oab__semigroup__mult(X28,X30) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_575])])]) ).
fof(c_0_923,plain,
! [X27,X28,X29,X30,X31] :
( hAPP(X29,X28) != c_Option_Ooption_OSome(X27,X31)
| c_Set_Oinsert(X28,c_Map_Odom(X29,X30,X31),X30) = c_Map_Odom(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_924,plain,
! [X26,X27,X28,X29,X30] :
( hAPP(hAPP(X26,X29),hAPP(hAPP(X26,X28),X27)) = hAPP(hAPP(X26,X28),hAPP(hAPP(X26,X29),X27))
| ~ c_OrderedGroup_Oab__semigroup__mult(X26,X30) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_577])])]) ).
fof(c_0_925,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_lessequals(X19,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X22)
| ~ c_lessequals(X19,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_578]) ).
fof(c_0_926,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_lessequals(X19,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X22)
| ~ c_lessequals(X19,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_579]) ).
fof(c_0_927,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22),X21),X20),X19,X22)
| ~ c_lessequals(X21,X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_580]) ).
fof(c_0_928,plain,
! [X19,X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22),X21),X20),X19,X22)
| ~ c_lessequals(X20,X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_581]) ).
fof(c_0_929,plain,
! [X12,X13,X14] :
( X13 = X12
| ~ c_lessequals(X12,X13,tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_582])])]) ).
fof(c_0_930,plain,
! [X12,X13,X14] :
( X13 = X12
| ~ c_lessequals(X12,X13,tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_583])])]) ).
fof(c_0_931,plain,
! [X47,X48,X49,X50,X51] :
( ~ class_HOL_Oord(X50)
| c_lessequals(hAPP(X49,X47),hAPP(X48,X47),X50)
| ~ c_lessequals(X49,X48,tc_fun(X51,X50)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_584])])]) ).
fof(c_0_932,plain,
! [X17,X18,X19] :
( c_Set_Oinsert(X18,X17,X19) != c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| hBOOL(c_in(X18,X17,X19)) ),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_933,plain,
! [X42,X43,X44,X45] :
( ~ class_Orderings_Oorder(X45)
| c_lessequals(X42,X44,X45)
| ~ c_lessequals(X42,X43,X45)
| ~ c_lessequals(X43,X44,X45) ),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_934,plain,
! [X42,X43,X44,X45] :
( ~ class_Orderings_Opreorder(X45)
| c_lessequals(X44,X42,X45)
| ~ c_lessequals(X43,X42,X45)
| ~ c_lessequals(X44,X43,X45) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_935,plain,
! [X7,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_936,plain,
! [X7,X8] :
( ~ class_Orderings_Olinorder(X8)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_937,plain,
! [X7,X8] :
( ~ class_Orderings_Olinorder(X8)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_938,plain,
! [X7,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_939,plain,
! [X8,X9] :
( X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_lessequals(X8,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_940,plain,
! [X8,X9,X10] :
( c_Set_Oinsert(X8,X9,X10) = X9
| ~ hBOOL(c_in(X8,X9,X10)) ),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_941,plain,
! [X24,X25,X26,X27] :
( c_Hoare__Mirabelle_Ohoare__derivs(X26,X24,X27)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X26,X25,X27)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X25,X24,X27) ),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_942,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) = c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_595]) ).
fof(c_0_943,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) = c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_944,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Oorder(X21)
| c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X21)
| ~ c_lessequals(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_945,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Oorder(X21)
| c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X21) != c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))
| ~ c_lessequals(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_946,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X8,X9),X8,X9))
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_947,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X8,X9),X8,X9))
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_948,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13) ),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_949,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13) ),
inference(variable_rename,[status(thm)],[c_0_602]) ).
fof(c_0_950,plain,
! [X12,X13,X14] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X14,tc_bool)),X14)
| ~ c_Finite__Set_Ofinite(X13,X14)
| ~ c_Finite__Set_Ofinite(X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_603]) ).
fof(c_0_951,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X60,X59,tc_fun(X61,tc_bool)),X61)
| ~ c_Finite__Set_Ofinite(X59,X61)
| ~ c_Finite__Set_Ofinite(X60,X61) ),
inference(variable_rename,[status(thm)],[c_0_604]) ).
fof(c_0_952,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X60,X59,tc_fun(X61,tc_bool)),X61)
| ~ c_Finite__Set_Ofinite(X59,X61)
| ~ c_Finite__Set_Ofinite(X60,X61) ),
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_953,plain,
! [X18,X19,X20] :
( hBOOL(c_in(X18,c_Collect(X19,X20),X20))
| ~ hBOOL(hAPP(X19,X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_606])])]) ).
fof(c_0_954,plain,
! [X8,X9,X10] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X10)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X8,X9,X10),X10) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Complete__Lattice_OSup__class_OSup(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_955,plain,
! [X8,X9,X10] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X10)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X8,X9,X10),X10) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10),X8),c_Complete__Lattice_OInf__class_OInf(X9,X10)) ),
inference(variable_rename,[status(thm)],[c_0_608]) ).
fof(c_0_956,plain,
! [X20,X21,X22] :
( hBOOL(hAPP(X21,X20))
| ~ hBOOL(c_in(X20,X21,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_609])])]) ).
fof(c_0_957,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ofinite(X9,X10)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_958,plain,
! [X12,X13,X14] :
( c_Lattices_Oupper__semilattice__class_Osup(X13,X12,tc_fun(X14,tc_bool)) != X12
| c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_959,plain,
! [X12,X13,X14] :
( c_Lattices_Oupper__semilattice__class_Osup(X13,X12,tc_fun(X14,tc_bool)) = X12
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_960,plain,
! [X12,X13,X14] :
( c_Lattices_Oupper__semilattice__class_Osup(X13,X12,tc_fun(X14,tc_bool)) = X13
| ~ c_lessequals(X12,X13,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_961,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(X29,X28))
| ~ hBOOL(hAPP(X30,X28))
| ~ c_lessequals(X30,X29,tc_fun(X31,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_614])])]) ).
fof(c_0_962,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(X29,X28))
| ~ c_lessequals(X30,X29,tc_fun(X31,tc_bool))
| ~ hBOOL(hAPP(X30,X28)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_615])])]) ).
fof(c_0_963,plain,
! [X12,X13,X14] :
( c_Lattices_Oupper__semilattice__class_Osup(X13,X12,tc_fun(X14,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_616]) ).
fof(c_0_964,plain,
! [X12,X13,X14] :
( c_Lattices_Oupper__semilattice__class_Osup(X13,X12,tc_fun(X14,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_617]) ).
fof(c_0_965,plain,
! [X12,X13,X14] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X14,tc_bool)),X14)
| ~ c_Finite__Set_Ofinite(X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_966,plain,
! [X18,X19,X20] :
( c_Com_OWT(c_Com_Ocom_OBODY(X20))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X19,X20,X18)) ),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_967,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| X14 = X13
| ~ c_lessequals(X13,X14,X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_968,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| X14 = X13
| ~ c_lessequals(X13,X14,X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_969,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| X14 = X13
| ~ c_lessequals(X14,X13,X15)
| ~ c_lessequals(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_970,plain,
! [X45,X46,X47,X48] :
( ~ class_OrderedGroup_Oab__group__add(X48)
| c_HOL_Ominus__class_Ominus(X47,X47,X48) != c_HOL_Ominus__class_Ominus(X46,X45,X48)
| X46 = X45 ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_971,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Oab__group__add(X20)
| c_HOL_Ominus__class_Ominus(X18,X17,X20) != c_HOL_Ominus__class_Ominus(X19,X19,X20)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_972,plain,
! [X69,X70,X71,X72,X73,X74] :
( c_Com_Ocom_OCall(X70,X72,X74) != c_Com_Ocom_OCall(X69,X71,X73)
| X74 = X73 ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_973,plain,
! [X69,X70,X71,X72,X73,X74] :
( c_Com_Ocom_OCall(X70,X72,X74) != c_Com_Ocom_OCall(X69,X71,X73)
| X72 = X71 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_626])])]) ).
fof(c_0_974,plain,
! [X69,X70,X71,X72,X73,X74] :
( c_Com_Ocom_OCall(X70,X72,X74) != c_Com_Ocom_OCall(X69,X71,X73)
| X70 = X69 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_627])])]) ).
fof(c_0_975,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_lessequals(X14,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_976,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_lessequals(X13,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_977,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_lessequals(X13,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_978,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_lessequals(X14,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_979,plain,
! [X7,X8] :
( ~ class_Orderings_Oorder(X8)
| c_SetInterval_Oord__class_OatLeastAtMost(X7,X7,X8) = c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8) ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_980,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15)) = X14 ),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_981,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13),X15) = X14 ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_982,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_983,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_984,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_985,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_986,plain,
! [X12,X13,X14] :
( c_Finite__Set_Ofinite(X13,X14)
| ~ c_Finite__Set_Ofinite(X12,X14)
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_987,plain,
! [X12,X13,X14] :
( c_Finite__Set_Ofinite(X13,X14)
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| ~ c_Finite__Set_Ofinite(X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_640]) ).
fof(c_0_988,plain,
! [X20,X21,X22] :
( hBOOL(c_in(X20,X21,X22))
| ~ hBOOL(hAPP(X21,X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_641])])]) ).
fof(c_0_989,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) != X13
| c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_990,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) = X14
| ~ c_lessequals(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_991,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) = X13
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_992,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13) = X13
| ~ c_lessequals(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_993,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13) = X14
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_994,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13) != X14
| c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_995,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X9,X10),X10)
| ~ c_Finite__Set_Ofinite(X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_648]) ).
fof(c_0_996,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Oorder(X21)
| c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X21)
| c_lessequals(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_997,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Oorder(X21)
| c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X21) = c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))
| c_lessequals(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_998,plain,
! [X16,X17,X18] :
( c_Hoare__Mirabelle_Ohoare__valids(X17,X16,X18)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_999,plain,
! [X4,X5,X6] :
( X5 = X4
| ~ hBOOL(hAPP(c_fequal(X5,X6),X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_652])])]) ).
fof(c_0_1000,plain,
! [X25,X26,X27] :
( c_Com_OWT(c_Com_Ocom_OCall(X27,X25,X26))
| ~ c_Com_OWT(c_Com_Ocom_OBODY(X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_653])])]) ).
fof(c_0_1001,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| c_lessequals(X13,X14,X15)
| c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1002,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) = c_Lattices_Oupper__semilattice__class_Osup(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1003,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) = c_Lattices_Oupper__semilattice__class_Osup(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1004,plain,
! [X18,X19,X20] :
( c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) != c_Collect(X19,X20)
| ~ hBOOL(hAPP(X19,X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_657])])]) ).
fof(c_0_1005,plain,
! [X18,X19,X20] :
( c_Collect(X19,X20) != c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))
| ~ hBOOL(hAPP(X19,X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_658])])]) ).
fof(c_0_1006,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X13),X14) ),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1007,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X14),X13) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X15),X13),X14) ),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1008,plain,
! [X12,X13,X14] :
( ~ class_Lattices_Obounded__lattice(X14)
| c_Lattices_Oupper__semilattice__class_Osup(X13,X12,X14) != c_Orderings_Obot__class_Obot(X14)
| X13 = c_Orderings_Obot__class_Obot(X14) ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1009,plain,
! [X12,X13,X14] :
( ~ class_Lattices_Obounded__lattice(X14)
| c_Lattices_Oupper__semilattice__class_Osup(X13,X12,X14) != c_Orderings_Obot__class_Obot(X14)
| X12 = c_Orderings_Obot__class_Obot(X14) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1010,plain,
! [X26,X27,X28,X29] :
( hAPP(hAPP(X26,X28),X27) = hAPP(hAPP(X26,X27),X28)
| ~ c_OrderedGroup_Oab__semigroup__mult(X26,X29) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_663])])]) ).
fof(c_0_1011,plain,
! [X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) = c_Orderings_Obot__class_Obot(X4) ),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1012,plain,
! [X11,X12] :
( ~ class_Lattices_Obounded__lattice(X12)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12),c_Orderings_Obot__class_Obot(X12)),X11) = c_Orderings_Obot__class_Obot(X12) ),
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1013,plain,
! [X21] :
( ~ class_Orderings_Obot(X21)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X21)),v_x) = c_Orderings_Obot__class_Obot(X21) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1014,plain,
! [X11,X12] :
( ~ class_Lattices_Obounded__lattice(X12)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12),X11),c_Orderings_Obot__class_Obot(X12)) = c_Orderings_Obot__class_Obot(X12) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1015,plain,
! [X11,X12] :
( ~ class_Lattices_Obounded__lattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X12),X11,X12) = X11 ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1016,plain,
! [X11,X12] :
( ~ class_Lattices_Obounded__lattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Orderings_Obot__class_Obot(X12),X12) = X11 ),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1017,plain,
! [X11,X12] :
( ~ class_Orderings_Obot(X12)
| c_lessequals(c_Orderings_Obot__class_Obot(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1018,plain,
! [X11,X12] :
( ~ class_Lattices_Oupper__semilattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X11,X12) = X11 ),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1019,plain,
! [X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_lessequals(X11,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1020,plain,
! [X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_lessequals(X11,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1021,plain,
! [X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12),X11),X11) = X11 ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1022,plain,
! [X63,X64,X65] :
( c_Option_Ooption_OSome(X64,X65) != c_Option_Ooption_OSome(X63,X65)
| X64 = X63 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_675])])]) ).
fof(c_0_1023,plain,
! [X25,X26] :
( hAPP(c_Com_Obody,X25) != c_Option_Ooption_OSome(X26,tc_Com_Ocom)
| ~ c_Com_OWT__bodies
| c_Com_OWT(X26) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1024,plain,
! [X6,X7] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X6,X7))
| ~ class_Finite__Set_Ofinite_Ofinite(X7)
| ~ class_Finite__Set_Ofinite_Ofinite(X6) ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1025,plain,
! [X6,X7] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X6,X7))
| ~ class_Complete__Lattice_Ocomplete__lattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1026,plain,
! [X6,X7] :
( class_Lattices_Oupper__semilattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1027,plain,
! [X6,X7] :
( class_Lattices_Olower__semilattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1028,plain,
! [X6,X7] :
( class_Lattices_Odistrib__lattice(tc_fun(X6,X7))
| ~ class_Lattices_Odistrib__lattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1029,plain,
! [X6,X7] :
( class_Lattices_Obounded__lattice(tc_fun(X6,X7))
| ~ class_Lattices_Obounded__lattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1030,plain,
! [X6,X7] :
( class_Orderings_Opreorder(tc_fun(X6,X7))
| ~ class_Orderings_Opreorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1031,plain,
! [X6,X7] :
( class_Lattices_Olattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1032,plain,
! [X6,X7] :
( class_Orderings_Oorder(tc_fun(X6,X7))
| ~ class_Orderings_Oorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1033,plain,
! [X6,X7] :
( class_Orderings_Obot(tc_fun(X6,X7))
| ~ class_Orderings_Obot(X7) ),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1034,plain,
! [X6,X7] :
( class_HOL_Ominus(tc_fun(X6,X7))
| ~ class_HOL_Ominus(X7) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1035,plain,
! [X6,X7] :
( class_HOL_Oord(tc_fun(X6,X7))
| ~ class_HOL_Oord(X7) ),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1036,plain,
! [X25] :
( c_Com_OWT(c_Com_Ocom_OBODY(X25))
| hAPP(c_Com_Obody,X25) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1037,plain,
! [X8,X9] :
( ~ class_Finite__Set_Ofinite_Ofinite(X9)
| c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1038,plain,
! [X5] :
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X5))
| ~ class_Finite__Set_Ofinite_Ofinite(X5) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1039,plain,
! [X10,X11] :
( c_Com_Ocom_OBODY(X11) != c_Com_Ocom_OBODY(X10)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1040,plain,
! [X17,X18] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| X18 = X17 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_693])])]) ).
cnf(c_0_1041,plain,
( hAPP(X1,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X5,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_694]) ).
cnf(c_0_1042,plain,
( hAPP(X2,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X6,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_695]) ).
cnf(c_0_1043,plain,
( hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(split_conjunct,[status(thm)],[c_0_696]) ).
cnf(c_0_1044,plain,
( hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(split_conjunct,[status(thm)],[c_0_697]) ).
cnf(c_0_1045,plain,
( hAPP(X1,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_698]) ).
cnf(c_0_1046,plain,
( hAPP(X2,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_699]) ).
cnf(c_0_1047,plain,
( hAPP(X1,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X5,X10),hAPP(X1,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_700]) ).
cnf(c_0_1048,plain,
( hAPP(X2,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X6,X10),hAPP(X2,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_701]) ).
cnf(c_0_1049,plain,
( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_702]) ).
cnf(c_0_1050,plain,
( hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X7
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_703]) ).
cnf(c_0_1051,plain,
( hBOOL(c_in(X3,X4,X2))
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),X5,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2)
| ~ hBOOL(c_in(X6,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_704]) ).
