TSTP Solution File: SCT027-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SCT027-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n020.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 : Mon Jul 18 21:36:45 EDT 2022
% Result : Unsatisfiable 6.56s 7.37s
% Output : CNFRefutation 7.19s
% 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(hAPP(c_fequal(T_a),V_x),V_x)),
input ).
fof(cls_ATP__Linkup_Oequal__imp__fequal_0_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),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__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__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
input ).
fof(clsarity_bool__Lattices_Oboolean__algebra_0,plain,
( class_Lattices_Oboolean__algebra(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Oboolean__algebra]) ).
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__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_CHAINED_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__CHAINED__1),c_Arrow__Order__Mirabelle_OLin)),
input ).
fof(cls_CHAINED_0_0,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__CHAINED__1),c_Arrow__Order__Mirabelle_OLin))
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_0]) ).
cnf(cls_linear__alt_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
input ).
fof(cls_linear__alt_0_0,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin))
| $false ),
inference(orientation,[status(thm)],[cls_linear__alt_0]) ).
cnf(cls_Pow__top_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_A),c_Set_OPow(V_A,T_a))),
input ).
fof(cls_Pow__top_0_0,plain,
! [T_a,V_A] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_A),c_Set_OPow(V_A,T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_Pow__top_0]) ).
cnf(cls_insertCI_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_B,T_a))),
input ).
fof(cls_insertCI_1_0,plain,
! [T_a,V_B,V_x] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_B,T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_insertCI_1]) ).
cnf(cls_insertI1_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_a,V_B,T_a))),
input ).
fof(cls_insertI1_0_0,plain,
! [T_a,V_B,V_a] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_a,V_B,T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_insertI1_0]) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_A,T_a))),
input ).
fof(cls_insert__iff_1_0,plain,
! [T_a,V_A,V_x] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_A,T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_insert__iff_1]) ).
cnf(cls_Collect__mem__eq_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),T_a) = V_A,
input ).
fof(cls_Collect__mem__eq_0_0,plain,
! [T_a,V_A] :
( c_Collect(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),T_a) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Collect__mem__eq_0]) ).
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_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(T_a),V_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(hAPP(c_fequal(T_a),V_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_Union__Pow__eq_0,axiom,
c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(V_A,T_a),tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Union__Pow__eq_0_0,plain,
! [T_a,V_A] :
( c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(V_A,T_a),tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Union__Pow__eq_0]) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),
input ).
fof(cls_singleton__iff_1_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_singleton__iff_1]) ).
cnf(cls_Int__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),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(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,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_Int__Diff_0]) ).
cnf(cls_singleton__conv_0,axiom,
c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_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__conv_0_0,plain,
! [T_a,V_a] :
( c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_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__conv_0]) ).
cnf(cls_Int__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Int__absorb_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Int__absorb_0]) ).
cnf(cls_UN__empty2_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_UN__empty2_0_0,plain,
! [T_a,T_b,V_A] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_UN__empty2_0]) ).
cnf(cls_Int__left__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__left__absorb_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__left__absorb_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_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_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_in__mktop_1,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x))),
input ).
fof(cls_in__mktop_1_0,plain,
! [V_L,V_x] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x)))
| $false ),
inference(orientation,[status(thm)],[cls_in__mktop_1]) ).
cnf(cls_in__mktop_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x))),
input ).
fof(cls_in__mktop_0_0,plain,
! [V_L,V_x,V_y] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x)))
| $false ),
inference(orientation,[status(thm)],[cls_in__mktop_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_psubset__eq_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_fun(T_a,tc_bool)),
input ).
fof(cls_psubset__eq_1_0,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_psubset__eq_1]) ).
cnf(cls_Diff__Int2_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),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(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int2_0]) ).
cnf(cls_Pow__bottom_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Set_OPow(V_B,T_a))),
input ).
fof(cls_Pow__bottom_0_0,plain,
! [T_a,V_B] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Set_OPow(V_B,T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_Pow__bottom_0]) ).
cnf(cls_Diff__Int__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Int__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int__distrib2_0]) ).
cnf(cls_Diff__Int__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_C,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Int__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(V_C,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int__distrib_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_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_Int__left__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__left__commute_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__left__commute_0]) ).
cnf(cls_Int__assoc_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__assoc_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__assoc_0]) ).
cnf(cls_converse__converse_0,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r,
input ).
fof(cls_converse__converse_0_0,plain,
! [T_a,T_b,V_r] :
( c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r
| $false ),
inference(orientation,[status(thm)],[cls_converse__converse_0]) ).
cnf(cls_not__psubset__empty_0,axiom,
~ c_HOL_Oord__class_Oless(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_not__psubset__empty_0_0,plain,
! [T_a,V_A] :
( ~ c_HOL_Oord__class_Oless(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_not__psubset__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_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_emptyE_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
input ).
fof(cls_emptyE_0_0,plain,
! [T_a,V_a] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| $false ),
inference(orientation,[status(thm)],[cls_emptyE_0]) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
input ).
fof(cls_empty__iff_0_0,plain,
! [T_a,V_c] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| $false ),
inference(orientation,[status(thm)],[cls_empty__iff_0]) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
input ).
fof(cls_ex__in__conv_0_0,plain,
! [T_a,V_x] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| $false ),
inference(orientation,[status(thm)],[cls_ex__in__conv_0]) ).
cnf(cls_vimage__Int_0,axiom,
c_Set_Ovimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(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__Int_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Ovimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(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__Int_0]) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)) = V_A,
input ).
fof(cls_double__complement_0_0,plain,
! [T_a,V_A] :
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_double__complement_0]) ).
cnf(cls_override__on__emptyset_0,axiom,
c_Fun_Ooverride__on(V_f,V_g,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b) = V_f,
input ).
fof(cls_override__on__emptyset_0_0,plain,
! [T_a,T_b,V_f,V_g] :
( c_Fun_Ooverride__on(V_f,V_g,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b) = V_f
| $false ),
inference(orientation,[status(thm)],[cls_override__on__emptyset_0]) ).
cnf(cls_Diff__Compl_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Compl_0_0,plain,
! [T_a,V_A,V_B] :
( c_HOL_Ominus__class_Ominus(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Compl_0]) ).
cnf(cls_Diff__disjoint_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,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_Diff__disjoint_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,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_Diff__disjoint_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_UN__constant_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),c_COMBK(V_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_UN__constant_0_0,plain,
! [T_a,T_b,V_c] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),c_COMBK(V_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_UN__constant_0]) ).
cnf(cls_vimage__Compl_0,axiom,
c_Set_Ovimage(V_f,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_b,tc_bool)),V_A),T_a,T_b) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),
input ).
fof(cls_vimage__Compl_0_0,plain,
! [T_a,T_b,V_A,V_f] :
( c_Set_Ovimage(V_f,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_b,tc_bool)),V_A),T_a,T_b) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__Compl_0]) ).
cnf(cls_image__constant__conv_0,axiom,
c_Set_Oimage(c_COMBK(V_c,T_a,T_b),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__constant__conv_0_0,plain,
! [T_a,T_b,V_c] :
( c_Set_Oimage(c_COMBK(V_c,T_a,T_b),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__constant__conv_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_Int__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__commute_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__commute_0]) ).
cnf(cls_inj__on__empty_0,axiom,
c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b),
input ).
fof(cls_inj__on__empty_0_0,plain,
! [T_a,T_b,V_f] :
( c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_inj__on__empty_0]) ).
cnf(cls_Compl__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A) = c_Collect(c_COMBB(c_Not,hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),tc_bool,tc_bool,T_a),T_a),
input ).
fof(cls_Compl__eq_0_0,plain,
! [T_a,V_A] :
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A) = c_Collect(c_COMBB(c_Not,hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),tc_bool,tc_bool,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Compl__eq_0]) ).
cnf(cls_vimage__def_0,axiom,
c_Set_Ovimage(V_f,V_B,T_a,T_b) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(T_b),V_f,T_b,tc_fun(tc_fun(T_b,tc_bool),tc_bool),T_a),T_a,tc_fun(T_b,tc_bool),tc_bool),V_B),T_a),
input ).
fof(cls_vimage__def_0_0,plain,
! [T_a,T_b,V_B,V_f] :
( c_Set_Ovimage(V_f,V_B,T_a,T_b) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(T_b),V_f,T_b,tc_fun(tc_fun(T_b,tc_bool),tc_bool),T_a),T_a,tc_fun(T_b,tc_bool),tc_bool),V_B),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_vimage__def_0]) ).
cnf(cls_Int__empty__right_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,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_Int__empty__right_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,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_Int__empty__right_0]) ).
cnf(cls_Int__empty__left_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__empty__left_0_0,plain,
! [T_a,V_B] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,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__left_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_insert__inter__insert_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_insert__inter__insert_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__inter__insert_0]) ).
cnf(cls_vimage__singleton__eq_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_aa),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))),
input ).
fof(cls_vimage__singleton__eq_1_0,plain,
! [T_a,T_aa,V_a,V_f] :
( hBOOL(hAPP(hAPP(c_in(T_aa),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)))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__singleton__eq_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_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_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_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_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_Compl__disjoint2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Compl__disjoint2_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),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_Compl__disjoint2_0]) ).
cnf(cls_Compl__disjoint_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(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_Compl__disjoint_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(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_Compl__disjoint_0]) ).
cnf(cls_in__mkbot_1,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x))),
input ).
fof(cls_in__mkbot_1_0,plain,
! [V_L,V_x] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x)))
| $false ),
inference(orientation,[status(thm)],[cls_in__mkbot_1]) ).
cnf(cls_in__mkbot_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x))),
input ).
fof(cls_in__mkbot_0_0,plain,
! [V_L,V_x,V_xa] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x)))
| $false ),
inference(orientation,[status(thm)],[cls_in__mkbot_0]) ).
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_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_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q),
input ).
fof(cls_COMBC__def_0_0,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q)
| $false ),
inference(orientation,[status(thm)],[cls_COMBC__def_0]) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P,
input ).
fof(cls_COMBK__def_0_0,plain,
! [T_a,T_b,V_P,V_Q] :
( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P
| $false ),
inference(orientation,[status(thm)],[cls_COMBK__def_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_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_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_Diff__eq_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__eq_0_0,plain,
! [T_a,V_A,V_B] :
( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__eq_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_insert__def_0,axiom,
c_Set_Oinsert(V_a,V_B,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a),V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_insert__def_0_0,plain,
! [T_a,V_B,V_a] :
( c_Set_Oinsert(V_a,V_B,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_insert__def_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_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]) ).
cnf(cls_fold__graph_H_Ointros_I1_J_0,axiom,
c_Nitpick_Ofold__graph_H(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_H_Ointros_I1_J_0_0,plain,
! [T_a,T_b,V_f,V_z] :
( c_Nitpick_Ofold__graph_H(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_H_Ointros_I1_J_0]) ).
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_Un__Int__crazy_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),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(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__crazy_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__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_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__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__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_Compl__Diff__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Compl__Diff__eq_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Compl__Diff__eq_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_Compl__Int_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Compl__Int_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Compl__Int_0]) ).
cnf(cls_Compl__Un_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Compl__Un_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Compl__Un_0]) ).
cnf(cls_vimage__Collect__eq_0,axiom,
c_Set_Ovimage(V_f,c_Collect(V_P,T_b),T_a,T_b) = c_Collect(c_COMBB(V_P,V_f,T_b,tc_bool,T_a),T_a),
input ).
fof(cls_vimage__Collect__eq_0_0,plain,
! [T_a,T_b,V_P,V_f] :
( c_Set_Ovimage(V_f,c_Collect(V_P,T_b),T_a,T_b) = c_Collect(c_COMBB(V_P,V_f,T_b,tc_bool,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_vimage__Collect__eq_0]) ).
cnf(cls_Collect__neg__eq_0,axiom,
c_Collect(c_COMBB(c_Not,V_P,tc_bool,tc_bool,T_a),T_a) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Collect(V_P,T_a)),
input ).
fof(cls_Collect__neg__eq_0_0,plain,
! [T_a,V_P] :
( c_Collect(c_COMBB(c_Not,V_P,tc_bool,tc_bool,T_a),T_a) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Collect(V_P,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_Collect__neg__eq_0]) ).
cnf(cls_subset__Compl__self__eq_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(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__Compl__self__eq_1_0,plain,
! [T_a] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(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__Compl__self__eq_1]) ).
cnf(cls_Diff__Int_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),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,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),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_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)) = c_Lattices_Olower__semilattice__class_Oinf(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__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)) = c_Lattices_Olower__semilattice__class_Oinf(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__Un_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)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),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)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__Diff__Int_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__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_c,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_b,tc_fun(T_a,tc_bool),T_c),T_c,tc_fun(T_a,tc_bool)),
input ).
fof(cls_UN__simps_I10_J_0_0,plain,
! [T_a,T_b,T_c,V_A,V_B,V_f] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_c,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_b,tc_fun(T_a,tc_bool),T_c),T_c,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_UN__simps_I10_J_0]) ).
cnf(cls_UN__extend__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_b,T_c),V_B,T_c,tc_fun(T_a,tc_bool)),
input ).
fof(cls_UN__extend__simps_I10_J_0_0,plain,
! [T_a,T_b,T_c,V_A,V_B,V_f] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_b,T_c),V_B,T_c,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_UN__extend__simps_I10_J_0]) ).
cnf(cls_image__Int__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(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)),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,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__Int__subset_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__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_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_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_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_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_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_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_COMBB__def_0,axiom,
hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)),
input ).
fof(cls_COMBB__def_0_0,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R))
| $false ),
inference(orientation,[status(thm)],[cls_COMBB__def_0]) ).
cnf(cls_Image__Un_0,axiom,
c_Relation_OImage(V_R,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_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,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_R] :
( c_Relation_OImage(V_R,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_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Image__Un_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__Un__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(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(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__Un__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(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(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Un__distrib_0]) ).
cnf(cls_Int__Un__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__Un__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Un__distrib2_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_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_Image__empty_0,axiom,
c_Relation_OImage(V_R,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_R] :
( c_Relation_OImage(V_R,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_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__Int__subset_0,axiom,
c_lessequals(c_Relation_OImage(V_R,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Image__Int__subset_0_0,plain,
! [T_a,T_b,V_A,V_B,V_R] :
( c_lessequals(c_Relation_OImage(V_R,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Image__Int__subset_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_fun__upd__upd_0,axiom,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b) = c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b),
input ).
fof(cls_fun__upd__upd_0_0,plain,
! [T_a,T_b,V_f,V_x,V_y,V_z] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b) = c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__upd_0]) ).
cnf(cls_fun__upd__idem_0,axiom,
c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_b,T_a) = V_f,
input ).
fof(cls_fun__upd__idem_0_0,plain,
! [T_a,T_b,V_f,V_x] :
( c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_b,T_a) = V_f
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__idem_0]) ).
cnf(cls_fun__upd__same_0,axiom,
hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_x) = V_y,
input ).
fof(cls_fun__upd__same_0_0,plain,
! [T_a,T_b,V_f,V_x,V_y] :
( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_x) = V_y
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__same_0]) ).
cnf(cls_fun__upd__triv_0,axiom,
c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_a,T_b) = V_f,
input ).
fof(cls_fun__upd__triv_0_0,plain,
! [T_a,T_b,V_f,V_x] :
( c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_a,T_b) = V_f
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__triv_0]) ).
cnf(cls_fun__upd__apply_0,axiom,
hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_aa),V_x) = V_y,
input ).
fof(cls_fun__upd__apply_0_0,plain,
! [T_a,T_aa,V_f,V_x,V_y] :
( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_aa),V_x) = V_y
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__apply_0]) ).
cnf(cls_fun__upd__idem__iff_1,axiom,
c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_aa,T_a) = V_f,
input ).
fof(cls_fun__upd__idem__iff_1_0,plain,
! [T_a,T_aa,V_f,V_x] :
( c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_aa,T_a) = V_f
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__idem__iff_1]) ).
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_Int__lower1_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__lower1_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__lower1_0]) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__lower2_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__lower2_0]) ).
cnf(cls_Un__Int__distrib_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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)),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,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__distrib_0]) ).
cnf(cls_Un__Int__distrib2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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)),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(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__distrib2_0]) ).
cnf(cls_image__image_0,axiom,
c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a),
input ).
fof(cls_image__image_0_0,plain,
! [T_a,T_b,T_c,V_A,V_f,V_g] :
( c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_image__image_0]) ).
fof(def_lhs_atom1,axiom,
! [V_g,V_f,V_A,T_c,T_b,T_a] :
( lhs_atom1(V_g,V_f,V_A,T_c,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [T_a,T_b,T_c,V_A,V_f,V_g] :
( lhs_atom1(V_g,V_f,V_A,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__image_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom2(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom2(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__distrib2_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_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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)),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__Int__distrib_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_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,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_Int__lower2_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_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,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_Int__lower1_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [T_a] :
( lhs_atom6(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_5,plain,
! [T_a] :
( lhs_atom6(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__empty_1_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_x,V_f,T_aa,T_a] :
( lhs_atom7(V_x,V_f,T_aa,T_a)
<=> c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_aa,T_a) = V_f ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [T_a,T_aa,V_f,V_x] :
( lhs_atom7(V_x,V_f,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__idem__iff_1_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_y,V_x,V_f,T_aa,T_a] :
( lhs_atom8(V_y,V_x,V_f,T_aa,T_a)
<=> hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_aa),V_x) = V_y ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [T_a,T_aa,V_f,V_x,V_y] :
( lhs_atom8(V_y,V_x,V_f,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__apply_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom9(V_x,V_f,T_b,T_a)
<=> c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_a,T_b) = V_f ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom9(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__triv_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_y,V_x,V_f,T_b,T_a] :
( lhs_atom10(V_y,V_x,V_f,T_b,T_a)
<=> hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_x) = V_y ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [T_a,T_b,V_f,V_x,V_y] :
( lhs_atom10(V_y,V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__same_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom11(V_x,V_f,T_b,T_a)
<=> c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_b,T_a) = V_f ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom11(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__idem_0_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [V_z,V_y,V_x,V_f,T_b,T_a] :
( lhs_atom12(V_z,V_y,V_x,V_f,T_b,T_a)
<=> c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b) = c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [T_a,T_b,V_f,V_x,V_y,V_z] :
( lhs_atom12(V_z,V_y,V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__upd_0_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_A,T_a] :
( lhs_atom13(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_12,plain,
! [T_a,V_A] :
( lhs_atom13(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty__right_0_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_B,T_a] :
( lhs_atom14(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_13,plain,
! [T_a,V_B] :
( lhs_atom14(V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty__left_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_R,V_B,V_A,T_b,T_a] :
( lhs_atom15(V_R,V_B,V_A,T_b,T_a)
<=> c_lessequals(c_Relation_OImage(V_R,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [T_a,T_b,V_A,V_B,V_R] :
( lhs_atom15(V_R,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Image__Int__subset_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [V_a,V_B,T_a] :
( lhs_atom16(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_15,plain,
! [T_a,V_B,V_a] :
( lhs_atom16(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__insertI_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V_R,T_b,T_a] :
( lhs_atom17(V_R,T_b,T_a)
<=> c_Relation_OImage(V_R,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_16,plain,
! [T_a,T_b,V_R] :
( lhs_atom17(V_R,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Image__empty_0_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [V_A,T_a] :
( lhs_atom18(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_17,plain,
! [T_a,V_A] :
( lhs_atom18(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__subsetI_0_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom19(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_18,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom19(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__right_0_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V_a,V_C,V_B,T_a] :
( lhs_atom20(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_19,plain,
! [T_a,V_B,V_C,V_a] :
( lhs_atom20(V_a,V_C,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__left_0_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom21(V_C,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom21(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Un__distrib2_0_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom22(V_C,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(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(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom22(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Un__distrib_0_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [V_A,T_a] :
( lhs_atom23(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_22,plain,
! [T_a,V_A] :
( lhs_atom23(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__absorb_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V_R,V_B,V_A,T_b,T_a] :
( lhs_atom24(V_R,V_B,V_A,T_b,T_a)
<=> c_Relation_OImage(V_R,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_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [T_a,T_b,V_A,V_B,V_R] :
( lhs_atom24(V_R,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Image__Un_0_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [V_R,V_Q,V_P,T_c,T_b,T_a] :
( lhs_atom25(V_R,V_Q,V_P,T_c,T_b,T_a)
<=> hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( lhs_atom25(V_R,V_Q,V_P,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_COMBB__def_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [V_x,T_a] :
( lhs_atom26(V_x,T_a)
<=> c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [T_a,V_x] :
( lhs_atom26(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_equalityE_0_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [V_A,T_a] :
( lhs_atom27(V_A,T_a)
<=> c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [T_a,V_A] :
( lhs_atom27(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__refl_0_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [V_M,V_B,V_A,T_b,T_a] :
( lhs_atom28(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_27,plain,
! [T_a,T_b,V_A,V_B,V_M] :
( lhs_atom28(V_M,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__Un_0_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [T_a] :
( lhs_atom29(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_28,plain,
! [T_a] :
( lhs_atom29(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty_2_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom30(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_29,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom30(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__Un_0_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [V_a,V_A,T_a] :
( lhs_atom31(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_30,plain,
! [T_a,V_A,V_a] :
( lhs_atom31(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__is__Un_0_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom32(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_31,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom32(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__extend__simps_I2_J_0_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom33(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_32,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom33(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__extend__simps_I3_J_0_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [V_a,V_B,V_A,T_b,T_a] :
( lhs_atom34(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_33,plain,
! [T_a,T_b,V_A,V_B,V_a] :
( lhs_atom34(V_a,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__insert_0_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom35(V_f,V_B,V_A,T_b,T_a)
<=> c_lessequals(c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom35(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__Int__subset_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [V_f,V_B,V_A,T_c,T_b,T_a] :
( lhs_atom36(V_f,V_B,V_A,T_c,T_b,T_a)
<=> c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_b,T_c),V_B,T_c,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [T_a,T_b,T_c,V_A,V_B,V_f] :
( lhs_atom36(V_f,V_B,V_A,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__extend__simps_I10_J_0_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [V_f,V_B,V_A,T_c,T_b,T_a] :
( lhs_atom37(V_f,V_B,V_A,T_c,T_b,T_a)
<=> c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_c,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_b,tc_fun(T_a,tc_bool),T_c),T_c,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [T_a,T_b,T_c,V_A,V_B,V_f] :
( lhs_atom37(V_f,V_B,V_A,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__simps_I10_J_0_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom38(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_37,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom38(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__diff__subset_0_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [V_B,V_A,T_a] :
( lhs_atom39(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)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
! [T_a,V_A,V_B] :
( lhs_atom39(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff__Int_0_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom40(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)) = c_Lattices_Olower__semilattice__class_Oinf(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_39,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom40(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Un_0_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom41(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),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_40,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom41(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int_0_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [T_a] :
( lhs_atom42(T_a)
<=> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(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_41,plain,
! [T_a] :
( lhs_atom42(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__Compl__self__eq_1_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [V_P,T_a] :
( lhs_atom43(V_P,T_a)
<=> c_Collect(c_COMBB(c_Not,V_P,tc_bool,tc_bool,T_a),T_a) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Collect(V_P,T_a)) ),
inference(definition,[],]) ).
fof(to_be_clausified_42,plain,
! [T_a,V_P] :
( lhs_atom43(V_P,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Collect__neg__eq_0_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [V_f,V_P,T_b,T_a] :
( lhs_atom44(V_f,V_P,T_b,T_a)
<=> c_Set_Ovimage(V_f,c_Collect(V_P,T_b),T_a,T_b) = c_Collect(c_COMBB(V_P,V_f,T_b,tc_bool,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
! [T_a,T_b,V_P,V_f] :
( lhs_atom44(V_f,V_P,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Collect__eq_0_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [V_B,V_A,T_a] :
( lhs_atom45(V_B,V_A,T_a)
<=> hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_44,plain,
! [T_a,V_A,V_B] :
( lhs_atom45(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Compl__Un_0_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [V_B,V_A,T_a] :
( lhs_atom46(V_B,V_A,T_a)
<=> hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_45,plain,
! [T_a,V_A,V_B] :
( lhs_atom46(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Compl__Int_0_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [V_f,V_A,T_b,T_a] :
( lhs_atom47(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_46,plain,
! [T_a,T_b,V_A,V_f] :
( lhs_atom47(V_f,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__vimage__subset_0_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [V_B,V_A,T_a] :
( lhs_atom48(V_B,V_A,T_a)
<=> hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_47,plain,
! [T_a,V_A,V_B] :
( lhs_atom48(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Compl__Diff__eq_0_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom49(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_48,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom49(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__commute_0_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom50(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_49,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom50(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__assoc_0_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [V_B,V_A,T_a] :
( lhs_atom51(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_50,plain,
! [T_a,V_A,V_B] :
( lhs_atom51(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper2_0_0,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
! [V_B,V_A,T_a] :
( lhs_atom52(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_51,plain,
! [T_a,V_A,V_B] :
( lhs_atom52(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper1_0_0,def_lhs_atom52]) ).
fof(def_lhs_atom53,axiom,
! [V_B,V_A,T_a] :
( lhs_atom53(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_52,plain,
! [T_a,V_A,V_B] :
( lhs_atom53(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__subset_0_0,def_lhs_atom53]) ).
fof(def_lhs_atom54,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom54(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_53,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom54(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__crazy_0_0,def_lhs_atom54]) ).
fof(def_lhs_atom55,axiom,
! [V_z,V_f,T_b,T_a] :
( lhs_atom55(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_54,plain,
! [T_a,T_b,V_f,V_z] :
( lhs_atom55(V_z,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold__graph_OemptyI_0_0,def_lhs_atom55]) ).
fof(def_lhs_atom56,axiom,
! [V_z,V_f,T_b,T_a] :
( lhs_atom56(V_z,V_f,T_b,T_a)
<=> c_Nitpick_Ofold__graph_H(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_55,plain,
! [T_a,T_b,V_f,V_z] :
( lhs_atom56(V_z,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold__graph_H_Ointros_I1_J_0_0,def_lhs_atom56]) ).
fof(def_lhs_atom57,axiom,
! [V_B,V_A,T_a] :
( lhs_atom57(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_56,plain,
! [T_a,V_A,V_B] :
( lhs_atom57(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff__cancel2_0_0,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
! [V_B,V_A,T_a] :
( lhs_atom58(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_57,plain,
! [T_a,V_A,V_B] :
( lhs_atom58(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff__cancel_0_0,def_lhs_atom58]) ).
fof(def_lhs_atom59,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom59(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_58,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom59(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff_0_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
! [V_B,V_A,T_a] :
( lhs_atom60(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_59,plain,
! [T_a,V_A,V_B] :
( lhs_atom60(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__commute_0_0,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
! [V_B,V_A,T_a] :
( lhs_atom61(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_60,plain,
! [T_a,V_A,V_B] :
( lhs_atom61(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__absorb_0_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom62(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_61,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom62(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Un_0_0,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
! [V_a,V_B,T_a] :
( lhs_atom63(V_a,V_B,T_a)
<=> c_Set_Oinsert(V_a,V_B,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_62,plain,
! [T_a,V_B,V_a] :
( lhs_atom63(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__def_0_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
! [V_f,V_a,V_B,T_b,T_a] :
( lhs_atom64(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_63,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( lhs_atom64(V_f,V_a,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__insert_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_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_64,plain,
! [T_a,V_A,V_B] :
( lhs_atom65(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__eq_0_0,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
! [V_f,T_b,T_a] :
( lhs_atom66(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_65,plain,
! [T_a,T_b,V_f] :
( lhs_atom66(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__empty_0_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
! [V_xa,V_x,T_a] :
( lhs_atom67(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_66,plain,
! [T_a,V_x,V_xa] :
( lhs_atom67(V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_doubleton__eq__iff_4_0,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
! [V_B,V_A,T_a] :
( lhs_atom68(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_67,plain,
! [T_a,V_A,V_B] :
( lhs_atom68(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__idemp_0_0,def_lhs_atom68]) ).
fof(def_lhs_atom69,axiom,
! [V_Q,V_P,T_b,T_a] :
( lhs_atom69(V_Q,V_P,T_b,T_a)
<=> hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ),
inference(definition,[],]) ).
fof(to_be_clausified_68,plain,
! [T_a,T_b,V_P,V_Q] :
( lhs_atom69(V_Q,V_P,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_COMBK__def_0_0,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
! [V_R,V_Q,V_P,T_c,T_b,T_a] :
( lhs_atom70(V_R,V_Q,V_P,T_c,T_b,T_a)
<=> hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ),
inference(definition,[],]) ).
fof(to_be_clausified_69,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( lhs_atom70(V_R,V_Q,V_P,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_COMBC__def_0_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom71(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_70,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom71(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_INT__extend__simps_I4_J_0_0,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
! [V_y,V_x,V_A,T_a] :
( lhs_atom72(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_71,plain,
! [T_a,V_A,V_x,V_y] :
( lhs_atom72(V_y,V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__commute_0_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
! [V_xa,V_x,V_L] :
( lhs_atom73(V_xa,V_x,V_L)
<=> ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x))) ),
inference(definition,[],]) ).
fof(to_be_clausified_72,plain,
! [V_L,V_x,V_xa] :
( lhs_atom73(V_xa,V_x,V_L)
| $false ),
inference(fold_definition,[status(thm)],[cls_in__mkbot_0_0,def_lhs_atom73]) ).
fof(def_lhs_atom74,axiom,
! [V_x,V_L] :
( lhs_atom74(V_x,V_L)
<=> ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x))) ),
inference(definition,[],]) ).
fof(to_be_clausified_73,plain,
! [V_L,V_x] :
( lhs_atom74(V_x,V_L)
| $false ),
inference(fold_definition,[status(thm)],[cls_in__mkbot_1_0,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
! [V_A,T_a] :
( lhs_atom75(V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(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_74,plain,
! [T_a,V_A] :
( lhs_atom75(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Compl__disjoint_0_0,def_lhs_atom75]) ).
fof(def_lhs_atom76,axiom,
! [V_A,T_a] :
( lhs_atom76(V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),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_75,plain,
! [T_a,V_A] :
( lhs_atom76(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Compl__disjoint2_0_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom77(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_76,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom77(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Diff_0_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
! [V_P,T_a] :
( lhs_atom78(V_P,T_a)
<=> c_Collect(V_P,T_a) = V_P ),
inference(definition,[],]) ).