cnf(c_0_1052,plain,
( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7)
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| ~ hBOOL(c_in(X4,X3,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_705]) ).
cnf(c_0_1053,plain,
( hBOOL(c_in(X3,X4,X2))
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,X4,X2),hAPP(hAPP(X1,X6),X5),X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_706]) ).
cnf(c_0_1054,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7) ),
inference(split_conjunct,[status(thm)],[c_0_707]) ).
cnf(c_0_1055,plain,
( hBOOL(c_in(X2,X3,X5))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5) ),
inference(split_conjunct,[status(thm)],[c_0_708]) ).
cnf(c_0_1056,plain,
( X4 = X2
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_709]) ).
cnf(c_0_1057,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_710]) ).
cnf(c_0_1058,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X5,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OBODY(X2),X3,X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OBODY(X2),X3,X4),X5,tc_Hoare__Mirabelle_Otriple(X4)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Option_Othe(hAPP(c_Com_Obody,X2),tc_Com_Ocom),X3,X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_711]) ).
cnf(c_0_1059,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(split_conjunct,[status(thm)],[c_0_712]) ).
cnf(c_0_1060,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
inference(split_conjunct,[status(thm)],[c_0_713]) ).
cnf(c_0_1061,plain,
( hAPP(X2,X1) = X3
| ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_714]) ).
cnf(c_0_1062,plain,
( c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_715]) ).
cnf(c_0_1063,plain,
( hBOOL(c_in(hAPP(X2,X1),X3,X5))
| ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_716]) ).
cnf(c_0_1064,plain,
( hBOOL(c_in(hAPP(X2,X1),X3,X5))
| ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_717]) ).
cnf(c_0_1065,plain,
( X2 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_718]) ).
cnf(c_0_1066,plain,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_719]) ).
cnf(c_0_1067,plain,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_720]) ).
cnf(c_0_1068,plain,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_721]) ).
cnf(c_0_1069,plain,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_722]) ).
cnf(c_0_1070,plain,
( c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
| c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_723]) ).
cnf(c_0_1071,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X1)),X2,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(split_conjunct,[status(thm)],[c_0_724]) ).
cnf(c_0_1072,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_725]) ).
cnf(c_0_1073,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_726]) ).
cnf(c_0_1074,plain,
( c_Map_Omap__le(X2,X5,X3,X4)
| ~ c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_727]) ).
cnf(c_0_1075,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_728]) ).
cnf(c_0_1076,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_729]) ).
cnf(c_0_1077,plain,
( hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_730]) ).
cnf(c_0_1078,plain,
( hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_731]) ).
cnf(c_0_1079,plain,
( hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_732]) ).
cnf(c_0_1080,plain,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_733]) ).
cnf(c_0_1081,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_734]) ).
cnf(c_0_1082,plain,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_735]) ).
cnf(c_0_1083,plain,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_736]) ).
cnf(c_0_1084,plain,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_737]) ).
cnf(c_0_1085,plain,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_738]) ).
cnf(c_0_1086,plain,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_739]) ).
cnf(c_0_1087,plain,
( hBOOL(hAPP(X4,X1))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_740]) ).
cnf(c_0_1088,plain,
( c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_741]) ).
cnf(c_0_1089,plain,
( hBOOL(c_in(hAPP(X1,X6),X5,X4))
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_742]) ).
cnf(c_0_1090,plain,
( c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_743]) ).
cnf(c_0_1091,plain,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_744]) ).
cnf(c_0_1092,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_745]) ).
cnf(c_0_1093,plain,
( hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_746]) ).
cnf(c_0_1094,plain,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_747]) ).
cnf(c_0_1095,plain,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_748]) ).
cnf(c_0_1096,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_749]) ).
cnf(c_0_1097,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X2)),X2)
| ~ class_Lattices_Olattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1098,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X1,tc_fun(X3,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_751]) ).
cnf(c_0_1099,plain,
( c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_752]) ).
cnf(c_0_1100,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_753]) ).
cnf(c_0_1101,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_754]) ).
cnf(c_0_1102,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_755]) ).
cnf(c_0_1103,plain,
( hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X2,X1)
| ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_756]) ).
cnf(c_0_1104,plain,
( c_Map_Omap__le(X1,X5,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_757]) ).
cnf(c_0_1105,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_758]) ).
cnf(c_0_1106,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_759]) ).
cnf(c_0_1107,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_760]) ).
cnf(c_0_1108,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_761]) ).
cnf(c_0_1109,plain,
( c_Finite__Set_Ofold1(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X2,X4)),c_Finite__Set_Ofold1(X1,X3,X4))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4)
| ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_762]) ).
cnf(c_0_1110,plain,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_763]) ).
cnf(c_0_1111,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_764]) ).
cnf(c_0_1112,plain,
( hAPP(X1,X5) = hAPP(X2,X5)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ hBOOL(c_in(X5,c_Map_Odom(X1,X3,X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_765]) ).
cnf(c_0_1113,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
inference(split_conjunct,[status(thm)],[c_0_766]) ).
cnf(c_0_1114,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)),X1)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_767]) ).
cnf(c_0_1115,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_768]) ).
cnf(c_0_1116,plain,
( hBOOL(c_in(X1,X2,X4))
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_769]) ).
cnf(c_0_1117,plain,
( hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(X5,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_770]) ).
cnf(c_0_1118,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2) = c_Set_Oinsert(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),X3)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_771]) ).
cnf(c_0_1119,plain,
( hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_772]) ).
cnf(c_0_1120,plain,
( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_773]) ).
cnf(c_0_1121,plain,
( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(c_Map_Omap__add(X2,X5,X3,X4),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_774]) ).
cnf(c_0_1122,plain,
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_775]) ).
cnf(c_0_1123,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_776]) ).
cnf(c_0_1124,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_777]) ).
cnf(c_0_1125,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_778]) ).
cnf(c_0_1126,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_779]) ).
cnf(c_0_1127,plain,
( ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_780]) ).
cnf(c_0_1128,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[c_0_781]) ).
cnf(c_0_1129,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[c_0_782]) ).
cnf(c_0_1130,plain,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_783]) ).
cnf(c_0_1131,plain,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_784]) ).
cnf(c_0_1132,plain,
( X1 = X2
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_785]) ).
cnf(c_0_1133,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X1,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_786]) ).
cnf(c_0_1134,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
inference(split_conjunct,[status(thm)],[c_0_787]) ).
cnf(c_0_1135,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
inference(split_conjunct,[status(thm)],[c_0_788]) ).
cnf(c_0_1136,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_789]) ).
cnf(c_0_1137,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_790]) ).
cnf(c_0_1138,plain,
( hBOOL(c_in(X1,X2,X4))
| ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_791]) ).
cnf(c_0_1139,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)) = c_Set_Oinsert(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_792]) ).
cnf(c_0_1140,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_793]) ).
cnf(c_0_1141,plain,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(split_conjunct,[status(thm)],[c_0_794]) ).
cnf(c_0_1142,plain,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_795]) ).
cnf(c_0_1143,plain,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_796]) ).
cnf(c_0_1144,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_797]) ).
cnf(c_0_1145,plain,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_798]) ).
cnf(c_0_1146,plain,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1147,plain,
( c_lessequals(c_Map_Odom(X1,X3,X4),c_Map_Odom(X2,X3,X4),tc_fun(X3,tc_bool))
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_800]) ).
cnf(c_0_1148,plain,
( c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_801]) ).
cnf(c_0_1149,plain,
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_802]) ).
cnf(c_0_1150,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_803]) ).
cnf(c_0_1151,plain,
( hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(X2) ),
inference(split_conjunct,[status(thm)],[c_0_804]) ).
cnf(c_0_1152,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_805]) ).
cnf(c_0_1153,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_806]) ).
cnf(c_0_1154,plain,
( X1 = X2
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_807]) ).
cnf(c_0_1155,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(c_in(X4,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_808]) ).
cnf(c_0_1156,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1157,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_810]) ).
cnf(c_0_1158,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1159,plain,
( c_lessequals(X2,X5,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1160,plain,
( c_lessequals(X4,X1,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_813]) ).
cnf(c_0_1161,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_814]) ).
cnf(c_0_1162,plain,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1163,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1164,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_OSome(X6,X4) ),
inference(split_conjunct,[status(thm)],[c_0_817]) ).
cnf(c_0_1165,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_818]) ).
cnf(c_0_1166,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_819]) ).
cnf(c_0_1167,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1168,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1169,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1170,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_823]) ).
cnf(c_0_1171,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1172,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_OSome(X6,X4) ),
inference(split_conjunct,[status(thm)],[c_0_825]) ).
cnf(c_0_1173,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_OSome(X6,X4) ),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1174,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_lessequals(X3,X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_827]) ).
cnf(c_0_1175,plain,
( ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(X2,X1) != c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[c_0_828]) ).
cnf(c_0_1176,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_829]) ).
cnf(c_0_1177,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X2))
| ~ class_Lattices_Odistrib__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_830]) ).
cnf(c_0_1178,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_831]) ).
cnf(c_0_1179,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_832]) ).
cnf(c_0_1180,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_833]) ).
cnf(c_0_1181,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_834]) ).
cnf(c_0_1182,plain,
( c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),c_Set_Oinsert(X4,X5,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),X5,tc_fun(X2,tc_bool))
| hAPP(X1,X4) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[c_0_835]) ).
cnf(c_0_1183,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_836]) ).
cnf(c_0_1184,plain,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_837]) ).
cnf(c_0_1185,plain,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_838]) ).
cnf(c_0_1186,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X4,X3,X2))
| c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X4,X3,X2),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_839]) ).
cnf(c_0_1187,plain,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_840]) ).
cnf(c_0_1188,plain,
( hBOOL(c_in(X2,X1,X4))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_841]) ).
cnf(c_0_1189,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_842]) ).
cnf(c_0_1190,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_843]) ).
cnf(c_0_1191,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_844]) ).
cnf(c_0_1192,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_845]) ).
cnf(c_0_1193,plain,
( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_846]) ).
cnf(c_0_1194,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_847]) ).
cnf(c_0_1195,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_848]) ).
cnf(c_0_1196,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_849]) ).
cnf(c_0_1197,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_850]) ).
cnf(c_0_1198,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_851]) ).
cnf(c_0_1199,plain,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_852]) ).
cnf(c_0_1200,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_853]) ).
cnf(c_0_1201,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_854]) ).
cnf(c_0_1202,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_855]) ).
cnf(c_0_1203,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_856]) ).
cnf(c_0_1204,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_857]) ).
cnf(c_0_1205,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1206,plain,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_859]) ).
cnf(c_0_1207,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_860]) ).
cnf(c_0_1208,plain,
( hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_861]) ).
cnf(c_0_1209,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_862]) ).
cnf(c_0_1210,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1211,plain,
( hBOOL(c_in(X1,X4,X3))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_864]) ).
cnf(c_0_1212,plain,
( X1 = X2
| hBOOL(c_in(X3,X1,X4))
| hBOOL(c_in(X3,X2,X4))
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1213,plain,
( ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1214,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1215,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1216,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_869]) ).
cnf(c_0_1217,plain,
( c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_870]) ).
cnf(c_0_1218,plain,
( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(X2,X1) != c_Option_Ooption_OSome(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_871]) ).
cnf(c_0_1219,plain,
( hBOOL(hAPP(X3,X1))
| ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_872]) ).
cnf(c_0_1220,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_873]) ).
cnf(c_0_1221,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_874]) ).
cnf(c_0_1222,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_875]) ).
cnf(c_0_1223,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_876]) ).
cnf(c_0_1224,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hBOOL(c_in(X2,c_Map_Odom(X1,X4,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_877]) ).
cnf(c_0_1225,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_878]) ).
cnf(c_0_1226,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_879]) ).
cnf(c_0_1227,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_880]) ).
cnf(c_0_1228,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_881]) ).
cnf(c_0_1229,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_882]) ).
cnf(c_0_1230,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_883]) ).
cnf(c_0_1231,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_884]) ).
cnf(c_0_1232,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_885]) ).
cnf(c_0_1233,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_886]) ).
cnf(c_0_1234,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_887]) ).
cnf(c_0_1235,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_888]) ).
cnf(c_0_1236,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_889]) ).
cnf(c_0_1237,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_890]) ).
cnf(c_0_1238,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_891]) ).
cnf(c_0_1239,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_892]) ).
cnf(c_0_1240,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_893]) ).
cnf(c_0_1241,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_894]) ).
cnf(c_0_1242,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_895]) ).
cnf(c_0_1243,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_896]) ).
cnf(c_0_1244,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_897]) ).
cnf(c_0_1245,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_898]) ).
cnf(c_0_1246,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_899]) ).
cnf(c_0_1247,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_900]) ).
cnf(c_0_1248,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_901]) ).
cnf(c_0_1249,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_902]) ).
cnf(c_0_1250,plain,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_903]) ).
cnf(c_0_1251,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_904]) ).
cnf(c_0_1252,plain,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_905]) ).
cnf(c_0_1253,plain,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_906]) ).
cnf(c_0_1254,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_907]) ).
cnf(c_0_1255,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_908]) ).
cnf(c_0_1256,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_909]) ).
cnf(c_0_1257,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_910]) ).
cnf(c_0_1258,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_911]) ).
cnf(c_0_1259,plain,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_912]) ).
cnf(c_0_1260,plain,
( c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_913]) ).
cnf(c_0_1261,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_914]) ).
cnf(c_0_1262,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_915]) ).
cnf(c_0_1263,plain,
( hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3)
| ~ class_HOL_Ominus(X3) ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1264,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(t_a,X3)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),hAPP(X2,v_x),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_917]) ).
cnf(c_0_1265,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_918]) ).
cnf(c_0_1266,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_919]) ).
cnf(c_0_1267,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_920]) ).
cnf(c_0_1268,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_921]) ).
cnf(c_0_1269,plain,
( hBOOL(c_in(X3,X4,X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Set_Oinsert(X3,X4,X5) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_922]) ).
cnf(c_0_1270,plain,
( c_Set_Oinsert(X1,c_Map_Odom(X2,X3,X4),X3) = c_Map_Odom(X2,X3,X4)
| hAPP(X2,X1) != c_Option_Ooption_OSome(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_923]) ).
cnf(c_0_1271,plain,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_924]) ).
cnf(c_0_1272,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_925]) ).
cnf(c_0_1273,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_926]) ).
cnf(c_0_1274,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_927]) ).
cnf(c_0_1275,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_928]) ).
cnf(c_0_1276,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_929]) ).
cnf(c_0_1277,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_930]) ).
cnf(c_0_1278,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_931]) ).
cnf(c_0_1279,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_932]) ).
cnf(c_0_1280,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_933]) ).
cnf(c_0_1281,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_934]) ).
cnf(c_0_1282,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_935]) ).
cnf(c_0_1283,plain,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_936]) ).
cnf(c_0_1284,plain,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_937]) ).
cnf(c_0_1285,plain,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_938]) ).
cnf(c_0_1286,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_939]) ).
cnf(c_0_1287,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_940]) ).
cnf(c_0_1288,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_941]) ).
cnf(c_0_1289,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_942]) ).
cnf(c_0_1290,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_943]) ).
cnf(c_0_1291,plain,
( ~ c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_944]) ).
cnf(c_0_1292,plain,
( ~ c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_945]) ).
cnf(c_0_1293,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_946]) ).
cnf(c_0_1294,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_947]) ).
cnf(c_0_1295,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_948]) ).
cnf(c_0_1296,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_949]) ).
cnf(c_0_1297,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_950]) ).
cnf(c_0_1298,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_951]) ).
cnf(c_0_1299,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_952]) ).
cnf(c_0_1300,plain,
( hBOOL(c_in(X2,c_Collect(X1,X3),X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_953]) ).
cnf(c_0_1301,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_954]) ).
cnf(c_0_1302,plain,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),c_Complete__Lattice_OInf__class_OInf(X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_955]) ).
cnf(c_0_1303,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_956]) ).
cnf(c_0_1304,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_957]) ).
cnf(c_0_1305,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_958]) ).
cnf(c_0_1306,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_959]) ).
cnf(c_0_1307,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_960]) ).
cnf(c_0_1308,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_961]) ).
cnf(c_0_1309,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_962]) ).
cnf(c_0_1310,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_963]) ).
cnf(c_0_1311,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_964]) ).
cnf(c_0_1312,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_965]) ).
cnf(c_0_1313,plain,
( c_Com_OWT(c_Com_Ocom_OBODY(X2))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_966]) ).
cnf(c_0_1314,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_967]) ).
cnf(c_0_1315,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_968]) ).
cnf(c_0_1316,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_969]) ).
cnf(c_0_1317,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_970]) ).
cnf(c_0_1318,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_971]) ).
cnf(c_0_1319,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_972]) ).
cnf(c_0_1320,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[c_0_973]) ).
cnf(c_0_1321,plain,
( X1 = X2
| c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_974]) ).
cnf(c_0_1322,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_975]) ).
cnf(c_0_1323,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_976]) ).
cnf(c_0_1324,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_977]) ).
cnf(c_0_1325,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_978]) ).
cnf(c_0_1326,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_979]) ).
cnf(c_0_1327,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_980]) ).
cnf(c_0_1328,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X1),X3),X2) = X1
| ~ class_Lattices_Olattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_981]) ).
cnf(c_0_1329,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_982]) ).
cnf(c_0_1330,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_983]) ).
cnf(c_0_1331,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_984]) ).
cnf(c_0_1332,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_985]) ).
cnf(c_0_1333,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_986]) ).
cnf(c_0_1334,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1335,plain,
( hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1336,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_989]) ).
cnf(c_0_1337,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1338,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_991]) ).
cnf(c_0_1339,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_992]) ).
cnf(c_0_1340,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_993]) ).
cnf(c_0_1341,plain,
( c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_994]) ).
cnf(c_0_1342,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_995]) ).
cnf(c_0_1343,plain,
( c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1344,plain,
( c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1345,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1346,plain,
( X1 = X3
| ~ hBOOL(hAPP(c_fequal(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_999]) ).
cnf(c_0_1347,plain,
( c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3))
| ~ c_Com_OWT(c_Com_Ocom_OBODY(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1348,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1349,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1350,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1003]) ).
cnf(c_0_1351,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1004]) ).
cnf(c_0_1352,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1005]) ).
cnf(c_0_1353,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1354,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1355,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1356,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1357,plain,
( hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1010]) ).
cnf(c_0_1358,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1011]) ).
cnf(c_0_1359,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1012]) ).
cnf(c_0_1360,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1013]) ).
cnf(c_0_1361,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1014]) ).
cnf(c_0_1362,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1363,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1364,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1365,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1366,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1367,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1020]) ).
cnf(c_0_1368,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1369,plain,
( X1 = X2
| c_Option_Ooption_OSome(X1,X3) != c_Option_Ooption_OSome(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1370,plain,
( c_Com_OWT(X1)
| ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X2) != c_Option_Ooption_OSome(X1,tc_Com_Ocom) ),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1371,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1372,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1373,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1026]) ).
cnf(c_0_1374,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1027]) ).
cnf(c_0_1375,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1028]) ).
cnf(c_0_1376,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1029]) ).
cnf(c_0_1377,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1378,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1031]) ).
cnf(c_0_1379,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1032]) ).
cnf(c_0_1380,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1381,plain,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1034]) ).
cnf(c_0_1382,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1035]) ).
cnf(c_0_1383,plain,
( hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(c_Com_Ocom_OBODY(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1036]) ).
cnf(c_0_1384,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1037]) ).
cnf(c_0_1385,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1038]) ).
cnf(c_0_1386,plain,
( X1 = X2
| c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1039]) ).
cnf(c_0_1387,plain,
( X1 = X2
| c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(split_conjunct,[status(thm)],[c_0_1040]) ).
cnf(c_0_1388,plain,
( hAPP(X1,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X5,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1041,
[final] ).
cnf(c_0_1389,plain,
( hAPP(X2,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X6,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1042,
[final] ).
cnf(c_0_1390,plain,
( hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
c_0_1043,
[final] ).
cnf(c_0_1391,plain,
( hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
c_0_1044,
[final] ).
cnf(c_0_1392,plain,
( hAPP(X1,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1045,
[final] ).
cnf(c_0_1393,plain,
( hAPP(X2,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1046,
[final] ).
cnf(c_0_1394,plain,
( hAPP(X1,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X5,X10),hAPP(X1,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1047,
[final] ).
cnf(c_0_1395,plain,
( hAPP(X2,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X6,X10),hAPP(X2,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1048,
[final] ).
cnf(c_0_1396,plain,
( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1049,
[final] ).
cnf(c_0_1397,plain,
( hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X7
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1050,
[final] ).
cnf(c_0_1398,plain,
( hBOOL(c_in(X3,X4,X2))
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),X5,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2)
| ~ hBOOL(c_in(X6,X4,X2)) ),
c_0_1051,
[final] ).
cnf(c_0_1399,plain,
( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7)
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| ~ hBOOL(c_in(X4,X3,X5)) ),
c_0_1052,
[final] ).
cnf(c_0_1400,plain,
( hBOOL(c_in(X3,X4,X2))
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,X4,X2),hAPP(hAPP(X1,X6),X5),X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2) ),
c_0_1053,
[final] ).
cnf(c_0_1401,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7) ),
c_0_1054,
[final] ).
cnf(c_0_1402,plain,
( hBOOL(c_in(X2,X3,X5))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5) ),
c_0_1055,
[final] ).
cnf(c_0_1403,plain,
( X4 = X2
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,X5) ),
c_0_1056,
[final] ).
cnf(c_0_1404,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X6) ),
c_0_1057,
[final] ).
cnf(c_0_1405,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X5,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OBODY(X2),X3,X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OBODY(X2),X3,X4),X5,tc_Hoare__Mirabelle_Otriple(X4)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Option_Othe(hAPP(c_Com_Obody,X2),tc_Com_Ocom),X3,X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
c_0_1058,
[final] ).
cnf(c_0_1406,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
c_0_1059,
[final] ).
cnf(c_0_1407,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
c_0_1060,
[final] ).
cnf(c_0_1408,plain,
( hAPP(X2,X1) = X3
| ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5)) ),
c_0_1061,
[final] ).
cnf(c_0_1409,plain,
( c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
c_0_1062,
[final] ).
cnf(c_0_1410,plain,
( hBOOL(c_in(hAPP(X2,X1),X3,X5))
| ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)) ),
c_0_1063,
[final] ).
cnf(c_0_1411,plain,
( hBOOL(c_in(hAPP(X2,X1),X3,X5))
| ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)) ),
c_0_1064,
[final] ).
cnf(c_0_1412,plain,
( X2 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X4)) ),
c_0_1065,
[final] ).
cnf(c_0_1413,plain,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
c_0_1066,
[final] ).
cnf(c_0_1414,plain,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
c_0_1067,
[final] ).
cnf(c_0_1415,plain,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
c_0_1068,
[final] ).
cnf(c_0_1416,plain,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
c_0_1069,
[final] ).
cnf(c_0_1417,plain,
( c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
| c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4) ),
c_0_1070,
[final] ).
cnf(c_0_1418,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X1)),X2,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
c_0_1071,
[final] ).
cnf(c_0_1419,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
c_0_1072,
[final] ).
cnf(c_0_1420,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
c_0_1073,
[final] ).
cnf(c_0_1421,plain,
( c_Map_Omap__le(X2,X5,X3,X4)
| ~ c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4) ),
c_0_1074,
[final] ).
cnf(c_0_1422,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X1,X3)) ),
c_0_1075,
[final] ).
cnf(c_0_1423,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X1,X3)) ),
c_0_1076,
[final] ).
cnf(c_0_1424,plain,
( hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
c_0_1077,
[final] ).
cnf(c_0_1425,plain,
( hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
c_0_1078,
[final] ).
cnf(c_0_1426,plain,
( hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
c_0_1079,
[final] ).
cnf(c_0_1427,plain,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
c_0_1080,
[final] ).
cnf(c_0_1428,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
c_0_1081,
[final] ).
cnf(c_0_1429,plain,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
c_0_1082,
[final] ).
cnf(c_0_1430,plain,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
c_0_1083,
[final] ).
cnf(c_0_1431,plain,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1084,
[final] ).
cnf(c_0_1432,plain,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1085,
[final] ).
cnf(c_0_1433,plain,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1086,
[final] ).
cnf(c_0_1434,plain,
( hBOOL(hAPP(X4,X1))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
c_0_1087,
[final] ).
cnf(c_0_1435,plain,
( c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X1,X3)) ),
c_0_1088,
[final] ).
cnf(c_0_1436,plain,
( hBOOL(c_in(hAPP(X1,X6),X5,X4))
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X2,X3)) ),
c_0_1089,
[final] ).
cnf(c_0_1437,plain,
( c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1090,
[final] ).
cnf(c_0_1438,plain,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1091,
[final] ).
cnf(c_0_1439,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
c_0_1092,
[final] ).
cnf(c_0_1440,plain,
( hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
c_0_1093,
[final] ).
cnf(c_0_1441,plain,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
c_0_1094,
[final] ).
cnf(c_0_1442,plain,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
c_0_1095,
[final] ).
cnf(c_0_1443,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X1,X4)) ),
c_0_1096,
[final] ).
cnf(c_0_1444,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X2)),X2)
| ~ class_Lattices_Olattice(X2) ),
c_0_1097,
[final] ).
cnf(c_0_1445,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X1,tc_fun(X3,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool))) ),
c_0_1098,
[final] ).
cnf(c_0_1446,plain,
( c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
c_0_1099,
[final] ).
cnf(c_0_1447,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1100,
[final] ).
cnf(c_0_1448,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
c_0_1101,
[final] ).
cnf(c_0_1449,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
c_0_1102,
[final] ).
cnf(c_0_1450,plain,
( hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X2,X1)
| ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3)) ),
c_0_1103,
[final] ).
cnf(c_0_1451,plain,
( c_Map_Omap__le(X1,X5,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X5,X3,X4) ),
c_0_1104,
[final] ).
cnf(c_0_1452,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X4,X1)) ),
c_0_1105,
[final] ).
cnf(c_0_1453,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1106,
[final] ).
cnf(c_0_1454,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
c_0_1107,
[final] ).
cnf(c_0_1455,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
c_0_1108,
[final] ).
cnf(c_0_1456,plain,
( hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X2,X4)),c_Finite__Set_Ofold1(X1,X3,X4)) = c_Finite__Set_Ofold1(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4)
| ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_1109,
[final] ).
cnf(c_0_1457,plain,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)) ),
c_0_1110,
[final] ).
cnf(c_0_1458,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
c_0_1111,
[final] ).
cnf(c_0_1459,plain,
( hAPP(X1,X5) = hAPP(X2,X5)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ hBOOL(c_in(X5,c_Map_Odom(X1,X3,X4),X3)) ),
c_0_1112,
[final] ).
cnf(c_0_1460,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
c_0_1113,
[final] ).
cnf(c_0_1461,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)),X1)
| ~ class_Lattices_Olattice(X1) ),
c_0_1114,
[final] ).
cnf(c_0_1462,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
c_0_1115,
[final] ).
cnf(c_0_1463,plain,
( hBOOL(c_in(X1,X2,X4))
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
c_0_1116,
[final] ).
cnf(c_0_1464,plain,
( hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(X5,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4) ),
c_0_1117,
[final] ).
cnf(c_0_1465,plain,
( c_Set_Oinsert(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2)
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1118,
[final] ).
cnf(c_0_1466,plain,
( hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4) ),
c_0_1119,
[final] ).
cnf(c_0_1467,plain,
( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X5,X1) ),
c_0_1120,
[final] ).
cnf(c_0_1468,plain,
( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(c_Map_Omap__add(X2,X5,X3,X4),X1) = hAPP(X5,X1) ),
c_0_1121,
[final] ).
cnf(c_0_1469,plain,
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
c_0_1122,
[final] ).
cnf(c_0_1470,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_1123,
[final] ).
cnf(c_0_1471,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_1124,
[final] ).
cnf(c_0_1472,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_1125,
[final] ).
cnf(c_0_1473,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_1126,
[final] ).
cnf(c_0_1474,plain,
( ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
c_0_1127,
[final] ).
cnf(c_0_1475,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
c_0_1128,
[final] ).
cnf(c_0_1476,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
c_0_1129,
[final] ).
cnf(c_0_1477,plain,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1130,
[final] ).
cnf(c_0_1478,plain,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1131,
[final] ).
cnf(c_0_1479,plain,
( X1 = X2
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X1,X3,X4) ),
c_0_1132,
[final] ).
cnf(c_0_1480,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X1,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1133,
[final] ).
cnf(c_0_1481,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
c_0_1134,
[final] ).
cnf(c_0_1482,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
c_0_1135,
[final] ).
cnf(c_0_1483,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
c_0_1136,
[final] ).
cnf(c_0_1484,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
c_0_1137,
[final] ).
cnf(c_0_1485,plain,
( hBOOL(c_in(X1,X2,X4))
| ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
c_0_1138,
[final] ).
cnf(c_0_1486,plain,
( c_Set_Oinsert(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1139,
[final] ).
cnf(c_0_1487,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) ),
c_0_1140,
[final] ).
cnf(c_0_1488,plain,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
c_0_1141,
[final] ).
cnf(c_0_1489,plain,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1142,
[final] ).
cnf(c_0_1490,plain,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1143,
[final] ).
cnf(c_0_1491,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_1144,
[final] ).
cnf(c_0_1492,plain,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1145,
[final] ).
cnf(c_0_1493,plain,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1146,
[final] ).
cnf(c_0_1494,plain,
( c_lessequals(c_Map_Odom(X1,X3,X4),c_Map_Odom(X2,X3,X4),tc_fun(X3,tc_bool))
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
c_0_1147,
[final] ).
cnf(c_0_1495,plain,
( c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
c_0_1148,
[final] ).
cnf(c_0_1496,plain,
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
c_0_1149,
[final] ).
cnf(c_0_1497,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1150,
[final] ).
cnf(c_0_1498,plain,
( hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(X2) ),
c_0_1151,
[final] ).
cnf(c_0_1499,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
c_0_1152,
[final] ).
cnf(c_0_1500,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
c_0_1153,
[final] ).
cnf(c_0_1501,plain,
( X1 = X2
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)) ),
c_0_1154,
[final] ).
cnf(c_0_1502,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(c_in(X4,X3,X1)) ),
c_0_1155,
[final] ).
cnf(c_0_1503,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) ),
c_0_1156,
[final] ).
cnf(c_0_1504,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
c_0_1157,
[final] ).
cnf(c_0_1505,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
c_0_1158,
[final] ).
cnf(c_0_1506,plain,
( c_lessequals(X2,X5,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1159,
[final] ).
cnf(c_0_1507,plain,
( c_lessequals(X4,X1,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1160,
[final] ).
cnf(c_0_1508,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1161,
[final] ).
cnf(c_0_1509,plain,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1162,
[final] ).
cnf(c_0_1510,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
c_0_1163,
[final] ).
cnf(c_0_1511,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_OSome(X6,X4) ),
c_0_1164,
[final] ).
cnf(c_0_1512,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
c_0_1165,
[final] ).
cnf(c_0_1513,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
c_0_1166,
[final] ).
cnf(c_0_1514,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1167,
[final] ).
cnf(c_0_1515,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1168,
[final] ).
cnf(c_0_1516,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
c_0_1169,
[final] ).
cnf(c_0_1517,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_1170,
[final] ).
cnf(c_0_1518,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
c_0_1171,
[final] ).
cnf(c_0_1519,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_OSome(X6,X4) ),
c_0_1172,
[final] ).
cnf(c_0_1520,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_OSome(X6,X4) ),
c_0_1173,
[final] ).
cnf(c_0_1521,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_lessequals(X3,X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1174,
[final] ).
cnf(c_0_1522,plain,
( ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(X2,X1) != c_Option_Ooption_ONone(X4) ),
c_0_1175,
[final] ).
cnf(c_0_1523,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_1176,
[final] ).
cnf(c_0_1524,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X2)) = c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Odistrib__lattice(X2) ),
c_0_1177,
[final] ).
cnf(c_0_1525,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_1178,
[final] ).
cnf(c_0_1526,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1179,
[final] ).
cnf(c_0_1527,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2 ),
c_0_1180,
[final] ).
cnf(c_0_1528,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4) ),
c_0_1181,
[final] ).
cnf(c_0_1529,plain,
( c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),c_Set_Oinsert(X4,X5,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),X5,tc_fun(X2,tc_bool))
| hAPP(X1,X4) != c_Option_Ooption_ONone(X3) ),
c_0_1182,
[final] ).
cnf(c_0_1530,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1183,
[final] ).
cnf(c_0_1531,plain,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1184,
[final] ).
cnf(c_0_1532,plain,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1185,
[final] ).
cnf(c_0_1533,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X4,X3,X2))
| c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X4,X3,X2),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1186,
[final] ).
cnf(c_0_1534,plain,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1187,
[final] ).
cnf(c_0_1535,plain,
( hBOOL(c_in(X2,X1,X4))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
c_0_1188,
[final] ).
cnf(c_0_1536,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
c_0_1189,
[final] ).
cnf(c_0_1537,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1190,
[final] ).
cnf(c_0_1538,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1191,
[final] ).
cnf(c_0_1539,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1192,
[final] ).
cnf(c_0_1540,plain,
( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1193,
[final] ).
cnf(c_0_1541,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_1194,
[final] ).
cnf(c_0_1542,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1195,
[final] ).
cnf(c_0_1543,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
c_0_1196,
[final] ).
cnf(c_0_1544,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
c_0_1197,
[final] ).
cnf(c_0_1545,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1198,
[final] ).
cnf(c_0_1546,plain,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
c_0_1199,
[final] ).
cnf(c_0_1547,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_1200,
[final] ).