fof(to_be_clausified_77,plain,
! [T_a,V_P] :
( lhs_atom78(V_P,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Collect__def_0_0,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom79(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_78,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom79(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__insert_0_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom80(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_79,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom80(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__insert2_0_0,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
! [V_a,V_A,T_a] :
( lhs_atom81(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_80,plain,
! [T_a,V_A,V_a] :
( lhs_atom81(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__not__empty_0_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
! [V_f,V_a,T_aa,T_a] :
( lhs_atom82(V_f,V_a,T_aa,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_aa),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))) ),
inference(definition,[],]) ).
fof(to_be_clausified_81,plain,
! [T_a,T_aa,V_a,V_f] :
( lhs_atom82(V_f,V_a,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__singleton__eq_1_0,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom83(V_a,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_82,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom83(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__inter__insert_0_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
! [V_x,V_A,T_a] :
( lhs_atom84(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_83,plain,
! [T_a,V_A,V_x] :
( lhs_atom84(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__absorb2_0_0,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
! [V_B,T_a] :
( lhs_atom85(V_B,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_84,plain,
! [T_a,V_B] :
( lhs_atom85(V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__empty__left_0_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
! [V_A,T_a] :
( lhs_atom86(V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,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_85,plain,
! [T_a,V_A] :
( lhs_atom86(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__empty__right_0_0,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
! [V_f,V_B,T_b,T_a] :
( lhs_atom87(V_f,V_B,T_b,T_a)
<=> c_Set_Ovimage(V_f,V_B,T_a,T_b) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(T_b),V_f,T_b,tc_fun(tc_fun(T_b,tc_bool),tc_bool),T_a),T_a,tc_fun(T_b,tc_bool),tc_bool),V_B),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_86,plain,
! [T_a,T_b,V_B,V_f] :
( lhs_atom87(V_f,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__def_0_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
! [V_A,T_a] :
( lhs_atom88(V_A,T_a)
<=> hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A) = c_Collect(c_COMBB(c_Not,hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),tc_bool,tc_bool,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_87,plain,
! [T_a,V_A] :
( lhs_atom88(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Compl__eq_0_0,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
! [V_f,T_b,T_a] :
( lhs_atom89(V_f,T_b,T_a)
<=> c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_88,plain,
! [T_a,T_b,V_f] :
( lhs_atom89(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_inj__on__empty_0_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
! [V_B,V_A,T_a] :
( lhs_atom90(V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_89,plain,
! [T_a,V_A,V_B] :
( lhs_atom90(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__commute_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_90,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_c,T_b,T_a] :
( lhs_atom92(V_c,T_b,T_a)
<=> c_Set_Oimage(c_COMBK(V_c,T_a,T_b),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_91,plain,
! [T_a,T_b,V_c] :
( lhs_atom92(V_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__constant__conv_0_0,def_lhs_atom92]) ).
fof(def_lhs_atom93,axiom,
! [V_f,V_A,T_b,T_a] :
( lhs_atom93(V_f,V_A,T_b,T_a)
<=> c_Set_Ovimage(V_f,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_b,tc_bool)),V_A),T_a,T_b) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)) ),
inference(definition,[],]) ).
fof(to_be_clausified_92,plain,
! [T_a,T_b,V_A,V_f] :
( lhs_atom93(V_f,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Compl_0_0,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
! [V_c,T_b,T_a] :
( lhs_atom94(V_c,T_b,T_a)
<=> c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),c_COMBK(V_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_93,plain,
! [T_a,T_b,V_c] :
( lhs_atom94(V_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__constant_0_0,def_lhs_atom94]) ).
fof(to_be_clausified_94,plain,
! [T_a,T_b,V_f] :
( lhs_atom66(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__is__image_1_0,def_lhs_atom66]) ).
fof(def_lhs_atom95,axiom,
! [V_B,V_A,T_a] :
( lhs_atom95(V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,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_95,plain,
! [T_a,V_A,V_B] :
( lhs_atom95(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__disjoint_0_0,def_lhs_atom95]) ).
fof(def_lhs_atom96,axiom,
! [V_B,V_A,T_a] :
( lhs_atom96(V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_96,plain,
! [T_a,V_A,V_B] :
( lhs_atom96(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Compl_0_0,def_lhs_atom96]) ).
fof(def_lhs_atom97,axiom,
! [V_g,V_f,T_b,T_a] :
( lhs_atom97(V_g,V_f,T_b,T_a)
<=> c_Fun_Ooverride__on(V_f,V_g,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b) = V_f ),
inference(definition,[],]) ).
fof(to_be_clausified_97,plain,
! [T_a,T_b,V_f,V_g] :
( lhs_atom97(V_g,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_override__on__emptyset_0_0,def_lhs_atom97]) ).
fof(def_lhs_atom98,axiom,
! [V_A,T_a] :
( lhs_atom98(V_A,T_a)
<=> hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_98,plain,
! [T_a,V_A] :
( lhs_atom98(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_double__complement_0_0,def_lhs_atom98]) ).
fof(def_lhs_atom99,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom99(V_f,V_B,V_A,T_b,T_a)
<=> c_Set_Ovimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(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_99,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom99(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Int_0_0,def_lhs_atom99]) ).
fof(def_lhs_atom100,axiom,
! [V_x,T_a] :
( lhs_atom100(V_x,T_a)
<=> ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_100,plain,
! [T_a,V_x] :
( lhs_atom100(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ex__in__conv_0_0,def_lhs_atom100]) ).
fof(def_lhs_atom101,axiom,
! [V_c,T_a] :
( lhs_atom101(V_c,T_a)
<=> ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_101,plain,
! [T_a,V_c] :
( lhs_atom101(V_c,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__iff_0_0,def_lhs_atom101]) ).
fof(def_lhs_atom102,axiom,
! [V_a,T_a] :
( lhs_atom102(V_a,T_a)
<=> ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_102,plain,
! [T_a,V_a] :
( lhs_atom102(V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_emptyE_0_0,def_lhs_atom102]) ).
fof(def_lhs_atom103,axiom,
! [V_A,T_a] :
( lhs_atom103(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_103,plain,
! [T_a,V_A] :
( lhs_atom103(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__empty_0_0,def_lhs_atom103]) ).
fof(def_lhs_atom104,axiom,
! [V_A,T_a] :
( lhs_atom104(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_104,plain,
! [T_a,V_A] :
( lhs_atom104(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__cancel_0_0,def_lhs_atom104]) ).
fof(def_lhs_atom105,axiom,
! [V_A,T_a] :
( lhs_atom105(V_A,T_a)
<=> ~ c_HOL_Oord__class_Oless(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_105,plain,
! [T_a,V_A] :
( lhs_atom105(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__psubset__empty_0_0,def_lhs_atom105]) ).
fof(def_lhs_atom106,axiom,
! [V_r,T_b,T_a] :
( lhs_atom106(V_r,T_b,T_a)
<=> c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r ),
inference(definition,[],]) ).
fof(to_be_clausified_106,plain,
! [T_a,T_b,V_r] :
( lhs_atom106(V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_converse__converse_0_0,def_lhs_atom106]) ).
fof(def_lhs_atom107,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom107(V_C,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_107,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom107(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__assoc_0_0,def_lhs_atom107]) ).
fof(def_lhs_atom108,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom108(V_C,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_108,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom108(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__left__commute_0_0,def_lhs_atom108]) ).
fof(def_lhs_atom109,axiom,
! [V_A,T_a] :
( lhs_atom109(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_109,plain,
! [T_a,V_A] :
( lhs_atom109(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__Diff_0_0,def_lhs_atom109]) ).
fof(def_lhs_atom110,axiom,
! [V_x,T_a] :
( lhs_atom110(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_110,plain,
! [T_a,V_x] :
( lhs_atom110(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_bot1E_0_0,def_lhs_atom110]) ).
fof(def_lhs_atom111,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom111(V_C,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_C,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_111,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom111(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int__distrib_0_0,def_lhs_atom111]) ).
fof(def_lhs_atom112,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom112(V_C,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_112,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom112(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int__distrib2_0_0,def_lhs_atom112]) ).
fof(def_lhs_atom113,axiom,
! [V_B,T_a] :
( lhs_atom113(V_B,T_a)
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Set_OPow(V_B,T_a))) ),
inference(definition,[],]) ).
fof(to_be_clausified_113,plain,
! [T_a,V_B] :
( lhs_atom113(V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Pow__bottom_0_0,def_lhs_atom113]) ).
fof(def_lhs_atom114,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom114(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_114,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom114(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int2_0_0,def_lhs_atom114]) ).
fof(def_lhs_atom115,axiom,
! [V_x,T_a] :
( lhs_atom115(V_x,T_a)
<=> ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_115,plain,
! [T_a,V_x] :
( lhs_atom115(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_psubset__eq_1_0,def_lhs_atom115]) ).
fof(def_lhs_atom116,axiom,
! [V_a,V_A,T_a] :
( lhs_atom116(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_116,plain,
! [T_a,V_A,V_a] :
( lhs_atom116(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__not__insert_0_0,def_lhs_atom116]) ).
fof(def_lhs_atom117,axiom,
! [V_y,V_x,V_L] :
( lhs_atom117(V_y,V_x,V_L)
<=> ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x))) ),
inference(definition,[],]) ).
fof(to_be_clausified_117,plain,
! [V_L,V_x,V_y] :
( lhs_atom117(V_y,V_x,V_L)
| $false ),
inference(fold_definition,[status(thm)],[cls_in__mktop_0_0,def_lhs_atom117]) ).
fof(def_lhs_atom118,axiom,
! [V_x,V_L] :
( lhs_atom118(V_x,V_L)
<=> ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x))) ),
inference(definition,[],]) ).
fof(to_be_clausified_118,plain,
! [V_L,V_x] :
( lhs_atom118(V_x,V_L)
| $false ),
inference(fold_definition,[status(thm)],[cls_in__mktop_1_0,def_lhs_atom118]) ).
fof(def_lhs_atom119,axiom,
! [V_f,V_a,V_B,T_b,T_a] :
( lhs_atom119(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_119,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( lhs_atom119(V_f,V_a,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__insert_0_0,def_lhs_atom119]) ).
fof(def_lhs_atom120,axiom,
! [V_a,V_B,T_b,T_a] :
( lhs_atom120(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_120,plain,
! [T_a,T_b,V_B,V_a] :
( lhs_atom120(V_a,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__extend__simps_I1_J_0_0,def_lhs_atom120]) ).
fof(def_lhs_atom121,axiom,
! [V_x,V_A,T_a] :
( lhs_atom121(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_121,plain,
! [T_a,V_A,V_x] :
( lhs_atom121(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__code_1_0,def_lhs_atom121]) ).
fof(def_lhs_atom122,axiom,
! [V_B,V_A,T_a] :
( lhs_atom122(V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_122,plain,
! [T_a,V_A,V_B] :
( lhs_atom122(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__left__absorb_0_0,def_lhs_atom122]) ).
fof(def_lhs_atom123,axiom,
! [V_A,T_b,T_a] :
( lhs_atom123(V_A,T_b,T_a)
<=> c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_123,plain,
! [T_a,T_b,V_A] :
( lhs_atom123(V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UN__empty2_0_0,def_lhs_atom123]) ).
fof(def_lhs_atom124,axiom,
! [V_A,T_a] :
( lhs_atom124(V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_124,plain,
! [T_a,V_A] :
( lhs_atom124(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__absorb_0_0,def_lhs_atom124]) ).
fof(def_lhs_atom125,axiom,
! [V_a,T_a] :
( lhs_atom125(V_a,T_a)
<=> c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_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_125,plain,
! [T_a,V_a] :
( lhs_atom125(V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_singleton__conv_0_0,def_lhs_atom125]) ).
fof(def_lhs_atom126,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom126(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,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_126,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom126(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Diff_0_0,def_lhs_atom126]) ).
fof(def_lhs_atom127,axiom,
! [V_x,T_a] :
( lhs_atom127(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))) ),
inference(definition,[],]) ).
fof(to_be_clausified_127,plain,
! [T_a,V_x] :
( lhs_atom127(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_singleton__iff_1_0,def_lhs_atom127]) ).
fof(def_lhs_atom128,axiom,
! [V_A,T_a] :
( lhs_atom128(V_A,T_a)
<=> c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(V_A,T_a),tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_128,plain,
! [T_a,V_A] :
( lhs_atom128(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Union__Pow__eq_0_0,def_lhs_atom128]) ).
fof(def_lhs_atom129,axiom,
! [V_a,T_a] :
( lhs_atom129(V_a,T_a)
<=> c_Collect(hAPP(c_fequal(T_a),V_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_129,plain,
! [T_a,V_a] :
( lhs_atom129(V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_singleton__conv2_0_0,def_lhs_atom129]) ).
fof(def_lhs_atom130,axiom,
! [V_f,T_b,T_a] :
( lhs_atom130(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_130,plain,
! [T_a,T_b,V_f] :
( lhs_atom130(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__empty_0_0,def_lhs_atom130]) ).
fof(def_lhs_atom131,axiom,
! [V_A,T_a] :
( lhs_atom131(V_A,T_a)
<=> c_Collect(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),T_a) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_131,plain,
! [T_a,V_A] :
( lhs_atom131(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Collect__mem__eq_0_0,def_lhs_atom131]) ).
fof(def_lhs_atom132,axiom,
! [V_x,V_A,T_a] :
( lhs_atom132(V_x,V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_A,T_a))) ),
inference(definition,[],]) ).
fof(to_be_clausified_132,plain,
! [T_a,V_A,V_x] :
( lhs_atom132(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__iff_1_0,def_lhs_atom132]) ).
fof(def_lhs_atom133,axiom,
! [V_a,V_B,T_a] :
( lhs_atom133(V_a,V_B,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_a,V_B,T_a))) ),
inference(definition,[],]) ).
fof(to_be_clausified_133,plain,
! [T_a,V_B,V_a] :
( lhs_atom133(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertI1_0_0,def_lhs_atom133]) ).
fof(def_lhs_atom134,axiom,
! [V_x,V_B,T_a] :
( lhs_atom134(V_x,V_B,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_B,T_a))) ),
inference(definition,[],]) ).
fof(to_be_clausified_134,plain,
! [T_a,V_B,V_x] :
( lhs_atom134(V_x,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertCI_1_0,def_lhs_atom134]) ).
fof(def_lhs_atom135,axiom,
! [V_A,T_a] :
( lhs_atom135(V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_A),c_Set_OPow(V_A,T_a))) ),
inference(definition,[],]) ).
fof(to_be_clausified_135,plain,
! [T_a,V_A] :
( lhs_atom135(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Pow__top_0_0,def_lhs_atom135]) ).
fof(def_lhs_atom136,axiom,
( lhs_atom136
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(definition,[],]) ).
fof(to_be_clausified_136,plain,
( lhs_atom136
| $false ),
inference(fold_definition,[status(thm)],[cls_linear__alt_0_0,def_lhs_atom136]) ).
fof(def_lhs_atom137,axiom,
( lhs_atom137
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__CHAINED__1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(definition,[],]) ).
fof(to_be_clausified_137,plain,
( lhs_atom137
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_0,def_lhs_atom137]) ).
fof(def_lhs_atom138,axiom,
( lhs_atom138
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_138,plain,
( lhs_atom138
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Oupper__semilattice_0,def_lhs_atom138]) ).
fof(def_lhs_atom139,axiom,
( lhs_atom139
<=> class_Lattices_Olower__semilattice(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_139,plain,
( lhs_atom139
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Olower__semilattice_0,def_lhs_atom139]) ).
fof(def_lhs_atom140,axiom,
( lhs_atom140
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_140,plain,
( lhs_atom140
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Odistrib__lattice_0,def_lhs_atom140]) ).
fof(def_lhs_atom141,axiom,
( lhs_atom141
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_141,plain,
( lhs_atom141
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom141]) ).
fof(def_lhs_atom142,axiom,
( lhs_atom142
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_142,plain,
( lhs_atom142
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom142]) ).
fof(def_lhs_atom143,axiom,
( lhs_atom143
<=> class_Lattices_Olattice(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_143,plain,
( lhs_atom143
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Olattice_0,def_lhs_atom143]) ).
fof(def_lhs_atom144,axiom,
( lhs_atom144
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_144,plain,
( lhs_atom144
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom144]) ).
fof(def_lhs_atom145,axiom,
( lhs_atom145
<=> class_Orderings_Obot(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_145,plain,
( lhs_atom145
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Obot_0,def_lhs_atom145]) ).
fof(def_lhs_atom146,axiom,
( lhs_atom146
<=> class_HOL_Oord(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_146,plain,
( lhs_atom146
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__HOL_Oord_0,def_lhs_atom146]) ).
fof(def_lhs_atom147,axiom,
( lhs_atom147
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_147,plain,
( lhs_atom147
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Complete__Lattice_Ocomplete__lattice_0,def_lhs_atom147]) ).
fof(def_lhs_atom148,axiom,
( lhs_atom148
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_148,plain,
( lhs_atom148
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Oupper__semilattice_0,def_lhs_atom148]) ).
fof(def_lhs_atom149,axiom,
( lhs_atom149
<=> class_Lattices_Olower__semilattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_149,plain,
( lhs_atom149
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Olower__semilattice_0,def_lhs_atom149]) ).
fof(def_lhs_atom150,axiom,
( lhs_atom150
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_150,plain,
( lhs_atom150
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Odistrib__lattice_0,def_lhs_atom150]) ).
fof(def_lhs_atom151,axiom,
( lhs_atom151
<=> class_Lattices_Obounded__lattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_151,plain,
( lhs_atom151
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Obounded__lattice_0,def_lhs_atom151]) ).
fof(def_lhs_atom152,axiom,
( lhs_atom152
<=> class_Lattices_Oboolean__algebra(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_152,plain,
( lhs_atom152
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Oboolean__algebra_0,def_lhs_atom152]) ).
fof(def_lhs_atom153,axiom,
( lhs_atom153
<=> class_Orderings_Opreorder(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_153,plain,
( lhs_atom153
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom153]) ).
fof(def_lhs_atom154,axiom,
( lhs_atom154
<=> class_Lattices_Olattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_154,plain,
( lhs_atom154
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Olattice_0,def_lhs_atom154]) ).
fof(def_lhs_atom155,axiom,
( lhs_atom155
<=> class_Orderings_Oorder(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_155,plain,
( lhs_atom155
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom155]) ).
fof(def_lhs_atom156,axiom,
( lhs_atom156
<=> class_Orderings_Obot(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_156,plain,
( lhs_atom156
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Obot_0,def_lhs_atom156]) ).
fof(def_lhs_atom157,axiom,
( lhs_atom157
<=> class_HOL_Oord(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_157,plain,
( lhs_atom157
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__HOL_Oord_0,def_lhs_atom157]) ).
fof(def_lhs_atom158,axiom,
! [V_x,T_a] :
( lhs_atom158(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_158,plain,
! [T_a,V_x] :
( lhs_atom158(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom158]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X13,X15,X16,X4,X5,X6] :
( lhs_atom70(X13,X15,X16,X4,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_1,axiom,
! [X2,X8,X3,X4,X5,X6] :
( lhs_atom37(X2,X8,X3,X4,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_2,axiom,
! [X2,X8,X3,X4,X5,X6] :
( lhs_atom36(X2,X8,X3,X4,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_3,axiom,
! [X13,X15,X16,X4,X5,X6] :
( lhs_atom25(X13,X15,X16,X4,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_4,axiom,
! [X12,X11,X9,X2,X5,X6] :
( lhs_atom12(X12,X11,X9,X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_5,axiom,
! [X1,X2,X3,X4,X5,X6] :
( lhs_atom1(X1,X2,X3,X4,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_6,axiom,
! [X2,X14,X8,X5,X6] :
( lhs_atom119(X2,X14,X8,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_119) ).
fof(c_0_7,axiom,
! [X2,X8,X3,X5,X6] :
( lhs_atom99(X2,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_8,axiom,
! [X2,X8,X3,X5,X6] :
( lhs_atom77(X2,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_9,axiom,
! [X2,X14,X8,X5,X6] :
( lhs_atom64(X2,X14,X8,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_10,axiom,
! [X2,X8,X3,X5,X6] :
( lhs_atom62(X2,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_11,axiom,
! [X2,X8,X3,X5,X6] :
( lhs_atom38(X2,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_12,axiom,
! [X2,X8,X3,X5,X6] :
( lhs_atom35(X2,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_13,axiom,
! [X14,X8,X3,X5,X6] :
( lhs_atom34(X14,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_14,axiom,
! [X2,X8,X3,X5,X6] :
( lhs_atom30(X2,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_15,axiom,
! [X17,X8,X3,X5,X6] :
( lhs_atom28(X17,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_16,axiom,
! [X13,X8,X3,X5,X6] :
( lhs_atom24(X13,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_17,axiom,
! [X13,X8,X3,X5,X6] :
( lhs_atom15(X13,X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_18,axiom,
! [X11,X9,X2,X5,X6] :
( lhs_atom10(X11,X9,X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_19,axiom,
! [X11,X9,X2,X10,X6] :
( lhs_atom8(X11,X9,X2,X10,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_20,axiom,
! [X7,X8,X3,X6] :
( lhs_atom126(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_126) ).
fof(c_0_21,axiom,
! [X14,X8,X5,X6] :
( lhs_atom120(X14,X8,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_120) ).
fof(c_0_22,axiom,
! [X7,X8,X3,X6] :
( lhs_atom114(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_23,axiom,
! [X7,X8,X3,X6] :
( lhs_atom112(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_24,axiom,
! [X7,X8,X3,X6] :
( lhs_atom111(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_25,axiom,
! [X7,X8,X3,X6] :
( lhs_atom108(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_26,axiom,
! [X7,X8,X3,X6] :
( lhs_atom107(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_27,axiom,
! [X1,X2,X5,X6] :
( lhs_atom97(X1,X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_28,axiom,
! [X2,X3,X5,X6] :
( lhs_atom93(X2,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_29,axiom,
! [X2,X8,X5,X6] :
( lhs_atom87(X2,X8,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_30,axiom,
! [X14,X8,X3,X6] :
( lhs_atom83(X14,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_31,axiom,
! [X2,X14,X10,X6] :
( lhs_atom82(X2,X14,X10,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_32,axiom,
! [X14,X8,X3,X6] :
( lhs_atom80(X14,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_33,axiom,
! [X14,X8,X3,X6] :
( lhs_atom79(X14,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_34,axiom,
! [X11,X9,X3,X6] :
( lhs_atom72(X11,X9,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_35,axiom,
! [X8,X3,X5,X6] :
( lhs_atom71(X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_36,axiom,
! [X15,X16,X5,X6] :
( lhs_atom69(X15,X16,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_37,axiom,
! [X7,X8,X3,X6] :
( lhs_atom59(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_38,axiom,
! [X12,X2,X5,X6] :
( lhs_atom56(X12,X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_39,axiom,
! [X12,X2,X5,X6] :
( lhs_atom55(X12,X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_40,axiom,
! [X7,X8,X3,X6] :
( lhs_atom54(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_41,axiom,
! [X7,X8,X3,X6] :
( lhs_atom50(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_42,axiom,
! [X7,X8,X3,X6] :
( lhs_atom49(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_43,axiom,
! [X2,X3,X5,X6] :
( lhs_atom47(X2,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_44,axiom,
! [X2,X16,X5,X6] :
( lhs_atom44(X2,X16,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_45,axiom,
! [X7,X8,X3,X6] :
( lhs_atom41(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_46,axiom,
! [X7,X8,X3,X6] :
( lhs_atom40(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_47,axiom,
! [X8,X3,X5,X6] :
( lhs_atom33(X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_48,axiom,
! [X8,X3,X5,X6] :
( lhs_atom32(X8,X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_49,axiom,
! [X7,X8,X3,X6] :
( lhs_atom22(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_50,axiom,
! [X7,X8,X3,X6] :
( lhs_atom21(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_51,axiom,
! [X14,X7,X8,X6] :
( lhs_atom20(X14,X7,X8,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_52,axiom,
! [X14,X8,X3,X6] :
( lhs_atom19(X14,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_53,axiom,
! [X9,X2,X5,X6] :
( lhs_atom11(X9,X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_54,axiom,
! [X9,X2,X5,X6] :
( lhs_atom9(X9,X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_55,axiom,
! [X9,X2,X10,X6] :
( lhs_atom7(X9,X2,X10,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_56,axiom,
! [X7,X8,X3,X6] :
( lhs_atom3(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_57,axiom,
! [X7,X8,X3,X6] :
( lhs_atom2(X7,X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_58,axiom,
! [X9,X8,X6] :
( lhs_atom134(X9,X8,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_134) ).
fof(c_0_59,axiom,
! [X14,X8,X6] :
( lhs_atom133(X14,X8,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_133) ).
fof(c_0_60,axiom,
! [X9,X3,X6] :
( lhs_atom132(X9,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_132) ).
fof(c_0_61,axiom,
! [X2,X5,X6] :
( lhs_atom130(X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_130) ).
fof(c_0_62,axiom,
! [X3,X5,X6] :
( lhs_atom123(X3,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_123) ).
fof(c_0_63,axiom,
! [X8,X3,X6] :
( lhs_atom122(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_122) ).
fof(c_0_64,axiom,
! [X9,X3,X6] :
( lhs_atom121(X9,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_121) ).
fof(c_0_65,axiom,
! [X11,X9,X19] :
( lhs_atom117(X11,X9,X19)
| ~ $true ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_66,axiom,
! [X14,X3,X6] :
( lhs_atom116(X14,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_67,axiom,
! [X21,X5,X6] :
( lhs_atom106(X21,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_68,axiom,
! [X8,X3,X6] :
( lhs_atom96(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_69,axiom,
! [X8,X3,X6] :
( lhs_atom95(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_70,axiom,
! [X2,X5,X6] :
( lhs_atom66(X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_71,axiom,
! [X20,X5,X6] :
( lhs_atom94(X20,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_72,axiom,
! [X20,X5,X6] :
( lhs_atom92(X20,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_73,axiom,
! [X14,X3,X6] :
( lhs_atom91(X14,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_74,axiom,
! [X8,X3,X6] :
( lhs_atom90(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_75,axiom,
! [X2,X5,X6] :
( lhs_atom89(X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_76,axiom,
! [X9,X3,X6] :
( lhs_atom84(X9,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_77,axiom,
! [X14,X3,X6] :
( lhs_atom81(X14,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_78,axiom,
! [X18,X9,X19] :
( lhs_atom73(X18,X9,X19)
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_79,axiom,
! [X8,X3,X6] :
( lhs_atom68(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_80,axiom,
! [X18,X9,X6] :
( lhs_atom67(X18,X9,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_81,axiom,
! [X2,X5,X6] :
( lhs_atom66(X2,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_82,axiom,
! [X8,X3,X6] :
( lhs_atom65(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_83,axiom,
! [X14,X8,X6] :
( lhs_atom63(X14,X8,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_84,axiom,
! [X8,X3,X6] :
( lhs_atom61(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_85,axiom,
! [X8,X3,X6] :
( lhs_atom60(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_86,axiom,
! [X8,X3,X6] :
( lhs_atom58(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_87,axiom,
! [X8,X3,X6] :
( lhs_atom57(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_88,axiom,
! [X8,X3,X6] :
( lhs_atom53(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_89,axiom,
! [X8,X3,X6] :
( lhs_atom52(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_90,axiom,
! [X8,X3,X6] :
( lhs_atom51(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_91,axiom,
! [X8,X3,X6] :
( lhs_atom48(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_92,axiom,
! [X8,X3,X6] :
( lhs_atom46(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_93,axiom,
! [X8,X3,X6] :
( lhs_atom45(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_94,axiom,
! [X8,X3,X6] :
( lhs_atom39(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_95,axiom,
! [X14,X3,X6] :
( lhs_atom31(X14,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_96,axiom,
! [X13,X5,X6] :
( lhs_atom17(X13,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_97,axiom,
! [X14,X8,X6] :
( lhs_atom16(X14,X8,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_98,axiom,
! [X8,X3,X6] :
( lhs_atom5(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_99,axiom,
! [X8,X3,X6] :
( lhs_atom4(X8,X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_100,axiom,
! [X9,X6] :
( lhs_atom158(X9,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_158) ).
fof(c_0_101,axiom,
! [X3,X6] :
( lhs_atom135(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_135) ).
fof(c_0_102,axiom,
! [X3,X6] :
( lhs_atom131(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_131) ).
fof(c_0_103,axiom,
! [X14,X6] :
( lhs_atom129(X14,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_129) ).
fof(c_0_104,axiom,
! [X3,X6] :
( lhs_atom128(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_128) ).
fof(c_0_105,axiom,
! [X9,X6] :
( lhs_atom127(X9,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_127) ).
fof(c_0_106,axiom,
! [X14,X6] :
( lhs_atom125(X14,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_125) ).
fof(c_0_107,axiom,
! [X3,X6] :
( lhs_atom124(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_124) ).
fof(c_0_108,axiom,
! [X9,X19] :
( lhs_atom118(X9,X19)
| ~ $true ),
file('<stdin>',to_be_clausified_118) ).
fof(c_0_109,axiom,
! [X9,X6] :
( lhs_atom115(X9,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_110,axiom,
! [X8,X6] :
( lhs_atom113(X8,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_111,axiom,
! [X9,X6] :
( lhs_atom110(X9,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_112,axiom,
! [X3,X6] :
( lhs_atom109(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_113,axiom,
! [X3,X6] :
( lhs_atom105(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_114,axiom,
! [X3,X6] :
( lhs_atom104(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_115,axiom,
! [X3,X6] :
( lhs_atom103(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_116,axiom,
! [X14,X6] :
( lhs_atom102(X14,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_117,axiom,
! [X20,X6] :
( lhs_atom101(X20,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_118,axiom,
! [X9,X6] :
( lhs_atom100(X9,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_119,axiom,
! [X3,X6] :
( lhs_atom98(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_120,axiom,
! [X3,X6] :
( lhs_atom88(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_121,axiom,
! [X3,X6] :
( lhs_atom86(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_122,axiom,
! [X8,X6] :
( lhs_atom85(X8,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_123,axiom,
! [X16,X6] :
( lhs_atom78(X16,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_124,axiom,
! [X3,X6] :
( lhs_atom76(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_125,axiom,
! [X3,X6] :
( lhs_atom75(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_126,axiom,
! [X9,X19] :
( lhs_atom74(X9,X19)
| ~ $true ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_127,axiom,
! [X16,X6] :
( lhs_atom43(X16,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_128,axiom,
! [X3,X6] :
( lhs_atom27(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_129,axiom,
! [X9,X6] :
( lhs_atom26(X9,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_130,axiom,
! [X3,X6] :
( lhs_atom23(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_131,axiom,
! [X3,X6] :
( lhs_atom18(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_132,axiom,
! [X8,X6] :
( lhs_atom14(X8,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_133,axiom,
! [X3,X6] :
( lhs_atom13(X3,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_134,axiom,
! [X6] :
( lhs_atom42(X6)
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_135,axiom,
! [X6] :
( lhs_atom29(X6)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_136,axiom,
! [X6] :
( lhs_atom6(X6)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_137,axiom,
( lhs_atom157
| ~ $true ),
file('<stdin>',to_be_clausified_157) ).