cnf(c_0_1548,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_1201,
[final] ).
cnf(c_0_1549,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1202,
[final] ).
cnf(c_0_1550,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1203,
[final] ).
cnf(c_0_1551,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1204,
[final] ).
cnf(c_0_1552,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
c_0_1205,
[final] ).
cnf(c_0_1553,plain,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1206,
[final] ).
cnf(c_0_1554,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
c_0_1207,
[final] ).
cnf(c_0_1555,plain,
( hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1208,
[final] ).
cnf(c_0_1556,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
c_0_1209,
[final] ).
cnf(c_0_1557,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
c_0_1210,
[final] ).
cnf(c_0_1558,plain,
( hBOOL(c_in(X1,X4,X3))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_1211,
[final] ).
cnf(c_0_1559,plain,
( X1 = X2
| hBOOL(c_in(X3,X1,X4))
| hBOOL(c_in(X3,X2,X4))
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
c_0_1212,
[final] ).
cnf(c_0_1560,plain,
( ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X1)) ),
c_0_1213,
[final] ).
cnf(c_0_1561,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1214,
[final] ).
cnf(c_0_1562,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1215,
[final] ).
cnf(c_0_1563,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X1) ),
c_0_1216,
[final] ).
cnf(c_0_1564,plain,
( c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1217,
[final] ).
cnf(c_0_1565,plain,
( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(X2,X1) != c_Option_Ooption_OSome(X5,X4) ),
c_0_1218,
[final] ).
cnf(c_0_1566,plain,
( hBOOL(hAPP(X3,X1))
| ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
c_0_1219,
[final] ).
cnf(c_0_1567,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_1220,
[final] ).
cnf(c_0_1568,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_1221,
[final] ).
cnf(c_0_1569,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1222,
[final] ).
cnf(c_0_1570,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1223,
[final] ).
cnf(c_0_1571,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hBOOL(c_in(X2,c_Map_Odom(X1,X4,X3),X4)) ),
c_0_1224,
[final] ).
cnf(c_0_1572,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1225,
[final] ).
cnf(c_0_1573,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1226,
[final] ).
cnf(c_0_1574,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1227,
[final] ).
cnf(c_0_1575,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1228,
[final] ).
cnf(c_0_1576,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1229,
[final] ).
cnf(c_0_1577,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1230,
[final] ).
cnf(c_0_1578,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
c_0_1231,
[final] ).
cnf(c_0_1579,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_1232,
[final] ).
cnf(c_0_1580,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1233,
[final] ).
cnf(c_0_1581,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
c_0_1234,
[final] ).
cnf(c_0_1582,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
c_0_1235,
[final] ).
cnf(c_0_1583,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1236,
[final] ).
cnf(c_0_1584,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
c_0_1237,
[final] ).
cnf(c_0_1585,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1238,
[final] ).
cnf(c_0_1586,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1239,
[final] ).
cnf(c_0_1587,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1240,
[final] ).
cnf(c_0_1588,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1241,
[final] ).
cnf(c_0_1589,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1242,
[final] ).
cnf(c_0_1590,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1243,
[final] ).
cnf(c_0_1591,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1244,
[final] ).
cnf(c_0_1592,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1245,
[final] ).
cnf(c_0_1593,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1246,
[final] ).
cnf(c_0_1594,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_1247,
[final] ).
cnf(c_0_1595,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1248,
[final] ).
cnf(c_0_1596,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1249,
[final] ).
cnf(c_0_1597,plain,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1250,
[final] ).
cnf(c_0_1598,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1251,
[final] ).
cnf(c_0_1599,plain,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1252,
[final] ).
cnf(c_0_1600,plain,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1253,
[final] ).
cnf(c_0_1601,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
c_0_1254,
[final] ).
cnf(c_0_1602,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1255,
[final] ).
cnf(c_0_1603,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1256,
[final] ).
cnf(c_0_1604,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1257,
[final] ).
cnf(c_0_1605,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3)) ),
c_0_1258,
[final] ).
cnf(c_0_1606,plain,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
c_0_1259,
[final] ).
cnf(c_0_1607,plain,
( c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
c_0_1260,
[final] ).
cnf(c_0_1608,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1261,
[final] ).
cnf(c_0_1609,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1262,
[final] ).
cnf(c_0_1610,plain,
( c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_HOL_Ominus(X3) ),
c_0_1263,
[final] ).
cnf(c_0_1611,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_Lattices_Olattice(X3) ),
c_0_1264,
[final] ).
cnf(c_0_1612,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1265,
[final] ).
cnf(c_0_1613,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1266,
[final] ).
cnf(c_0_1614,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1267,
[final] ).
cnf(c_0_1615,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1268,
[final] ).
cnf(c_0_1616,plain,
( hBOOL(c_in(X3,X4,X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Set_Oinsert(X3,X4,X5) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1269,
[final] ).
cnf(c_0_1617,plain,
( c_Set_Oinsert(X1,c_Map_Odom(X2,X3,X4),X3) = c_Map_Odom(X2,X3,X4)
| hAPP(X2,X1) != c_Option_Ooption_OSome(X5,X4) ),
c_0_1270,
[final] ).
cnf(c_0_1618,plain,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_1271,
[final] ).
cnf(c_0_1619,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1272,
[final] ).
cnf(c_0_1620,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1273,
[final] ).
cnf(c_0_1621,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1274,
[final] ).
cnf(c_0_1622,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1275,
[final] ).
cnf(c_0_1623,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_1276,
[final] ).
cnf(c_0_1624,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_1277,
[final] ).
cnf(c_0_1625,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_1278,
[final] ).
cnf(c_0_1626,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1279,
[final] ).
cnf(c_0_1627,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1280,
[final] ).
cnf(c_0_1628,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1281,
[final] ).
cnf(c_0_1629,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
c_0_1282,
[final] ).
cnf(c_0_1630,plain,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
c_0_1283,
[final] ).
cnf(c_0_1631,plain,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
c_0_1284,
[final] ).
cnf(c_0_1632,plain,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
c_0_1285,
[final] ).
cnf(c_0_1633,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
c_0_1286,
[final] ).
cnf(c_0_1634,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1287,
[final] ).
cnf(c_0_1635,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
c_0_1288,
[final] ).
cnf(c_0_1636,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1289,
[final] ).
cnf(c_0_1637,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1290,
[final] ).
cnf(c_0_1638,plain,
( ~ c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1291,
[final] ).
cnf(c_0_1639,plain,
( ~ c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_1292,
[final] ).
cnf(c_0_1640,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1293,
[final] ).
cnf(c_0_1641,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1294,
[final] ).
cnf(c_0_1642,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
c_0_1295,
[final] ).
cnf(c_0_1643,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1296,
[final] ).
cnf(c_0_1644,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1297,
[final] ).
cnf(c_0_1645,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1298,
[final] ).
cnf(c_0_1646,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1299,
[final] ).
cnf(c_0_1647,plain,
( hBOOL(c_in(X2,c_Collect(X1,X3),X3))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1300,
[final] ).
cnf(c_0_1648,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1301,
[final] ).
cnf(c_0_1649,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),c_Complete__Lattice_OInf__class_OInf(X2,X3)) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1302,
[final] ).
cnf(c_0_1650,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1303,
[final] ).
cnf(c_0_1651,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
c_0_1304,
[final] ).
cnf(c_0_1652,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
c_0_1305,
[final] ).
cnf(c_0_1653,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1306,
[final] ).
cnf(c_0_1654,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1307,
[final] ).
cnf(c_0_1655,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
c_0_1308,
[final] ).
cnf(c_0_1656,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
c_0_1309,
[final] ).
cnf(c_0_1657,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1310,
[final] ).
cnf(c_0_1658,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1311,
[final] ).
cnf(c_0_1659,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1312,
[final] ).
cnf(c_0_1660,plain,
( c_Com_OWT(c_Com_Ocom_OBODY(X2))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3)) ),
c_0_1313,
[final] ).
cnf(c_0_1661,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1314,
[final] ).
cnf(c_0_1662,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1315,
[final] ).
cnf(c_0_1663,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1316,
[final] ).
cnf(c_0_1664,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_1317,
[final] ).
cnf(c_0_1665,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1318,
[final] ).
cnf(c_0_1666,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2) ),
c_0_1319,
[final] ).
cnf(c_0_1667,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6) ),
c_0_1320,
[final] ).
cnf(c_0_1668,plain,
( X1 = X2
| c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6) ),
c_0_1321,
[final] ).
cnf(c_0_1669,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1322,
[final] ).
cnf(c_0_1670,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1323,
[final] ).
cnf(c_0_1671,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1324,
[final] ).
cnf(c_0_1672,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1325,
[final] ).
cnf(c_0_1673,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1326,
[final] ).
cnf(c_0_1674,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = X2
| ~ class_Lattices_Olattice(X1) ),
c_0_1327,
[final] ).
cnf(c_0_1675,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X1),X3),X2) = X1
| ~ class_Lattices_Olattice(X2) ),
c_0_1328,
[final] ).
cnf(c_0_1676,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
c_0_1329,
[final] ).
cnf(c_0_1677,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
c_0_1330,
[final] ).
cnf(c_0_1678,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1331,
[final] ).
cnf(c_0_1679,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1332,
[final] ).
cnf(c_0_1680,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
c_0_1333,
[final] ).
cnf(c_0_1681,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
c_0_1334,
[final] ).
cnf(c_0_1682,plain,
( hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1335,
[final] ).
cnf(c_0_1683,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1336,
[final] ).
cnf(c_0_1684,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1337,
[final] ).
cnf(c_0_1685,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1338,
[final] ).
cnf(c_0_1686,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1339,
[final] ).
cnf(c_0_1687,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1340,
[final] ).
cnf(c_0_1688,plain,
( c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1341,
[final] ).
cnf(c_0_1689,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1342,
[final] ).
cnf(c_0_1690,plain,
( c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1343,
[final] ).
cnf(c_0_1691,plain,
( c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_1344,
[final] ).
cnf(c_0_1692,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
c_0_1345,
[final] ).
cnf(c_0_1693,plain,
( X1 = X3
| ~ hBOOL(hAPP(c_fequal(X1,X2),X3)) ),
c_0_1346,
[final] ).
cnf(c_0_1694,plain,
( c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3))
| ~ c_Com_OWT(c_Com_Ocom_OBODY(X1)) ),
c_0_1347,
[final] ).
cnf(c_0_1695,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1348,
[final] ).
cnf(c_0_1696,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1349,
[final] ).
cnf(c_0_1697,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1350,
[final] ).
cnf(c_0_1698,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3) ),
c_0_1351,
[final] ).
cnf(c_0_1699,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1352,
[final] ).
cnf(c_0_1700,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
c_0_1353,
[final] ).
cnf(c_0_1701,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1354,
[final] ).
cnf(c_0_1702,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1355,
[final] ).
cnf(c_0_1703,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1356,
[final] ).
cnf(c_0_1704,plain,
( hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_1357,
[final] ).
cnf(c_0_1705,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1358,
[final] ).
cnf(c_0_1706,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_1359,
[final] ).
cnf(c_0_1707,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
c_0_1360,
[final] ).
cnf(c_0_1708,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_1361,
[final] ).
cnf(c_0_1709,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_1362,
[final] ).
cnf(c_0_1710,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1363,
[final] ).
cnf(c_0_1711,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
c_0_1364,
[final] ).
cnf(c_0_1712,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_1365,
[final] ).
cnf(c_0_1713,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1366,
[final] ).
cnf(c_0_1714,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1367,
[final] ).
cnf(c_0_1715,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1368,
[final] ).
cnf(c_0_1716,plain,
( X1 = X2
| c_Option_Ooption_OSome(X1,X3) != c_Option_Ooption_OSome(X2,X3) ),
c_0_1369,
[final] ).
cnf(c_0_1717,plain,
( c_Com_OWT(X1)
| ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X2) != c_Option_Ooption_OSome(X1,tc_Com_Ocom) ),
c_0_1370,
[final] ).
cnf(c_0_1718,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_1371,
[final] ).
cnf(c_0_1719,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1372,
[final] ).
cnf(c_0_1720,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1373,
[final] ).
cnf(c_0_1721,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1374,
[final] ).
cnf(c_0_1722,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_1375,
[final] ).
cnf(c_0_1723,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_1376,
[final] ).
cnf(c_0_1724,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1377,
[final] ).
cnf(c_0_1725,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1378,
[final] ).
cnf(c_0_1726,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_1379,
[final] ).
cnf(c_0_1727,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
c_0_1380,
[final] ).
cnf(c_0_1728,plain,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
c_0_1381,
[final] ).
cnf(c_0_1729,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
c_0_1382,
[final] ).
cnf(c_0_1730,plain,
( hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(c_Com_Ocom_OBODY(X1)) ),
c_0_1383,
[final] ).
cnf(c_0_1731,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_1384,
[final] ).
cnf(c_0_1732,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
c_0_1385,
[final] ).
cnf(c_0_1733,plain,
( X1 = X2
| c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2) ),
c_0_1386,
[final] ).
cnf(c_0_1734,plain,
( X1 = X2
| c_Hoare__Mirabelle_Ostate__not__singleton ),
c_0_1387,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1388_0,axiom,
( hAPP(X1,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X5,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1388]) ).
cnf(c_0_1388_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X5,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_1388]) ).
cnf(c_0_1389_0,axiom,
( hAPP(X2,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X6,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1389]) ).
cnf(c_0_1389_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X6,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_1389]) ).
cnf(c_0_1390_0,axiom,
( hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1390]) ).
cnf(c_0_1390_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1390]) ).
cnf(c_0_1390_2,axiom,
( ~ hBOOL(c_in(X10,X11,X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_1390]) ).
cnf(c_0_1391_0,axiom,
( hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1391]) ).
cnf(c_0_1391_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1391]) ).
cnf(c_0_1391_2,axiom,
( ~ hBOOL(c_in(X10,X11,X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11))) ),
inference(literals_permutation,[status(thm)],[c_0_1391]) ).
cnf(c_0_1392_0,axiom,
( hAPP(X1,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1392]) ).
cnf(c_0_1392_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10 ),
inference(literals_permutation,[status(thm)],[c_0_1392]) ).
cnf(c_0_1393_0,axiom,
( hAPP(X2,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1393]) ).
cnf(c_0_1393_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10 ),
inference(literals_permutation,[status(thm)],[c_0_1393]) ).
cnf(c_0_1394_0,axiom,
( hAPP(X1,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X5,X10),hAPP(X1,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1394]) ).
cnf(c_0_1394_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X5,X10),hAPP(X1,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_1394]) ).
cnf(c_0_1395_0,axiom,
( hAPP(X2,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X6,X10),hAPP(X2,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1395]) ).
cnf(c_0_1395_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X6,X10),hAPP(X2,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_1395]) ).
cnf(c_0_1396_0,axiom,
( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1396]) ).
cnf(c_0_1396_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X8 ),
inference(literals_permutation,[status(thm)],[c_0_1396]) ).
cnf(c_0_1397_0,axiom,
( hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X7
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1397]) ).
cnf(c_0_1397_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1397]) ).
cnf(c_0_1398_0,axiom,
( hBOOL(c_in(X3,X4,X2))
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),X5,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2)
| ~ hBOOL(c_in(X6,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1398]) ).
cnf(c_0_1398_1,axiom,
( c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),X5,X2,X2)
| hBOOL(c_in(X3,X4,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2)
| ~ hBOOL(c_in(X6,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1398]) ).
cnf(c_0_1398_2,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),X5,X2,X2)
| hBOOL(c_in(X3,X4,X2))
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2)
| ~ hBOOL(c_in(X6,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1398]) ).
cnf(c_0_1398_3,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),X5,X2,X2)
| hBOOL(c_in(X3,X4,X2))
| ~ hBOOL(c_in(X6,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1398]) ).
cnf(c_0_1398_4,axiom,
( ~ hBOOL(c_in(X6,X4,X2))
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),X5,X2,X2)
| hBOOL(c_in(X3,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1398]) ).
cnf(c_0_1399_0,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7)
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| ~ hBOOL(c_in(X4,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1399]) ).
cnf(c_0_1399_1,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7)
| ~ hBOOL(c_in(X4,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1399]) ).
cnf(c_0_1399_2,axiom,
( ~ hBOOL(c_in(X4,X3,X5))
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1399]) ).
cnf(c_0_1400_0,axiom,
( hBOOL(c_in(X3,X4,X2))
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,X4,X2),hAPP(hAPP(X1,X6),X5),X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1400]) ).
cnf(c_0_1400_1,axiom,
( c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,X4,X2),hAPP(hAPP(X1,X6),X5),X2,X2)
| hBOOL(c_in(X3,X4,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1400]) ).
cnf(c_0_1400_2,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,X4,X2),hAPP(hAPP(X1,X6),X5),X2,X2)
| hBOOL(c_in(X3,X4,X2))
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1400]) ).