fof(c_0_138,axiom,
( lhs_atom156
| ~ $true ),
file('<stdin>',to_be_clausified_156) ).
fof(c_0_139,axiom,
( lhs_atom155
| ~ $true ),
file('<stdin>',to_be_clausified_155) ).
fof(c_0_140,axiom,
( lhs_atom154
| ~ $true ),
file('<stdin>',to_be_clausified_154) ).
fof(c_0_141,axiom,
( lhs_atom153
| ~ $true ),
file('<stdin>',to_be_clausified_153) ).
fof(c_0_142,axiom,
( lhs_atom152
| ~ $true ),
file('<stdin>',to_be_clausified_152) ).
fof(c_0_143,axiom,
( lhs_atom151
| ~ $true ),
file('<stdin>',to_be_clausified_151) ).
fof(c_0_144,axiom,
( lhs_atom150
| ~ $true ),
file('<stdin>',to_be_clausified_150) ).
fof(c_0_145,axiom,
( lhs_atom149
| ~ $true ),
file('<stdin>',to_be_clausified_149) ).
fof(c_0_146,axiom,
( lhs_atom148
| ~ $true ),
file('<stdin>',to_be_clausified_148) ).
fof(c_0_147,axiom,
( lhs_atom147
| ~ $true ),
file('<stdin>',to_be_clausified_147) ).
fof(c_0_148,axiom,
( lhs_atom146
| ~ $true ),
file('<stdin>',to_be_clausified_146) ).
fof(c_0_149,axiom,
( lhs_atom145
| ~ $true ),
file('<stdin>',to_be_clausified_145) ).
fof(c_0_150,axiom,
( lhs_atom144
| ~ $true ),
file('<stdin>',to_be_clausified_144) ).
fof(c_0_151,axiom,
( lhs_atom143
| ~ $true ),
file('<stdin>',to_be_clausified_143) ).
fof(c_0_152,axiom,
( lhs_atom142
| ~ $true ),
file('<stdin>',to_be_clausified_142) ).
fof(c_0_153,axiom,
( lhs_atom141
| ~ $true ),
file('<stdin>',to_be_clausified_141) ).
fof(c_0_154,axiom,
( lhs_atom140
| ~ $true ),
file('<stdin>',to_be_clausified_140) ).
fof(c_0_155,axiom,
( lhs_atom139
| ~ $true ),
file('<stdin>',to_be_clausified_139) ).
fof(c_0_156,axiom,
( lhs_atom138
| ~ $true ),
file('<stdin>',to_be_clausified_138) ).
fof(c_0_157,axiom,
( lhs_atom137
| ~ $true ),
file('<stdin>',to_be_clausified_137) ).
fof(c_0_158,axiom,
( lhs_atom136
| ~ $true ),
file('<stdin>',to_be_clausified_136) ).
fof(c_0_159,plain,
! [X13,X15,X16,X4,X5,X6] : lhs_atom70(X13,X15,X16,X4,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_160,plain,
! [X2,X8,X3,X4,X5,X6] : lhs_atom37(X2,X8,X3,X4,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_161,plain,
! [X2,X8,X3,X4,X5,X6] : lhs_atom36(X2,X8,X3,X4,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_162,plain,
! [X13,X15,X16,X4,X5,X6] : lhs_atom25(X13,X15,X16,X4,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_163,plain,
! [X12,X11,X9,X2,X5,X6] : lhs_atom12(X12,X11,X9,X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_164,plain,
! [X1,X2,X3,X4,X5,X6] : lhs_atom1(X1,X2,X3,X4,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_165,plain,
! [X2,X14,X8,X5,X6] : lhs_atom119(X2,X14,X8,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_166,plain,
! [X2,X8,X3,X5,X6] : lhs_atom99(X2,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_167,plain,
! [X2,X8,X3,X5,X6] : lhs_atom77(X2,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_168,plain,
! [X2,X14,X8,X5,X6] : lhs_atom64(X2,X14,X8,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_169,plain,
! [X2,X8,X3,X5,X6] : lhs_atom62(X2,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_170,plain,
! [X2,X8,X3,X5,X6] : lhs_atom38(X2,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_171,plain,
! [X2,X8,X3,X5,X6] : lhs_atom35(X2,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_172,plain,
! [X14,X8,X3,X5,X6] : lhs_atom34(X14,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_173,plain,
! [X2,X8,X3,X5,X6] : lhs_atom30(X2,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_174,plain,
! [X17,X8,X3,X5,X6] : lhs_atom28(X17,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_175,plain,
! [X13,X8,X3,X5,X6] : lhs_atom24(X13,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_176,plain,
! [X13,X8,X3,X5,X6] : lhs_atom15(X13,X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_177,plain,
! [X11,X9,X2,X5,X6] : lhs_atom10(X11,X9,X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_178,plain,
! [X11,X9,X2,X10,X6] : lhs_atom8(X11,X9,X2,X10,X6),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_179,plain,
! [X7,X8,X3,X6] : lhs_atom126(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_180,plain,
! [X14,X8,X5,X6] : lhs_atom120(X14,X8,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_181,plain,
! [X7,X8,X3,X6] : lhs_atom114(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_182,plain,
! [X7,X8,X3,X6] : lhs_atom112(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_183,plain,
! [X7,X8,X3,X6] : lhs_atom111(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_184,plain,
! [X7,X8,X3,X6] : lhs_atom108(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_185,plain,
! [X7,X8,X3,X6] : lhs_atom107(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_186,plain,
! [X1,X2,X5,X6] : lhs_atom97(X1,X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_187,plain,
! [X2,X3,X5,X6] : lhs_atom93(X2,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_188,plain,
! [X2,X8,X5,X6] : lhs_atom87(X2,X8,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_189,plain,
! [X14,X8,X3,X6] : lhs_atom83(X14,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_190,plain,
! [X2,X14,X10,X6] : lhs_atom82(X2,X14,X10,X6),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_191,plain,
! [X14,X8,X3,X6] : lhs_atom80(X14,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_192,plain,
! [X14,X8,X3,X6] : lhs_atom79(X14,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_193,plain,
! [X11,X9,X3,X6] : lhs_atom72(X11,X9,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_194,plain,
! [X8,X3,X5,X6] : lhs_atom71(X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_195,plain,
! [X15,X16,X5,X6] : lhs_atom69(X15,X16,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_196,plain,
! [X7,X8,X3,X6] : lhs_atom59(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_197,plain,
! [X12,X2,X5,X6] : lhs_atom56(X12,X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_198,plain,
! [X12,X2,X5,X6] : lhs_atom55(X12,X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_199,plain,
! [X7,X8,X3,X6] : lhs_atom54(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_200,plain,
! [X7,X8,X3,X6] : lhs_atom50(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_201,plain,
! [X7,X8,X3,X6] : lhs_atom49(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_202,plain,
! [X2,X3,X5,X6] : lhs_atom47(X2,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_203,plain,
! [X2,X16,X5,X6] : lhs_atom44(X2,X16,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_204,plain,
! [X7,X8,X3,X6] : lhs_atom41(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_205,plain,
! [X7,X8,X3,X6] : lhs_atom40(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_206,plain,
! [X8,X3,X5,X6] : lhs_atom33(X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_207,plain,
! [X8,X3,X5,X6] : lhs_atom32(X8,X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_208,plain,
! [X7,X8,X3,X6] : lhs_atom22(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_209,plain,
! [X7,X8,X3,X6] : lhs_atom21(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_210,plain,
! [X14,X7,X8,X6] : lhs_atom20(X14,X7,X8,X6),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_211,plain,
! [X14,X8,X3,X6] : lhs_atom19(X14,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_212,plain,
! [X9,X2,X5,X6] : lhs_atom11(X9,X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_213,plain,
! [X9,X2,X5,X6] : lhs_atom9(X9,X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_214,plain,
! [X9,X2,X10,X6] : lhs_atom7(X9,X2,X10,X6),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_215,plain,
! [X7,X8,X3,X6] : lhs_atom3(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_216,plain,
! [X7,X8,X3,X6] : lhs_atom2(X7,X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_217,plain,
! [X9,X8,X6] : lhs_atom134(X9,X8,X6),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_218,plain,
! [X14,X8,X6] : lhs_atom133(X14,X8,X6),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_219,plain,
! [X9,X3,X6] : lhs_atom132(X9,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_220,plain,
! [X2,X5,X6] : lhs_atom130(X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_221,plain,
! [X3,X5,X6] : lhs_atom123(X3,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_222,plain,
! [X8,X3,X6] : lhs_atom122(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_223,plain,
! [X9,X3,X6] : lhs_atom121(X9,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_224,plain,
! [X11,X9,X19] : lhs_atom117(X11,X9,X19),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_225,plain,
! [X14,X3,X6] : lhs_atom116(X14,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_226,plain,
! [X21,X5,X6] : lhs_atom106(X21,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_227,plain,
! [X8,X3,X6] : lhs_atom96(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_228,plain,
! [X8,X3,X6] : lhs_atom95(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_229,plain,
! [X2,X5,X6] : lhs_atom66(X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_230,plain,
! [X20,X5,X6] : lhs_atom94(X20,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_231,plain,
! [X20,X5,X6] : lhs_atom92(X20,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_232,plain,
! [X14,X3,X6] : lhs_atom91(X14,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_233,plain,
! [X8,X3,X6] : lhs_atom90(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_234,plain,
! [X2,X5,X6] : lhs_atom89(X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_235,plain,
! [X9,X3,X6] : lhs_atom84(X9,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_236,plain,
! [X14,X3,X6] : lhs_atom81(X14,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_237,plain,
! [X18,X9,X19] : lhs_atom73(X18,X9,X19),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_238,plain,
! [X8,X3,X6] : lhs_atom68(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_239,plain,
! [X18,X9,X6] : lhs_atom67(X18,X9,X6),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_240,plain,
! [X2,X5,X6] : lhs_atom66(X2,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_241,plain,
! [X8,X3,X6] : lhs_atom65(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_242,plain,
! [X14,X8,X6] : lhs_atom63(X14,X8,X6),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_243,plain,
! [X8,X3,X6] : lhs_atom61(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_244,plain,
! [X8,X3,X6] : lhs_atom60(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_245,plain,
! [X8,X3,X6] : lhs_atom58(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_246,plain,
! [X8,X3,X6] : lhs_atom57(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_247,plain,
! [X8,X3,X6] : lhs_atom53(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_248,plain,
! [X8,X3,X6] : lhs_atom52(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_249,plain,
! [X8,X3,X6] : lhs_atom51(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_250,plain,
! [X8,X3,X6] : lhs_atom48(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_251,plain,
! [X8,X3,X6] : lhs_atom46(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_252,plain,
! [X8,X3,X6] : lhs_atom45(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_253,plain,
! [X8,X3,X6] : lhs_atom39(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_254,plain,
! [X14,X3,X6] : lhs_atom31(X14,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_255,plain,
! [X13,X5,X6] : lhs_atom17(X13,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_256,plain,
! [X14,X8,X6] : lhs_atom16(X14,X8,X6),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_257,plain,
! [X8,X3,X6] : lhs_atom5(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_258,plain,
! [X8,X3,X6] : lhs_atom4(X8,X3,X6),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_259,plain,
! [X9,X6] : lhs_atom158(X9,X6),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_260,plain,
! [X3,X6] : lhs_atom135(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_261,plain,
! [X3,X6] : lhs_atom131(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_262,plain,
! [X14,X6] : lhs_atom129(X14,X6),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_263,plain,
! [X3,X6] : lhs_atom128(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_264,plain,
! [X9,X6] : lhs_atom127(X9,X6),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_265,plain,
! [X14,X6] : lhs_atom125(X14,X6),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_266,plain,
! [X3,X6] : lhs_atom124(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_267,plain,
! [X9,X19] : lhs_atom118(X9,X19),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_268,plain,
! [X9,X6] : lhs_atom115(X9,X6),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_269,plain,
! [X8,X6] : lhs_atom113(X8,X6),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_270,plain,
! [X9,X6] : lhs_atom110(X9,X6),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_271,plain,
! [X3,X6] : lhs_atom109(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_272,plain,
! [X3,X6] : lhs_atom105(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_273,plain,
! [X3,X6] : lhs_atom104(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_274,plain,
! [X3,X6] : lhs_atom103(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_275,plain,
! [X14,X6] : lhs_atom102(X14,X6),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_276,plain,
! [X20,X6] : lhs_atom101(X20,X6),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_277,plain,
! [X9,X6] : lhs_atom100(X9,X6),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_278,plain,
! [X3,X6] : lhs_atom98(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_279,plain,
! [X3,X6] : lhs_atom88(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_280,plain,
! [X3,X6] : lhs_atom86(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_281,plain,
! [X8,X6] : lhs_atom85(X8,X6),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_282,plain,
! [X16,X6] : lhs_atom78(X16,X6),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_283,plain,
! [X3,X6] : lhs_atom76(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_284,plain,
! [X3,X6] : lhs_atom75(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_285,plain,
! [X9,X19] : lhs_atom74(X9,X19),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_286,plain,
! [X16,X6] : lhs_atom43(X16,X6),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_287,plain,
! [X3,X6] : lhs_atom27(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_288,plain,
! [X9,X6] : lhs_atom26(X9,X6),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_289,plain,
! [X3,X6] : lhs_atom23(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_290,plain,
! [X3,X6] : lhs_atom18(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_291,plain,
! [X8,X6] : lhs_atom14(X8,X6),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_292,plain,
! [X3,X6] : lhs_atom13(X3,X6),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_293,plain,
! [X6] : lhs_atom42(X6),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_294,plain,
! [X6] : lhs_atom29(X6),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_295,plain,
! [X6] : lhs_atom6(X6),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_296,plain,
lhs_atom157,
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_297,plain,
lhs_atom156,
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_298,plain,
lhs_atom155,
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_299,plain,
lhs_atom154,
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_300,plain,
lhs_atom153,
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_301,plain,
lhs_atom152,
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_302,plain,
lhs_atom151,
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_303,plain,
lhs_atom150,
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_304,plain,
lhs_atom149,
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_305,plain,
lhs_atom148,
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_306,plain,
lhs_atom147,
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_307,plain,
lhs_atom146,
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_308,plain,
lhs_atom145,
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_309,plain,
lhs_atom144,
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_310,plain,
lhs_atom143,
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_311,plain,
lhs_atom142,
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_312,plain,
lhs_atom141,
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_313,plain,
lhs_atom140,
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_314,plain,
lhs_atom139,
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_315,plain,
lhs_atom138,
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_316,plain,
lhs_atom137,
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_317,plain,
lhs_atom136,
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_318,plain,
! [X17,X18,X19,X20,X21,X22] : lhs_atom70(X17,X18,X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_159]) ).
fof(c_0_319,plain,
! [X9,X10,X11,X12,X13,X14] : lhs_atom37(X9,X10,X11,X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_320,plain,
! [X9,X10,X11,X12,X13,X14] : lhs_atom36(X9,X10,X11,X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_161]) ).
fof(c_0_321,plain,
! [X17,X18,X19,X20,X21,X22] : lhs_atom25(X17,X18,X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_162]) ).
fof(c_0_322,plain,
! [X13,X14,X15,X16,X17,X18] : lhs_atom12(X13,X14,X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_163]) ).
fof(c_0_323,plain,
! [X7,X8,X9,X10,X11,X12] : lhs_atom1(X7,X8,X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_164]) ).
fof(c_0_324,plain,
! [X15,X16,X17,X18,X19] : lhs_atom119(X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_325,plain,
! [X9,X10,X11,X12,X13] : lhs_atom99(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_326,plain,
! [X9,X10,X11,X12,X13] : lhs_atom77(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_327,plain,
! [X15,X16,X17,X18,X19] : lhs_atom64(X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_328,plain,
! [X9,X10,X11,X12,X13] : lhs_atom62(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_329,plain,
! [X9,X10,X11,X12,X13] : lhs_atom38(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_330,plain,
! [X9,X10,X11,X12,X13] : lhs_atom35(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_331,plain,
! [X15,X16,X17,X18,X19] : lhs_atom34(X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_332,plain,
! [X9,X10,X11,X12,X13] : lhs_atom30(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_333,plain,
! [X18,X19,X20,X21,X22] : lhs_atom28(X18,X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_334,plain,
! [X14,X15,X16,X17,X18] : lhs_atom24(X14,X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_335,plain,
! [X14,X15,X16,X17,X18] : lhs_atom15(X14,X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_336,plain,
! [X12,X13,X14,X15,X16] : lhs_atom10(X12,X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_337,plain,
! [X12,X13,X14,X15,X16] : lhs_atom8(X12,X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_338,plain,
! [X9,X10,X11,X12] : lhs_atom126(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_339,plain,
! [X15,X16,X17,X18] : lhs_atom120(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_340,plain,
! [X9,X10,X11,X12] : lhs_atom114(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_341,plain,
! [X9,X10,X11,X12] : lhs_atom112(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_342,plain,
! [X9,X10,X11,X12] : lhs_atom111(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_343,plain,
! [X9,X10,X11,X12] : lhs_atom108(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_344,plain,
! [X9,X10,X11,X12] : lhs_atom107(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_185]) ).
fof(c_0_345,plain,
! [X7,X8,X9,X10] : lhs_atom97(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_346,plain,
! [X7,X8,X9,X10] : lhs_atom93(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_347,plain,
! [X9,X10,X11,X12] : lhs_atom87(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_348,plain,
! [X15,X16,X17,X18] : lhs_atom83(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_349,plain,
! [X15,X16,X17,X18] : lhs_atom82(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_350,plain,
! [X15,X16,X17,X18] : lhs_atom80(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_351,plain,
! [X15,X16,X17,X18] : lhs_atom79(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_352,plain,
! [X12,X13,X14,X15] : lhs_atom72(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_353,plain,
! [X9,X10,X11,X12] : lhs_atom71(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_354,plain,
! [X17,X18,X19,X20] : lhs_atom69(X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_355,plain,
! [X9,X10,X11,X12] : lhs_atom59(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_356,plain,
! [X13,X14,X15,X16] : lhs_atom56(X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_357,plain,
! [X13,X14,X15,X16] : lhs_atom55(X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_358,plain,
! [X9,X10,X11,X12] : lhs_atom54(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_359,plain,
! [X9,X10,X11,X12] : lhs_atom50(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_360,plain,
! [X9,X10,X11,X12] : lhs_atom49(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_361,plain,
! [X7,X8,X9,X10] : lhs_atom47(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_362,plain,
! [X17,X18,X19,X20] : lhs_atom44(X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_363,plain,
! [X9,X10,X11,X12] : lhs_atom41(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_364,plain,
! [X9,X10,X11,X12] : lhs_atom40(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_365,plain,
! [X9,X10,X11,X12] : lhs_atom33(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_366,plain,
! [X9,X10,X11,X12] : lhs_atom32(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_367,plain,
! [X9,X10,X11,X12] : lhs_atom22(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_368,plain,
! [X9,X10,X11,X12] : lhs_atom21(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_369,plain,
! [X15,X16,X17,X18] : lhs_atom20(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_370,plain,
! [X15,X16,X17,X18] : lhs_atom19(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_371,plain,
! [X10,X11,X12,X13] : lhs_atom11(X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_372,plain,
! [X10,X11,X12,X13] : lhs_atom9(X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_373,plain,
! [X11,X12,X13,X14] : lhs_atom7(X11,X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_374,plain,
! [X9,X10,X11,X12] : lhs_atom3(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_375,plain,
! [X9,X10,X11,X12] : lhs_atom2(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_376,plain,
! [X10,X11,X12] : lhs_atom134(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_377,plain,
! [X15,X16,X17] : lhs_atom133(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_378,plain,
! [X10,X11,X12] : lhs_atom132(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_379,plain,
! [X7,X8,X9] : lhs_atom130(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_380,plain,
! [X7,X8,X9] : lhs_atom123(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_381,plain,
! [X9,X10,X11] : lhs_atom122(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_382,plain,
! [X10,X11,X12] : lhs_atom121(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_383,plain,
! [X20,X21,X22] : lhs_atom117(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_384,plain,
! [X15,X16,X17] : lhs_atom116(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_385,plain,
! [X22,X23,X24] : lhs_atom106(X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_386,plain,
! [X9,X10,X11] : lhs_atom96(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_387,plain,
! [X9,X10,X11] : lhs_atom95(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_388,plain,
! [X7,X8,X9] : lhs_atom66(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_389,plain,
! [X21,X22,X23] : lhs_atom94(X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_390,plain,
! [X21,X22,X23] : lhs_atom92(X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_391,plain,
! [X15,X16,X17] : lhs_atom91(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_392,plain,
! [X9,X10,X11] : lhs_atom90(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_393,plain,
! [X7,X8,X9] : lhs_atom89(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_394,plain,
! [X10,X11,X12] : lhs_atom84(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_235]) ).
fof(c_0_395,plain,
! [X15,X16,X17] : lhs_atom81(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_396,plain,
! [X20,X21,X22] : lhs_atom73(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_237]) ).
fof(c_0_397,plain,
! [X9,X10,X11] : lhs_atom68(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_238]) ).
fof(c_0_398,plain,
! [X19,X20,X21] : lhs_atom67(X19,X20,X21),
inference(variable_rename,[status(thm)],[c_0_239]) ).
fof(c_0_399,plain,
! [X7,X8,X9] : lhs_atom66(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_240]) ).
fof(c_0_400,plain,
! [X9,X10,X11] : lhs_atom65(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_401,plain,
! [X15,X16,X17] : lhs_atom63(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_242]) ).
fof(c_0_402,plain,
! [X9,X10,X11] : lhs_atom61(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_243]) ).
fof(c_0_403,plain,
! [X9,X10,X11] : lhs_atom60(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_244]) ).
fof(c_0_404,plain,
! [X9,X10,X11] : lhs_atom58(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_245]) ).
fof(c_0_405,plain,
! [X9,X10,X11] : lhs_atom57(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_246]) ).
fof(c_0_406,plain,
! [X9,X10,X11] : lhs_atom53(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_247]) ).
fof(c_0_407,plain,
! [X9,X10,X11] : lhs_atom52(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_248]) ).
fof(c_0_408,plain,
! [X9,X10,X11] : lhs_atom51(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_249]) ).
fof(c_0_409,plain,
! [X9,X10,X11] : lhs_atom48(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_250]) ).
fof(c_0_410,plain,
! [X9,X10,X11] : lhs_atom46(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_251]) ).
fof(c_0_411,plain,
! [X9,X10,X11] : lhs_atom45(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_412,plain,
! [X9,X10,X11] : lhs_atom39(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_253]) ).
fof(c_0_413,plain,
! [X15,X16,X17] : lhs_atom31(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_254]) ).
fof(c_0_414,plain,
! [X14,X15,X16] : lhs_atom17(X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_415,plain,
! [X15,X16,X17] : lhs_atom16(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_256]) ).
fof(c_0_416,plain,
! [X9,X10,X11] : lhs_atom5(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_257]) ).
fof(c_0_417,plain,
! [X9,X10,X11] : lhs_atom4(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_258]) ).
fof(c_0_418,plain,
! [X10,X11] : lhs_atom158(X10,X11),
inference(variable_rename,[status(thm)],[c_0_259]) ).
fof(c_0_419,plain,
! [X7,X8] : lhs_atom135(X7,X8),
inference(variable_rename,[status(thm)],[c_0_260]) ).
fof(c_0_420,plain,
! [X7,X8] : lhs_atom131(X7,X8),
inference(variable_rename,[status(thm)],[c_0_261]) ).
fof(c_0_421,plain,
! [X15,X16] : lhs_atom129(X15,X16),
inference(variable_rename,[status(thm)],[c_0_262]) ).
fof(c_0_422,plain,
! [X7,X8] : lhs_atom128(X7,X8),
inference(variable_rename,[status(thm)],[c_0_263]) ).
fof(c_0_423,plain,
! [X10,X11] : lhs_atom127(X10,X11),
inference(variable_rename,[status(thm)],[c_0_264]) ).
fof(c_0_424,plain,
! [X15,X16] : lhs_atom125(X15,X16),
inference(variable_rename,[status(thm)],[c_0_265]) ).
fof(c_0_425,plain,
! [X7,X8] : lhs_atom124(X7,X8),
inference(variable_rename,[status(thm)],[c_0_266]) ).
fof(c_0_426,plain,
! [X20,X21] : lhs_atom118(X20,X21),
inference(variable_rename,[status(thm)],[c_0_267]) ).
fof(c_0_427,plain,
! [X10,X11] : lhs_atom115(X10,X11),
inference(variable_rename,[status(thm)],[c_0_268]) ).
fof(c_0_428,plain,
! [X9,X10] : lhs_atom113(X9,X10),
inference(variable_rename,[status(thm)],[c_0_269]) ).
fof(c_0_429,plain,
! [X10,X11] : lhs_atom110(X10,X11),
inference(variable_rename,[status(thm)],[c_0_270]) ).
fof(c_0_430,plain,
! [X7,X8] : lhs_atom109(X7,X8),
inference(variable_rename,[status(thm)],[c_0_271]) ).
fof(c_0_431,plain,
! [X7,X8] : lhs_atom105(X7,X8),
inference(variable_rename,[status(thm)],[c_0_272]) ).
fof(c_0_432,plain,
! [X7,X8] : lhs_atom104(X7,X8),
inference(variable_rename,[status(thm)],[c_0_273]) ).
fof(c_0_433,plain,
! [X7,X8] : lhs_atom103(X7,X8),
inference(variable_rename,[status(thm)],[c_0_274]) ).
fof(c_0_434,plain,
! [X15,X16] : lhs_atom102(X15,X16),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_435,plain,
! [X21,X22] : lhs_atom101(X21,X22),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_436,plain,
! [X10,X11] : lhs_atom100(X10,X11),
inference(variable_rename,[status(thm)],[c_0_277]) ).
fof(c_0_437,plain,
! [X7,X8] : lhs_atom98(X7,X8),
inference(variable_rename,[status(thm)],[c_0_278]) ).
fof(c_0_438,plain,
! [X7,X8] : lhs_atom88(X7,X8),
inference(variable_rename,[status(thm)],[c_0_279]) ).
fof(c_0_439,plain,
! [X7,X8] : lhs_atom86(X7,X8),
inference(variable_rename,[status(thm)],[c_0_280]) ).
fof(c_0_440,plain,
! [X9,X10] : lhs_atom85(X9,X10),
inference(variable_rename,[status(thm)],[c_0_281]) ).
fof(c_0_441,plain,
! [X17,X18] : lhs_atom78(X17,X18),
inference(variable_rename,[status(thm)],[c_0_282]) ).
fof(c_0_442,plain,
! [X7,X8] : lhs_atom76(X7,X8),
inference(variable_rename,[status(thm)],[c_0_283]) ).
fof(c_0_443,plain,
! [X7,X8] : lhs_atom75(X7,X8),
inference(variable_rename,[status(thm)],[c_0_284]) ).
fof(c_0_444,plain,
! [X20,X21] : lhs_atom74(X20,X21),
inference(variable_rename,[status(thm)],[c_0_285]) ).
fof(c_0_445,plain,
! [X17,X18] : lhs_atom43(X17,X18),
inference(variable_rename,[status(thm)],[c_0_286]) ).
fof(c_0_446,plain,
! [X7,X8] : lhs_atom27(X7,X8),
inference(variable_rename,[status(thm)],[c_0_287]) ).
fof(c_0_447,plain,
! [X10,X11] : lhs_atom26(X10,X11),
inference(variable_rename,[status(thm)],[c_0_288]) ).
fof(c_0_448,plain,
! [X7,X8] : lhs_atom23(X7,X8),
inference(variable_rename,[status(thm)],[c_0_289]) ).
fof(c_0_449,plain,
! [X7,X8] : lhs_atom18(X7,X8),
inference(variable_rename,[status(thm)],[c_0_290]) ).
fof(c_0_450,plain,
! [X9,X10] : lhs_atom14(X9,X10),
inference(variable_rename,[status(thm)],[c_0_291]) ).
fof(c_0_451,plain,
! [X7,X8] : lhs_atom13(X7,X8),
inference(variable_rename,[status(thm)],[c_0_292]) ).
fof(c_0_452,plain,
! [X7] : lhs_atom42(X7),
inference(variable_rename,[status(thm)],[c_0_293]) ).
fof(c_0_453,plain,
! [X7] : lhs_atom29(X7),
inference(variable_rename,[status(thm)],[c_0_294]) ).
fof(c_0_454,plain,
! [X7] : lhs_atom6(X7),
inference(variable_rename,[status(thm)],[c_0_295]) ).
fof(c_0_455,plain,
lhs_atom157,
c_0_296 ).
fof(c_0_456,plain,
lhs_atom156,
c_0_297 ).
fof(c_0_457,plain,
lhs_atom155,
c_0_298 ).
fof(c_0_458,plain,
lhs_atom154,
c_0_299 ).
fof(c_0_459,plain,
lhs_atom153,
c_0_300 ).
fof(c_0_460,plain,
lhs_atom152,
c_0_301 ).
fof(c_0_461,plain,
lhs_atom151,
c_0_302 ).
fof(c_0_462,plain,
lhs_atom150,
c_0_303 ).
fof(c_0_463,plain,
lhs_atom149,
c_0_304 ).
fof(c_0_464,plain,
lhs_atom148,
c_0_305 ).
fof(c_0_465,plain,
lhs_atom147,
c_0_306 ).
fof(c_0_466,plain,
lhs_atom146,
c_0_307 ).
fof(c_0_467,plain,
lhs_atom145,
c_0_308 ).
fof(c_0_468,plain,
lhs_atom144,
c_0_309 ).
fof(c_0_469,plain,
lhs_atom143,
c_0_310 ).
fof(c_0_470,plain,
lhs_atom142,
c_0_311 ).
fof(c_0_471,plain,
lhs_atom141,
c_0_312 ).
fof(c_0_472,plain,
lhs_atom140,
c_0_313 ).
fof(c_0_473,plain,
lhs_atom139,
c_0_314 ).
fof(c_0_474,plain,
lhs_atom138,
c_0_315 ).
fof(c_0_475,plain,
lhs_atom137,
c_0_316 ).
fof(c_0_476,plain,
lhs_atom136,
c_0_317 ).
cnf(c_0_477,plain,
lhs_atom70(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_478,plain,
lhs_atom37(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_479,plain,
lhs_atom36(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_480,plain,
lhs_atom25(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_481,plain,
lhs_atom12(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_482,plain,
lhs_atom1(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_483,plain,
lhs_atom119(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_484,plain,
lhs_atom99(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_485,plain,
lhs_atom77(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_486,plain,
lhs_atom64(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_487,plain,
lhs_atom62(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_488,plain,
lhs_atom38(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_489,plain,
lhs_atom35(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_490,plain,
lhs_atom34(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_491,plain,
lhs_atom30(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_492,plain,
lhs_atom28(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_493,plain,
lhs_atom24(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_494,plain,
lhs_atom15(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_495,plain,
lhs_atom10(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_496,plain,
lhs_atom8(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_497,plain,
lhs_atom126(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_498,plain,
lhs_atom120(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_499,plain,
lhs_atom114(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_500,plain,
lhs_atom112(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_501,plain,
lhs_atom111(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_502,plain,
lhs_atom108(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_503,plain,
lhs_atom107(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_504,plain,
lhs_atom97(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_505,plain,
lhs_atom93(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_506,plain,
lhs_atom87(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_507,plain,
lhs_atom83(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_508,plain,
lhs_atom82(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_509,plain,
lhs_atom80(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_510,plain,
lhs_atom79(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_511,plain,
lhs_atom72(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_512,plain,
lhs_atom71(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_513,plain,
lhs_atom69(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_514,plain,
lhs_atom59(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_515,plain,
lhs_atom56(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_516,plain,
lhs_atom55(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_517,plain,
lhs_atom54(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_518,plain,
lhs_atom50(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_519,plain,
lhs_atom49(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_520,plain,
lhs_atom47(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_521,plain,
lhs_atom44(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_522,plain,
lhs_atom41(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_523,plain,
lhs_atom40(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_524,plain,
lhs_atom33(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_525,plain,
lhs_atom32(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_526,plain,
lhs_atom22(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_527,plain,
lhs_atom21(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_528,plain,
lhs_atom20(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_529,plain,
lhs_atom19(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_530,plain,
lhs_atom11(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_531,plain,
lhs_atom9(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_532,plain,
lhs_atom7(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_533,plain,
lhs_atom3(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_534,plain,
lhs_atom2(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_535,plain,
lhs_atom134(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_536,plain,
lhs_atom133(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_537,plain,
lhs_atom132(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_538,plain,
lhs_atom130(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_539,plain,
lhs_atom123(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_540,plain,
lhs_atom122(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_541,plain,
lhs_atom121(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_542,plain,
lhs_atom117(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_543,plain,
lhs_atom116(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_544,plain,
lhs_atom106(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_545,plain,
lhs_atom96(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_546,plain,
lhs_atom95(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_547,plain,
lhs_atom66(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_548,plain,
lhs_atom94(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_549,plain,
lhs_atom92(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_550,plain,
lhs_atom91(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_551,plain,
lhs_atom90(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_552,plain,
lhs_atom89(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_553,plain,
lhs_atom84(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_554,plain,
lhs_atom81(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_555,plain,
lhs_atom73(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_556,plain,
lhs_atom68(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_557,plain,
lhs_atom67(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_558,plain,
lhs_atom66(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_559,plain,
lhs_atom65(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_560,plain,
lhs_atom63(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_561,plain,
lhs_atom61(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_562,plain,
lhs_atom60(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_563,plain,
lhs_atom58(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_564,plain,
lhs_atom57(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_565,plain,
lhs_atom53(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_566,plain,
lhs_atom52(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_567,plain,
lhs_atom51(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_568,plain,
lhs_atom48(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_569,plain,
lhs_atom46(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_570,plain,
lhs_atom45(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_571,plain,
lhs_atom39(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_572,plain,
lhs_atom31(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_573,plain,
lhs_atom17(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_574,plain,
lhs_atom16(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_575,plain,
lhs_atom5(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_576,plain,
lhs_atom4(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_577,plain,
lhs_atom158(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_578,plain,
lhs_atom135(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_579,plain,
lhs_atom131(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_580,plain,
lhs_atom129(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_581,plain,
lhs_atom128(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_582,plain,
lhs_atom127(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_583,plain,
lhs_atom125(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_584,plain,
lhs_atom124(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_585,plain,
lhs_atom118(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_586,plain,
lhs_atom115(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_587,plain,
lhs_atom113(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_588,plain,
lhs_atom110(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_589,plain,
lhs_atom109(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_590,plain,
lhs_atom105(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_591,plain,
lhs_atom104(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_592,plain,
lhs_atom103(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_593,plain,
lhs_atom102(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_594,plain,
lhs_atom101(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_595,plain,
lhs_atom100(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_596,plain,
lhs_atom98(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_597,plain,
lhs_atom88(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_438]) ).
cnf(c_0_598,plain,
lhs_atom86(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_599,plain,
lhs_atom85(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_440]) ).
cnf(c_0_600,plain,
lhs_atom78(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_601,plain,
lhs_atom76(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_602,plain,
lhs_atom75(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_603,plain,
lhs_atom74(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_604,plain,
lhs_atom43(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_605,plain,
lhs_atom27(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_606,plain,
lhs_atom26(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_607,plain,
lhs_atom23(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_608,plain,
lhs_atom18(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_609,plain,
lhs_atom14(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_450]) ).
cnf(c_0_610,plain,
lhs_atom13(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_451]) ).
cnf(c_0_611,plain,
lhs_atom42(X1),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_612,plain,
lhs_atom29(X1),
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_613,plain,
lhs_atom6(X1),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_614,plain,
lhs_atom157,
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_615,plain,
lhs_atom156,
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_616,plain,
lhs_atom155,
inference(split_conjunct,[status(thm)],[c_0_457]) ).
cnf(c_0_617,plain,
lhs_atom154,
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_618,plain,
lhs_atom153,
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_619,plain,
lhs_atom152,
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_620,plain,
lhs_atom151,
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_621,plain,
lhs_atom150,
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_622,plain,
lhs_atom149,
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_623,plain,
lhs_atom148,
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_624,plain,
lhs_atom147,
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_625,plain,
lhs_atom146,
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_626,plain,
lhs_atom145,
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_627,plain,
lhs_atom144,
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_628,plain,
lhs_atom143,
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_629,plain,
lhs_atom142,
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_630,plain,
lhs_atom141,
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_631,plain,
lhs_atom140,
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_632,plain,
lhs_atom139,
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_633,plain,
lhs_atom138,
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_634,plain,
lhs_atom137,
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_635,plain,
lhs_atom136,
inference(split_conjunct,[status(thm)],[c_0_476]) ).
cnf(c_0_636,plain,
lhs_atom70(X1,X2,X3,X4,X5,X6),
c_0_477,
[final] ).
cnf(c_0_637,plain,
lhs_atom37(X1,X2,X3,X4,X5,X6),
c_0_478,
[final] ).
cnf(c_0_638,plain,
lhs_atom36(X1,X2,X3,X4,X5,X6),
c_0_479,
[final] ).
cnf(c_0_639,plain,
lhs_atom25(X1,X2,X3,X4,X5,X6),
c_0_480,
[final] ).
cnf(c_0_640,plain,
lhs_atom12(X1,X2,X3,X4,X5,X6),
c_0_481,
[final] ).
cnf(c_0_641,plain,
lhs_atom1(X1,X2,X3,X4,X5,X6),
c_0_482,
[final] ).
cnf(c_0_642,plain,
lhs_atom119(X1,X2,X3,X4,X5),
c_0_483,
[final] ).
cnf(c_0_643,plain,
lhs_atom99(X1,X2,X3,X4,X5),
c_0_484,
[final] ).
cnf(c_0_644,plain,
lhs_atom77(X1,X2,X3,X4,X5),
c_0_485,
[final] ).
cnf(c_0_645,plain,
lhs_atom64(X1,X2,X3,X4,X5),
c_0_486,
[final] ).
cnf(c_0_646,plain,
lhs_atom62(X1,X2,X3,X4,X5),
c_0_487,
[final] ).
cnf(c_0_647,plain,
lhs_atom38(X1,X2,X3,X4,X5),
c_0_488,
[final] ).
cnf(c_0_648,plain,
lhs_atom35(X1,X2,X3,X4,X5),
c_0_489,
[final] ).
cnf(c_0_649,plain,
lhs_atom34(X1,X2,X3,X4,X5),
c_0_490,
[final] ).
cnf(c_0_650,plain,
lhs_atom30(X1,X2,X3,X4,X5),
c_0_491,
[final] ).
cnf(c_0_651,plain,
lhs_atom28(X1,X2,X3,X4,X5),
c_0_492,
[final] ).
cnf(c_0_652,plain,
lhs_atom24(X1,X2,X3,X4,X5),
c_0_493,
[final] ).
cnf(c_0_653,plain,
lhs_atom15(X1,X2,X3,X4,X5),
c_0_494,
[final] ).
cnf(c_0_654,plain,
lhs_atom10(X1,X2,X3,X4,X5),
c_0_495,
[final] ).
cnf(c_0_655,plain,
lhs_atom8(X1,X2,X3,X4,X5),
c_0_496,
[final] ).
cnf(c_0_656,plain,
lhs_atom126(X1,X2,X3,X4),
c_0_497,
[final] ).
cnf(c_0_657,plain,
lhs_atom120(X1,X2,X3,X4),
c_0_498,
[final] ).
cnf(c_0_658,plain,
lhs_atom114(X1,X2,X3,X4),
c_0_499,
[final] ).
cnf(c_0_659,plain,
lhs_atom112(X1,X2,X3,X4),
c_0_500,
[final] ).
cnf(c_0_660,plain,
lhs_atom111(X1,X2,X3,X4),
c_0_501,
[final] ).
cnf(c_0_661,plain,
lhs_atom108(X1,X2,X3,X4),
c_0_502,
[final] ).
cnf(c_0_662,plain,
lhs_atom107(X1,X2,X3,X4),
c_0_503,
[final] ).
cnf(c_0_663,plain,
lhs_atom97(X1,X2,X3,X4),
c_0_504,
[final] ).
cnf(c_0_664,plain,
lhs_atom93(X1,X2,X3,X4),
c_0_505,
[final] ).
cnf(c_0_665,plain,
lhs_atom87(X1,X2,X3,X4),
c_0_506,
[final] ).
cnf(c_0_666,plain,
lhs_atom83(X1,X2,X3,X4),
c_0_507,
[final] ).
cnf(c_0_667,plain,
lhs_atom82(X1,X2,X3,X4),
c_0_508,
[final] ).
cnf(c_0_668,plain,
lhs_atom80(X1,X2,X3,X4),
c_0_509,
[final] ).
cnf(c_0_669,plain,
lhs_atom79(X1,X2,X3,X4),
c_0_510,
[final] ).
cnf(c_0_670,plain,
lhs_atom72(X1,X2,X3,X4),
c_0_511,
[final] ).
cnf(c_0_671,plain,
lhs_atom71(X1,X2,X3,X4),
c_0_512,
[final] ).
cnf(c_0_672,plain,
lhs_atom69(X1,X2,X3,X4),
c_0_513,
[final] ).
cnf(c_0_673,plain,
lhs_atom59(X1,X2,X3,X4),
c_0_514,
[final] ).
cnf(c_0_674,plain,
lhs_atom56(X1,X2,X3,X4),
c_0_515,
[final] ).
cnf(c_0_675,plain,
lhs_atom55(X1,X2,X3,X4),
c_0_516,
[final] ).
cnf(c_0_676,plain,
lhs_atom54(X1,X2,X3,X4),
c_0_517,
[final] ).
cnf(c_0_677,plain,
lhs_atom50(X1,X2,X3,X4),
c_0_518,
[final] ).
cnf(c_0_678,plain,
lhs_atom49(X1,X2,X3,X4),
c_0_519,
[final] ).
cnf(c_0_679,plain,
lhs_atom47(X1,X2,X3,X4),
c_0_520,
[final] ).
cnf(c_0_680,plain,
lhs_atom44(X1,X2,X3,X4),
c_0_521,
[final] ).
cnf(c_0_681,plain,
lhs_atom41(X1,X2,X3,X4),
c_0_522,
[final] ).
cnf(c_0_682,plain,
lhs_atom40(X1,X2,X3,X4),
c_0_523,
[final] ).
cnf(c_0_683,plain,
lhs_atom33(X1,X2,X3,X4),
c_0_524,
[final] ).
cnf(c_0_684,plain,
lhs_atom32(X1,X2,X3,X4),
c_0_525,
[final] ).
cnf(c_0_685,plain,
lhs_atom22(X1,X2,X3,X4),
c_0_526,
[final] ).
cnf(c_0_686,plain,
lhs_atom21(X1,X2,X3,X4),
c_0_527,
[final] ).
cnf(c_0_687,plain,
lhs_atom20(X1,X2,X3,X4),
c_0_528,
[final] ).
cnf(c_0_688,plain,
lhs_atom19(X1,X2,X3,X4),
c_0_529,
[final] ).
cnf(c_0_689,plain,
lhs_atom11(X1,X2,X3,X4),
c_0_530,
[final] ).
cnf(c_0_690,plain,
lhs_atom9(X1,X2,X3,X4),
c_0_531,
[final] ).
cnf(c_0_691,plain,
lhs_atom7(X1,X2,X3,X4),
c_0_532,
[final] ).
cnf(c_0_692,plain,
lhs_atom3(X1,X2,X3,X4),
c_0_533,
[final] ).
cnf(c_0_693,plain,
lhs_atom2(X1,X2,X3,X4),
c_0_534,
[final] ).
cnf(c_0_694,plain,
lhs_atom134(X1,X2,X3),
c_0_535,
[final] ).
cnf(c_0_695,plain,
lhs_atom133(X1,X2,X3),
c_0_536,
[final] ).
cnf(c_0_696,plain,
lhs_atom132(X1,X2,X3),
c_0_537,
[final] ).
cnf(c_0_697,plain,
lhs_atom130(X1,X2,X3),
c_0_538,
[final] ).
cnf(c_0_698,plain,
lhs_atom123(X1,X2,X3),
c_0_539,
[final] ).
cnf(c_0_699,plain,
lhs_atom122(X1,X2,X3),
c_0_540,
[final] ).
cnf(c_0_700,plain,
lhs_atom121(X1,X2,X3),
c_0_541,
[final] ).
cnf(c_0_701,plain,
lhs_atom117(X1,X2,X3),
c_0_542,
[final] ).
cnf(c_0_702,plain,
lhs_atom116(X1,X2,X3),
c_0_543,
[final] ).
cnf(c_0_703,plain,
lhs_atom106(X1,X2,X3),
c_0_544,
[final] ).
cnf(c_0_704,plain,
lhs_atom96(X1,X2,X3),
c_0_545,
[final] ).
cnf(c_0_705,plain,
lhs_atom95(X1,X2,X3),
c_0_546,
[final] ).
cnf(c_0_706,plain,
lhs_atom66(X1,X2,X3),
c_0_547,
[final] ).
cnf(c_0_707,plain,
lhs_atom94(X1,X2,X3),
c_0_548,
[final] ).
cnf(c_0_708,plain,
lhs_atom92(X1,X2,X3),
c_0_549,
[final] ).
cnf(c_0_709,plain,
lhs_atom91(X1,X2,X3),
c_0_550,
[final] ).
cnf(c_0_710,plain,
lhs_atom90(X1,X2,X3),
c_0_551,
[final] ).
cnf(c_0_711,plain,
lhs_atom89(X1,X2,X3),
c_0_552,
[final] ).
cnf(c_0_712,plain,
lhs_atom84(X1,X2,X3),
c_0_553,
[final] ).
cnf(c_0_713,plain,
lhs_atom81(X1,X2,X3),
c_0_554,
[final] ).
cnf(c_0_714,plain,
lhs_atom73(X1,X2,X3),
c_0_555,
[final] ).
cnf(c_0_715,plain,
lhs_atom68(X1,X2,X3),
c_0_556,
[final] ).
cnf(c_0_716,plain,
lhs_atom67(X1,X2,X3),
c_0_557,
[final] ).
cnf(c_0_717,plain,
lhs_atom66(X1,X2,X3),
c_0_558,
[final] ).
cnf(c_0_718,plain,
lhs_atom65(X1,X2,X3),
c_0_559,
[final] ).
cnf(c_0_719,plain,
lhs_atom63(X1,X2,X3),
c_0_560,
[final] ).
cnf(c_0_720,plain,
lhs_atom61(X1,X2,X3),
c_0_561,
[final] ).
cnf(c_0_721,plain,
lhs_atom60(X1,X2,X3),
c_0_562,
[final] ).
cnf(c_0_722,plain,
lhs_atom58(X1,X2,X3),
c_0_563,
[final] ).
cnf(c_0_723,plain,
lhs_atom57(X1,X2,X3),
c_0_564,
[final] ).
cnf(c_0_724,plain,
lhs_atom53(X1,X2,X3),
c_0_565,
[final] ).
cnf(c_0_725,plain,
lhs_atom52(X1,X2,X3),
c_0_566,
[final] ).
cnf(c_0_726,plain,
lhs_atom51(X1,X2,X3),
c_0_567,
[final] ).
cnf(c_0_727,plain,
lhs_atom48(X1,X2,X3),
c_0_568,
[final] ).
cnf(c_0_728,plain,
lhs_atom46(X1,X2,X3),
c_0_569,
[final] ).
cnf(c_0_729,plain,
lhs_atom45(X1,X2,X3),
c_0_570,
[final] ).
cnf(c_0_730,plain,
lhs_atom39(X1,X2,X3),
c_0_571,
[final] ).
cnf(c_0_731,plain,
lhs_atom31(X1,X2,X3),
c_0_572,
[final] ).
cnf(c_0_732,plain,
lhs_atom17(X1,X2,X3),
c_0_573,
[final] ).
cnf(c_0_733,plain,
lhs_atom16(X1,X2,X3),
c_0_574,
[final] ).
cnf(c_0_734,plain,
lhs_atom5(X1,X2,X3),
c_0_575,
[final] ).
cnf(c_0_735,plain,
lhs_atom4(X1,X2,X3),
c_0_576,
[final] ).
cnf(c_0_736,plain,
lhs_atom158(X1,X2),
c_0_577,
[final] ).
cnf(c_0_737,plain,
lhs_atom135(X1,X2),
c_0_578,
[final] ).
cnf(c_0_738,plain,
lhs_atom131(X1,X2),
c_0_579,
[final] ).
cnf(c_0_739,plain,
lhs_atom129(X1,X2),
c_0_580,
[final] ).
cnf(c_0_740,plain,
lhs_atom128(X1,X2),
c_0_581,
[final] ).
cnf(c_0_741,plain,
lhs_atom127(X1,X2),
c_0_582,
[final] ).
cnf(c_0_742,plain,
lhs_atom125(X1,X2),
c_0_583,
[final] ).
cnf(c_0_743,plain,
lhs_atom124(X1,X2),
c_0_584,
[final] ).
cnf(c_0_744,plain,
lhs_atom118(X1,X2),
c_0_585,
[final] ).
cnf(c_0_745,plain,
lhs_atom115(X1,X2),
c_0_586,
[final] ).
cnf(c_0_746,plain,
lhs_atom113(X1,X2),
c_0_587,
[final] ).
cnf(c_0_747,plain,
lhs_atom110(X1,X2),
c_0_588,
[final] ).
cnf(c_0_748,plain,
lhs_atom109(X1,X2),
c_0_589,
[final] ).
cnf(c_0_749,plain,
lhs_atom105(X1,X2),
c_0_590,
[final] ).
cnf(c_0_750,plain,
lhs_atom104(X1,X2),
c_0_591,
[final] ).
cnf(c_0_751,plain,
lhs_atom103(X1,X2),
c_0_592,
[final] ).
cnf(c_0_752,plain,
lhs_atom102(X1,X2),
c_0_593,
[final] ).
cnf(c_0_753,plain,
lhs_atom101(X1,X2),
c_0_594,
[final] ).
cnf(c_0_754,plain,
lhs_atom100(X1,X2),
c_0_595,
[final] ).
cnf(c_0_755,plain,
lhs_atom98(X1,X2),
c_0_596,
[final] ).
cnf(c_0_756,plain,
lhs_atom88(X1,X2),
c_0_597,
[final] ).
cnf(c_0_757,plain,
lhs_atom86(X1,X2),
c_0_598,
[final] ).
cnf(c_0_758,plain,
lhs_atom85(X1,X2),
c_0_599,
[final] ).
cnf(c_0_759,plain,
lhs_atom78(X1,X2),
c_0_600,
[final] ).
cnf(c_0_760,plain,
lhs_atom76(X1,X2),
c_0_601,
[final] ).
cnf(c_0_761,plain,
lhs_atom75(X1,X2),
c_0_602,
[final] ).
cnf(c_0_762,plain,
lhs_atom74(X1,X2),
c_0_603,
[final] ).
cnf(c_0_763,plain,
lhs_atom43(X1,X2),
c_0_604,
[final] ).
cnf(c_0_764,plain,
lhs_atom27(X1,X2),
c_0_605,
[final] ).
cnf(c_0_765,plain,
lhs_atom26(X1,X2),
c_0_606,
[final] ).
cnf(c_0_766,plain,
lhs_atom23(X1,X2),
c_0_607,
[final] ).
cnf(c_0_767,plain,
lhs_atom18(X1,X2),
c_0_608,
[final] ).
cnf(c_0_768,plain,
lhs_atom14(X1,X2),
c_0_609,
[final] ).
cnf(c_0_769,plain,
lhs_atom13(X1,X2),
c_0_610,
[final] ).
cnf(c_0_770,plain,
lhs_atom42(X1),
c_0_611,
[final] ).
cnf(c_0_771,plain,
lhs_atom29(X1),
c_0_612,
[final] ).
cnf(c_0_772,plain,
lhs_atom6(X1),
c_0_613,
[final] ).
cnf(c_0_773,plain,
lhs_atom157,
c_0_614,
[final] ).
cnf(c_0_774,plain,
lhs_atom156,
c_0_615,
[final] ).
cnf(c_0_775,plain,
lhs_atom155,
c_0_616,
[final] ).
cnf(c_0_776,plain,
lhs_atom154,
c_0_617,
[final] ).
cnf(c_0_777,plain,
lhs_atom153,
c_0_618,
[final] ).
cnf(c_0_778,plain,
lhs_atom152,
c_0_619,
[final] ).
cnf(c_0_779,plain,
lhs_atom151,
c_0_620,
[final] ).
cnf(c_0_780,plain,
lhs_atom150,
c_0_621,
[final] ).
cnf(c_0_781,plain,
lhs_atom149,
c_0_622,
[final] ).
cnf(c_0_782,plain,
lhs_atom148,
c_0_623,
[final] ).
cnf(c_0_783,plain,
lhs_atom147,
c_0_624,
[final] ).
cnf(c_0_784,plain,
lhs_atom146,
c_0_625,
[final] ).
cnf(c_0_785,plain,
lhs_atom145,
c_0_626,
[final] ).
cnf(c_0_786,plain,
lhs_atom144,
c_0_627,
[final] ).
cnf(c_0_787,plain,
lhs_atom143,
c_0_628,
[final] ).
cnf(c_0_788,plain,
lhs_atom142,
c_0_629,
[final] ).
cnf(c_0_789,plain,
lhs_atom141,
c_0_630,
[final] ).
cnf(c_0_790,plain,
lhs_atom140,
c_0_631,
[final] ).
cnf(c_0_791,plain,
lhs_atom139,
c_0_632,
[final] ).
cnf(c_0_792,plain,
lhs_atom138,
c_0_633,
[final] ).
cnf(c_0_793,plain,
lhs_atom137,
c_0_634,
[final] ).
cnf(c_0_794,plain,
lhs_atom136,
c_0_635,
[final] ).
% End CNF derivation
cnf(c_0_636_0,axiom,
hAPP(hAPP(c_COMBC(X3,X5,X4,X6),X2),X1) = hAPP(hAPP(X3,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_636,def_lhs_atom70]) ).
cnf(c_0_637_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(X1,X3,X4,X5),X2,X5,tc_fun(X6,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(X2,X1,X5,tc_fun(X6,tc_bool),X4),X4,tc_fun(X6,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_637,def_lhs_atom37]) ).
cnf(c_0_638_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(X2,X1,X4,tc_fun(X6,tc_bool),X5),X5,tc_fun(X6,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(X1,X3,X5,X4),X2,X4,tc_fun(X6,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_638,def_lhs_atom36]) ).
cnf(c_0_639_0,axiom,
hAPP(c_COMBB(X3,X2,X5,X6,X4),X1) = hAPP(X3,hAPP(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_639,def_lhs_atom25]) ).
cnf(c_0_640_0,axiom,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X3,X2,X6,X5),X3,X1,X6,X5) = c_Fun_Ofun__upd(X4,X3,X1,X6,X5),
inference(unfold_definition,[status(thm)],[c_0_640,def_lhs_atom12]) ).
cnf(c_0_641_0,axiom,
c_Set_Oimage(X2,c_Set_Oimage(X1,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X2,X1,X5,X6,X4),X3,X4,X6),
inference(unfold_definition,[status(thm)],[c_0_641,def_lhs_atom1]) ).
cnf(c_0_642_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_642,def_lhs_atom119]) ).
cnf(c_0_643_0,axiom,
c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(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_643,def_lhs_atom99]) ).
cnf(c_0_644_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_644,def_lhs_atom77]) ).
cnf(c_0_645_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_645,def_lhs_atom64]) ).
cnf(c_0_646_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_646,def_lhs_atom62]) ).
cnf(c_0_647_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_647,def_lhs_atom38]) ).
cnf(c_0_648_0,axiom,
c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X3,X4,X5),c_Set_Oimage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_648,def_lhs_atom35]) ).
cnf(c_0_649_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_649,def_lhs_atom34]) ).
cnf(c_0_650_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_650,def_lhs_atom30]) ).
cnf(c_0_651_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_651,def_lhs_atom28]) ).
cnf(c_0_652_0,axiom,
c_Relation_OImage(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X3,X4,X5),c_Relation_OImage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_652,def_lhs_atom24]) ).
cnf(c_0_653_0,axiom,
c_lessequals(c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X3,X4,X5),c_Relation_OImage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_653,def_lhs_atom15]) ).
cnf(c_0_654_0,axiom,
hAPP(c_Fun_Ofun__upd(X3,X2,X1,X4,X5),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_654,def_lhs_atom10]) ).
cnf(c_0_655_0,axiom,
hAPP(c_Fun_Ofun__upd(X3,X2,X1,X5,X4),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_655,def_lhs_atom8]) ).
cnf(c_0_656_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_656,def_lhs_atom126]) ).
cnf(c_0_657_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_657,def_lhs_atom120]) ).
cnf(c_0_658_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_658,def_lhs_atom114]) ).
cnf(c_0_659_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_659,def_lhs_atom112]) ).
cnf(c_0_660_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_660,def_lhs_atom111]) ).
cnf(c_0_661_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_661,def_lhs_atom108]) ).
cnf(c_0_662_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_662,def_lhs_atom107]) ).
cnf(c_0_663_0,axiom,
c_Fun_Ooverride__on(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_663,def_lhs_atom97]) ).
cnf(c_0_664_0,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),X4,X3) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X2,X4,X3)),
inference(unfold_definition,[status(thm)],[c_0_664,def_lhs_atom93]) ).
cnf(c_0_665_0,axiom,
c_Set_Ovimage(X1,X2,X4,X3) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X3),X1,X3,tc_fun(tc_fun(X3,tc_bool),tc_bool),X4),X4,tc_fun(X3,tc_bool),tc_bool),X2),X4),
inference(unfold_definition,[status(thm)],[c_0_665,def_lhs_atom87]) ).
cnf(c_0_666_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X3,X4),c_Set_Oinsert(X1,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_666,def_lhs_atom83]) ).
cnf(c_0_667_0,axiom,
hBOOL(hAPP(hAPP(c_in(X3),X2),c_Set_Ovimage(X1,c_Set_Oinsert(hAPP(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X3,X4))),
inference(unfold_definition,[status(thm)],[c_0_667,def_lhs_atom82]) ).
cnf(c_0_668_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_668,def_lhs_atom80]) ).
cnf(c_0_669_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_669,def_lhs_atom79]) ).
cnf(c_0_670_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_670,def_lhs_atom72]) ).
cnf(c_0_671_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_671,def_lhs_atom71]) ).
cnf(c_0_672_0,axiom,
hAPP(c_COMBK(X2,X4,X3),X1) = X2,
inference(unfold_definition,[status(thm)],[c_0_672,def_lhs_atom69]) ).
cnf(c_0_673_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_673,def_lhs_atom59]) ).
cnf(c_0_674_0,axiom,
c_Nitpick_Ofold__graph_H(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X1,X4,X3),
inference(unfold_definition,[status(thm)],[c_0_674,def_lhs_atom56]) ).
cnf(c_0_675_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_675,def_lhs_atom55]) ).
cnf(c_0_676_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_676,def_lhs_atom54]) ).
cnf(c_0_677_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_677,def_lhs_atom50]) ).
cnf(c_0_678_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_678,def_lhs_atom49]) ).
cnf(c_0_679_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_679,def_lhs_atom47]) ).
cnf(c_0_680_0,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(c_COMBB(X2,X1,X3,tc_bool,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_680,def_lhs_atom44]) ).