cnf(c_0_1400_3,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold__graph(X1,X6,c_Set_Oinsert(X3,X4,X2),hAPP(hAPP(X1,X6),X5),X2,X2)
| hBOOL(c_in(X3,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1400]) ).
cnf(c_0_1401_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1401]) ).
cnf(c_0_1401_1,axiom,
( c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| hBOOL(c_in(X1,X2,X3))
| ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1401]) ).
cnf(c_0_1401_2,axiom,
( ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7)
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1401]) ).
cnf(c_0_1402_0,axiom,
( hBOOL(c_in(X2,X3,X5))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1402]) ).
cnf(c_0_1402_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| hBOOL(c_in(X2,X3,X5))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1402]) ).
cnf(c_0_1402_2,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5)
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| hBOOL(c_in(X2,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1402]) ).
cnf(c_0_1403_0,axiom,
( X4 = X2
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1403]) ).
cnf(c_0_1403_1,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,X5)
| X4 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1403]) ).
cnf(c_0_1404_0,axiom,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1404]) ).
cnf(c_0_1404_1,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X6)
| c_Finite__Set_Ofinite(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1404]) ).
cnf(c_0_1405_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X5,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OBODY(X2),X3,X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OBODY(X2),X3,X4),X5,tc_Hoare__Mirabelle_Otriple(X4)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Option_Othe(hAPP(c_Com_Obody,X2),tc_Com_Ocom),X3,X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1405]) ).
cnf(c_0_1405_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OBODY(X2),X3,X4),X5,tc_Hoare__Mirabelle_Otriple(X4)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Option_Othe(hAPP(c_Com_Obody,X2),tc_Com_Ocom),X3,X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X5,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OBODY(X2),X3,X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1405]) ).
cnf(c_0_1406_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1406]) ).
cnf(c_0_1406_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1406]) ).
cnf(c_0_1406_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1406]) ).
cnf(c_0_1407_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1407]) ).
cnf(c_0_1407_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1407]) ).
cnf(c_0_1408_0,axiom,
( hAPP(X2,X1) = X3
| ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1408]) ).
cnf(c_0_1408_1,axiom,
( ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5))
| hAPP(X2,X1) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1408]) ).
cnf(c_0_1409_0,axiom,
( c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1409]) ).
cnf(c_0_1409_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1409]) ).
cnf(c_0_1409_2,axiom,
( ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1409]) ).
cnf(c_0_1409_3,axiom,
( ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1409]) ).
cnf(c_0_1410_0,axiom,
( hBOOL(c_in(hAPP(X2,X1),X3,X5))
| ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1410]) ).
cnf(c_0_1410_1,axiom,
( ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
| hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1410]) ).
cnf(c_0_1411_0,axiom,
( hBOOL(c_in(hAPP(X2,X1),X3,X5))
| ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1411]) ).
cnf(c_0_1411_1,axiom,
( ~ hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
| hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1411]) ).
cnf(c_0_1412_0,axiom,
( X2 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1412]) ).
cnf(c_0_1412_1,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X4))
| X2 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1412]) ).
cnf(c_0_1413_0,axiom,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1413]) ).
cnf(c_0_1413_1,axiom,
( ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
| hBOOL(hAPP(X2,hAPP(X1,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_1413]) ).
cnf(c_0_1414_0,axiom,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1414]) ).
cnf(c_0_1414_1,axiom,
( ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
| c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1414]) ).
cnf(c_0_1415_0,axiom,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1415]) ).
cnf(c_0_1415_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1415]) ).
cnf(c_0_1415_2,axiom,
( ~ hBOOL(c_in(X4,hAPP(X5,X1),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1415]) ).
cnf(c_0_1416_0,axiom,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1416]) ).
cnf(c_0_1416_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1416]) ).
cnf(c_0_1416_2,axiom,
( ~ hBOOL(c_in(X4,hAPP(X5,X1),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1416]) ).
cnf(c_0_1417_0,axiom,
( c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
| c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1417]) ).
cnf(c_0_1417_1,axiom,
( c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4)
| c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1417]) ).
cnf(c_0_1418_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X1)),X2,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1418]) ).
cnf(c_0_1418_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X1)),X2,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1418]) ).
cnf(c_0_1419_0,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1419]) ).
cnf(c_0_1419_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1419]) ).
cnf(c_0_1419_2,axiom,
( ~ hBOOL(hAPP(hAPP(X4,X1),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1419]) ).
cnf(c_0_1420_0,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1420]) ).
cnf(c_0_1420_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1420]) ).
cnf(c_0_1420_2,axiom,
( ~ hBOOL(hAPP(hAPP(X4,X1),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1420]) ).
cnf(c_0_1421_0,axiom,
( c_Map_Omap__le(X2,X5,X3,X4)
| ~ c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1421]) ).
cnf(c_0_1421_1,axiom,
( ~ c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4)
| c_Map_Omap__le(X2,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1421]) ).
cnf(c_0_1422_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1422]) ).
cnf(c_0_1422_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1422]) ).
cnf(c_0_1422_2,axiom,
( ~ hBOOL(c_in(X2,X1,X3))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1422]) ).
cnf(c_0_1423_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1423]) ).
cnf(c_0_1423_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1423]) ).
cnf(c_0_1423_2,axiom,
( ~ hBOOL(c_in(X2,X1,X3))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1423]) ).
cnf(c_0_1424_0,axiom,
( hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1424]) ).
cnf(c_0_1424_1,axiom,
( ~ hBOOL(c_in(hAPP(X1,X2),X3,X4))
| hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1424]) ).
cnf(c_0_1425_0,axiom,
( hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1425]) ).
cnf(c_0_1425_1,axiom,
( ~ hBOOL(c_in(hAPP(X1,X2),X3,X4))
| hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1425]) ).
cnf(c_0_1426_0,axiom,
( hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1426]) ).
cnf(c_0_1426_1,axiom,
( ~ hBOOL(c_in(hAPP(X1,X2),X3,X4))
| hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1426]) ).
cnf(c_0_1427_0,axiom,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1427]) ).
cnf(c_0_1427_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2))
| hBOOL(c_in(X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1427]) ).
cnf(c_0_1428_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1428]) ).
cnf(c_0_1428_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1428]) ).
cnf(c_0_1428_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1428]) ).
cnf(c_0_1429_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1429]) ).
cnf(c_0_1429_1,axiom,
( ~ hBOOL(c_in(X2,X3,X4))
| hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1429]) ).
cnf(c_0_1430_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1430]) ).
cnf(c_0_1430_1,axiom,
( ~ hBOOL(c_in(X2,X3,X4))
| hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1430]) ).
cnf(c_0_1431_0,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1431]) ).
cnf(c_0_1431_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1431]) ).
cnf(c_0_1432_0,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1432]) ).
cnf(c_0_1432_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1432]) ).
cnf(c_0_1433_0,axiom,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1433]) ).
cnf(c_0_1433_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1433]) ).
cnf(c_0_1434_0,axiom,
( hBOOL(hAPP(X4,X1))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1434]) ).
cnf(c_0_1434_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2))
| hBOOL(hAPP(X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1434]) ).
cnf(c_0_1435_0,axiom,
( c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1435]) ).
cnf(c_0_1435_1,axiom,
( ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1435]) ).
cnf(c_0_1435_2,axiom,
( ~ hBOOL(c_in(X6,X1,X3))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1435]) ).
cnf(c_0_1436_0,axiom,
( hBOOL(c_in(hAPP(X1,X6),X5,X4))
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1436]) ).
cnf(c_0_1436_1,axiom,
( ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| hBOOL(c_in(hAPP(X1,X6),X5,X4))
| ~ hBOOL(c_in(X6,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1436]) ).
cnf(c_0_1436_2,axiom,
( ~ hBOOL(c_in(X6,X2,X3))
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| hBOOL(c_in(hAPP(X1,X6),X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1436]) ).
cnf(c_0_1437_0,axiom,
( c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1437]) ).
cnf(c_0_1437_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1437]) ).
cnf(c_0_1438_0,axiom,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1438]) ).
cnf(c_0_1438_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1438]) ).
cnf(c_0_1439_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1439]) ).
cnf(c_0_1439_1,axiom,
( ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1439]) ).
cnf(c_0_1440_0,axiom,
( hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1440]) ).
cnf(c_0_1440_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
| hBOOL(c_in(X1,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1440]) ).
cnf(c_0_1441_0,axiom,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1441]) ).
cnf(c_0_1441_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
| hBOOL(c_in(X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1441]) ).
cnf(c_0_1442_0,axiom,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1442]) ).
cnf(c_0_1442_1,axiom,
( ~ hBOOL(hAPP(X1,hAPP(X2,X3)))
| hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1442]) ).
cnf(c_0_1443_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1443]) ).
cnf(c_0_1443_1,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1443]) ).
cnf(c_0_1443_2,axiom,
( ~ hBOOL(c_in(X2,X1,X4))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1443]) ).
cnf(c_0_1444_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X2)),X2)
| ~ class_Lattices_Olattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1444]) ).
cnf(c_0_1444_1,axiom,
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1444]) ).
cnf(c_0_1445_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X1,tc_fun(X3,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_1445]) ).
cnf(c_0_1445_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X1,tc_fun(X3,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)))
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1445]) ).
cnf(c_0_1446_0,axiom,
( c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1446]) ).
cnf(c_0_1446_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1446]) ).
cnf(c_0_1446_2,axiom,
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1446]) ).
cnf(c_0_1446_3,axiom,
( ~ hBOOL(c_in(X5,X1,X2))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(X3,X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1446]) ).
cnf(c_0_1447_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1447]) ).
cnf(c_0_1447_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1447]) ).
cnf(c_0_1448_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1448]) ).
cnf(c_0_1448_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1448]) ).
cnf(c_0_1448_2,axiom,
( ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1448]) ).
cnf(c_0_1449_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1449]) ).
cnf(c_0_1449_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1449]) ).
cnf(c_0_1449_2,axiom,
( ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1449]) ).
cnf(c_0_1450_0,axiom,
( hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X2,X1)
| ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1450]) ).
cnf(c_0_1450_1,axiom,
( ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1450]) ).
cnf(c_0_1451_0,axiom,
( c_Map_Omap__le(X1,X5,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1451]) ).
cnf(c_0_1451_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(X1,X5,X3,X4)
| ~ c_Map_Omap__le(X2,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1451]) ).
cnf(c_0_1451_2,axiom,
( ~ c_Map_Omap__le(X2,X5,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(X1,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1451]) ).
cnf(c_0_1452_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1452]) ).
cnf(c_0_1452_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3))
| ~ hBOOL(hAPP(X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1452]) ).
cnf(c_0_1452_2,axiom,
( ~ hBOOL(hAPP(X4,X1))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1452]) ).
cnf(c_0_1453_0,axiom,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1453]) ).
cnf(c_0_1453_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1453]) ).
cnf(c_0_1454_0,axiom,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1454]) ).
cnf(c_0_1454_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| hBOOL(hAPP(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1454]) ).
cnf(c_0_1455_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1455]) ).
cnf(c_0_1455_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1455]) ).
cnf(c_0_1456_0,axiom,
( hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X2,X4)),c_Finite__Set_Ofold1(X1,X3,X4)) = c_Finite__Set_Ofold1(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4)
| ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1456]) ).
cnf(c_0_1456_1,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X2,X4)),c_Finite__Set_Ofold1(X1,X3,X4)) = c_Finite__Set_Ofold1(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4)
| ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1456]) ).
cnf(c_0_1456_2,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X2,X4)),c_Finite__Set_Ofold1(X1,X3,X4)) = c_Finite__Set_Ofold1(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4)
| ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1456]) ).
cnf(c_0_1456_3,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X2,X4)),c_Finite__Set_Ofold1(X1,X3,X4)) = c_Finite__Set_Ofold1(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1456]) ).
cnf(c_0_1456_4,axiom,
( ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X2,X4)),c_Finite__Set_Ofold1(X1,X3,X4)) = c_Finite__Set_Ofold1(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1456]) ).
cnf(c_0_1456_5,axiom,
( ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X2,X4)),c_Finite__Set_Ofold1(X1,X3,X4)) = c_Finite__Set_Ofold1(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1456]) ).
cnf(c_0_1456_6,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X2,X4)),c_Finite__Set_Ofold1(X1,X3,X4)) = c_Finite__Set_Ofold1(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1456]) ).
cnf(c_0_1457_0,axiom,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1457]) ).
cnf(c_0_1457_1,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3))
| X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1457]) ).
cnf(c_0_1458_0,axiom,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1458]) ).
cnf(c_0_1458_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1458]) ).
cnf(c_0_1458_2,axiom,
( ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1458]) ).
cnf(c_0_1459_0,axiom,
( hAPP(X1,X5) = hAPP(X2,X5)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ hBOOL(c_in(X5,c_Map_Odom(X1,X3,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1459]) ).
cnf(c_0_1459_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| hAPP(X1,X5) = hAPP(X2,X5)
| ~ hBOOL(c_in(X5,c_Map_Odom(X1,X3,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1459]) ).
cnf(c_0_1459_2,axiom,
( ~ hBOOL(c_in(X5,c_Map_Odom(X1,X3,X4),X3))
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| hAPP(X1,X5) = hAPP(X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1459]) ).
cnf(c_0_1460_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1460]) ).
cnf(c_0_1460_1,axiom,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1460]) ).
cnf(c_0_1460_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1460]) ).
cnf(c_0_1460_3,axiom,
( ~ c_Com_OWT(X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1460]) ).
cnf(c_0_1461_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)),X1)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1461]) ).
cnf(c_0_1461_1,axiom,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1461]) ).
cnf(c_0_1462_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1462]) ).
cnf(c_0_1462_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1462]) ).
cnf(c_0_1462_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1462]) ).
cnf(c_0_1463_0,axiom,
( hBOOL(c_in(X1,X2,X4))
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1463]) ).
cnf(c_0_1463_1,axiom,
( hBOOL(c_in(X1,X3,X4))
| hBOOL(c_in(X1,X2,X4))
| ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1463]) ).
cnf(c_0_1463_2,axiom,
( ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4))
| hBOOL(c_in(X1,X3,X4))
| hBOOL(c_in(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1463]) ).
cnf(c_0_1464_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(X5,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1464]) ).
cnf(c_0_1464_1,axiom,
( hAPP(X5,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1464]) ).
cnf(c_0_1464_2,axiom,
( hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4)
| hAPP(X5,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1464]) ).
cnf(c_0_1465_0,axiom,
( c_Set_Oinsert(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1465]) ).
cnf(c_0_1465_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1465]) ).
cnf(c_0_1466_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1466]) ).
cnf(c_0_1466_1,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X4)
| hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1466]) ).
cnf(c_0_1466_2,axiom,
( hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) != c_Option_Ooption_OSome(X3,X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X4)
| hAPP(X1,X2) = c_Option_Ooption_OSome(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1466]) ).
cnf(c_0_1467_0,axiom,
( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1467]) ).
cnf(c_0_1467_1,axiom,
( hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X5,X1)
| hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1467]) ).
cnf(c_0_1468_0,axiom,
( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(c_Map_Omap__add(X2,X5,X3,X4),X1) = hAPP(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1468]) ).
cnf(c_0_1468_1,axiom,
( hAPP(c_Map_Omap__add(X2,X5,X3,X4),X1) = hAPP(X5,X1)
| hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1468]) ).
cnf(c_0_1469_0,axiom,
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1469]) ).
cnf(c_0_1469_1,axiom,
( ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1469]) ).
cnf(c_0_1470_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1470]) ).
cnf(c_0_1470_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1470]) ).
cnf(c_0_1470_2,axiom,
( c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1470]) ).
cnf(c_0_1471_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1471]) ).
cnf(c_0_1471_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1471]) ).
cnf(c_0_1471_2,axiom,
( c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1471]) ).
cnf(c_0_1472_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1472]) ).
cnf(c_0_1472_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1472]) ).
cnf(c_0_1472_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1472]) ).
cnf(c_0_1473_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1473]) ).
cnf(c_0_1473_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1473]) ).
cnf(c_0_1473_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1473]) ).
cnf(c_0_1474_0,axiom,
( ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1474]) ).
cnf(c_0_1474_1,axiom,
( ~ hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1474]) ).
cnf(c_0_1475_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1475]) ).
cnf(c_0_1475_1,axiom,
( hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1475]) ).
cnf(c_0_1476_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1476]) ).
cnf(c_0_1476_1,axiom,
( hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1476]) ).
cnf(c_0_1477_0,axiom,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1477]) ).
cnf(c_0_1477_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1477]) ).
cnf(c_0_1478_0,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1478]) ).
cnf(c_0_1478_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1478]) ).
cnf(c_0_1479_0,axiom,
( X1 = X2
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1479]) ).
cnf(c_0_1479_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| X1 = X2
| ~ c_Map_Omap__le(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1479]) ).
cnf(c_0_1479_2,axiom,
( ~ c_Map_Omap__le(X2,X1,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1479]) ).
cnf(c_0_1480_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X1,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1480]) ).
cnf(c_0_1480_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X1,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_1480]) ).
cnf(c_0_1481_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1481]) ).
cnf(c_0_1481_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1481]) ).
cnf(c_0_1482_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1482]) ).
cnf(c_0_1482_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1482]) ).
cnf(c_0_1483_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1483]) ).
cnf(c_0_1483_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1483]) ).
cnf(c_0_1484_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1484]) ).
cnf(c_0_1484_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1484]) ).
cnf(c_0_1484_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1484]) ).
cnf(c_0_1485_0,axiom,
( hBOOL(c_in(X1,X2,X4))
| ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1485]) ).
cnf(c_0_1485_1,axiom,
( ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
| hBOOL(c_in(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1485]) ).
cnf(c_0_1486_0,axiom,
( c_Set_Oinsert(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1486]) ).
cnf(c_0_1486_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1486]) ).
cnf(c_0_1487_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1487]) ).
cnf(c_0_1487_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1487]) ).
cnf(c_0_1488_0,axiom,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1488]) ).
cnf(c_0_1488_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5)
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1488]) ).
cnf(c_0_1488_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1488]) ).
cnf(c_0_1489_0,axiom,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1489]) ).
cnf(c_0_1489_1,axiom,
( hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1489]) ).
cnf(c_0_1489_2,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1489]) ).
cnf(c_0_1490_0,axiom,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1490]) ).
cnf(c_0_1490_1,axiom,
( hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1490]) ).
cnf(c_0_1490_2,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1490]) ).
cnf(c_0_1491_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1491]) ).
cnf(c_0_1491_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1491]) ).
cnf(c_0_1491_2,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1491]) ).
cnf(c_0_1492_0,axiom,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1492]) ).
cnf(c_0_1492_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1492]) ).
cnf(c_0_1492_2,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1492]) ).
cnf(c_0_1493_0,axiom,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1493]) ).
cnf(c_0_1493_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1493]) ).
cnf(c_0_1493_2,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1493]) ).
cnf(c_0_1494_0,axiom,
( c_lessequals(c_Map_Odom(X1,X3,X4),c_Map_Odom(X2,X3,X4),tc_fun(X3,tc_bool))
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1494]) ).
cnf(c_0_1494_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_lessequals(c_Map_Odom(X1,X3,X4),c_Map_Odom(X2,X3,X4),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1494]) ).
cnf(c_0_1495_0,axiom,
( c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1495]) ).
cnf(c_0_1495_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
| c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1495]) ).
cnf(c_0_1496_0,axiom,
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1496]) ).
cnf(c_0_1496_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
| c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1496]) ).
cnf(c_0_1497_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1497]) ).
cnf(c_0_1497_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1497]) ).
cnf(c_0_1498_0,axiom,
( hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1498]) ).
cnf(c_0_1498_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1498]) ).
cnf(c_0_1498_2,axiom,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1498]) ).
cnf(c_0_1498_3,axiom,
( ~ c_Com_OWT(X2)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)) ),
inference(literals_permutation,[status(thm)],[c_0_1498]) ).
cnf(c_0_1499_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1499]) ).
cnf(c_0_1499_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1499]) ).
cnf(c_0_1499_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1499]) ).
cnf(c_0_1500_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1500]) ).
cnf(c_0_1500_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1500]) ).
cnf(c_0_1500_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1500]) ).
cnf(c_0_1501_0,axiom,
( X1 = X2
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1501]) ).
cnf(c_0_1501_1,axiom,
( hBOOL(c_in(X1,X3,X4))
| X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1501]) ).
cnf(c_0_1501_2,axiom,
( ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
| hBOOL(c_in(X1,X3,X4))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1501]) ).
cnf(c_0_1502_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(c_in(X4,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1502]) ).
cnf(c_0_1502_1,axiom,
( ~ hBOOL(c_in(X4,X2,X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X4,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1502]) ).
cnf(c_0_1502_2,axiom,
( ~ hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(c_in(X4,X2,X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1502]) ).
cnf(c_0_1503_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1503]) ).
cnf(c_0_1503_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2)
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1503]) ).
cnf(c_0_1504_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1504]) ).
cnf(c_0_1504_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1504]) ).
cnf(c_0_1504_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1504]) ).
cnf(c_0_1505_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1505]) ).
cnf(c_0_1505_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1505]) ).
cnf(c_0_1505_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1505]) ).
cnf(c_0_1506_0,axiom,
( c_lessequals(X2,X5,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1506]) ).
cnf(c_0_1506_1,axiom,
( ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1506]) ).
cnf(c_0_1506_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1506]) ).
cnf(c_0_1506_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1506]) ).
cnf(c_0_1507_0,axiom,
( c_lessequals(X4,X1,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1507]) ).
cnf(c_0_1507_1,axiom,
( ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1507]) ).
cnf(c_0_1507_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1507]) ).
cnf(c_0_1507_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1507]) ).
cnf(c_0_1508_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1508]) ).
cnf(c_0_1508_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1508]) ).
cnf(c_0_1509_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1509]) ).
cnf(c_0_1509_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1509]) ).
cnf(c_0_1510_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1510]) ).
cnf(c_0_1510_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1510]) ).
cnf(c_0_1511_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_OSome(X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1511]) ).
cnf(c_0_1511_1,axiom,
( hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X1,X5) != c_Option_Ooption_OSome(X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1511]) ).
cnf(c_0_1511_2,axiom,
( hAPP(X1,X5) != c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1511]) ).
cnf(c_0_1512_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1512]) ).
cnf(c_0_1512_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1512]) ).
cnf(c_0_1513_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1513]) ).
cnf(c_0_1513_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1513]) ).
cnf(c_0_1514_0,axiom,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1514]) ).
cnf(c_0_1514_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1514]) ).
cnf(c_0_1515_0,axiom,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1515]) ).
cnf(c_0_1515_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1515]) ).
cnf(c_0_1516_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1516]) ).
cnf(c_0_1516_1,axiom,
( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1516]) ).
cnf(c_0_1516_2,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1516]) ).
cnf(c_0_1517_0,axiom,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1517]) ).
cnf(c_0_1517_1,axiom,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1517]) ).
cnf(c_0_1517_2,axiom,
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1517]) ).
cnf(c_0_1518_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1518]) ).
cnf(c_0_1518_1,axiom,
( hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1518]) ).
cnf(c_0_1518_2,axiom,
( hAPP(X1,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1518]) ).
cnf(c_0_1519_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_OSome(X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1519]) ).
cnf(c_0_1519_1,axiom,
( hAPP(X2,X5) != c_Option_Ooption_OSome(X6,X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1519]) ).
cnf(c_0_1520_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4)
| hAPP(X2,X5) != c_Option_Ooption_OSome(X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1520]) ).
cnf(c_0_1520_1,axiom,
( hAPP(X2,X5) != c_Option_Ooption_OSome(X6,X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_OSome(X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1520]) ).
cnf(c_0_1521_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_lessequals(X3,X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1521]) ).
cnf(c_0_1521_1,axiom,
( c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1521]) ).
cnf(c_0_1521_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1521]) ).
cnf(c_0_1521_3,axiom,
( ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1521]) ).
cnf(c_0_1521_4,axiom,
( ~ hBOOL(c_in(X4,X1,X2))
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1521]) ).
cnf(c_0_1521_5,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1521]) ).
cnf(c_0_1522_0,axiom,
( ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(X2,X1) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1522]) ).
cnf(c_0_1522_1,axiom,
( hAPP(X2,X1) != c_Option_Ooption_ONone(X4)
| ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1522]) ).
cnf(c_0_1523_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1523]) ).
cnf(c_0_1523_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1523]) ).
cnf(c_0_1524_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X2)) = c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Odistrib__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1524]) ).
cnf(c_0_1524_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X2)) = c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1524]) ).
cnf(c_0_1525_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1525]) ).
cnf(c_0_1525_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1525]) ).
cnf(c_0_1526_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1526]) ).
cnf(c_0_1526_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1526]) ).
cnf(c_0_1527_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1527]) ).
cnf(c_0_1527_1,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1527]) ).
cnf(c_0_1528_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1528]) ).
cnf(c_0_1528_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1528]) ).
cnf(c_0_1529_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),c_Set_Oinsert(X4,X5,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),X5,tc_fun(X2,tc_bool))
| hAPP(X1,X4) != c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1529]) ).
cnf(c_0_1529_1,axiom,
( hAPP(X1,X4) != c_Option_Ooption_ONone(X3)
| c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),c_Set_Oinsert(X4,X5,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1529]) ).
cnf(c_0_1530_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1530]) ).
cnf(c_0_1530_1,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3)
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1530]) ).
cnf(c_0_1531_0,axiom,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1531]) ).
cnf(c_0_1531_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1531]) ).
cnf(c_0_1532_0,axiom,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1532]) ).
cnf(c_0_1532_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1532]) ).
cnf(c_0_1533_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X4,X3,X2))
| c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X4,X3,X2),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1533]) ).
cnf(c_0_1533_1,axiom,
( hBOOL(c_in(X4,X3,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X4,X3,X2),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1533]) ).
cnf(c_0_1533_2,axiom,
( c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X4,X3,X2),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| hBOOL(c_in(X4,X3,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1533]) ).
cnf(c_0_1533_3,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X4,X3,X2),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| hBOOL(c_in(X4,X3,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1533]) ).
cnf(c_0_1533_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X4,X3,X2),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| hBOOL(c_in(X4,X3,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1533]) ).
cnf(c_0_1534_0,axiom,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1534]) ).
cnf(c_0_1534_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1534]) ).
cnf(c_0_1534_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1534]) ).
cnf(c_0_1535_0,axiom,
( hBOOL(c_in(X2,X1,X4))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1535]) ).
cnf(c_0_1535_1,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| hBOOL(c_in(X2,X1,X4))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1535]) ).
cnf(c_0_1535_2,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| hBOOL(c_in(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1535]) ).
cnf(c_0_1536_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1536]) ).
cnf(c_0_1536_1,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1536]) ).
cnf(c_0_1536_2,axiom,
( ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1536]) ).
cnf(c_0_1537_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1537]) ).
cnf(c_0_1537_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1537]) ).
cnf(c_0_1537_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1537]) ).
cnf(c_0_1538_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1538]) ).
cnf(c_0_1538_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1538]) ).
cnf(c_0_1538_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1538]) ).
cnf(c_0_1539_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1539]) ).
cnf(c_0_1539_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1539]) ).
cnf(c_0_1539_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1539]) ).
cnf(c_0_1540_0,axiom,
( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1540]) ).
cnf(c_0_1540_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1540]) ).
cnf(c_0_1540_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1540]) ).
cnf(c_0_1540_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1540]) ).
cnf(c_0_1541_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1541]) ).
cnf(c_0_1541_1,axiom,
( c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1541]) ).
cnf(c_0_1542_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1542]) ).
cnf(c_0_1542_1,axiom,
( c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1542]) ).
cnf(c_0_1543_0,axiom,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1543]) ).
cnf(c_0_1543_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1543]) ).
cnf(c_0_1544_0,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1544]) ).
cnf(c_0_1544_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1544]) ).
cnf(c_0_1545_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1545]) ).
cnf(c_0_1545_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1545]) ).
cnf(c_0_1546_0,axiom,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1546]) ).
cnf(c_0_1546_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x)) ),
inference(literals_permutation,[status(thm)],[c_0_1546]) ).
cnf(c_0_1547_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1547]) ).
cnf(c_0_1547_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1547]) ).
cnf(c_0_1548_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1548]) ).
cnf(c_0_1548_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1548]) ).
cnf(c_0_1549_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1549]) ).
cnf(c_0_1549_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1549]) ).
cnf(c_0_1550_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1550_1,axiom,
( c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1550_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1551_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1551_1,axiom,
( c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1551_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1552_0,axiom,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1552]) ).
cnf(c_0_1552_1,axiom,
( hBOOL(hAPP(X2,X4))
| X1 = X4
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1552]) ).
cnf(c_0_1552_2,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| hBOOL(hAPP(X2,X4))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1552]) ).
cnf(c_0_1553_0,axiom,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1553]) ).
cnf(c_0_1553_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1553]) ).
cnf(c_0_1554_0,axiom,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1554]) ).
cnf(c_0_1554_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1554]) ).
cnf(c_0_1554_2,axiom,
( ~ hBOOL(c_in(X4,X1,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1554]) ).
cnf(c_0_1555_0,axiom,
( hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1555]) ).
cnf(c_0_1555_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1555]) ).
cnf(c_0_1555_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1555]) ).
cnf(c_0_1556_0,axiom,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1556]) ).
cnf(c_0_1556_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1556]) ).
cnf(c_0_1556_2,axiom,
( ~ hBOOL(c_in(X4,X1,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1556]) ).
cnf(c_0_1557_0,axiom,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1557]) ).
cnf(c_0_1557_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1557]) ).
cnf(c_0_1557_2,axiom,
( ~ hBOOL(c_in(X4,X1,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1557]) ).
cnf(c_0_1558_0,axiom,
( hBOOL(c_in(X1,X4,X3))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1558]) ).
cnf(c_0_1558_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1558]) ).
cnf(c_0_1559_0,axiom,
( X1 = X2
| hBOOL(c_in(X3,X1,X4))
| hBOOL(c_in(X3,X2,X4))
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1559]) ).
cnf(c_0_1559_1,axiom,
( hBOOL(c_in(X3,X1,X4))
| X1 = X2
| hBOOL(c_in(X3,X2,X4))
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1559]) ).
cnf(c_0_1559_2,axiom,
( hBOOL(c_in(X3,X2,X4))
| hBOOL(c_in(X3,X1,X4))
| X1 = X2
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1559]) ).
cnf(c_0_1559_3,axiom,
( c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4)
| hBOOL(c_in(X3,X2,X4))
| hBOOL(c_in(X3,X1,X4))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1559]) ).
cnf(c_0_1560_0,axiom,
( ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_1,axiom,
( ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1561_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1562_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1563_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_1,axiom,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_2,axiom,
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_3,axiom,
( ~ c_Com_OWT(X1)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1564_0,axiom,
( c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_3,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1565_0,axiom,
( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
| hAPP(X2,X1) != c_Option_Ooption_OSome(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_1,axiom,
( hAPP(X2,X1) != c_Option_Ooption_OSome(X5,X4)
| hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1566_0,axiom,
( hBOOL(hAPP(X3,X1))
| ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_1,axiom,
( ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1567_0,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1568_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_1,axiom,
( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1569_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1570_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1571_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hBOOL(c_in(X2,c_Map_Odom(X1,X4,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_1,axiom,
( hBOOL(c_in(X2,c_Map_Odom(X1,X4,X3),X4))
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1572_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1573_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1574_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1575_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1576_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1577_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1578_0,axiom,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_1,axiom,
( c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1579_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1580_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1581_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_1,axiom,
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1582_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1583_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1584_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1585_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1586_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1587_0,axiom,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1588_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1589_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_2,axiom,
( c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1590_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1591_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1592_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1593_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1594_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1595_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1595_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1596_0,axiom,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1596_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1596_2,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1597_0,axiom,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1597]) ).
cnf(c_0_1597_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X4,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1597]) ).
cnf(c_0_1597_2,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1597]) ).
cnf(c_0_1598_0,axiom,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1598]) ).
cnf(c_0_1598_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1598]) ).
cnf(c_0_1598_2,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1598]) ).
cnf(c_0_1599_0,axiom,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X4,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_2,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1600_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1600_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1601_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_2,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1602_0,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1603_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_1,axiom,
( c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_3,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_4,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1604_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_1,axiom,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_3,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_4,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1605_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_1,axiom,
( ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3))
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1606_0,axiom,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1607_0,axiom,
( c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1608_0,axiom,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1609_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1610_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_HOL_Ominus(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_1,axiom,
( ~ class_HOL_Ominus(X3)
| c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1611_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(t_a,X3)),v_x) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1612_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1613_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1614_0,axiom,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1614_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1614_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1615_0,axiom,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1615_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1615_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1616_0,axiom,
( hBOOL(c_in(X3,X4,X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Set_Oinsert(X3,X4,X5) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(c_in(X3,X4,X5))
| c_Set_Oinsert(X3,X4,X5) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_2,axiom,
( c_Set_Oinsert(X3,X4,X5) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(c_in(X3,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1617_0,axiom,
( c_Set_Oinsert(X1,c_Map_Odom(X2,X3,X4),X3) = c_Map_Odom(X2,X3,X4)
| hAPP(X2,X1) != c_Option_Ooption_OSome(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_1,axiom,
( hAPP(X2,X1) != c_Option_Ooption_OSome(X5,X4)
| c_Set_Oinsert(X1,c_Map_Odom(X2,X3,X4),X3) = c_Map_Odom(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1618_0,axiom,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1618_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1619_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1620_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1621_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1621_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1621_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1622_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1622_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1622_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1623_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1623_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1623_2,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1624_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_2,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1625_0,axiom,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1626_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_1,axiom,
( c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1627_0,axiom,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1628_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1629_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1630_0,axiom,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1631_0,axiom,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1631_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1632_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1632_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1633_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_1,axiom,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1634_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1635_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1636_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1637_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1638_0,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1639_0,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_1,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1640_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_1,axiom,
( hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1641_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_1,axiom,
( hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1642_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1642_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1643_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1643_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1644_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1645_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1646_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1646_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1646_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1647_0,axiom,
( hBOOL(c_in(X2,c_Collect(X1,X3),X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1648_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1648]) ).