cnf(c_0_681_0,axiom,
c_HOL_Ominus__class_Ominus(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),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_681,def_lhs_atom41]) ).
cnf(c_0_682_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)) = c_Lattices_Olower__semilattice__class_Oinf(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_682,def_lhs_atom40]) ).
cnf(c_0_683_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_683,def_lhs_atom33]) ).
cnf(c_0_684_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_684,def_lhs_atom32]) ).
cnf(c_0_685_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(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(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_685,def_lhs_atom22]) ).
cnf(c_0_686_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_686,def_lhs_atom21]) ).
cnf(c_0_687_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_687,def_lhs_atom20]) ).
cnf(c_0_688_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_688,def_lhs_atom19]) ).
cnf(c_0_689_0,axiom,
c_Fun_Ofun__upd(X2,X1,hAPP(X2,X1),X3,X4) = X2,
inference(unfold_definition,[status(thm)],[c_0_689,def_lhs_atom11]) ).
cnf(c_0_690_0,axiom,
c_Fun_Ofun__upd(X2,X1,hAPP(X2,X1),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_690,def_lhs_atom9]) ).
cnf(c_0_691_0,axiom,
c_Fun_Ofun__upd(X2,X1,hAPP(X2,X1),X3,X4) = X2,
inference(unfold_definition,[status(thm)],[c_0_691,def_lhs_atom7]) ).
cnf(c_0_692_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_692,def_lhs_atom3]) ).
cnf(c_0_693_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_693,def_lhs_atom2]) ).
cnf(c_0_694_0,axiom,
hBOOL(hAPP(hAPP(c_in(X3),X1),c_Set_Oinsert(X1,X2,X3))),
inference(unfold_definition,[status(thm)],[c_0_694,def_lhs_atom134]) ).
cnf(c_0_695_0,axiom,
hBOOL(hAPP(hAPP(c_in(X3),X1),c_Set_Oinsert(X1,X2,X3))),
inference(unfold_definition,[status(thm)],[c_0_695,def_lhs_atom133]) ).
cnf(c_0_696_0,axiom,
hBOOL(hAPP(hAPP(c_in(X3),X1),c_Set_Oinsert(X1,X2,X3))),
inference(unfold_definition,[status(thm)],[c_0_696,def_lhs_atom132]) ).
cnf(c_0_697_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_697,def_lhs_atom130]) ).
cnf(c_0_698_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_698,def_lhs_atom123]) ).
cnf(c_0_699_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_699,def_lhs_atom122]) ).
cnf(c_0_700_0,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_700,def_lhs_atom121]) ).
cnf(c_0_701_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X2))),
inference(unfold_definition,[status(thm)],[c_0_701,def_lhs_atom117]) ).
cnf(c_0_702_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_702,def_lhs_atom116]) ).
cnf(c_0_703_0,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(X1,X3,X2),X2,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_703,def_lhs_atom106]) ).
cnf(c_0_704_0,axiom,
c_HOL_Ominus__class_Ominus(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_704,def_lhs_atom96]) ).
cnf(c_0_705_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_705,def_lhs_atom95]) ).
cnf(c_0_706_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_706,def_lhs_atom66]) ).
cnf(c_0_707_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_COMBK(X1,tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_707,def_lhs_atom94]) ).
cnf(c_0_708_0,axiom,
c_Set_Oimage(c_COMBK(X1,X3,X2),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_708,def_lhs_atom92]) ).
cnf(c_0_709_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_709,def_lhs_atom91]) ).
cnf(c_0_710_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_710,def_lhs_atom90]) ).
cnf(c_0_711_0,axiom,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2),
inference(unfold_definition,[status(thm)],[c_0_711,def_lhs_atom89]) ).
cnf(c_0_712_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_712,def_lhs_atom84]) ).
cnf(c_0_713_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_713,def_lhs_atom81]) ).
cnf(c_0_714_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))),
inference(unfold_definition,[status(thm)],[c_0_714,def_lhs_atom73]) ).
cnf(c_0_715_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_715,def_lhs_atom68]) ).
cnf(c_0_716_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_716,def_lhs_atom67]) ).
cnf(c_0_717_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_717,def_lhs_atom66]) ).
cnf(c_0_718_0,axiom,
c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_718,def_lhs_atom65]) ).
cnf(c_0_719_0,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_719,def_lhs_atom63]) ).
cnf(c_0_720_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_720,def_lhs_atom61]) ).
cnf(c_0_721_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_721,def_lhs_atom60]) ).
cnf(c_0_722_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_722,def_lhs_atom58]) ).
cnf(c_0_723_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_723,def_lhs_atom57]) ).
cnf(c_0_724_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_724,def_lhs_atom53]) ).
cnf(c_0_725_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_725,def_lhs_atom52]) ).
cnf(c_0_726_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_726,def_lhs_atom51]) ).
cnf(c_0_727_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_727,def_lhs_atom48]) ).
cnf(c_0_728_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_728,def_lhs_atom46]) ).
cnf(c_0_729_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_729,def_lhs_atom45]) ).
cnf(c_0_730_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2,
inference(unfold_definition,[status(thm)],[c_0_730,def_lhs_atom39]) ).
cnf(c_0_731_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_731,def_lhs_atom31]) ).
cnf(c_0_732_0,axiom,
c_Relation_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_732,def_lhs_atom17]) ).
cnf(c_0_733_0,axiom,
c_lessequals(X2,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_733,def_lhs_atom16]) ).
cnf(c_0_734_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_734,def_lhs_atom5]) ).
cnf(c_0_735_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_735,def_lhs_atom4]) ).
cnf(c_0_736_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_736,def_lhs_atom158]) ).
cnf(c_0_737_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),X1),c_Set_OPow(X1,X2))),
inference(unfold_definition,[status(thm)],[c_0_737,def_lhs_atom135]) ).
cnf(c_0_738_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X1),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_738,def_lhs_atom131]) ).
cnf(c_0_739_0,axiom,
c_Collect(hAPP(c_fequal(X2),X1),X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_739,def_lhs_atom129]) ).
cnf(c_0_740_0,axiom,
c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X1,X2),tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_740,def_lhs_atom128]) ).
cnf(c_0_741_0,axiom,
hBOOL(hAPP(hAPP(c_in(X2),X1),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))),
inference(unfold_definition,[status(thm)],[c_0_741,def_lhs_atom127]) ).
cnf(c_0_742_0,axiom,
c_Collect(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_742,def_lhs_atom125]) ).
cnf(c_0_743_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_743,def_lhs_atom124]) ).
cnf(c_0_744_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X2,X1))),
inference(unfold_definition,[status(thm)],[c_0_744,def_lhs_atom118]) ).
cnf(c_0_745_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_745,def_lhs_atom115]) ).
cnf(c_0_746_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_Set_OPow(X1,X2))),
inference(unfold_definition,[status(thm)],[c_0_746,def_lhs_atom113]) ).
cnf(c_0_747_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1)),
inference(unfold_definition,[status(thm)],[c_0_747,def_lhs_atom110]) ).
cnf(c_0_748_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_748,def_lhs_atom109]) ).
cnf(c_0_749_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_749,def_lhs_atom105]) ).
cnf(c_0_750_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_750,def_lhs_atom104]) ).
cnf(c_0_751_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_751,def_lhs_atom103]) ).
cnf(c_0_752_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
inference(unfold_definition,[status(thm)],[c_0_752,def_lhs_atom102]) ).
cnf(c_0_753_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
inference(unfold_definition,[status(thm)],[c_0_753,def_lhs_atom101]) ).
cnf(c_0_754_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
inference(unfold_definition,[status(thm)],[c_0_754,def_lhs_atom100]) ).
cnf(c_0_755_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1)) = X1,
inference(unfold_definition,[status(thm)],[c_0_755,def_lhs_atom98]) ).
cnf(c_0_756_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1) = c_Collect(c_COMBB(c_Not,hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X1),tc_bool,tc_bool,X2),X2),
inference(unfold_definition,[status(thm)],[c_0_756,def_lhs_atom88]) ).
cnf(c_0_757_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_757,def_lhs_atom86]) ).
cnf(c_0_758_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(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_758,def_lhs_atom85]) ).
cnf(c_0_759_0,axiom,
c_Collect(X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_759,def_lhs_atom78]) ).
cnf(c_0_760_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_760,def_lhs_atom76]) ).
cnf(c_0_761_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(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_761,def_lhs_atom75]) ).
cnf(c_0_762_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X2,X1))),
inference(unfold_definition,[status(thm)],[c_0_762,def_lhs_atom74]) ).
cnf(c_0_763_0,axiom,
c_Collect(c_COMBB(c_Not,X1,tc_bool,tc_bool,X2),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Collect(X1,X2)),
inference(unfold_definition,[status(thm)],[c_0_763,def_lhs_atom43]) ).
cnf(c_0_764_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_764,def_lhs_atom27]) ).
cnf(c_0_765_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_765,def_lhs_atom26]) ).
cnf(c_0_766_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_766,def_lhs_atom23]) ).
cnf(c_0_767_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_767,def_lhs_atom18]) ).
cnf(c_0_768_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_768,def_lhs_atom14]) ).
cnf(c_0_769_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_769,def_lhs_atom13]) ).
cnf(c_0_770_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(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_770,def_lhs_atom42]) ).
cnf(c_0_771_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_771,def_lhs_atom29]) ).
cnf(c_0_772_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_772,def_lhs_atom6]) ).
cnf(c_0_773_0,axiom,
class_HOL_Oord(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_773,def_lhs_atom157]) ).
cnf(c_0_774_0,axiom,
class_Orderings_Obot(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_774,def_lhs_atom156]) ).
cnf(c_0_775_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_775,def_lhs_atom155]) ).
cnf(c_0_776_0,axiom,
class_Lattices_Olattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_776,def_lhs_atom154]) ).
cnf(c_0_777_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_777,def_lhs_atom153]) ).
cnf(c_0_778_0,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_778,def_lhs_atom152]) ).
cnf(c_0_779_0,axiom,
class_Lattices_Obounded__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_779,def_lhs_atom151]) ).
cnf(c_0_780_0,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_780,def_lhs_atom150]) ).
cnf(c_0_781_0,axiom,
class_Lattices_Olower__semilattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_781,def_lhs_atom149]) ).
cnf(c_0_782_0,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_782,def_lhs_atom148]) ).
cnf(c_0_783_0,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_783,def_lhs_atom147]) ).
cnf(c_0_784_0,axiom,
class_HOL_Oord(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_784,def_lhs_atom146]) ).
cnf(c_0_785_0,axiom,
class_Orderings_Obot(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_785,def_lhs_atom145]) ).
cnf(c_0_786_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_786,def_lhs_atom144]) ).
cnf(c_0_787_0,axiom,
class_Lattices_Olattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_787,def_lhs_atom143]) ).
cnf(c_0_788_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_788,def_lhs_atom142]) ).
cnf(c_0_789_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_789,def_lhs_atom141]) ).
cnf(c_0_790_0,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_790,def_lhs_atom140]) ).
cnf(c_0_791_0,axiom,
class_Lattices_Olower__semilattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_791,def_lhs_atom139]) ).
cnf(c_0_792_0,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_792,def_lhs_atom138]) ).
cnf(c_0_793_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__CHAINED__1),c_Arrow__Order__Mirabelle_OLin)),
inference(unfold_definition,[status(thm)],[c_0_793,def_lhs_atom137]) ).
cnf(c_0_794_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
inference(unfold_definition,[status(thm)],[c_0_794,def_lhs_atom136]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X31,X32,X23,X24,X33,X34,X35,X36,X3] :
( c_Complete__Lattice_Ocomplete__lattice(X35,X36,c_COMBC(X23,X3,X3,tc_bool),c_COMBC(X24,X3,X3,tc_bool),X32,X33,X31,X34,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_Odual__complete__lattice_0) ).
fof(c_0_1_002,axiom,
! [X31,X32,X23,X24,X33,X34,X16,X17,X35,X36,X3] :
( hAPP(X35,c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X32,X17),X16)
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OSup__binary_0) ).
fof(c_0_2_003,axiom,
! [X31,X32,X23,X24,X33,X34,X16,X17,X35,X36,X3] :
( hAPP(X36,c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X33,X17),X16)
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OInf__binary_0) ).
fof(c_0_3_004,axiom,
! [X6,X31,X32,X23,X24,X33,X34,X35,X36,X12,X3] :
( hBOOL(hAPP(hAPP(X23,hAPP(X36,X12)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OInf__lower_0) ).
fof(c_0_4_005,axiom,
! [X6,X31,X32,X23,X24,X33,X34,X35,X36,X12,X3] :
( hBOOL(hAPP(hAPP(X23,X6),hAPP(X35,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OSup__upper_0) ).
fof(c_0_5_006,axiom,
! [X31,X32,X23,X24,X33,X34,X17,X35,X36,X3] :
( hAPP(X35,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X17
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OSup__singleton_0) ).
fof(c_0_6_007,axiom,
! [X31,X32,X23,X24,X33,X34,X17,X35,X36,X3] :
( hAPP(X36,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X17
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OInf__singleton_0) ).
fof(c_0_7_008,axiom,
! [X31,X32,X23,X24,X33,X34,X17,X35,X36,X12,X3] :
( hAPP(X35,c_Set_Oinsert(X17,X12,X3)) = hAPP(hAPP(X32,X17),hAPP(X35,X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OSup__insert_0) ).
fof(c_0_8_009,axiom,
! [X31,X32,X23,X24,X33,X34,X17,X35,X36,X12,X3] :
( hAPP(X36,c_Set_Oinsert(X17,X12,X3)) = hAPP(hAPP(X33,X17),hAPP(X36,X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OInf__insert_0) ).
fof(c_0_9_010,axiom,
! [X31,X32,X23,X24,X33,X34,X35,X36,X3] :
( hAPP(X35,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X34
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OSup__empty_0) ).
fof(c_0_10_011,axiom,
! [X31,X32,X23,X24,X33,X34,X35,X36,X3] :
( hAPP(X36,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X31
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
file('<stdin>',cls_complete__lattice_OInf__empty_0) ).
fof(c_0_11_012,axiom,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X12,X14,X13,X3,X15))),hAPP(X14,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X12,X14,X13,X3,X15)))) ),
file('<stdin>',cls_Pi__I_1) ).
fof(c_0_12_013,axiom,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X12,X14,X13,X3,X15))),hAPP(X14,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X12,X14,X13,X3,X15)))) ),
file('<stdin>',cls_Pi__I_H_1) ).
fof(c_0_13_014,axiom,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,c_COMBK(X14,tc_fun(X15,tc_bool),X3),X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X12,X14,X13,X3,X15))),X14)) ),
file('<stdin>',cls_funcsetI_1) ).
fof(c_0_14_015,axiom,
! [X45,X9,X6,X13,X12,X15,X3] :
( c_Nitpick_Ofold__graph_H(X13,X45,X12,hAPP(hAPP(X13,X6),X9),X3,X15)
| ~ c_Nitpick_Ofold__graph_H(X13,X45,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,X3,X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_fold__graph_H_Ointros_I2_J_0) ).
fof(c_0_15_016,axiom,
! [X45,X9,X6,X13,X12,X15,X3] :
( c_Finite__Set_Ofold__graph(X13,X45,X12,hAPP(hAPP(X13,X6),X9),X3,X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Finite__Set_Ofold__graph(X13,X45,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,X3,X15) ),
file('<stdin>',cls_Diff1__fold__graph_0) ).
fof(c_0_16_017,axiom,
! [X45,X9,X6,X13,X12,X15,X3] :
( c_Finite__Set_Ofold__graph(X13,X45,c_Set_Oinsert(X6,X12,X3),hAPP(hAPP(X13,X6),X9),X3,X15)
| ~ c_Finite__Set_Ofold__graph(X13,X45,X12,X9,X3,X15)
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_fold__graph_OinsertI_0) ).
fof(c_0_17_018,axiom,
! [X6,X18,X16,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_equiv__class__nondisjoint_0) ).
fof(c_0_18_019,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__above_14) ).
fof(c_0_19_020,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__below_14) ).
fof(c_0_20_021,axiom,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,c_COMBK(X14,tc_fun(X15,tc_bool),X3),X3,X15)))
| hBOOL(hAPP(hAPP(c_in(X3),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X12,X14,X13,X3,X15)),X12)) ),
file('<stdin>',cls_funcsetI_0) ).
fof(c_0_21_022,axiom,
! [X19,X13,X12,X15,X3] :
( X13 = X19
| hBOOL(hAPP(hAPP(c_in(X3),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X12,X13,X19,X3,X15)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X19),c_FuncSet_Oextensional(X12,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_Oextensional(X12,X3,X15))) ),
file('<stdin>',cls_extensionalityI_0) ).
fof(c_0_22_023,axiom,
! [X30,X6,X21,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X12,X14,X21,X15,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X15,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
file('<stdin>',cls_bex__UN_3) ).
fof(c_0_23_024,axiom,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15)))
| hBOOL(hAPP(hAPP(c_in(X3),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X12,X14,X13,X3,X15)),X12)) ),
file('<stdin>',cls_Pi__I_0) ).
fof(c_0_24_025,axiom,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15)))
| hBOOL(hAPP(hAPP(c_in(X3),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X12,X14,X13,X3,X15)),X12)) ),
file('<stdin>',cls_Pi__I_H_0) ).
fof(c_0_25_026,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__below_10) ).
fof(c_0_26_027,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X17
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__below_8) ).
fof(c_0_27_028,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X16
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__above_10) ).
fof(c_0_28_029,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X16
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__above_8) ).
fof(c_0_29_030,axiom,
! [X9,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16))) ),
file('<stdin>',cls_in__below_13) ).
fof(c_0_30_031,axiom,
! [X30,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
file('<stdin>',cls_in__below_12) ).
fof(c_0_31_032,axiom,
! [X30,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6))) ),
file('<stdin>',cls_in__above_13) ).
fof(c_0_32_033,axiom,
! [X9,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X6,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
file('<stdin>',cls_in__above_12) ).
fof(c_0_33_034,axiom,
! [X45,X6,X13,X15,X3] :
( X6 = X45
| ~ c_Finite__Set_Ofold__graph(X13,X45,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X6,X3,X15) ),
file('<stdin>',cls_empty__fold__graphE_0) ).
fof(c_0_34_035,axiom,
! [X19,X13,X12,X15,X3] :
( hAPP(X13,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X12,X13,X19,X3,X15)) != hAPP(X19,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X12,X13,X19,X3,X15))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X19),c_FuncSet_Oextensional(X12,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_Oextensional(X12,X3,X15)))
| X13 = X19 ),
file('<stdin>',cls_extensionalityI_1) ).
fof(c_0_35_036,axiom,
! [X9,X6,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X9,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
file('<stdin>',cls_notin__Lin__iff_1) ).
fof(c_0_36_037,axiom,
! [X16,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
file('<stdin>',cls_Lin__irrefl_0) ).
fof(c_0_37_038,axiom,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X25),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanAtMost(X23,X24,X25,X22,X3))) ),
file('<stdin>',cls_ord_OgreaterThanAtMost__iff_0) ).
fof(c_0_38_039,axiom,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X26),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanAtMost(X23,X24,X25,X22,X3))) ),
file('<stdin>',cls_ord_OgreaterThanAtMost__iff_1) ).
fof(c_0_39_040,axiom,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X26),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastLessThan(X23,X24,X25,X22,X3))) ),
file('<stdin>',cls_ord_OatLeastLessThan__iff_1) ).
fof(c_0_40_041,axiom,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X25),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastLessThan(X23,X24,X25,X22,X3))) ),
file('<stdin>',cls_ord_OatLeastLessThan__iff_0) ).
fof(c_0_41_042,axiom,
! [X56,X50,X27,X16,X17,X15,X3] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X56,X17,X16,X3,X15),X27,X50,X3,X15) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X56,X27,X50,X3,X15),X17,X16,X3,X15)
| X17 = X27 ),
file('<stdin>',cls_fun__upd__twist_0) ).
fof(c_0_42_043,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X16
| X6 = X16
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__above_3) ).
fof(c_0_43_044,axiom,
! [X30,X6,X17,X10] :
( X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X17 ),
file('<stdin>',cls_in__above_2) ).
fof(c_0_44_045,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X17
| X9 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__below_3) ).
fof(c_0_45_046,axiom,
! [X9,X6,X16,X10] :
( X9 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X16 ),
file('<stdin>',cls_in__below_2) ).
fof(c_0_46_047,axiom,
! [X9,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
file('<stdin>',cls_in__above_1) ).
fof(c_0_47_048,axiom,
! [X30,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
file('<stdin>',cls_in__below_1) ).
fof(c_0_48_049,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X16
| X6 = X16
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__above_4) ).
fof(c_0_49_050,axiom,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X17
| X9 = X17
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__below_4) ).
fof(c_0_50_051,axiom,
! [X30,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6))) ),
file('<stdin>',cls_in__above_7) ).
fof(c_0_51_052,axiom,
! [X9,X6,X16,X10] :
( X6 = X16
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X6,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
file('<stdin>',cls_in__above_6) ).
fof(c_0_52_053,axiom,
! [X9,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X6
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16))) ),
file('<stdin>',cls_in__below_7) ).
fof(c_0_53_054,axiom,
! [X30,X6,X17,X10] :
( X6 = X17
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
file('<stdin>',cls_in__below_6) ).
fof(c_0_54_055,axiom,
! [X30,X6,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X30 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X30,X6))) ),
file('<stdin>',cls_in__above_11) ).
fof(c_0_55_056,axiom,
! [X9,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6))) ),
file('<stdin>',cls_in__above_9) ).
fof(c_0_56_057,axiom,
! [X30,X6,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X30,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X30
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X30,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X30))) ),
file('<stdin>',cls_in__below_11) ).
fof(c_0_57_058,axiom,
! [X30,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16))) ),
file('<stdin>',cls_in__below_9) ).
fof(c_0_58_059,axiom,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X16,X17,X15,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X15)),c_Pair(X17,X16,X3,X15)),c_Relation_Oconverse(X18,X15,X3))) ),
file('<stdin>',cls_converseD_0) ).
fof(c_0_59_060,axiom,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X16,X17,X15,X3)),c_Relation_Oconverse(X18,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X15)),c_Pair(X17,X16,X3,X15)),X18)) ),
file('<stdin>',cls_converseI_0) ).
fof(c_0_60_061,axiom,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X15)),c_Pair(X17,X16,X3,X15)),c_Relation_Oconverse(X18,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X16,X17,X15,X3)),X18)) ),
file('<stdin>',cls_converse__iff_1) ).
fof(c_0_61_062,axiom,
! [X13,X17,X12,X15,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X15)))
| ~ c_Fun_Oinj__on(X13,c_Set_Oinsert(X17,X12,X3),X3,X15) ),
file('<stdin>',cls_inj__on__insert_1) ).
fof(c_0_62_063,axiom,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X45
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X10,X45))) ),
file('<stdin>',cls_in__mkbot_2) ).
fof(c_0_63_064,axiom,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X45
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X10,X45))) ),
file('<stdin>',cls_in__mktop_2) ).
fof(c_0_64_065,axiom,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X10,X45)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X45
| X9 = X45 ),
file('<stdin>',cls_in__mkbot_3) ).
fof(c_0_65_066,axiom,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X10,X45)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| X9 = X45 ),
file('<stdin>',cls_in__mkbot_5) ).
fof(c_0_66_067,axiom,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X10,X45)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X45
| X6 = X45 ),
file('<stdin>',cls_in__mktop_3) ).
fof(c_0_67_068,axiom,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X10,X45)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| X6 = X45 ),
file('<stdin>',cls_in__mktop_5) ).
fof(c_0_68_069,axiom,
! [X9,X6,X18,X1,X2,X12,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_quotient__eqI_0) ).
fof(c_0_69_070,axiom,
! [X18,X16,X17,X12,X3] :
( c_lessequals(c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_equiv__class__subset_0) ).
fof(c_0_70_071,axiom,
! [X18,X16,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),X12))
| ~ c_lessequals(c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_subset__equiv__class_0) ).
fof(c_0_71_072,axiom,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X16),c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X17,X16,X15,X3)),X18)) ),
file('<stdin>',cls_Image__singleton__iff_1) ).
fof(c_0_72_073,axiom,
! [X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X9,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
file('<stdin>',cls_notin__Lin__iff_0) ).
fof(c_0_73_074,axiom,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X17,X16,X15,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),X15,X3))) ),
file('<stdin>',cls_Image__singleton__iff_0) ).
fof(c_0_74_075,axiom,
! [X30,X6,X21,X14,X12,X15,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X12,X14,X21,X15,X3)))
| ~ hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
file('<stdin>',cls_bex__UN_4) ).
fof(c_0_75_076,axiom,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastLessThan(X23,X24,X25,X22,X3)))
| ~ hBOOL(hAPP(hAPP(X24,X26),X22))
| ~ hBOOL(hAPP(hAPP(X23,X25),X26)) ),
file('<stdin>',cls_ord_OatLeastLessThan__iff_2) ).
fof(c_0_76_077,axiom,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanAtMost(X23,X24,X25,X22,X3)))
| ~ hBOOL(hAPP(hAPP(X23,X26),X22))
| ~ hBOOL(hAPP(hAPP(X24,X25),X26)) ),
file('<stdin>',cls_ord_OgreaterThanAtMost__iff_2) ).
fof(c_0_77_078,axiom,
! [X9,X6,X18,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X18,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_eq__equiv__class__iff_1) ).
fof(c_0_78_079,axiom,
! [X18,X16,X17,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),X16),c_Relation_OImage(X18,X12,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X15)),c_Pair(X17,X16,X3,X15)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_rev__ImageI_0) ).
fof(c_0_79_080,axiom,
! [X6,X18,X16,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X16),c_Relation_OImage(X18,X12,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X6,X16,X15,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
file('<stdin>',cls_Image__iff_2) ).
fof(c_0_80_081,axiom,
! [X6,X16,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__above_0) ).
fof(c_0_81_082,axiom,
! [X6,X16,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
file('<stdin>',cls_in__below_0) ).
fof(c_0_82_083,axiom,
! [X18,X16,X17,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_equiv__class__eq_0) ).
fof(c_0_83_084,axiom,
! [X9,X6,X18,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X18,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_equiv__class__eq__iff_0) ).
fof(c_0_84_085,axiom,
! [X9,X6,X18,X12,X3] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X18,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X18,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_eq__equiv__class__iff2_1) ).
fof(c_0_85_086,axiom,
! [X9,X6,X13,X12,X15,X3] :
( c_Set_Oimage(c_Fun_Ofun__upd(X13,X6,X9,X15,X3),X12,X15,X3) = c_Set_Oinsert(X9,c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),tc_fun(X15,tc_bool)),X15,X3),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
file('<stdin>',cls_fun__upd__image_0) ).
fof(c_0_86_087,axiom,
! [X6,X18,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_quotientI_0) ).
fof(c_0_87_088,axiom,
! [X9,X30,X6,X18,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X6),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X6),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X30,X9,X3,X3)),X18)) ),
file('<stdin>',cls_quotient__eq__iff_0) ).
fof(c_0_88_089,axiom,
! [X13,X17,X12,X15,X3] :
( c_Fun_Oinj__on(X13,c_Set_Oinsert(X17,X12,X3),X3,X15)
| hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X15)))
| ~ c_Fun_Oinj__on(X13,X12,X3,X15) ),
file('<stdin>',cls_inj__on__insert_2) ).
fof(c_0_89_090,axiom,
! [X9,X6,X18,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X18,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18)) ),
file('<stdin>',cls_eq__equiv__class__iff_0) ).
fof(c_0_90_091,axiom,
! [X9,X6,X18,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X18,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_equiv__class__eq__iff_3) ).
fof(c_0_91_092,axiom,
! [X9,X6,X13,X12,X15,X3] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X13,X6,X9,X3,X15),X12,X3,X15)
| hBOOL(hAPP(hAPP(c_in(X15),X9),c_Set_Oimage(X13,X12,X3,X15)))
| ~ c_Fun_Oinj__on(X13,X12,X3,X15) ),
file('<stdin>',cls_inj__on__fun__updI_0) ).
fof(c_0_92_093,axiom,
! [X18,X16,X17,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_eq__equiv__class_0) ).
fof(c_0_93_094,axiom,
! [X18,X14,X12,X15,X3] :
( c_lessequals(c_Relation_OImage(X18,X12,X15,X3),X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X15,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X18,X15,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),X3,X15)),tc_fun(X15,tc_bool)) ),
file('<stdin>',cls_Image__subset__eq_1) ).
fof(c_0_94_095,axiom,
! [X13,X14,X12,X15,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3,X15),c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X14,X12,tc_fun(X3,tc_bool)),X3,X15),tc_fun(X15,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| ~ c_Fun_Oinj__on(X13,X14,X3,X15)
| ~ c_Fun_Oinj__on(X13,X12,X3,X15)
| c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15) ),
file('<stdin>',cls_inj__on__Un_3) ).
fof(c_0_95_096,axiom,
! [X9,X6,X18,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_equiv__class__eq__iff_2) ).
fof(c_0_96_097,axiom,
! [X9,X6,X18,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_equiv__class__eq__iff_1) ).
fof(c_0_97_098,axiom,
! [X7,X8,X3] :
( c_lessequals(X8,X7,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X8),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X7),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_pred__subset__eq_0) ).
fof(c_0_98_099,axiom,
! [X13,X14,X12,X15,X3] :
( c_lessequals(c_Set_Oimage(X13,X12,X3,X15),X14,tc_fun(X15,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,c_COMBK(X14,tc_fun(X15,tc_bool),X3),X3,X15))) ),
file('<stdin>',cls_funcset__image_0) ).
fof(c_0_99_100,axiom,
! [X9,X6,X18,X12,X3] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X18,X3) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X18,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18)) ),
file('<stdin>',cls_eq__equiv__class__iff2_0) ).
fof(c_0_100_101,axiom,
! [X41,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X41))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X41),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3)))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3))) ),
file('<stdin>',cls_ball__conj__distrib_3) ).
fof(c_0_101_102,axiom,
! [X40,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X40))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X40),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3)))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3))) ),
file('<stdin>',cls_ball__conj__distrib_2) ).