cnf(c_0_1648_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1648]) ).
cnf(c_0_1649_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),c_Complete__Lattice_OInf__class_OInf(X2,X3)) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1649_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),c_Complete__Lattice_OInf__class_OInf(X2,X3)) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1650_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1650_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1651_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1651_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1652_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1652_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1653_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1654_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1655_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_2,axiom,
( ~ hBOOL(hAPP(X1,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1656_0,axiom,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_2,axiom,
( ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1657_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1658_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1659_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1659_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1660_0,axiom,
( c_Com_OWT(c_Com_Ocom_OBODY(X2))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1660_1,axiom,
( ~ c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3))
| c_Com_OWT(c_Com_Ocom_OBODY(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1661_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1661_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1661_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1661_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1662_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1662_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1662_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1662_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1663_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1664_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_1,axiom,
( c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1665_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1666_0,axiom,
( X1 = X2
| c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_1,axiom,
( c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1667_0,axiom,
( X1 = X2
| c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1667_1,axiom,
( c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1668_0,axiom,
( X1 = X2
| c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1668_1,axiom,
( c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1669_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1670_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1671_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1672_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1672_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1673_0,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1674_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1675_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X1),X3),X2) = X1
| ~ class_Lattices_Olattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1675_1,axiom,
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X1),X3),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1676_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_1,axiom,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1677_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_1,axiom,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1678_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1679_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1679_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1680_0,axiom,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_2,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1681_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1681_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1681_2,axiom,
( ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1682_0,axiom,
( hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1682_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(c_in(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1683_0,axiom,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1684_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1685_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1686_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1687_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1687_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1687_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1688_0,axiom,
( c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1688_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1688_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1689_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1689_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1690_0,axiom,
( c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1691_0,axiom,
( c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_1,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1692_0,axiom,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1692_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1693_0,axiom,
( X1 = X3
| ~ hBOOL(hAPP(c_fequal(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_1,axiom,
( ~ hBOOL(hAPP(c_fequal(X1,X2),X3))
| X1 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1694_0,axiom,
( c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3))
| ~ c_Com_OWT(c_Com_Ocom_OBODY(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_1,axiom,
( ~ c_Com_OWT(c_Com_Ocom_OBODY(X1))
| c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1695_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1695_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1695_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1696_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1696_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1697_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1697_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1698_0,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1699_0,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_1,axiom,
( c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1700_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1701_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1702_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1703_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1704_0,axiom,
( hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1705_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1706_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1707_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_1,axiom,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1708_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1709_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1710_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_1,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1711_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_1,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1712_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1713_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1714_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1715_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1715_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1716_0,axiom,
( X1 = X2
| c_Option_Ooption_OSome(X1,X3) != c_Option_Ooption_OSome(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_1,axiom,
( c_Option_Ooption_OSome(X1,X3) != c_Option_Ooption_OSome(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1717_0,axiom,
( c_Com_OWT(X1)
| ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X2) != c_Option_Ooption_OSome(X1,tc_Com_Ocom) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_1,axiom,
( ~ c_Com_OWT__bodies
| c_Com_OWT(X1)
| hAPP(c_Com_Obody,X2) != c_Option_Ooption_OSome(X1,tc_Com_Ocom) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_2,axiom,
( hAPP(c_Com_Obody,X2) != c_Option_Ooption_OSome(X1,tc_Com_Ocom)
| ~ c_Com_OWT__bodies
| c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1718_0,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_2,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1719_0,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1719_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1720_0,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1720_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Oupper__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1721_0,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1721_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olower__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1722_0,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1722_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1723_0,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1723_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1724_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1725_0,axiom,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1726_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1727_0,axiom,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_1,axiom,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1728_0,axiom,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_1,axiom,
( ~ class_HOL_Ominus(X1)
| class_HOL_Ominus(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1729_0,axiom,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_1,axiom,
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1730_0,axiom,
( hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(c_Com_Ocom_OBODY(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_1,axiom,
( c_Com_OWT(c_Com_Ocom_OBODY(X1))
| hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1731_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1732_0,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1733_0,axiom,
( X1 = X2
| c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1733_1,axiom,
( c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1734_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_1,axiom,
( c_Hoare__Mirabelle_Ostate__not__singleton
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_671,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
file('<stdin>',cls_conjecture_4) ).
fof(c_0_1_672,negated_conjecture,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
file('<stdin>',cls_conjecture_3) ).
fof(c_0_2_673,negated_conjecture,
c_Com_OWT(v_c),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_3_674,negated_conjecture,
c_Com_OWT__bodies,
file('<stdin>',cls_conjecture_1) ).
fof(c_0_4_675,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('<stdin>',cls_conjecture_0) ).
fof(c_0_5_676,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_6_677,negated_conjecture,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
c_0_1 ).
fof(c_0_7_678,negated_conjecture,
c_Com_OWT(v_c),
c_0_2 ).
fof(c_0_8_679,negated_conjecture,
c_Com_OWT__bodies,
c_0_3 ).
fof(c_0_9_680,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
c_0_4 ).
fof(c_0_10_681,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
c_0_5 ).
fof(c_0_11_682,negated_conjecture,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
c_0_6 ).
fof(c_0_12_683,negated_conjecture,
c_Com_OWT(v_c),
c_0_7 ).
fof(c_0_13_684,negated_conjecture,
c_Com_OWT__bodies,
c_0_8 ).
fof(c_0_14_685,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
c_0_9 ).
cnf(c_0_15_686,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16_687,negated_conjecture,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17_688,negated_conjecture,
c_Com_OWT(v_c),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18_689,negated_conjecture,
c_Com_OWT__bodies,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19_690,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20_691,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
c_0_15,
[final] ).
cnf(c_0_21_692,negated_conjecture,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
c_0_16,
[final] ).
cnf(c_0_22_693,negated_conjecture,
c_Com_OWT(v_c),
c_0_17,
[final] ).
cnf(c_0_23_694,negated_conjecture,
c_Com_OWT__bodies,
c_0_18,
[final] ).
cnf(c_0_24_695,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
c_0_19,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_447,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X0),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_ec7453.p',c_0_1563_3) ).
cnf(c_1828,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X0),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X0) ),
inference(copy,[status(esa)],[c_447]) ).
cnf(c_134041,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| ~ c_Com_OWT__bodies ),
inference(instantiation,[status(thm)],[c_1828]) ).
cnf(c_869,plain,
( hAPP(c_Com_Obody,X0) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(c_Com_Ocom_OBODY(X0)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_ec7453.p',c_0_1730_1) ).
cnf(c_2250,plain,
( hAPP(c_Com_Obody,X0) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(c_Com_Ocom_OBODY(X0)) ),
inference(copy,[status(esa)],[c_869]) ).
cnf(c_131480,plain,
( c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| hAPP(c_Com_Obody,v_x) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(instantiation,[status(thm)],[c_2250]) ).
cnf(c_342,plain,
( hAPP(X0,X1) != c_Option_Ooption_ONone(X2)
| ~ hBOOL(c_in(X1,c_Map_Odom(X0,X3,X2),X3)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_ec7453.p',c_0_1522_0) ).
cnf(c_1723,plain,
( hAPP(X0,X1) != c_Option_Ooption_ONone(X2)
| ~ hBOOL(c_in(X1,c_Map_Odom(X0,X3,X2),X3)) ),
inference(copy,[status(esa)],[c_342]) ).
cnf(c_34730,plain,
( ~ hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| hAPP(c_Com_Obody,v_x) != c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(instantiation,[status(thm)],[c_1723]) ).
cnf(c_1012,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
file('/export/starexec/sandbox/tmp/iprover_modulo_ec7453.p',c_0_20) ).
cnf(c_1013,negated_conjecture,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
file('/export/starexec/sandbox/tmp/iprover_modulo_ec7453.p',c_0_21) ).
cnf(c_1015,negated_conjecture,
c_Com_OWT__bodies,
file('/export/starexec/sandbox/tmp/iprover_modulo_ec7453.p',c_0_23) ).
cnf(c_1016,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox/tmp/iprover_modulo_ec7453.p',c_0_24) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_134041,c_131480,c_34730,c_1012,c_1013,c_1015,c_1016]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV905-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 08:26:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.20/0.50 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.50 % Orientation found
% 0.20/0.50 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_5ca9c6.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_ec7453.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_f6d5a2 | grep -v "SZS"
% 0.36/0.52
% 0.36/0.52 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.36/0.52
% 0.36/0.52 %
% 0.36/0.52 % ------ iProver source info
% 0.36/0.52
% 0.36/0.52 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.36/0.52 % git: non_committed_changes: true
% 0.36/0.52 % git: last_make_outside_of_git: true
% 0.36/0.52
% 0.36/0.52 %
% 0.36/0.52 % ------ Input Options
% 0.36/0.52
% 0.36/0.52 % --out_options all
% 0.36/0.52 % --tptp_safe_out true
% 0.36/0.52 % --problem_path ""
% 0.36/0.52 % --include_path ""
% 0.36/0.52 % --clausifier .//eprover
% 0.36/0.52 % --clausifier_options --tstp-format
% 0.36/0.52 % --stdin false
% 0.36/0.52 % --dbg_backtrace false
% 0.36/0.52 % --dbg_dump_prop_clauses false
% 0.36/0.52 % --dbg_dump_prop_clauses_file -
% 0.36/0.52 % --dbg_out_stat false
% 0.36/0.52
% 0.36/0.52 % ------ General Options
% 0.36/0.52
% 0.36/0.52 % --fof false
% 0.36/0.52 % --time_out_real 150.
% 0.36/0.52 % --time_out_prep_mult 0.2
% 0.36/0.52 % --time_out_virtual -1.
% 0.36/0.52 % --schedule none
% 0.36/0.52 % --ground_splitting input
% 0.36/0.52 % --splitting_nvd 16
% 0.36/0.52 % --non_eq_to_eq false
% 0.36/0.52 % --prep_gs_sim true
% 0.36/0.52 % --prep_unflatten false
% 0.36/0.52 % --prep_res_sim true
% 0.36/0.52 % --prep_upred true
% 0.36/0.52 % --res_sim_input true
% 0.36/0.52 % --clause_weak_htbl true
% 0.36/0.52 % --gc_record_bc_elim false
% 0.36/0.52 % --symbol_type_check false
% 0.36/0.52 % --clausify_out false
% 0.36/0.52 % --large_theory_mode false
% 0.36/0.52 % --prep_sem_filter none
% 0.36/0.52 % --prep_sem_filter_out false
% 0.36/0.52 % --preprocessed_out false
% 0.36/0.52 % --sub_typing false
% 0.36/0.52 % --brand_transform false
% 0.36/0.52 % --pure_diseq_elim true
% 0.36/0.52 % --min_unsat_core false
% 0.36/0.52 % --pred_elim true
% 0.36/0.52 % --add_important_lit false
% 0.36/0.52 % --soft_assumptions false
% 0.36/0.52 % --reset_solvers false
% 0.36/0.52 % --bc_imp_inh []
% 0.36/0.52 % --conj_cone_tolerance 1.5
% 0.36/0.52 % --prolific_symb_bound 500
% 0.36/0.52 % --lt_threshold 2000
% 0.36/0.52
% 0.36/0.52 % ------ SAT Options
% 0.36/0.52
% 0.36/0.52 % --sat_mode false
% 0.36/0.52 % --sat_fm_restart_options ""
% 0.36/0.52 % --sat_gr_def false
% 0.36/0.52 % --sat_epr_types true
% 0.36/0.52 % --sat_non_cyclic_types false
% 0.36/0.52 % --sat_finite_models false
% 0.36/0.52 % --sat_fm_lemmas false
% 0.36/0.52 % --sat_fm_prep false
% 0.36/0.52 % --sat_fm_uc_incr true
% 0.36/0.52 % --sat_out_model small
% 0.36/0.52 % --sat_out_clauses false
% 0.36/0.52
% 0.36/0.52 % ------ QBF Options
% 0.36/0.52
% 0.36/0.52 % --qbf_mode false
% 0.36/0.52 % --qbf_elim_univ true
% 0.36/0.52 % --qbf_sk_in true
% 0.36/0.52 % --qbf_pred_elim true
% 0.36/0.52 % --qbf_split 32
% 0.36/0.52
% 0.36/0.52 % ------ BMC1 Options
% 0.36/0.52
% 0.36/0.52 % --bmc1_incremental false
% 0.36/0.52 % --bmc1_axioms reachable_all
% 0.36/0.52 % --bmc1_min_bound 0
% 0.36/0.52 % --bmc1_max_bound -1
% 0.36/0.52 % --bmc1_max_bound_default -1
% 0.36/0.52 % --bmc1_symbol_reachability true
% 0.36/0.52 % --bmc1_property_lemmas false
% 0.36/0.52 % --bmc1_k_induction false
% 0.36/0.52 % --bmc1_non_equiv_states false
% 0.36/0.52 % --bmc1_deadlock false
% 0.36/0.52 % --bmc1_ucm false
% 0.36/0.52 % --bmc1_add_unsat_core none
% 0.36/0.52 % --bmc1_unsat_core_children false
% 0.36/0.52 % --bmc1_unsat_core_extrapolate_axioms false
% 0.36/0.52 % --bmc1_out_stat full
% 0.36/0.52 % --bmc1_ground_init false
% 0.36/0.52 % --bmc1_pre_inst_next_state false
% 0.36/0.52 % --bmc1_pre_inst_state false
% 0.36/0.52 % --bmc1_pre_inst_reach_state false
% 0.36/0.52 % --bmc1_out_unsat_core false
% 0.36/0.52 % --bmc1_aig_witness_out false
% 0.36/0.52 % --bmc1_verbose false
% 0.36/0.52 % --bmc1_dump_clauses_tptp false
% 6.87/7.16 % --bmc1_dump_unsat_core_tptp false
% 6.87/7.16 % --bmc1_dump_file -
% 6.87/7.16 % --bmc1_ucm_expand_uc_limit 128
% 6.87/7.16 % --bmc1_ucm_n_expand_iterations 6
% 6.87/7.16 % --bmc1_ucm_extend_mode 1
% 6.87/7.16 % --bmc1_ucm_init_mode 2
% 6.87/7.16 % --bmc1_ucm_cone_mode none
% 6.87/7.16 % --bmc1_ucm_reduced_relation_type 0
% 6.87/7.16 % --bmc1_ucm_relax_model 4
% 6.87/7.16 % --bmc1_ucm_full_tr_after_sat true
% 6.87/7.16 % --bmc1_ucm_expand_neg_assumptions false
% 6.87/7.16 % --bmc1_ucm_layered_model none
% 6.87/7.16 % --bmc1_ucm_max_lemma_size 10
% 6.87/7.16
% 6.87/7.16 % ------ AIG Options
% 6.87/7.16
% 6.87/7.16 % --aig_mode false
% 6.87/7.16
% 6.87/7.16 % ------ Instantiation Options
% 6.87/7.16
% 6.87/7.16 % --instantiation_flag true
% 6.87/7.16 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 6.87/7.16 % --inst_solver_per_active 750
% 6.87/7.16 % --inst_solver_calls_frac 0.5
% 6.87/7.16 % --inst_passive_queue_type priority_queues
% 6.87/7.16 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 6.87/7.16 % --inst_passive_queues_freq [25;2]
% 6.87/7.16 % --inst_dismatching true
% 6.87/7.16 % --inst_eager_unprocessed_to_passive true
% 6.87/7.16 % --inst_prop_sim_given true
% 6.87/7.16 % --inst_prop_sim_new false
% 6.87/7.16 % --inst_orphan_elimination true
% 6.87/7.16 % --inst_learning_loop_flag true
% 6.87/7.16 % --inst_learning_start 3000
% 6.87/7.16 % --inst_learning_factor 2
% 6.87/7.16 % --inst_start_prop_sim_after_learn 3
% 6.87/7.16 % --inst_sel_renew solver
% 6.87/7.16 % --inst_lit_activity_flag true
% 6.87/7.16 % --inst_out_proof true
% 6.87/7.16
% 6.87/7.16 % ------ Resolution Options
% 6.87/7.16
% 6.87/7.16 % --resolution_flag true
% 6.87/7.16 % --res_lit_sel kbo_max
% 6.87/7.16 % --res_to_prop_solver none
% 6.87/7.16 % --res_prop_simpl_new false
% 6.87/7.16 % --res_prop_simpl_given false
% 6.87/7.16 % --res_passive_queue_type priority_queues
% 6.87/7.16 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 6.87/7.16 % --res_passive_queues_freq [15;5]
% 6.87/7.16 % --res_forward_subs full
% 6.87/7.16 % --res_backward_subs full
% 6.87/7.16 % --res_forward_subs_resolution true
% 6.87/7.16 % --res_backward_subs_resolution true
% 6.87/7.16 % --res_orphan_elimination false
% 6.87/7.16 % --res_time_limit 1000.