fof(c_0_102_103,axiom,
! [X30,X6,X10] :
( X30 = X6
| X6 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X30
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X30,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X30))) ),
file('<stdin>',cls_in__below_5) ).
fof(c_0_103_104,axiom,
! [X30,X6,X10] :
( X30 = X6
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X30 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X30,X6))) ),
file('<stdin>',cls_in__above_5) ).
fof(c_0_104_105,axiom,
! [X6,X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X6)),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,c_COMBK(X14,tc_fun(X15,tc_bool),X3),X3,X15))) ),
file('<stdin>',cls_funcset__mem_0) ).
fof(c_0_105_106,axiom,
! [X13,X12,X15,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X3),X13,X3,X3,X15),X12,X15,X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Finite__Set_Osetsum(X13,X12,X15,X3)) ),
file('<stdin>',cls_setsum__negf_0) ).
fof(c_0_106_107,axiom,
! [X6,X27,X16,X14,X12,X28,X15,X3] :
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_fun(X28,tc_bool))),X16),X27))
| ~ hBOOL(hAPP(hAPP(hAPP(X14,X6),X16),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_SUP2__iff_2) ).
fof(c_0_107_108,axiom,
! [X27,X16,X17,X14,X12,X28,X15,X3] :
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_fun(X28,tc_bool))),X16),X27))
| ~ hBOOL(hAPP(hAPP(hAPP(X14,X17),X16),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_SUP2__I_0) ).
fof(c_0_108_109,axiom,
! [X13,X16,X17,X15,X3] :
( hAPP(X13,X17) = X16
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Ovimage(X13,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),X3,X15))) ),
file('<stdin>',cls_vimage__singleton__eq_0) ).
fof(c_0_109_110,axiom,
! [X18,X14,X12,X15,X3] :
( c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X15,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X18,X15,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),X3,X15)),tc_fun(X15,tc_bool))
| ~ c_lessequals(c_Relation_OImage(X18,X12,X15,X3),X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Image__subset__eq_0) ).
fof(c_0_110_111,axiom,
! [X9,X6,X13,X12,X15,X3] :
( c_Set_Oimage(c_Fun_Ofun__upd(X13,X6,X9,X15,X3),X12,X15,X3) = c_Set_Oimage(X13,X12,X15,X3)
| hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
file('<stdin>',cls_fun__upd__image_1) ).
fof(c_0_111_112,axiom,
! [X18,X2,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_List_Osko__Equiv__Relations__XquotientE__1__1(X12,X2,X18,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),c_Equiv__Relations_Oquotient(X12,X18,X3))) ),
file('<stdin>',cls_quotientE_1) ).
fof(c_0_112_113,axiom,
! [X19,X13,X17,X12,X15,X3] :
( hAPP(c_Fun_Ooverride__on(X13,X19,X12,X3,X15),X17) = hAPP(X19,X17)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_override__on__apply__in_0) ).
fof(c_0_113_114,axiom,
! [X6,X21,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X12,X14,X21,X3)),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
file('<stdin>',cls_bex__Un_6) ).
fof(c_0_114_115,axiom,
! [X30,X21,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X12,X14,X21,X3)),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12)) ),
file('<stdin>',cls_bex__Un_4) ).
fof(c_0_115_116,axiom,
! [X19,X13,X17,X12,X15,X3] :
( hAPP(c_Fun_Ooverride__on(X13,X19,X12,X3,X15),X17) = hAPP(X13,X17)
| hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_override__on__apply__notin_0) ).
fof(c_0_116_117,axiom,
! [X6,X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X6)),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15))) ),
file('<stdin>',cls_Pi__mem_0) ).
fof(c_0_117_118,axiom,
! [X6,X13,X14,X12,X15,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X6)),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15))) ),
file('<stdin>',cls_PiE_0) ).
fof(c_0_118_119,axiom,
! [X7,X8,X3] :
( c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X8),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X7),tc_fun(X3,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_pred__subset__eq_1) ).
fof(c_0_119_120,axiom,
! [X45,X9,X6,X13,X15,X3] :
( hAPP(c_Fun_Ofun__upd(X13,X6,X9,X15,X3),X45) = hAPP(X13,X45)
| X45 = X6 ),
file('<stdin>',cls_fun__upd__apply_1) ).
fof(c_0_120_121,axiom,
! [X45,X9,X6,X13,X15,X3] :
( hAPP(c_Fun_Ofun__upd(X13,X6,X9,X3,X15),X45) = hAPP(X13,X45)
| X45 = X6 ),
file('<stdin>',cls_fun__upd__other_0) ).
fof(c_0_121_122,axiom,
! [X13,X14,X12,X15,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3,X15),c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X14,X12,tc_fun(X3,tc_bool)),X3,X15),tc_fun(X15,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| ~ c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15) ),
file('<stdin>',cls_inj__on__Un_2) ).
fof(c_0_122_123,axiom,
! [X39,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X39))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X39),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3)),X12)) ),
file('<stdin>',cls_ball__conj__distrib_1) ).
fof(c_0_123_124,axiom,
! [X37,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X37))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X37),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3)),X12)) ),
file('<stdin>',cls_ball__conj__distrib_0) ).
fof(c_0_124_125,axiom,
! [X9,X6,X43,X44,X12,X15,X3] :
( hAPP(X44,X6) != hAPP(X44,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X15),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12))
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15)
| X6 = X9 ),
file('<stdin>',cls_type__definition_OAbs__inject_0) ).
fof(c_0_125_126,axiom,
! [X30,X6,X10] :
( X30 = X6
| X30 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X10,X6))) ),
file('<stdin>',cls_in__mktop_4) ).
fof(c_0_126_127,axiom,
! [X9,X6,X10] :
( X6 = X9
| X9 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X10,X6))) ),
file('<stdin>',cls_in__mkbot_4) ).
fof(c_0_127_128,axiom,
! [X18,X2,X12,X3] :
( X2 = c_Relation_OImage(X18,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(X12,X2,X18,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),c_Equiv__Relations_Oquotient(X12,X18,X3))) ),
file('<stdin>',cls_quotientE_0) ).
fof(c_0_128_129,axiom,
! [X18,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_equiv__class__self_0) ).
fof(c_0_129_130,axiom,
! [X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
file('<stdin>',cls_converse__in__Lin_0) ).
fof(c_0_130_131,axiom,
! [X6,X43,X44,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X43,X6)),X12))
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15) ),
file('<stdin>',cls_type__definition_ORep_0) ).
fof(c_0_131_132,axiom,
! [X9,X43,X44,X12,X15,X3] :
( hAPP(X43,hAPP(X44,X9)) = X9
| ~ hBOOL(hAPP(hAPP(c_in(X15),X9),X12))
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15) ),
file('<stdin>',cls_type__definition_OAbs__inverse_0) ).
fof(c_0_132_133,axiom,
! [X13,X11,X14,X12,X15,X3] :
( c_Set_Oimage(X13,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X3,X15) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X13,X12,X3,X15),c_Set_Oimage(X13,X14,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X13,X11,X3,X15) ),
file('<stdin>',cls_inj__on__image__Int_0) ).
fof(c_0_133_134,axiom,
! [X13,X11,X14,X12,X15,X3] :
( c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3,X15) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X13,X12,X3,X15),c_Set_Oimage(X13,X14,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X13,X11,X3,X15) ),
file('<stdin>',cls_inj__on__image__set__diff_0) ).
fof(c_0_134_135,axiom,
! [X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X9)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X9 ),
file('<stdin>',cls_below__Lin_0) ).
fof(c_0_135_136,axiom,
! [X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X10,X6,X9)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X9 ),
file('<stdin>',cls_above__Lin_0) ).
fof(c_0_136_137,axiom,
! [X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
file('<stdin>',cls_converse__in__Lin_1) ).
fof(c_0_137_138,axiom,
! [X9,X6,X43,X44,X12,X15,X3] :
( hAPP(X43,X6) != hAPP(X43,X9)
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15)
| X6 = X9 ),
file('<stdin>',cls_type__definition_ORep__inject_0) ).
fof(c_0_138_139,axiom,
! [X6,X43,X44,X12,X15,X3] :
( hAPP(X44,hAPP(X43,X6)) = X6
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15) ),
file('<stdin>',cls_type__definition_ORep__inverse_0) ).
fof(c_0_139_140,axiom,
! [X13,X17,X14,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Ovimage(X13,X14,X3,X15))) ),
file('<stdin>',cls_vimageE_0) ).
fof(c_0_140_141,axiom,
! [X13,X17,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Ovimage(X13,X12,X3,X15))) ),
file('<stdin>',cls_vimageD_0) ).
fof(c_0_141_142,axiom,
! [X9,X6,X13,X15,X3] :
( c_Fun_Ofun__upd(X13,X6,X9,X3,X15) != X13
| hAPP(X13,X6) = X9 ),
file('<stdin>',cls_fun__upd__idem__iff_0) ).
fof(c_0_142_143,axiom,
! [X22,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X25),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanLessThan(X24,X25,X22,X3))) ),
file('<stdin>',cls_ord_OgreaterThanLessThan__iff_0) ).
fof(c_0_143_144,axiom,
! [X22,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X26),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanLessThan(X24,X25,X22,X3))) ),
file('<stdin>',cls_ord_OgreaterThanLessThan__iff_1) ).
fof(c_0_144_145,axiom,
! [X22,X23,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X26),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastAtMost(X23,X25,X22,X3))) ),
file('<stdin>',cls_ord_OatLeastAtMost__iff_1) ).
fof(c_0_145_146,axiom,
! [X22,X23,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X25),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastAtMost(X23,X25,X22,X3))) ),
file('<stdin>',cls_ord_OatLeastAtMost__iff_0) ).
fof(c_0_146_147,axiom,
! [X18,X1,X2,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_quotient__disj_0) ).
fof(c_0_147_148,axiom,
! [X7,X8,X3] :
( hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X8) != hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X7)
| X8 = X7 ),
file('<stdin>',cls_pred__equals__eq_0) ).
fof(c_0_148_149,axiom,
! [X6,X13,X12,X15,X3] :
( hBOOL(hAPP(X12,hAPP(X13,X6)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X13,X12,X3,X15),X6)) ),
file('<stdin>',cls_vimage__code_0) ).
fof(c_0_149_150,axiom,
! [X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X10,X6)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
file('<stdin>',cls_mktop__Lin_0) ).
fof(c_0_150_151,axiom,
! [X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X10,X6)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
file('<stdin>',cls_mkbot__Lin_0) ).
fof(c_0_151_152,axiom,
! [X6,X16,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X16),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X15,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
file('<stdin>',cls_UN__iff_2) ).
fof(c_0_152_153,axiom,
! [X16,X17,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),X16),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X16),hAPP(X14,X17)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_UN__I_0) ).
fof(c_0_153_154,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_8) ).
fof(c_0_154_155,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
file('<stdin>',cls_psubset__insert__iff_4) ).
fof(c_0_155_156,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_9) ).
fof(c_0_156_157,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
file('<stdin>',cls_psubset__insert__iff_5) ).
fof(c_0_157_158,axiom,
! [X13,X17,X14,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Ovimage(X13,X14,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),X14)) ),
file('<stdin>',cls_vimage__eq_1) ).
fof(c_0_158_159,axiom,
! [X13,X17,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),X17),c_Set_Ovimage(X13,X12,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X17)),X12)) ),
file('<stdin>',cls_vimageI2_0) ).
fof(c_0_159_160,axiom,
! [X13,X17,X14,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),X17),c_Set_Ovimage(X13,X14,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X17)),X14)) ),
file('<stdin>',cls_vimageI_0) ).
fof(c_0_160_161,axiom,
! [X13,X14,X12,X15,X3] :
( c_Set_Oimage(X13,X12,X3,X15) != c_Set_Oimage(X13,X14,X3,X15)
| ~ c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15)
| X12 = X14 ),
file('<stdin>',cls_inj__on__Un__image__eq__iff_0) ).
fof(c_0_161_162,axiom,
! [X6,X16,X14,X12,X15,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_bool)),X16))
| ~ hBOOL(hAPP(hAPP(X14,X6),X16))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_SUP1__iff_2) ).
fof(c_0_162_163,axiom,
! [X16,X17,X14,X12,X15,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_bool)),X16))
| ~ hBOOL(hAPP(hAPP(X14,X17),X16))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_SUP1__I_0) ).
fof(c_0_163_164,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_3) ).
fof(c_0_164_165,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_diff__single__insert_0) ).
fof(c_0_165_166,axiom,
! [X6,X13,X12,X20,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X20),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X6)),c_Set_Oimage(X13,X12,X20,X3))) ),
file('<stdin>',cls_rev__image__eqI_0) ).
fof(c_0_166_167,axiom,
! [X6,X13,X12,X15,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X6)),c_Set_Oimage(X13,X12,X15,X3))) ),
file('<stdin>',cls_image__iff_2) ).
fof(c_0_167_168,axiom,
! [X6,X13,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X6)),c_Set_Oimage(X13,X12,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
file('<stdin>',cls_image__eqI_0) ).
fof(c_0_168_169,axiom,
! [X6,X13,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X6)),c_Set_Oimage(X13,X12,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_imageI_0) ).
fof(c_0_169_170,axiom,
! [X22,X23,X25,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastAtMost(X23,X25,X22,X3)))
| ~ hBOOL(hAPP(hAPP(X23,X26),X22))
| ~ hBOOL(hAPP(hAPP(X23,X25),X26)) ),
file('<stdin>',cls_ord_OatLeastAtMost__iff_2) ).
fof(c_0_170_171,axiom,
! [X22,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanLessThan(X24,X25,X22,X3)))
| ~ hBOOL(hAPP(hAPP(X24,X26),X22))
| ~ hBOOL(hAPP(hAPP(X24,X25),X26)) ),
file('<stdin>',cls_ord_OgreaterThanLessThan__iff_2) ).
fof(c_0_171_172,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_4) ).
fof(c_0_172_173,axiom,
! [X6,X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X6)),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12))
| ~ c_lessequals(c_Set_Oimage(X13,X12,X15,X3),X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_image__subset__iff_0) ).
fof(c_0_173_174,axiom,
! [X6,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3)),X12)) ),
file('<stdin>',cls_ball__conj__distrib_5) ).
fof(c_0_174_175,axiom,
! [X6,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3)),X12)) ),
file('<stdin>',cls_ball__conj__distrib_4) ).
fof(c_0_175_176,axiom,
! [X6,X54,X14,X12,X15,X3] :
( c_lessequals(hAPP(X12,X6),X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X54))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X12,X15,tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_UN__subset__iff_0) ).
fof(c_0_176_177,axiom,
! [X6,X21,X14,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X12,X14,X21,X3)))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
file('<stdin>',cls_bex__Un_7) ).
fof(c_0_177_178,axiom,
! [X30,X21,X14,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X12,X14,X21,X3)))
| ~ hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12)) ),
file('<stdin>',cls_bex__Un_5) ).
fof(c_0_178_179,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_1) ).
fof(c_0_179_180,axiom,
! [X13,X14,X12,X15,X3] :
( c_lessequals(c_Set_Oimage(X13,X12,X3,X15),c_Set_Oimage(X13,X14,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_image__mono_0) ).
fof(c_0_180_181,axiom,
! [X6,X13,X12,X15,X3] :
( ~ c_lessequals(X6,X12,tc_fun(X15,tc_bool))
| c_lessequals(c_Set_Oimage(X13,X6,X15,X3),c_Set_Oimage(X13,X12,X15,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__image__iff_2) ).
fof(c_0_181_182,axiom,
! [X13,X14,X12,X15,X3] :
( c_lessequals(c_Set_Ovimage(X13,X12,X15,X3),c_Set_Ovimage(X13,X14,X15,X3),tc_fun(X15,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_vimage__mono_0) ).
fof(c_0_182_183,axiom,
! [X13,X17,X12,X3] :
( c_Finite__Set_Osetsum(X13,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X13,X12,X3,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_setsum__diff1__nat_1) ).
fof(c_0_183_184,axiom,
! [X6,X13,X12,X15,X3] :
( hBOOL(hAPP(c_Set_Ovimage(X13,X12,X3,X15),X6))
| ~ hBOOL(hAPP(X12,hAPP(X13,X6))) ),
file('<stdin>',cls_vimage__code_1) ).
fof(c_0_184_185,axiom,
! [X51,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X51))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X51),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)),X12))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3))) ),
file('<stdin>',cls_ball__conj__distrib_9) ).
fof(c_0_185_186,axiom,
! [X51,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X51))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X51),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)),X12))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3))) ),
file('<stdin>',cls_ball__conj__distrib_8) ).
fof(c_0_186_187,axiom,
! [X30,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3)),X12)) ),
file('<stdin>',cls_ball__conj__distrib_7) ).
fof(c_0_187_188,axiom,
! [X30,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3)),X12)) ),
file('<stdin>',cls_ball__conj__distrib_6) ).
fof(c_0_188_189,axiom,
! [X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X12,X11,X3)),X11))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_UnionE_1) ).
fof(c_0_189_190,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_0) ).
fof(c_0_190_191,axiom,
! [X29,X54,X12,X15,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X12,X29),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X12,X3,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X12,X3,tc_fun(X15,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X29),X54)) ),
file('<stdin>',cls_UN__absorb_0) ).
fof(c_0_191_192,axiom,
! [X6,X13,X12,X15,X3] :
( c_Set_Oinsert(hAPP(X13,X6),c_Set_Oimage(X13,X12,X3,X15),X15) = c_Set_Oimage(X13,X12,X3,X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_insert__image_0) ).
fof(c_0_192_193,axiom,
! [X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OInf__class_OInf(X11,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X12,X11,X3)),X11)) ),
file('<stdin>',cls_InterI_0) ).
fof(c_0_193_194,axiom,
! [X42,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X42))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X42),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3))) ),
file('<stdin>',cls_ball__conj__distrib_11) ).
fof(c_0_194_195,axiom,
! [X42,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X42))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X42),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3))) ),
file('<stdin>',cls_ball__conj__distrib_10) ).
fof(c_0_195_196,axiom,
! [X2,X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),X11))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OInf__class_OInf(X11,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_InterD_0) ).
fof(c_0_196_197,axiom,
! [X6,X13,X12,X15,X3] :
( hAPP(X13,X6) = c_HOL_Oundefined(X15)
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_Oextensional(X12,X3,X15))) ),
file('<stdin>',cls_extensional__arb_0) ).
fof(c_0_197_198,axiom,
! [X8] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X8),c_Arrow__Order__Mirabelle_OLin)) ),
file('<stdin>',cls_that_0) ).
fof(c_0_198_199,axiom,
! [X6,X17,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_bexCI_0) ).
fof(c_0_199_200,axiom,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Lattices_Olower__semilattice__class_Oinf(X12,c_Collect(X21,X3),tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_Int__Collect_0) ).
fof(c_0_200_201,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),c_Lattices_Oupper__semilattice__class_Osup(X6,X45,X3),X3),X3) ),
file('<stdin>',cls_distrib__sup__le_0) ).
fof(c_0_201_202,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X45,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3),X3) ),
file('<stdin>',cls_distrib__inf__le_0) ).
fof(c_0_202_203,axiom,
! [X11,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)),X12,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X12,X11,X3)),X11)) ),
file('<stdin>',cls_Union__disjoint_1) ).
fof(c_0_203_204,axiom,
! [X13,X14,X12,X15,X3] :
( c_Fun_Oinj__on(X13,X14,X3,X15)
| ~ c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15) ),
file('<stdin>',cls_inj__on__Un_1) ).
fof(c_0_204_205,axiom,
! [X13,X14,X12,X15,X3] :
( c_Fun_Oinj__on(X13,X12,X3,X15)
| ~ c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15) ),
file('<stdin>',cls_inj__on__Un_0) ).
fof(c_0_205_206,axiom,
! [X2,X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),X11)) ),
file('<stdin>',cls_UnionI_0) ).
fof(c_0_206_207,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_UnE_0) ).
fof(c_0_207_208,axiom,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Lattices_Olower__semilattice__class_Oinf(X12,c_Collect(X21,X3),tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_Int__Collect_1) ).
fof(c_0_208_209,axiom,
! [X50,X27,X16,X17,X3] :
( c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X27,c_Set_Oinsert(X50,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X17 = X50
| X17 = X27 ),
file('<stdin>',cls_doubleton__eq__iff_0) ).
fof(c_0_209_210,axiom,
! [X50,X27,X16,X17,X3] :
( c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X27,c_Set_Oinsert(X50,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X27
| X17 = X27 ),
file('<stdin>',cls_doubleton__eq__iff_1) ).
fof(c_0_210_211,axiom,
! [X50,X27,X16,X17,X3] :
( c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X27,c_Set_Oinsert(X50,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X17 = X50
| X16 = X50 ),
file('<stdin>',cls_doubleton__eq__iff_2) ).
fof(c_0_211_212,axiom,
! [X50,X27,X16,X17,X3] :
( c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X27,c_Set_Oinsert(X50,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X27
| X16 = X50 ),
file('<stdin>',cls_doubleton__eq__iff_3) ).
fof(c_0_212_213,axiom,
! [X6,X11,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)),X12,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X12,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X6),X11)) ),
file('<stdin>',cls_Union__disjoint_0) ).
fof(c_0_213_214,axiom,
! [X16,X17,X3] :
( X16 = X17
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3))) ),
file('<stdin>',cls_singletonE_0) ).
fof(c_0_214_215,axiom,
! [X27,X14,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_DiffE_1) ).
fof(c_0_215_216,axiom,
! [X17,X14,X12,X15,X3] :
( c_lessequals(hAPP(X14,X17),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_UN__upper_0) ).
fof(c_0_216_217,axiom,
! [X13,X17,X12,X15,X3] :
( c_Fun_Oinj__on(X13,X12,X3,X15)
| ~ c_Fun_Oinj__on(X13,c_Set_Oinsert(X17,X12,X3),X3,X15) ),
file('<stdin>',cls_inj__on__insert_0) ).
fof(c_0_217_218,axiom,
! [X11,X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Oupper__semilattice__class_Osup(X14,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X11,X12,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_0) ).
fof(c_0_218_219,axiom,
! [X17,X12,X3] :
( c_Set_Oinsert(X17,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_insert__Diff_0) ).
fof(c_0_219_220,axiom,
! [X13,X14,X12,X15,X3] :
( c_Fun_Oinj__on(X13,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3,X15)
| ~ c_Fun_Oinj__on(X13,X12,X3,X15) ),
file('<stdin>',cls_inj__on__diff_0) ).
fof(c_0_220_221,axiom,
! [X48,X16,X49,X17,X15,X3] :
( c_Pair(X17,X16,X3,X15) != c_Pair(X49,X48,X3,X15)
| X17 = X49 ),
file('<stdin>',cls_Pair__eq_0) ).
fof(c_0_221_222,axiom,
! [X48,X16,X49,X17,X15,X3] :
( c_Pair(X17,X16,X3,X15) != c_Pair(X49,X48,X3,X15)
| X16 = X48 ),
file('<stdin>',cls_Pair__eq_1) ).
fof(c_0_222_223,axiom,
! [X9,X6,X13,X12,X15,X3] :
( hAPP(X13,X6) != hAPP(X13,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| X6 = X9
| ~ c_Fun_Oinj__on(X13,X12,X3,X15) ),
file('<stdin>',cls_inj__on__contraD_0) ).
fof(c_0_223_224,axiom,
! [X9,X6,X13,X12,X15,X3] :
( hAPP(X13,X6) != hAPP(X13,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Fun_Oinj__on(X13,X12,X3,X15)
| X6 = X9 ),
file('<stdin>',cls_inj__on__iff_0) ).
fof(c_0_224_225,axiom,
! [X30,X6,X13,X12,X15,X3] :
( hAPP(X13,X6) != hAPP(X13,X30)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Fun_Oinj__on(X13,X12,X3,X15)
| X6 = X30 ),
file('<stdin>',cls_inj__on__def_0) ).
fof(c_0_225_226,axiom,
! [X9,X6,X13,X12,X15,X3] :
( hAPP(X13,X6) != hAPP(X13,X9)
| ~ c_Fun_Oinj__on(X13,X12,X3,X15)
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_inj__onD_0) ).
fof(c_0_226_227,axiom,
! [X13,X14,X12,X15,X3] :
( c_Fun_Oinj__on(X13,X12,X3,X15)
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X13,X14,X3,X15) ),
file('<stdin>',cls_subset__inj__on_0) ).
fof(c_0_227_228,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_DiffE_0) ).
fof(c_0_228_229,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_IntE_1) ).
fof(c_0_229_230,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_IntE_0) ).
fof(c_0_230_231,axiom,
! [X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OInf__class_OInf(X11,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X12,X11,X3))) ),
file('<stdin>',cls_InterI_1) ).
fof(c_0_231_232,axiom,
! [X17,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ hBOOL(hAPP(X21,X17)) ),
file('<stdin>',cls_bexCI_2) ).
fof(c_0_232_233,axiom,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexI__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(X21,X6)) ),
file('<stdin>',cls_bexI_0) ).
fof(c_0_233_234,axiom,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexE__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_bexE_0) ).
fof(c_0_234_235,axiom,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_rev__bexI_0) ).
fof(c_0_235_236,axiom,
! [X26,X52,X12,X15,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X15)
| c_lessequals(hAPP(X52,X26),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X52,X3,X15),X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),X12)) ),
file('<stdin>',cls_le__SUPI_0) ).
fof(c_0_236_237,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
file('<stdin>',cls_Int__iff_2) ).
fof(c_0_237_238,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
file('<stdin>',cls_IntI_0) ).
fof(c_0_238_239,axiom,
! [X27,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12))) ),
file('<stdin>',cls_ComplD_0) ).
fof(c_0_239_240,axiom,
! [X6,X21,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(X21,X6))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XballE__1__1(X12,X21,X3)),X12)) ),
file('<stdin>',cls_ballE_0) ).
fof(c_0_240_241,axiom,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),c_Lattices_Olower__semilattice__class_Oinf(X12,c_Collect(X21,X3),tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_Int__Collect_2) ).
fof(c_0_241_242,axiom,
! [X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X12,X11,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_UnionE_0) ).
fof(c_0_242_243,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
file('<stdin>',cls_Diff__iff_2) ).
fof(c_0_243_244,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
file('<stdin>',cls_DiffI_0) ).
fof(c_0_244_245,axiom,
! [X6,X14,X12,X15,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X15,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hAPP(X14,X6) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
file('<stdin>',cls_UNION__empty__conv_I2_J_0) ).
fof(c_0_245_246,axiom,
! [X6,X14,X12,X15,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X15,tc_fun(X3,tc_bool))
| hAPP(X14,X6) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
file('<stdin>',cls_UNION__empty__conv_I1_J_0) ).
fof(c_0_246_247,axiom,
! [X6,X27,X12,X15,X3] :
( c_Set_Oimage(c_COMBK(X27,X15,X3),X12,X3,X15) = c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_image__constant_0) ).
fof(c_0_247_248,axiom,
! [X6,X17,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_bexCI_1) ).
fof(c_0_248_249,axiom,
! [X55,X11,X14,X12,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X11,X55,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X55,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__mono_0) ).
fof(c_0_249_250,axiom,
! [X55,X11,X14,X12,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X11,X55,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X55,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Diff__mono_0) ).
fof(c_0_250_251,axiom,
! [X55,X11,X14,X12,X3] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X55,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X55,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__mono_0) ).
fof(c_0_251_252,axiom,
! [X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X12),c_Set_OPow(X14,X3))) ),
file('<stdin>',cls_PowD_0) ).
fof(c_0_252_253,axiom,
! [X16,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| X17 = X16
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Oinsert(X16,X12,X3))) ),
file('<stdin>',cls_insertE_0) ).
fof(c_0_253_254,axiom,
! [X14,X12,X3] :
( c_lessequals(X14,X12,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Compl__subset__Compl__iff_0) ).
fof(c_0_254_255,axiom,
! [X14,X12,X3] :
( c_lessequals(X14,c_Complete__Lattice_OSup__class_OSup(X12,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X14),X12)) ),
file('<stdin>',cls_Union__upper_0) ).
fof(c_0_255_256,axiom,
! [X14,X12,X3] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X12,tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X14),X12)) ),
file('<stdin>',cls_Inter__lower_0) ).
fof(c_0_256_257,axiom,
! [X16,X17,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3) ),
file('<stdin>',cls_Sup__binary_0) ).
fof(c_0_257_258,axiom,
! [X16,X17,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3) ),
file('<stdin>',cls_Inf__binary_0) ).
fof(c_0_258_259,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X14,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Diff__subset__conv_1) ).
fof(c_0_259_260,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X14,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Diff__subset__conv_0) ).
fof(c_0_260_261,axiom,
! [X6,X12,X3] :
( X12 = c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,c_Set_Oinsert(X6,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_261_262,axiom,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(X14,X6))
| hBOOL(hAPP(X12,X6))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X6)) ),
file('<stdin>',cls_sup1E_0) ).
fof(c_0_262_263,axiom,
! [X23,X29,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X26),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatMost(X23,X29,X3))) ),
file('<stdin>',cls_ord_OatMost__iff_0) ).
fof(c_0_263_264,axiom,
! [X24,X29,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X29),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThan(X24,X29,X3))) ),
file('<stdin>',cls_ord_OgreaterThan__iff_0) ).
fof(c_0_264_265,axiom,
! [X24,X29,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X26),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OlessThan(X24,X29,X3))) ),
file('<stdin>',cls_ord_OlessThan__iff_0) ).
fof(c_0_265_266,axiom,
! [X11,X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Oupper__semilattice__class_Osup(X14,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X12,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_1) ).
fof(c_0_266_267,axiom,
! [X6,X21,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XballE__1__1(X12,X21,X3))) ),
file('<stdin>',cls_ballE_1) ).
fof(c_0_267_268,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_2) ).
fof(c_0_268_269,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
file('<stdin>',cls_UnCI_1) ).
fof(c_0_269_270,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X14)) ),
file('<stdin>',cls_UnCI_0) ).
fof(c_0_270_271,axiom,
! [X17,X11,X14,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X17,X14,X3),X11,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X17,c_Lattices_Olower__semilattice__class_Oinf(X14,X11,tc_fun(X3,tc_bool)),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X11)) ),
file('<stdin>',cls_Int__insert__left_0) ).
fof(c_0_271_272,axiom,
! [X17,X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,c_Set_Oinsert(X17,X14,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X17,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_Int__insert__right_0) ).