% 6.87/7.16 % --res_out_proof true
% 6.87/7.16 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_5ca9c6.s
% 6.87/7.16 % --modulo true
% 6.87/7.16
% 6.87/7.16 % ------ Combination Options
% 6.87/7.16
% 6.87/7.16 % --comb_res_mult 1000
% 6.87/7.16 % --comb_inst_mult 300
% 6.87/7.16 % ------
% 6.87/7.16
% 6.87/7.16 % ------ Parsing...% successful
% 6.87/7.16
% 6.87/7.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 6.87/7.16
% 6.87/7.16 % ------ Proving...
% 6.87/7.16 % ------ Problem Properties
% 6.87/7.16
% 6.87/7.16 %
% 6.87/7.16 % EPR false
% 6.87/7.16 % Horn false
% 6.87/7.16 % Has equality true
% 6.87/7.16
% 6.87/7.16 % % ------ Input Options Time Limit: Unbounded
% 6.87/7.16
% 6.87/7.16
% 6.87/7.16 Compiling...
% 6.87/7.16 Loading plugin: done.
% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
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% 6.87/7.16 Compiling...
% 6.87/7.16 Loading plugin: done.
% 6.87/7.16 Compiling...
% 6.87/7.16 Loading plugin: done.
% 6.87/7.16 Compiling...
% 6.87/7.16 Loading plugin: done.
% 6.87/7.16 Compiling...
% 6.87/7.16 Loading plugin: done.
% 6.87/7.16 Compiling...
% 6.87/7.16 Loading plugin: done.
% 6.87/7.16 Compiling...
% 6.87/7.16 Loading plugin: done.
% 6.87/7.16 Compiling...
% 6.87/7.16 Loading plugin: done.
% 6.87/7.16 % % ------ Current options:
% 6.87/7.16
% 6.87/7.16 % ------ Input Options
% 6.87/7.16
% 6.87/7.16 % --out_options all
% 6.87/7.16 % --tptp_safe_out true
% 6.87/7.16 % --problem_path ""
% 6.87/7.16 % --include_path ""
% 6.87/7.16 % --clausifier .//eprover
% 6.87/7.16 % --clausifier_options --tstp-format
% 6.87/7.16 % --stdin false
% 6.87/7.16 % --dbg_backtrace false
% 6.87/7.16 % --dbg_dump_prop_clauses false
% 6.87/7.16 % --dbg_dump_prop_clauses_file -
% 6.87/7.16 % --dbg_out_stat false
% 6.87/7.16
% 6.87/7.16 % ------ General Options
% 6.87/7.16
% 6.87/7.16 % --fof false
% 6.87/7.16 % --time_out_real 150.
% 6.87/7.16 % --time_out_prep_mult 0.2
% 6.87/7.16 % --time_out_virtual -1.
% 6.87/7.16 % --schedule none
% 6.87/7.16 % --ground_splitting input
% 6.87/7.16 % --splitting_nvd 16
% 6.87/7.16 % --non_eq_to_eq false
% 6.87/7.16 % --prep_gs_sim true
% 6.87/7.16 % --prep_unflatten false
% 6.87/7.16 % --prep_res_sim true
% 6.87/7.16 % --prep_upred true
% 6.87/7.16 % --res_sim_input true
% 6.87/7.16 % --clause_weak_htbl true
% 6.87/7.16 % --gc_record_bc_elim false
% 6.87/7.16 % --symbol_type_check false
% 6.87/7.16 % --clausify_out false
% 6.87/7.16 % --large_theory_mode false
% 6.87/7.16 % --prep_sem_filter none
% 6.87/7.16 % --prep_sem_filter_out false
% 6.87/7.16 % --preprocessed_out false
% 6.87/7.16 % --sub_typing false
% 6.87/7.16 % --brand_transform false
% 6.87/7.16 % --pure_diseq_elim true
% 6.87/7.16 % --min_unsat_core false
% 6.87/7.16 % --pred_elim true
% 6.87/7.16 % --add_important_lit false
% 6.87/7.16 % --soft_assumptions false
% 6.87/7.16 % --reset_solvers false
% 6.87/7.16 % --bc_imp_inh []
% 6.87/7.16 % --conj_cone_tolerance 1.5
% 6.87/7.16 % --prolific_symb_bound 500
% 6.87/7.16 % --lt_threshold 2000
% 6.87/7.16
% 6.87/7.16 % ------ SAT Options
% 6.87/7.16
% 6.87/7.16 % --sat_mode false
% 6.87/7.16 % --sat_fm_restart_options ""
% 6.87/7.16 % --sat_gr_def false
% 6.87/7.16 % --sat_epr_types true
% 6.87/7.16 % --sat_non_cyclic_types false
% 6.87/7.16 % --sat_finite_models false
% 6.87/7.16 % --sat_fm_lemmas false
% 6.87/7.16 % --sat_fm_prep false
% 6.87/7.16 % --sat_fm_uc_incr true
% 6.87/7.16 % --sat_out_model small
% 6.87/7.16 % --sat_out_clauses false
% 6.87/7.16
% 6.87/7.16 % ------ QBF Options
% 6.87/7.16
% 6.87/7.16 % --qbf_mode false
% 6.87/7.16 % --qbf_elim_univ true
% 6.87/7.16 % --qbf_sk_in true
% 6.87/7.16 % --qbf_pred_elim true
% 6.87/7.16 % --qbf_split 32
% 6.87/7.16
% 6.87/7.16 % ------ BMC1 Options
% 6.87/7.16
% 6.87/7.16 % --bmc1_incremental false
% 6.87/7.16 % --bmc1_axioms reachable_all
% 6.87/7.16 % --bmc1_min_bound 0
% 6.87/7.16 % --bmc1_max_bound -1
% 6.87/7.16 % --bmc1_max_bound_default -1
% 6.87/7.16 % --bmc1_symbol_reachability true
% 6.87/7.16 % --bmc1_property_lemmas false
% 6.87/7.16 % --bmc1_k_induction false
% 6.87/7.16 % --bmc1_non_equiv_states false
% 6.87/7.16 % --bmc1_deadlock false
% 6.87/7.16 % --bmc1_ucm false
% 6.87/7.16 % --bmc1_add_unsat_core none
% 6.87/7.16 % --bmc1_unsat_core_children false
% 6.87/7.16 % --bmc1_unsat_core_extrapolate_axioms false
% 6.87/7.16 % --bmc1_out_stat full
% 6.87/7.16 % --bmc1_ground_init false
% 6.87/7.16 % --bmc1_pre_inst_next_state false
% 6.87/7.16 % --bmc1_pre_inst_state false
% 6.87/7.16 % --bmc1_pre_inst_reach_state false
% 6.87/7.16 % --bmc1_out_unsat_core false
% 6.87/7.16 % --bmc1_aig_witness_out false
% 6.87/7.16 % --bmc1_verbose false
% 6.87/7.16 % --bmc1_dump_clauses_tptp false
% 6.87/7.16 % --bmc1_dump_unsat_core_tptp false
% 6.87/7.16 % --bmc1_dump_file -
% 6.87/7.16 % --bmc1_ucm_expand_uc_limit 128
% 6.87/7.16 % --bmc1_ucm_n_expand_iterations 6
% 6.87/7.16 % --bmc1_ucm_extend_mode 1
% 6.87/7.16 % --bmc1_ucm_init_mode 2
% 6.87/7.16 % --bmc1_ucm_cone_mode none
% 12.89/13.13 % --bmc1_ucm_reduced_relation_type 0
% 12.89/13.13 % --bmc1_ucm_relax_model 4
% 12.89/13.13 % --bmc1_ucm_full_tr_after_sat true
% 12.89/13.13 % --bmc1_ucm_expand_neg_assumptions false
% 12.89/13.13 % --bmc1_ucm_layered_model none
% 12.89/13.13 % --bmc1_ucm_max_lemma_size 10
% 12.89/13.13
% 12.89/13.13 % ------ AIG Options
% 12.89/13.13
% 12.89/13.13 % --aig_mode false
% 12.89/13.13
% 12.89/13.13 % ------ Instantiation Options
% 12.89/13.13
% 12.89/13.13 % --instantiation_flag true
% 12.89/13.13 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 12.89/13.13 % --inst_solver_per_active 750
% 12.89/13.13 % --inst_solver_calls_frac 0.5
% 12.89/13.13 % --inst_passive_queue_type priority_queues
% 12.89/13.13 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 12.89/13.13 % --inst_passive_queues_freq [25;2]
% 12.89/13.13 % --inst_dismatching true
% 12.89/13.13 % --inst_eager_unprocessed_to_passive true
% 12.89/13.13 % --inst_prop_sim_given true
% 12.89/13.13 % --inst_prop_sim_new false
% 12.89/13.13 % --inst_orphan_elimination true
% 12.89/13.13 % --inst_learning_loop_flag true
% 12.89/13.13 % --inst_learning_start 3000
% 12.89/13.13 % --inst_learning_factor 2
% 12.89/13.13 % --inst_start_prop_sim_after_learn 3
% 12.89/13.13 % --inst_sel_renew solver
% 12.89/13.13 % --inst_lit_activity_flag true
% 12.89/13.13 % --inst_out_proof true
% 12.89/13.13
% 12.89/13.13 % ------ Resolution Options
% 12.89/13.13
% 12.89/13.13 % --resolution_flag true
% 12.89/13.13 % --res_lit_sel kbo_max
% 12.89/13.13 % --res_to_prop_solver none
% 12.89/13.13 % --res_prop_simpl_new false
% 12.89/13.13 % --res_prop_simpl_given false
% 12.89/13.13 % --res_passive_queue_type priority_queues
% 12.89/13.13 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 12.89/13.13 % --res_passive_queues_freq [15;5]
% 12.89/13.13 % --res_forward_subs full
% 12.89/13.13 % --res_backward_subs full
% 12.89/13.13 % --res_forward_subs_resolution true
% 12.89/13.13 % --res_backward_subs_resolution true
% 12.89/13.13 % --res_orphan_elimination false
% 12.89/13.13 % --res_time_limit 1000.
% 12.89/13.13 % --res_out_proof true
% 12.89/13.13 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_5ca9c6.s
% 12.89/13.13 % --modulo true
% 12.89/13.13
% 12.89/13.13 % ------ Combination Options
% 12.89/13.13
% 12.89/13.13 % --comb_res_mult 1000
% 12.89/13.13 % --comb_inst_mult 300
% 12.89/13.13 % ------
% 12.89/13.13
% 12.89/13.13
% 12.89/13.13
% 12.89/13.13 % ------ Proving...
% 12.89/13.13 %
% 12.89/13.13
% 12.89/13.13
% 12.89/13.13 % ------ Statistics
% 12.89/13.13
% 12.89/13.13 % ------ General
% 12.89/13.13
% 12.89/13.13 % num_of_input_clauses: 1017
% 12.89/13.13 % num_of_input_neg_conjectures: 5
% 12.89/13.13 % num_of_splits: 0
% 12.89/13.13 % num_of_split_atoms: 0
% 12.89/13.13 % num_of_sem_filtered_clauses: 0
% 12.89/13.13 % num_of_subtypes: 0
% 12.89/13.13 % monotx_restored_types: 0
% 12.89/13.13 % sat_num_of_epr_types: 0
% 12.89/13.13 % sat_num_of_non_cyclic_types: 0
% 12.89/13.13 % sat_guarded_non_collapsed_types: 0
% 12.89/13.13 % is_epr: 0
% 12.89/13.13 % is_horn: 0
% 12.89/13.13 % has_eq: 1
% 12.89/13.13 % num_pure_diseq_elim: 0
% 12.89/13.13 % simp_replaced_by: 0
% 12.89/13.13 % res_preprocessed: 10
% 12.89/13.13 % prep_upred: 0
% 12.89/13.13 % prep_unflattend: 0
% 12.89/13.13 % pred_elim_cands: 0
% 12.89/13.13 % pred_elim: 0
% 12.89/13.13 % pred_elim_cl: 0
% 12.89/13.13 % pred_elim_cycles: 0
% 12.89/13.13 % forced_gc_time: 0
% 12.89/13.13 % gc_basic_clause_elim: 0
% 12.89/13.13 % parsing_time: 0.063
% 12.89/13.13 % sem_filter_time: 0.
% 12.89/13.13 % pred_elim_time: 0.
% 12.89/13.13 % out_proof_time: 0.
% 12.89/13.13 % monotx_time: 0.
% 12.89/13.13 % subtype_inf_time: 0.
% 12.89/13.13 % unif_index_cands_time: 0.02
% 12.89/13.13 % unif_index_add_time: 0.009
% 12.89/13.13 % total_time: 12.62
% 12.89/13.13 % num_of_symbols: 96
% 12.89/13.13 % num_of_terms: 206239
% 12.89/13.13
% 12.89/13.13 % ------ Propositional Solver
% 12.89/13.13
% 12.89/13.13 % prop_solver_calls: 4
% 12.89/13.13 % prop_fast_solver_calls: 15
% 12.89/13.13 % prop_num_of_clauses: 3214
% 12.89/13.13 % prop_preprocess_simplified: 7478
% 12.89/13.13 % prop_fo_subsumed: 0
% 12.89/13.13 % prop_solver_time: 0.
% 12.89/13.13 % prop_fast_solver_time: 0.
% 12.89/13.13 % prop_unsat_core_time: 0.
% 12.89/13.13
% 12.89/13.13 % ------ QBF
% 12.89/13.13
% 12.89/13.13 % qbf_q_res: 0
% 12.89/13.13 % qbf_num_tautologies: 0
% 12.89/13.13 % qbf_prep_cycles: 0
% 12.89/13.13
% 12.89/13.13 % ------ BMC1
% 12.89/13.13
% 12.89/13.13 % bmc1_current_bound: -1
% 12.89/13.13 % bmc1_last_solved_bound: -1
% 12.89/13.13 % bmc1_unsat_core_size: -1
% 12.89/13.13 % bmc1_unsat_core_parents_size: -1
% 12.89/13.13 % bmc1_merge_next_fun: 0
% 12.89/13.13 % bmc1_unsat_core_clauses_time: 0.
% 12.89/13.13
% 12.89/13.13 % ------ Instantiation
% 12.89/13.13
% 12.89/13.13 % inst_num_of_clauses: 2097
% 12.89/13.13 % inst_num_in_passive: 1342
% 12.89/13.13 % inst_num_in_active: 736
% 12.89/13.13 % inst_num_in_unprocessed: 13
% 12.89/13.13 % inst_num_of_loops: 748
% 12.89/13.13 % inst_num_of_learning_restarts: 0
% 12.89/13.13 % inst_num_moves_active_passive: 8
% 12.89/13.13 % inst_lit_activity: 303
% 12.89/13.13 % inst_lit_activity_moves: 0
% 12.89/13.13 % inst_num_tautologies: 2
% 12.89/13.13 % inst_num_prop_implied: 0
% 12.89/13.13 % inst_num_existing_simplified: 0
% 12.89/13.13 % inst_num_eq_res_simplified: 0
% 12.89/13.13 % inst_num_child_elim: 0
% 12.89/13.13 % inst_num_of_dismatching_blockings: 607
% 12.89/13.13 % inst_num_of_non_proper_insts: 1272
% 12.89/13.13 % inst_num_of_duplicates: 2134
% 12.89/13.13 % inst_inst_num_from_inst_to_res: 0
% 12.89/13.13 % inst_dismatching_checking_time: 0.002
% 12.89/13.13
% 12.89/13.13 % ------ Resolution
% 12.89/13.13
% 12.89/13.13 % res_num_of_clauses: 51067
% 12.89/13.13 % res_num_in_passive: 48965
% 12.89/13.13 % res_num_in_active: 2186
% 12.89/13.13 % res_num_of_loops: 3000
% 12.89/13.13 % res_forward_subset_subsumed: 3861
% 12.89/13.13 % res_backward_subset_subsumed: 723
% 12.89/13.13 % res_forward_subsumed: 1219
% 12.89/13.13 % res_backward_subsumed: 5
% 12.89/13.13 % res_forward_subsumption_resolution: 29
% 12.89/13.13 % res_backward_subsumption_resolution: 4
% 12.89/13.13 % res_clause_to_clause_subsumption: 49123
% 12.89/13.13 % res_orphan_elimination: 0
% 12.89/13.13 % res_tautology_del: 626
% 12.89/13.13 % res_num_eq_res_simplified: 0
% 12.89/13.13 % res_num_sel_changes: 0
% 12.89/13.13 % res_moves_from_active_to_pass: 0
% 12.89/13.13
% 12.89/13.13 % Status Unsatisfiable
% 12.89/13.13 % SZS status Unsatisfiable
% 12.89/13.13 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------