fof(c_0_272_273,axiom,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(X14,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X6)) ),
file('<stdin>',cls_inf1E_1) ).
fof(c_0_273_274,axiom,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(X12,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X6)) ),
file('<stdin>',cls_inf1E_0) ).
fof(c_0_274_275,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_7) ).
fof(c_0_275_276,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_0) ).
fof(c_0_276_277,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
file('<stdin>',cls_psubset__insert__iff_3) ).
fof(c_0_277_278,axiom,
! [X11,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X12,X11,X3),X12,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)),X12,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Union__disjoint_2) ).
fof(c_0_278_279,axiom,
! [X6,X12,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X12,X3),c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X12
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_Diff__insert__absorb_0) ).
fof(c_0_279_280,axiom,
! [X6,X14,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_disjoint__iff__not__equal_0) ).
fof(c_0_280_281,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X6,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3)
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
file('<stdin>',cls_insert__Diff__if_1) ).
fof(c_0_281_282,axiom,
! [X27,X12,X15,X3] :
( c_Set_Oimage(c_COMBK(X27,X3,X15),X12,X15,X3) = c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
file('<stdin>',cls_image__constant__conv_1) ).
fof(c_0_282_283,axiom,
! [X16,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Oinsert(X16,X12,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_insert__iff_2) ).
fof(c_0_283_284,axiom,
! [X16,X17,X14,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Oinsert(X16,X14,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X14)) ),
file('<stdin>',cls_insertCI_0) ).
fof(c_0_284_285,axiom,
! [X27,X12,X15,X3] :
( c_Set_Ovimage(c_COMBK(X27,X15,X3),X12,X3,X15) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X15),X27),X12)) ),
file('<stdin>',cls_vimage__const_1) ).
fof(c_0_285_286,axiom,
! [X11,X14,X12,X3] :
( c_HOL_Ominus__class_Ominus(X14,c_HOL_Ominus__class_Ominus(X11,X12,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X12
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_double__diff_0) ).
fof(c_0_286_287,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X12,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_2) ).
fof(c_0_287_288,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X12,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__greatest_0) ).
fof(c_0_288_289,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_2) ).
fof(c_0_289_290,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__least_0) ).
fof(c_0_290_291,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_subset__insert_0) ).
fof(c_0_291_292,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_1) ).
fof(c_0_292_293,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
file('<stdin>',cls_insert__subset_2) ).
fof(c_0_293_294,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_6) ).
fof(c_0_294_295,axiom,
! [X27,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12)))
| hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
file('<stdin>',cls_ComplI_0) ).
fof(c_0_295_296,axiom,
! [X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X12),c_Set_OPow(X14,X3)))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_PowI_0) ).
fof(c_0_296_297,axiom,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XbexI__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(X21,X6)) ),
file('<stdin>',cls_bexI_1) ).
fof(c_0_297_298,axiom,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XbexE__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_bexE_1) ).
fof(c_0_298_299,axiom,
! [X17,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ hBOOL(hAPP(X21,X17)) ),
file('<stdin>',cls_bexCI_3) ).
fof(c_0_299_300,axiom,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_rev__bexI_1) ).
fof(c_0_300_301,axiom,
! [X13,X12,X15,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X13,X12,X15,X3)
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
file('<stdin>',cls_empty__is__image_0) ).
fof(c_0_301_302,axiom,
! [X13,X12,X15,X3] :
( c_Set_Oimage(X13,X12,X15,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
file('<stdin>',cls_image__is__empty_0) ).
fof(c_0_302_303,axiom,
! [X14,X12,X3] :
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Compl__subset__Compl__iff_1) ).
fof(c_0_303_304,axiom,
! [X14,X12,X3] :
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Compl__anti__mono_0) ).
fof(c_0_304_305,axiom,
! [X27,X12,X15,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,c_COMBK(X27,tc_fun(X3,tc_bool),X15),X15,tc_fun(X3,tc_bool)) = X27
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
file('<stdin>',cls_UN__constant_1) ).
fof(c_0_305_306,axiom,
! [X23,X29,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatMost(X23,X29,X3)))
| ~ hBOOL(hAPP(hAPP(X23,X26),X29)) ),
file('<stdin>',cls_ord_OatMost__iff_1) ).
fof(c_0_306_307,axiom,
! [X24,X29,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThan(X24,X29,X3)))
| ~ hBOOL(hAPP(hAPP(X24,X29),X26)) ),
file('<stdin>',cls_ord_OgreaterThan__iff_1) ).
fof(c_0_307_308,axiom,
! [X24,X29,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OlessThan(X24,X29,X3)))
| ~ hBOOL(hAPP(hAPP(X24,X26),X29)) ),
file('<stdin>',cls_ord_OlessThan__iff_1) ).
fof(c_0_308_309,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(X12,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_0) ).
fof(c_0_309_310,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_1) ).
fof(c_0_310_311,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(X11,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_1) ).
fof(c_0_311_312,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(X11,X12,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_0) ).
fof(c_0_312_313,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),c_Lattices_Oupper__semilattice__class_Osup(X6,X45,X3),X3) ),
file('<stdin>',cls_sup__inf__distrib1_0) ).
fof(c_0_313_314,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X6,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X9,X6,X3),c_Lattices_Oupper__semilattice__class_Osup(X45,X6,X3),X3) ),
file('<stdin>',cls_sup__inf__distrib2_0) ).
fof(c_0_314_315,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X45,X3),X3) ),
file('<stdin>',cls_inf__sup__distrib1_0) ).
fof(c_0_315_316,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X6,X3),c_Lattices_Olower__semilattice__class_Oinf(X45,X6,X3),X3) ),
file('<stdin>',cls_inf__sup__distrib2_0) ).
fof(c_0_316_317,axiom,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X6))
| ~ hBOOL(hAPP(X14,X6))
| ~ hBOOL(hAPP(X12,X6)) ),
file('<stdin>',cls_inf1I_0) ).
fof(c_0_317_318,axiom,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_disjoint__eq__subset__Compl_1) ).
fof(c_0_318_319,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
file('<stdin>',cls_insert__Diff1_0) ).
fof(c_0_319_320,axiom,
! [X9,X6,X12,X3] :
( hBOOL(hAPP(X12,X6))
| X9 = X6
| ~ hBOOL(hAPP(c_Set_Oinsert(X9,X12,X3),X6)) ),
file('<stdin>',cls_insert__code_0) ).
fof(c_0_320_321,axiom,
! [X17,X55,X11,X3] :
( c_lessequals(c_Set_Oinsert(X17,X11,X3),c_Set_Oinsert(X17,X55,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X55,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__mono_0) ).
fof(c_0_321_322,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_subset__insert_1) ).
fof(c_0_322_323,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_subset__insert__iff_2) ).
fof(c_0_323_324,axiom,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_lessequals(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__subset_0) ).
fof(c_0_324_325,axiom,
! [X53,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X53),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X53),X12))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__iff_0) ).
fof(c_0_325_326,axiom,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_set__rev__mp_0) ).
fof(c_0_326_327,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subsetD_0) ).
fof(c_0_327_328,axiom,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_set__mp_0) ).
fof(c_0_328_329,axiom,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubsetD_0) ).
fof(c_0_329_330,axiom,
! [X52,X12,X15,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X15)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,c_COMBK(X52,X15,X3),X3,X15) = X52
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_SUP__const_0) ).
fof(c_0_330_331,axiom,
! [X6,X14,X12,X3] :
( c_Set_Oinsert(X6,X12,X3) != c_Set_Oinsert(X6,X14,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| X12 = X14 ),
file('<stdin>',cls_insert__ident_0) ).
fof(c_0_331_332,axiom,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X6))
| ~ hBOOL(hAPP(X12,X6)) ),
file('<stdin>',cls_sup1CI_1) ).
fof(c_0_332_333,axiom,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X6))
| ~ hBOOL(hAPP(X14,X6)) ),
file('<stdin>',cls_sup1CI_0) ).
fof(c_0_333_334,axiom,
! [X6,X21,X3] :
( ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_bex__empty_0) ).
fof(c_0_334_335,axiom,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_disjoint__eq__subset__Compl_0) ).
fof(c_0_335_336,axiom,
! [X17,X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,c_Set_Oinsert(X17,X14,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_Int__insert__right_1) ).
fof(c_0_336_337,axiom,
! [X17,X11,X14,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X17,X14,X3),X11,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X14,X11,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X17),X11)) ),
file('<stdin>',cls_Int__insert__left_1) ).
fof(c_0_337_338,axiom,
! [X6,X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__subset_1) ).
fof(c_0_338_339,axiom,
! [X6,X21,X3] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_ball__empty_0) ).
fof(c_0_339_340,axiom,
! [X12,X3] :
( X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__Compl__self__eq_0) ).
fof(c_0_340_341,axiom,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,c_HOL_Ominus__class_Ominus(X14,X12,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X14
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Diff__partition_0) ).
fof(c_0_341_342,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X3)
| ~ c_lessequals(X6,X16,X3)
| ~ c_lessequals(X6,X17,X3) ),
file('<stdin>',cls_le__infI_0) ).
fof(c_0_342_343,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3)
| ~ c_lessequals(X6,X45,X3)
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_le__inf__iff_2) ).
fof(c_0_343_344,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3)
| ~ c_lessequals(X6,X45,X3)
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_inf__greatest_0) ).
fof(c_0_344_345,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X6,X3)
| ~ c_lessequals(X16,X6,X3)
| ~ c_lessequals(X17,X6,X3) ),
file('<stdin>',cls_le__supI_0) ).
fof(c_0_345_346,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X6,X3)
| ~ c_lessequals(X45,X6,X3)
| ~ c_lessequals(X9,X6,X3) ),
file('<stdin>',cls_sup__least_0) ).
fof(c_0_346_347,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3)
| ~ c_lessequals(X9,X45,X3)
| ~ c_lessequals(X6,X45,X3) ),
file('<stdin>',cls_le__sup__iff_2) ).
fof(c_0_347_348,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3)) ),
file('<stdin>',cls_inf__eq__neg__sup_0) ).
fof(c_0_348_349,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3)) ),
file('<stdin>',cls_sup__eq__neg__inf_0) ).
fof(c_0_349_350,axiom,
! [X16,X17,X3] :
( c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X17 = X16 ),
file('<stdin>',cls_singleton__inject_0) ).
fof(c_0_350_351,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) ),
file('<stdin>',cls_sup__assoc_0) ).
fof(c_0_351_352,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X6,X45,X3),X3) ),
file('<stdin>',cls_sup__left__commute_0) ).
fof(c_0_352_353,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X6,X45,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I7_J_0) ).
fof(c_0_353_354,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I6_J_0) ).
fof(c_0_354_355,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X45,X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I2_J_0) ).
fof(c_0_355_356,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X6,X45,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I3_J_0) ).
fof(c_0_356_357,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X6,X45,X3),X3) ),
file('<stdin>',cls_inf__left__commute_0) ).
fof(c_0_357_358,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X45,X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) ),
file('<stdin>',cls_inf__assoc_0) ).
fof(c_0_358_359,axiom,
! [X11,X14,X12,X3] :
( c_lessequals(X12,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__trans_0) ).
fof(c_0_359_360,axiom,
! [X11,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__subset__trans_0) ).
fof(c_0_360_361,axiom,
! [X11,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__psubset__trans_0) ).
fof(c_0_361_362,axiom,
! [X11,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X14,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__trans_0) ).
fof(c_0_362_363,axiom,
! [X46,X9,X47,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| c_lessequals(X46,X47,X3)
| ~ c_lessequals(X9,X6,X3) ),
file('<stdin>',cls_le__eqI_0) ).
fof(c_0_363_364,axiom,
! [X46,X9,X47,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| c_lessequals(X9,X6,X3)
| ~ c_lessequals(X46,X47,X3) ),
file('<stdin>',cls_le__eqI_1) ).
fof(c_0_364_365,axiom,
! [X46,X9,X47,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| c_HOL_Oord__class_Oless(X47,X46,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_less__eqI_0) ).
fof(c_0_365_366,axiom,
! [X46,X9,X47,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X47,X46,X3) ),
file('<stdin>',cls_less__eqI_1) ).
fof(c_0_366_367,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X16,X6,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X6,X3) ),
file('<stdin>',cls_le__supE_1) ).
fof(c_0_367_368,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,X45,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3) ),
file('<stdin>',cls_le__sup__iff_0) ).
fof(c_0_368_369,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,X45,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3) ),
file('<stdin>',cls_le__sup__iff_1) ).
fof(c_0_369_370,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X17,X6,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X6,X3) ),
file('<stdin>',cls_le__supE_0) ).
fof(c_0_370_371,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,X17,X3)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X3) ),
file('<stdin>',cls_le__infE_0) ).
fof(c_0_371_372,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,X16,X3)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X3) ),
file('<stdin>',cls_le__infE_1) ).
fof(c_0_372_373,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,X9,X3)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) ),
file('<stdin>',cls_le__inf__iff_0) ).
fof(c_0_373_374,axiom,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,X45,X3)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) ),
file('<stdin>',cls_le__inf__iff_1) ).
fof(c_0_374_375,axiom,
! [X16,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X16,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insertI2_0) ).
fof(c_0_375_376,axiom,
! [X19,X13,X15,X3] :
( ~ class_HOL_Oord(X15)
| c_HOL_Oord__class_Oless(X13,X19,tc_fun(X3,X15))
| c_lessequals(X19,X13,tc_fun(X3,X15))
| ~ c_lessequals(X13,X19,tc_fun(X3,X15)) ),
file('<stdin>',cls_less__fun__def_2) ).
fof(c_0_376_377,axiom,
! [X9,X6,X12,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X9,X12,X3),X6))
| ~ hBOOL(hAPP(X12,X6)) ),
file('<stdin>',cls_insert__code_2) ).
fof(c_0_377_378,axiom,
! [X17,X21,X3] :
( hBOOL(hAPP(X21,X17))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Collect(X21,X3))) ),
file('<stdin>',cls_CollectD_0) ).
fof(c_0_378_379,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X17,X16,X3)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3) ),
file('<stdin>',cls_neg__le__iff__le_0) ).
fof(c_0_379_380,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X17,X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3) ),
file('<stdin>',cls_neg__less__iff__less_0) ).
fof(c_0_380_381,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3) ),
file('<stdin>',cls_neg__sup__eq__inf_0) ).
fof(c_0_381_382,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X9),X3) ),
file('<stdin>',cls_compl__sup_0) ).
fof(c_0_382_383,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3) ),
file('<stdin>',cls_neg__inf__eq__sup_0) ).
fof(c_0_383_384,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X9),X3) ),
file('<stdin>',cls_compl__inf_0) ).
fof(c_0_384_385,axiom,
! [X19,X13,X15,X3] :
( ~ class_HOL_Oord(X15)
| ~ c_lessequals(X19,X13,tc_fun(X3,X15))
| ~ c_HOL_Oord__class_Oless(X13,X19,tc_fun(X3,X15)) ),
file('<stdin>',cls_less__fun__def_1) ).
fof(c_0_385_386,axiom,
! [X6,X12,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(X6,c_Complete__Lattice_OSup__class_OSup(X12,X3),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_Sup__upper_0) ).
fof(c_0_386_387,axiom,
! [X6,X12,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X12,X3),X6,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
file('<stdin>',cls_Inf__lower_0) ).
fof(c_0_387_388,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X3)
| ~ c_lessequals(X6,X17,X3) ),
file('<stdin>',cls_le__supI1_0) ).
fof(c_0_388_389,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X3)
| ~ c_lessequals(X6,X16,X3) ),
file('<stdin>',cls_le__supI2_0) ).
fof(c_0_389_390,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X6,X3)
| ~ c_lessequals(X17,X6,X3) ),
file('<stdin>',cls_le__infI1_0) ).
fof(c_0_390_391,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X6,X3)
| ~ c_lessequals(X16,X6,X3) ),
file('<stdin>',cls_le__infI2_0) ).
fof(c_0_391_392,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_HOL_Oord__class_Oless(X6,c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,X17,X3) ),
file('<stdin>',cls_less__supI1_0) ).
fof(c_0_392_393,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_HOL_Oord__class_Oless(X6,c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,X16,X3) ),
file('<stdin>',cls_less__supI2_0) ).
fof(c_0_393_394,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(X16,X6,X3) ),
file('<stdin>',cls_less__infI2_0) ).
fof(c_0_394_395,axiom,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(X17,X6,X3) ),
file('<stdin>',cls_less__infI1_0) ).
fof(c_0_395_396,axiom,
! [X14,X12,X3] :
( X12 = X14
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_set__eq__subset_2) ).
fof(c_0_396_397,axiom,
! [X14,X12,X3] :
( X12 = X14
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_equalityI_0) ).
fof(c_0_397_398,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X16,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3)
| ~ c_lessequals(X17,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3) ),
file('<stdin>',cls_le__minus__iff_0) ).
fof(c_0_398_399,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X17,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3)
| ~ c_lessequals(X16,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3) ),
file('<stdin>',cls_le__minus__iff_1) ).
fof(c_0_399_400,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X17,X3)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X16,X3) ),
file('<stdin>',cls_minus__le__iff_0) ).
fof(c_0_400_401,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X16,X3)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X17,X3) ),
file('<stdin>',cls_minus__le__iff_1) ).
fof(c_0_401_402,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X16,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3)
| ~ c_HOL_Oord__class_Oless(X17,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3) ),
file('<stdin>',cls_less__minus__iff_0) ).
fof(c_0_402_403,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X17,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3)
| ~ c_HOL_Oord__class_Oless(X16,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3) ),
file('<stdin>',cls_less__minus__iff_1) ).
fof(c_0_403_404,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X17,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X16,X3) ),
file('<stdin>',cls_minus__less__iff_0) ).
fof(c_0_404_405,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X17,X3) ),
file('<stdin>',cls_minus__less__iff_1) ).
fof(c_0_405_406,axiom,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)) = X12 ),
file('<stdin>',cls_Diff__triv_0) ).
fof(c_0_406_407,axiom,
! [X6,X19,X13,X15,X3] :
( ~ class_HOL_Oord(X15)
| c_lessequals(hAPP(X13,X6),hAPP(X19,X6),X15)
| ~ c_lessequals(X13,X19,tc_fun(X3,X15)) ),
file('<stdin>',cls_le__funD_0) ).
fof(c_0_407_408,axiom,
! [X30,X6,X3] :
( c_Set_Oinsert(X6,X30,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X30)) ),
file('<stdin>',cls_comm__monoid__add_Ononempty__iff_2) ).
fof(c_0_408_409,axiom,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X45,X6,X3)
| ~ c_lessequals(X45,X9,X3)
| ~ c_lessequals(X9,X6,X3) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_409_410,axiom,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X45,X6,X3)
| ~ c_lessequals(X45,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3) ),
file('<stdin>',cls_xt1_I7_J_0) ).
fof(c_0_410_411,axiom,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X45,X6,X3)
| ~ c_HOL_Oord__class_Oless(X45,X9,X3)
| ~ c_lessequals(X9,X6,X3) ),
file('<stdin>',cls_xt1_I8_J_0) ).
fof(c_0_411_412,axiom,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X6,X45,X3)
| ~ c_lessequals(X9,X45,X3)
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_412_413,axiom,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X6,X45,X3)
| ~ c_HOL_Oord__class_Oless(X9,X45,X3)
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_order__le__less__trans_0) ).
fof(c_0_413_414,axiom,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X6,X45,X3)
| ~ c_lessequals(X9,X45,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_order__less__le__trans_0) ).
fof(c_0_414_415,axiom,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X45,X6,X3)
| ~ c_HOL_Oord__class_Oless(X45,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_415_416,axiom,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X6,X45,X3)
| ~ c_HOL_Oord__class_Oless(X9,X45,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_416_417,axiom,
! [X17,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X17 ),
file('<stdin>',cls_Inf__singleton_0) ).
fof(c_0_417_418,axiom,
! [X17,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X17 ),
file('<stdin>',cls_Sup__singleton_0) ).
fof(c_0_418_419,axiom,
! [X12,X3] :
( X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__empty_0) ).
fof(c_0_419_420,axiom,
! [X18,X12,X3] :
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X12,X18,X3),tc_fun(X3,tc_bool)) = X12
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
file('<stdin>',cls_Union__quotient_0) ).
fof(c_0_420_421,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3)
| ~ c_lessequals(X17,X16,X3) ),
file('<stdin>',cls_le__imp__neg__le_0) ).
fof(c_0_421_422,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3)
| ~ c_HOL_Oord__class_Oless(X17,X16,X3) ),
file('<stdin>',cls_neg__less__iff__less_1) ).
fof(c_0_422_423,axiom,
! [X17,X12,X3] :
( c_Set_Oinsert(X17,X12,X3) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
file('<stdin>',cls_insert__absorb_0) ).
fof(c_0_423_424,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) ),
file('<stdin>',cls_sup__left__idem_0) ).
fof(c_0_424_425,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) ),
file('<stdin>',cls_inf__sup__aci_I8_J_0) ).
fof(c_0_425_426,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) ),
file('<stdin>',cls_inf__sup__aci_I4_J_0) ).
fof(c_0_426_427,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) ),
file('<stdin>',cls_inf__left__idem_0) ).
fof(c_0_427_428,axiom,
! [X19,X13,X15,X3] :
( ~ class_HOL_Oord(X15)
| c_lessequals(X13,X19,tc_fun(X3,X15))
| ~ c_HOL_Oord__class_Oless(X13,X19,tc_fun(X3,X15)) ),
file('<stdin>',cls_less__fun__def_0) ).
fof(c_0_428_429,axiom,
! [X14,X12,X3] :
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14)
| X12 = X14 ),
file('<stdin>',cls_Compl__eq__Compl__iff_0) ).
fof(c_0_429_430,axiom,
! [X17,X12,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X17,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X17,c_Complete__Lattice_OSup__class_OSup(X12,X3),X3) ),
file('<stdin>',cls_Sup__insert_0) ).
fof(c_0_430_431,axiom,
! [X17,X12,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X17,X12,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X17,c_Complete__Lattice_OInf__class_OInf(X12,X3),X3) ),
file('<stdin>',cls_Inf__insert_0) ).
fof(c_0_431_432,axiom,
! [X17,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Collect(X21,X3)))
| ~ hBOOL(hAPP(X21,X17)) ),
file('<stdin>',cls_CollectI_0) ).
fof(c_0_432_433,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| c_lessequals(X9,X6,X3)
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_less__le__not__le_2) ).
fof(c_0_433_434,axiom,
! [X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool))
| X12 = X14
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__eq_2) ).
fof(c_0_434_435,axiom,
! [X14,X12,X3] :
( X12 = X14
| c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__iff__psubset__eq_0) ).
fof(c_0_435_436,axiom,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) != X14
| c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__Un__eq_1) ).
fof(c_0_436_437,axiom,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) = X12
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__absorb2_0) ).
fof(c_0_437_438,axiom,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) = X14
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__absorb1_0) ).
fof(c_0_438_439,axiom,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) = X12
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__absorb2_0) ).
fof(c_0_439_440,axiom,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) = X14
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__absorb1_0) ).
fof(c_0_440_441,axiom,
! [X6,X38,X21,X3] :
( hBOOL(hAPP(X38,X6))
| ~ hBOOL(hAPP(X21,X6))
| ~ c_lessequals(X21,X38,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_predicate1D_0) ).
fof(c_0_441_442,axiom,
! [X6,X38,X21,X3] :
( hBOOL(hAPP(X38,X6))
| ~ c_lessequals(X21,X38,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X21,X6)) ),
file('<stdin>',cls_rev__predicate1D_0) ).
fof(c_0_442_443,axiom,
! [X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__eq_0) ).
fof(c_0_443_444,axiom,
! [X6,X7,X3] :
( hBOOL(hAPP(X7,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X7)) ),
file('<stdin>',cls_mem__def_0) ).
fof(c_0_444_445,axiom,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_1) ).
fof(c_0_445_446,axiom,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_0) ).
fof(c_0_446_447,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_HOL_Ominus__class_Ominus(X17,X16,X3)) = c_HOL_Ominus__class_Ominus(X16,X17,X3) ),
file('<stdin>',cls_minus__diff__eq_0) ).
fof(c_0_447_448,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| X6 = X9
| ~ c_lessequals(X6,X9,X3)
| ~ c_lessequals(X9,X6,X3) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_448_449,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| X6 = X9
| ~ c_lessequals(X9,X6,X3)
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_449_450,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| X6 = X9
| ~ c_lessequals(X9,X6,X3)
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_450_451,axiom,
! [X46,X47,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X6,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| X47 = X46 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_451_452,axiom,
! [X9,X30,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X30,X9,X3) != c_HOL_Ominus__class_Ominus(X6,X6,X3)
| X30 = X9 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_452_453,axiom,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X6,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X6,X3) ),
file('<stdin>',cls_linorder__antisym__conv2_1) ).
fof(c_0_453_454,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_lessequals(X9,X6,X3) ),
file('<stdin>',cls_linorder__not__less_1) ).
fof(c_0_454_455,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3) ),
file('<stdin>',cls_linorder__not__le_1) ).
fof(c_0_455_456,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_less__le__not__le_1) ).
fof(c_0_456_457,axiom,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X17,X16,X3)
| ~ c_HOL_Oord__class_Oless(X16,X17,X3) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_457_458,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_458_459,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_459_460,axiom,
! [X16,X17,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X16,X3) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_460_461,axiom,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_461_462,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) = X6 ),
file('<stdin>',cls_inf__sup__absorb_0) ).
fof(c_0_462_463,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X3) = X6 ),
file('<stdin>',cls_sup__inf__absorb_0) ).
fof(c_0_463_464,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X6,X3) ),
file('<stdin>',cls_inf__le1_0) ).
fof(c_0_464_465,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X9,X3) ),
file('<stdin>',cls_inf__le2_0) ).
fof(c_0_465_466,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X9,X3) ),
file('<stdin>',cls_inf__sup__ord_I2_J_0) ).
fof(c_0_466_467,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X6,X3) ),
file('<stdin>',cls_inf__sup__ord_I1_J_0) ).
fof(c_0_467_468,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) ),
file('<stdin>',cls_sup__ge1_0) ).
fof(c_0_468_469,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) ),
file('<stdin>',cls_sup__ge2_0) ).
fof(c_0_469_470,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) ),
file('<stdin>',cls_inf__sup__ord_I4_J_0) ).
fof(c_0_470_471,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) ),
file('<stdin>',cls_inf__sup__ord_I3_J_0) ).
fof(c_0_471_472,axiom,
! [X6,X7,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X7))
| ~ hBOOL(hAPP(X7,X6)) ),
file('<stdin>',cls_mem__def_1) ).
fof(c_0_472_473,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X9),X3) ),
file('<stdin>',cls_diff__eq_0) ).
fof(c_0_473_474,axiom,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X17,X3)
| X17 = X16
| ~ c_lessequals(X16,X17,X3) ),
file('<stdin>',cls_xt1_I11_J_0) ).
fof(c_0_474_475,axiom,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X17,X3)
| ~ c_lessequals(X16,X17,X3)
| X17 = X16 ),
file('<stdin>',cls_xt1_I12_J_0) ).
fof(c_0_475_476,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_order__le__less_0) ).
fof(c_0_476_477,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| X6 = X9
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_order__less__le_2) ).
fof(c_0_477_478,axiom,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X17,X16,X3)
| X17 = X16
| ~ c_lessequals(X17,X16,X3) ),
file('<stdin>',cls_order__le__neq__trans_0) ).
fof(c_0_478_479,axiom,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X17,X16,X3)
| ~ c_lessequals(X17,X16,X3)
| X17 = X16 ),
file('<stdin>',cls_order__neq__le__trans_0) ).
fof(c_0_479_480,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| X6 = X9
| ~ c_lessequals(X6,X9,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_linorder__antisym__conv1_0) ).
fof(c_0_480_481,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_linorder__antisym__conv2_0) ).
fof(c_0_481_482,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) != X9
| c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_le__iff__sup_1) ).
fof(c_0_482_483,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) != X6
| c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_le__iff__inf_1) ).
fof(c_0_483_484,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) = X9
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_le__iff__sup_0) ).
fof(c_0_484_485,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) = X6
| ~ c_lessequals(X9,X6,X3) ),
file('<stdin>',cls_sup__absorb1_0) ).
fof(c_0_485_486,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) = X6
| ~ c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_le__iff__inf_0) ).
fof(c_0_486_487,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) = X9
| ~ c_lessequals(X9,X6,X3) ),
file('<stdin>',cls_inf__absorb2_0) ).
fof(c_0_487_488,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_order__less__imp__le_0) ).
fof(c_0_488_489,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_order__le__less_1) ).
fof(c_0_489_490,axiom,
! [X9,X6,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X9,X6,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| X6 = X9 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_490_491,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X9,X6,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_491_492,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X6,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| X6 = X9 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_492_493,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X6,X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_493_494,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X6,X9,X3)
| c_HOL_Oord__class_Oless(X9,X6,X3) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_494_495,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| c_lessequals(X9,X6,X3) ),
file('<stdin>',cls_not__leE_0) ).
fof(c_0_495_496,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X6,X3)
| c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_496_497,axiom,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X6,X6,X3)
| c_lessequals(X6,X6,X3) ),
file('<stdin>',cls_linorder__antisym__conv1_1) ).
fof(c_0_497_498,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X6,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3) ),
file('<stdin>',cls_linorder__not__less_0) ).
fof(c_0_498_499,axiom,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X6,X3)
| c_lessequals(X6,X9,X3) ),
file('<stdin>',cls_linorder__not__le_0) ).
fof(c_0_499_500,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,X6,X3) ),
file('<stdin>',cls_sup__commute_0) ).
fof(c_0_500_501,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,X6,X3) ),
file('<stdin>',cls_inf__sup__aci_I5_J_0) ).
fof(c_0_501_502,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) = c_Lattices_Olower__semilattice__class_Oinf(X9,X6,X3) ),
file('<stdin>',cls_inf__commute_0) ).
fof(c_0_502_503,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) = c_Lattices_Olower__semilattice__class_Oinf(X9,X6,X3) ),
file('<stdin>',cls_inf__sup__aci_I1_J_0) ).
fof(c_0_503_504,axiom,
! [X6,X21,X3] :
( c_Collect(X21,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X21,X6)) ),
file('<stdin>',cls_Collect__empty__eq_0) ).
fof(c_0_504_505,axiom,
! [X6,X21,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X21,X3)
| ~ hBOOL(hAPP(X21,X6)) ),
file('<stdin>',cls_empty__Collect__eq_0) ).
fof(c_0_505_506,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X12,X14,X3) != c_Orderings_Obot__class_Obot(X3)
| X12 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq1_0) ).
fof(c_0_506_507,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X12,X14,X3) != c_Orderings_Obot__class_Obot(X3)
| X14 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq2_0) ).
fof(c_0_507_508,axiom,
! [X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6),X3) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_inf__compl__bot_0) ).
fof(c_0_508_509,axiom,
! [X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6),X6,X3) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_compl__inf__bot_0) ).
fof(c_0_509_510,axiom,
! [X6,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X6,X3) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_510_511,axiom,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X6,X3) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_511_512,axiom,
! [X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X6,X3) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_512_513,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_513_514,axiom,
! [X9,X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X9)
| X6 = X9 ),
file('<stdin>',cls_compl__eq__compl__iff_0) ).
fof(c_0_514_515,axiom,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16)
| X17 = X16 ),
file('<stdin>',cls_neg__equal__iff__equal_0) ).
fof(c_0_515_516,axiom,
! [X6,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X3),X3) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_inf__bot__right_0) ).
fof(c_0_516_517,axiom,
! [X6,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X3),X6,X3) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_inf__bot__left_0) ).
fof(c_0_517_518,axiom,
! [X6,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X6,X3) = X6 ),
file('<stdin>',cls_sup__bot__left_0) ).
fof(c_0_518_519,axiom,
! [X6,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X3),X3) = X6 ),
file('<stdin>',cls_sup__bot__right_0) ).
fof(c_0_519_520,axiom,
! [X6,X3] :
( ~ class_Orderings_Obot(X3)
| c_lessequals(c_Orderings_Obot__class_Obot(X3),X6,X3) ),
file('<stdin>',cls_bot__least_0) ).
fof(c_0_520_521,axiom,
! [X17,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17)) = X17 ),
file('<stdin>',cls_minus__minus_0) ).
fof(c_0_521_522,axiom,
! [X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6)) = X6 ),
file('<stdin>',cls_double__compl_0) ).
fof(c_0_522_523,axiom,
! [X16,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X16 = hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16)) ),
file('<stdin>',cls_equation__minus__iff_0) ).
fof(c_0_523_524,axiom,
! [X17,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X17 = hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17)) ),
file('<stdin>',cls_equation__minus__iff_1) ).
fof(c_0_524_525,axiom,
! [X16,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16)) = X16 ),
file('<stdin>',cls_minus__equation__iff_1) ).
fof(c_0_525_526,axiom,
! [X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X3) = X6 ),
file('<stdin>',cls_sup__idem_0) ).
fof(c_0_526_527,axiom,
! [X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X3) = X6 ),
file('<stdin>',cls_inf__idem_0) ).
fof(c_0_527_528,axiom,
! [X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X6,X6,X3) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_528_529,axiom,
! [X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X6,X6,X3) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_529_530,axiom,
! [X4,X5] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X4,X5))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
file('<stdin>',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_530_531,axiom,
! [X4,X5] :
( class_Lattices_Oupper__semilattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
file('<stdin>',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(c_0_531_532,axiom,
! [X4,X5] :
( class_Lattices_Olower__semilattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
file('<stdin>',clsarity_fun__Lattices_Olower__semilattice) ).
fof(c_0_532_533,axiom,
! [X4,X5] :
( class_Lattices_Odistrib__lattice(tc_fun(X4,X5))
| ~ class_Lattices_Odistrib__lattice(X5) ),
file('<stdin>',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(c_0_533_534,axiom,
! [X4,X5] :
( class_Lattices_Obounded__lattice(tc_fun(X4,X5))
| ~ class_Lattices_Obounded__lattice(X5) ),
file('<stdin>',clsarity_fun__Lattices_Obounded__lattice) ).
fof(c_0_534_535,axiom,
! [X4,X5] :
( class_Lattices_Oboolean__algebra(tc_fun(X4,X5))
| ~ class_Lattices_Oboolean__algebra(X5) ),
file('<stdin>',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(c_0_535_536,axiom,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_536_537,axiom,
! [X4,X5] :
( class_Lattices_Olattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
file('<stdin>',clsarity_fun__Lattices_Olattice) ).
fof(c_0_537_538,axiom,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_538_539,axiom,
! [X4,X5] :
( class_Orderings_Obot(tc_fun(X4,X5))
| ~ class_Orderings_Obot(X5) ),
file('<stdin>',clsarity_fun__Orderings_Obot) ).
fof(c_0_539_540,axiom,
! [X4,X5] :
( class_HOL_Oord(tc_fun(X4,X5))
| ~ class_HOL_Oord(X5) ),
file('<stdin>',clsarity_fun__HOL_Oord) ).
fof(c_0_540_541,plain,
! [X31,X32,X23,X24,X33,X34,X35,X36,X3] :
( c_Complete__Lattice_Ocomplete__lattice(X35,X36,c_COMBC(X23,X3,X3,tc_bool),c_COMBC(X24,X3,X3,tc_bool),X32,X33,X31,X34,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_541_542,plain,
! [X31,X32,X23,X24,X33,X34,X16,X17,X35,X36,X3] :
( hAPP(X35,c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X32,X17),X16)
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_542_543,plain,
! [X31,X32,X23,X24,X33,X34,X16,X17,X35,X36,X3] :
( hAPP(X36,c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X33,X17),X16)
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_543_544,plain,
! [X6,X31,X32,X23,X24,X33,X34,X35,X36,X12,X3] :
( hBOOL(hAPP(hAPP(X23,hAPP(X36,X12)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_544_545,plain,
! [X6,X31,X32,X23,X24,X33,X34,X35,X36,X12,X3] :
( hBOOL(hAPP(hAPP(X23,X6),hAPP(X35,X12)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_545_546,plain,
! [X31,X32,X23,X24,X33,X34,X17,X35,X36,X3] :
( hAPP(X35,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X17
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_546_547,plain,
! [X31,X32,X23,X24,X33,X34,X17,X35,X36,X3] :
( hAPP(X36,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X17
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_547_548,plain,
! [X31,X32,X23,X24,X33,X34,X17,X35,X36,X12,X3] :
( hAPP(X35,c_Set_Oinsert(X17,X12,X3)) = hAPP(hAPP(X32,X17),hAPP(X35,X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_548_549,plain,
! [X31,X32,X23,X24,X33,X34,X17,X35,X36,X12,X3] :
( hAPP(X36,c_Set_Oinsert(X17,X12,X3)) = hAPP(hAPP(X33,X17),hAPP(X36,X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_549_550,plain,
! [X31,X32,X23,X24,X33,X34,X35,X36,X3] :
( hAPP(X35,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X34
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_550_551,plain,
! [X31,X32,X23,X24,X33,X34,X35,X36,X3] :
( hAPP(X36,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X31
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X23,X24,X33,X32,X34,X31,X3) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_551_552,plain,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X12,X14,X13,X3,X15))),hAPP(X14,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X12,X14,X13,X3,X15)))) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_552_553,plain,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X12,X14,X13,X3,X15))),hAPP(X14,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X12,X14,X13,X3,X15)))) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_553_554,plain,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,c_COMBK(X14,tc_fun(X15,tc_bool),X3),X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X12,X14,X13,X3,X15))),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_554_555,plain,
! [X45,X9,X6,X13,X12,X15,X3] :
( c_Nitpick_Ofold__graph_H(X13,X45,X12,hAPP(hAPP(X13,X6),X9),X3,X15)
| ~ c_Nitpick_Ofold__graph_H(X13,X45,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,X3,X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_555_556,plain,
! [X45,X9,X6,X13,X12,X15,X3] :
( c_Finite__Set_Ofold__graph(X13,X45,X12,hAPP(hAPP(X13,X6),X9),X3,X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Finite__Set_Ofold__graph(X13,X45,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_556_557,plain,
! [X45,X9,X6,X13,X12,X15,X3] :
( c_Finite__Set_Ofold__graph(X13,X45,c_Set_Oinsert(X6,X12,X3),hAPP(hAPP(X13,X6),X9),X3,X15)
| ~ c_Finite__Set_Ofold__graph(X13,X45,X12,X9,X3,X15)
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_557_558,plain,
! [X6,X18,X16,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_558_559,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_559_560,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_560_561,axiom,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,c_COMBK(X14,tc_fun(X15,tc_bool),X3),X3,X15)))
| hBOOL(hAPP(hAPP(c_in(X3),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X12,X14,X13,X3,X15)),X12)) ),
c_0_20 ).
fof(c_0_561_562,plain,
! [X19,X13,X12,X15,X3] :
( X13 = X19
| hBOOL(hAPP(hAPP(c_in(X3),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X12,X13,X19,X3,X15)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X19),c_FuncSet_Oextensional(X12,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_Oextensional(X12,X3,X15))) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_562_563,plain,
! [X30,X6,X21,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X12,X14,X21,X15,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X15,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_563_564,axiom,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15)))
| hBOOL(hAPP(hAPP(c_in(X3),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X12,X14,X13,X3,X15)),X12)) ),
c_0_23 ).
fof(c_0_564_565,axiom,
! [X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15)))
| hBOOL(hAPP(hAPP(c_in(X3),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X12,X14,X13,X3,X15)),X12)) ),
c_0_24 ).
fof(c_0_565_566,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_566_567,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X17
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_567_568,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X16
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_568_569,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X16
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_569_570,plain,
! [X9,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16))) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_570_571,plain,
! [X30,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_571_572,plain,
! [X30,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6))) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_572_573,plain,
! [X9,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X6,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_573_574,plain,
! [X45,X6,X13,X15,X3] :
( X6 = X45
| ~ c_Finite__Set_Ofold__graph(X13,X45,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X6,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_574_575,plain,
! [X19,X13,X12,X15,X3] :
( hAPP(X13,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X12,X13,X19,X3,X15)) != hAPP(X19,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X12,X13,X19,X3,X15))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X19),c_FuncSet_Oextensional(X12,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_Oextensional(X12,X3,X15)))
| X13 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_575_576,plain,
! [X9,X6,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X9,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_576_577,plain,
! [X16,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_577_578,plain,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X25),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanAtMost(X23,X24,X25,X22,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_578_579,plain,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X26),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanAtMost(X23,X24,X25,X22,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_579_580,plain,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X26),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastLessThan(X23,X24,X25,X22,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_580_581,plain,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X25),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastLessThan(X23,X24,X25,X22,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_581_582,axiom,
! [X56,X50,X27,X16,X17,X15,X3] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X56,X17,X16,X3,X15),X27,X50,X3,X15) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X56,X27,X50,X3,X15),X17,X16,X3,X15)
| X17 = X27 ),
c_0_41 ).
fof(c_0_582_583,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X16
| X6 = X16
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_583_584,plain,
! [X30,X6,X17,X10] :
( X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X17 ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_584_585,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X17
| X9 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_585_586,plain,
! [X9,X6,X16,X10] :
( X9 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_586_587,plain,
! [X9,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_587_588,plain,
! [X30,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_588_589,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X16
| X6 = X16
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_589_590,plain,
! [X9,X6,X16,X17,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X17
| X9 = X17
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_590_591,plain,
! [X30,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6))) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_591_592,plain,
! [X9,X6,X16,X10] :
( X6 = X16
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X6,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_592_593,plain,
! [X9,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X16,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X6
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16))) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_593_594,plain,
! [X30,X6,X17,X10] :
( X6 = X17
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_594_595,plain,
! [X30,X6,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X30 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X30,X6))) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_595_596,plain,
! [X9,X6,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X17,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X6))) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_596_597,plain,
! [X30,X6,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X30,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X30
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X30,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X30))) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_597_598,plain,
! [X30,X6,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X16
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X16))) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_598_599,plain,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X16,X17,X15,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X15)),c_Pair(X17,X16,X3,X15)),c_Relation_Oconverse(X18,X15,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_599_600,plain,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X16,X17,X15,X3)),c_Relation_Oconverse(X18,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X15)),c_Pair(X17,X16,X3,X15)),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_600_601,plain,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X15)),c_Pair(X17,X16,X3,X15)),c_Relation_Oconverse(X18,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X16,X17,X15,X3)),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_601_602,plain,
! [X13,X17,X12,X15,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X15)))
| ~ c_Fun_Oinj__on(X13,c_Set_Oinsert(X17,X12,X3),X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_602_603,plain,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X45
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X10,X45))) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_603_604,plain,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X45
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X10,X45))) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_604_605,plain,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X10,X45)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X45
| X9 = X45 ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_605_606,plain,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X10,X45)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| X9 = X45 ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_606_607,plain,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X10,X45)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X9 = X45
| X6 = X45 ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_607_608,plain,
! [X45,X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X10,X45)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| X6 = X45 ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_608_609,plain,
! [X9,X6,X18,X1,X2,X12,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_609_610,plain,
! [X18,X16,X17,X12,X3] :
( c_lessequals(c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_610_611,plain,
! [X18,X16,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),X12))
| ~ c_lessequals(c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_611_612,plain,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X16),c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X17,X16,X15,X3)),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_612_613,plain,
! [X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X9,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X10))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_613_614,plain,
! [X18,X16,X17,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X17,X16,X15,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),X15,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_614_615,plain,
! [X30,X6,X21,X14,X12,X15,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X12,X14,X21,X15,X3)))
| ~ hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_615_616,plain,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastLessThan(X23,X24,X25,X22,X3)))
| ~ hBOOL(hAPP(hAPP(X24,X26),X22))
| ~ hBOOL(hAPP(hAPP(X23,X25),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_616_617,plain,
! [X22,X23,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanAtMost(X23,X24,X25,X22,X3)))
| ~ hBOOL(hAPP(hAPP(X23,X26),X22))
| ~ hBOOL(hAPP(hAPP(X24,X25),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_617_618,plain,
! [X9,X6,X18,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X18,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_618_619,plain,
! [X18,X16,X17,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),X16),c_Relation_OImage(X18,X12,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X15)),c_Pair(X17,X16,X3,X15)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_619_620,plain,
! [X6,X18,X16,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X16),c_Relation_OImage(X18,X12,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X15,X3)),c_Pair(X6,X16,X15,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_620_621,plain,
! [X6,X16,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_621_622,plain,
! [X6,X16,X17,X10] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X17,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_622_623,plain,
! [X18,X16,X17,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_623_624,plain,
! [X9,X6,X18,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X18,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_624_625,plain,
! [X9,X6,X18,X12,X3] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X18,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X18,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_625_626,plain,
! [X9,X6,X13,X12,X15,X3] :
( c_Set_Oimage(c_Fun_Ofun__upd(X13,X6,X9,X15,X3),X12,X15,X3) = c_Set_Oinsert(X9,c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),tc_fun(X15,tc_bool)),X15,X3),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_626_627,plain,
! [X6,X18,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_627_628,plain,
! [X9,X30,X6,X18,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X6),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X6),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X30,X9,X3,X3)),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_628_629,plain,
! [X13,X17,X12,X15,X3] :
( c_Fun_Oinj__on(X13,c_Set_Oinsert(X17,X12,X3),X3,X15)
| hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X15)))
| ~ c_Fun_Oinj__on(X13,X12,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_629_630,plain,
! [X9,X6,X18,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X18,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_630_631,plain,
! [X9,X6,X18,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X18,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_631_632,plain,
! [X9,X6,X13,X12,X15,X3] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X13,X6,X9,X3,X15),X12,X3,X15)
| hBOOL(hAPP(hAPP(c_in(X15),X9),c_Set_Oimage(X13,X12,X3,X15)))
| ~ c_Fun_Oinj__on(X13,X12,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_632_633,plain,
! [X18,X16,X17,X12,X3] :
( c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X18,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X17,X16,X3,X3)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_633_634,plain,
! [X18,X14,X12,X15,X3] :
( c_lessequals(c_Relation_OImage(X18,X12,X15,X3),X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X15,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X18,X15,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),X3,X15)),tc_fun(X15,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_634_635,plain,
! [X13,X14,X12,X15,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3,X15),c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X14,X12,tc_fun(X3,tc_bool)),X3,X15),tc_fun(X15,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| ~ c_Fun_Oinj__on(X13,X14,X3,X15)
| ~ c_Fun_Oinj__on(X13,X12,X3,X15)
| c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_635_636,plain,
! [X9,X6,X18,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_636_637,plain,
! [X9,X6,X18,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_637_638,plain,
! [X7,X8,X3] :
( c_lessequals(X8,X7,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X8),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X7),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_638_639,plain,
! [X13,X14,X12,X15,X3] :
( c_lessequals(c_Set_Oimage(X13,X12,X3,X15),X14,tc_fun(X15,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,c_COMBK(X14,tc_fun(X15,tc_bool),X3),X3,X15))) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_639_640,plain,
! [X9,X6,X18,X12,X3] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X18,X3) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X18,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X9,X3,X3)),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_640_641,plain,
! [X41,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X41))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X41),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3)))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_641_642,plain,
! [X40,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X40))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X40),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3)))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_642_643,plain,
! [X30,X6,X10] :
( X30 = X6
| X6 = X30
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X30
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X30,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X30))) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_643_644,plain,
! [X30,X6,X10] :
( X30 = X6
| X30 = X6
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X30 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X10,X30,X6))) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_644_645,plain,
! [X6,X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X6)),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,c_COMBK(X14,tc_fun(X15,tc_bool),X3),X3,X15))) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_645_646,plain,
! [X13,X12,X15,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X3),X13,X3,X3,X15),X12,X15,X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Finite__Set_Osetsum(X13,X12,X15,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_646_647,plain,
! [X6,X27,X16,X14,X12,X28,X15,X3] :
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_fun(X28,tc_bool))),X16),X27))
| ~ hBOOL(hAPP(hAPP(hAPP(X14,X6),X16),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_647_648,plain,
! [X27,X16,X17,X14,X12,X28,X15,X3] :
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_fun(X28,tc_bool))),X16),X27))
| ~ hBOOL(hAPP(hAPP(hAPP(X14,X17),X16),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_648_649,plain,
! [X13,X16,X17,X15,X3] :
( hAPP(X13,X17) = X16
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Ovimage(X13,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),X3,X15))) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_649_650,plain,
! [X18,X14,X12,X15,X3] :
( c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X15,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X18,X15,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),X3,X15)),tc_fun(X15,tc_bool))
| ~ c_lessequals(c_Relation_OImage(X18,X12,X15,X3),X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_650_651,axiom,
! [X9,X6,X13,X12,X15,X3] :
( c_Set_Oimage(c_Fun_Ofun__upd(X13,X6,X9,X15,X3),X12,X15,X3) = c_Set_Oimage(X13,X12,X15,X3)
| hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
c_0_110 ).
fof(c_0_651_652,plain,
! [X18,X2,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_List_Osko__Equiv__Relations__XquotientE__1__1(X12,X2,X18,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),c_Equiv__Relations_Oquotient(X12,X18,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_652_653,plain,
! [X19,X13,X17,X12,X15,X3] :
( hAPP(c_Fun_Ooverride__on(X13,X19,X12,X3,X15),X17) = hAPP(X19,X17)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_653_654,plain,
! [X6,X21,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X12,X14,X21,X3)),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_654_655,plain,
! [X30,X21,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X12,X14,X21,X3)),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_655_656,axiom,
! [X19,X13,X17,X12,X15,X3] :
( hAPP(c_Fun_Ooverride__on(X13,X19,X12,X3,X15),X17) = hAPP(X13,X17)
| hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
c_0_115 ).
fof(c_0_656_657,plain,
! [X6,X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X6)),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15))) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_657_658,plain,
! [X6,X13,X14,X12,X15,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X6)),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_OPi(X12,X14,X3,X15))) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_658_659,plain,
! [X7,X8,X3] :
( c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X8),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X7),tc_fun(X3,tc_bool))
| ~ c_lessequals(X8,X7,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_659_660,axiom,
! [X45,X9,X6,X13,X15,X3] :
( hAPP(c_Fun_Ofun__upd(X13,X6,X9,X15,X3),X45) = hAPP(X13,X45)
| X45 = X6 ),
c_0_119 ).
fof(c_0_660_661,axiom,
! [X45,X9,X6,X13,X15,X3] :
( hAPP(c_Fun_Ofun__upd(X13,X6,X9,X3,X15),X45) = hAPP(X13,X45)
| X45 = X6 ),
c_0_120 ).
fof(c_0_661_662,plain,
! [X13,X14,X12,X15,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3,X15),c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X14,X12,tc_fun(X3,tc_bool)),X3,X15),tc_fun(X15,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| ~ c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_662_663,plain,
! [X39,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X39))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X39),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_663_664,plain,
! [X37,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X37))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X37),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X12,X21,X38,X3)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_664_665,plain,
! [X9,X6,X43,X44,X12,X15,X3] :
( hAPP(X44,X6) != hAPP(X44,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X15),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12))
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15)
| X6 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_665_666,axiom,
! [X30,X6,X10] :
( X30 = X6
| X30 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X30,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X10,X6))) ),
c_0_125 ).
fof(c_0_666_667,axiom,
! [X9,X6,X10] :
( X6 = X9
| X9 = X6
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X6,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X10,X6))) ),
c_0_126 ).
fof(c_0_667_668,plain,
! [X18,X2,X12,X3] :
( X2 = c_Relation_OImage(X18,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(X12,X2,X18,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),c_Equiv__Relations_Oquotient(X12,X18,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_668_669,plain,
! [X18,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Relation_OImage(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_669_670,plain,
! [X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_670_671,plain,
! [X6,X43,X44,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X43,X6)),X12))
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_671_672,plain,
! [X9,X43,X44,X12,X15,X3] :
( hAPP(X43,hAPP(X44,X9)) = X9
| ~ hBOOL(hAPP(hAPP(c_in(X15),X9),X12))
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_672_673,plain,
! [X13,X11,X14,X12,X15,X3] :
( c_Set_Oimage(X13,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X3,X15) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X13,X12,X3,X15),c_Set_Oimage(X13,X14,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X13,X11,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_673_674,plain,
! [X13,X11,X14,X12,X15,X3] :
( c_Set_Oimage(X13,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3,X15) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X13,X12,X3,X15),c_Set_Oimage(X13,X14,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X13,X11,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_674_675,plain,
! [X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X10,X6,X9)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_675_676,plain,
! [X9,X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X10,X6,X9)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin))
| X6 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_676_677,plain,
! [X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_677_678,plain,
! [X9,X6,X43,X44,X12,X15,X3] :
( hAPP(X43,X6) != hAPP(X43,X9)
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15)
| X6 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_678_679,plain,
! [X6,X43,X44,X12,X15,X3] :
( hAPP(X44,hAPP(X43,X6)) = X6
| ~ c_Typedef_Otype__definition(X43,X44,X12,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_679_680,plain,
! [X13,X17,X14,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Ovimage(X13,X14,X3,X15))) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_680_681,plain,
! [X13,X17,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Ovimage(X13,X12,X3,X15))) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_681_682,axiom,
! [X9,X6,X13,X15,X3] :
( c_Fun_Ofun__upd(X13,X6,X9,X3,X15) != X13
| hAPP(X13,X6) = X9 ),
c_0_141 ).
fof(c_0_682_683,plain,
! [X22,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X25),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanLessThan(X24,X25,X22,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_683_684,plain,
! [X22,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X26),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanLessThan(X24,X25,X22,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_684_685,plain,
! [X22,X23,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X26),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastAtMost(X23,X25,X22,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_685_686,plain,
! [X22,X23,X25,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X25),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastAtMost(X23,X25,X22,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_686_687,plain,
! [X18,X1,X2,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),c_Equiv__Relations_Oquotient(X12,X18,X3)))
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_687_688,axiom,
! [X7,X8,X3] :
( hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X8) != hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X7)
| X8 = X7 ),
c_0_147 ).
fof(c_0_688_689,plain,
! [X6,X13,X12,X15,X3] :
( hBOOL(hAPP(X12,hAPP(X13,X6)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X13,X12,X3,X15),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_689_690,plain,
! [X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X10,X6)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_690_691,plain,
! [X6,X10] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X10,X6)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X10),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_691_692,plain,
! [X6,X16,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X16),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X15,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),hAPP(X14,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_692_693,plain,
! [X16,X17,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),X16),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X16),hAPP(X14,X17)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_693_694,plain,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_694_695,plain,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_695_696,plain,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_696_697,plain,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_697_698,plain,
! [X13,X17,X14,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Ovimage(X13,X14,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X17)),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_698_699,plain,
! [X13,X17,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),X17),c_Set_Ovimage(X13,X12,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X17)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_699_700,plain,
! [X13,X17,X14,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),X17),c_Set_Ovimage(X13,X14,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X17)),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_700_701,plain,
! [X13,X14,X12,X15,X3] :
( c_Set_Oimage(X13,X12,X3,X15) != c_Set_Oimage(X13,X14,X3,X15)
| ~ c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15)
| X12 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_701_702,plain,
! [X6,X16,X14,X12,X15,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_bool)),X16))
| ~ hBOOL(hAPP(hAPP(X14,X6),X16))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_702_703,plain,
! [X16,X17,X14,X12,X15,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_bool)),X16))
| ~ hBOOL(hAPP(hAPP(X14,X17),X16))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_703_704,plain,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_704_705,plain,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_705_706,plain,
! [X6,X13,X12,X20,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X20),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X6)),c_Set_Oimage(X13,X12,X20,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_706_707,plain,
! [X6,X13,X12,X15,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X6)),c_Set_Oimage(X13,X12,X15,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_707_708,plain,
! [X6,X13,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X6)),c_Set_Oimage(X13,X12,X15,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_708_709,plain,
! [X6,X13,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X15),hAPP(X13,X6)),c_Set_Oimage(X13,X12,X3,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_709_710,plain,
! [X22,X23,X25,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatLeastAtMost(X23,X25,X22,X3)))
| ~ hBOOL(hAPP(hAPP(X23,X26),X22))
| ~ hBOOL(hAPP(hAPP(X23,X25),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_710_711,plain,
! [X22,X24,X25,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThanLessThan(X24,X25,X22,X3)))
| ~ hBOOL(hAPP(hAPP(X24,X26),X22))
| ~ hBOOL(hAPP(hAPP(X24,X25),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_711_712,plain,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_712_713,plain,
! [X6,X13,X14,X12,X15,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),hAPP(X13,X6)),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12))
| ~ c_lessequals(c_Set_Oimage(X13,X12,X15,X3),X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_713_714,plain,
! [X6,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_714_715,plain,
! [X6,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_715_716,plain,
! [X6,X54,X14,X12,X15,X3] :
( c_lessequals(hAPP(X12,X6),X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X54))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X12,X15,tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_716_717,plain,
! [X6,X21,X14,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X12,X14,X21,X3)))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_717_718,plain,
! [X30,X21,X14,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X12,X14,X21,X3)))
| ~ hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_718_719,plain,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_719_720,plain,
! [X13,X14,X12,X15,X3] :
( c_lessequals(c_Set_Oimage(X13,X12,X3,X15),c_Set_Oimage(X13,X14,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_720_721,plain,
! [X6,X13,X12,X15,X3] :
( ~ c_lessequals(X6,X12,tc_fun(X15,tc_bool))
| c_lessequals(c_Set_Oimage(X13,X6,X15,X3),c_Set_Oimage(X13,X12,X15,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_721_722,plain,
! [X13,X14,X12,X15,X3] :
( c_lessequals(c_Set_Ovimage(X13,X12,X15,X3),c_Set_Ovimage(X13,X14,X15,X3),tc_fun(X15,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_722_723,axiom,
! [X13,X17,X12,X3] :
( c_Finite__Set_Osetsum(X13,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X13,X12,X3,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
c_0_182 ).
fof(c_0_723_724,plain,
! [X6,X13,X12,X15,X3] :
( hBOOL(hAPP(c_Set_Ovimage(X13,X12,X3,X15),X6))
| ~ hBOOL(hAPP(X12,hAPP(X13,X6))) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_724_725,plain,
! [X51,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X51))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X51),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)),X12))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_725_726,plain,
! [X51,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X51))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X51),X12))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)),X12))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_726_727,plain,
! [X30,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_727_728,plain,
! [X30,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X30))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_728_729,plain,
! [X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X12,X11,X3)),X11))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_729_730,plain,
! [X6,X14,X12,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_730_731,plain,
! [X29,X54,X12,X15,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X12,X29),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X12,X3,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X12,X3,tc_fun(X15,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X29),X54)) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_731_732,plain,
! [X6,X13,X12,X15,X3] :
( c_Set_Oinsert(hAPP(X13,X6),c_Set_Oimage(X13,X12,X3,X15),X15) = c_Set_Oimage(X13,X12,X3,X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_732_733,axiom,
! [X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OInf__class_OInf(X11,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X12,X11,X3)),X11)) ),
c_0_192 ).
fof(c_0_733_734,plain,
! [X42,X38,X21,X12,X3] :
( hBOOL(hAPP(X38,X42))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X42),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_734_735,plain,
! [X42,X38,X21,X12,X3] :
( hBOOL(hAPP(X21,X42))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X42),X12))
| ~ hBOOL(hAPP(X38,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X38,X3)))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X12,X21,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_735_736,plain,
! [X2,X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),X11))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OInf__class_OInf(X11,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_736_737,plain,
! [X6,X13,X12,X15,X3] :
( hAPP(X13,X6) = c_HOL_Oundefined(X15)
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X15)),X13),c_FuncSet_Oextensional(X12,X3,X15))) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_737_738,plain,
! [X8] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X8),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_738_739,plain,
! [X6,X17,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_739_740,plain,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Lattices_Olower__semilattice__class_Oinf(X12,c_Collect(X21,X3),tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_740_741,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),c_Lattices_Oupper__semilattice__class_Osup(X6,X45,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_741_742,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X45,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_742_743,axiom,
! [X11,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)),X12,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X12,X11,X3)),X11)) ),
c_0_202 ).
fof(c_0_743_744,plain,
! [X13,X14,X12,X15,X3] :
( c_Fun_Oinj__on(X13,X14,X3,X15)
| ~ c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_744_745,plain,
! [X13,X14,X12,X15,X3] :
( c_Fun_Oinj__on(X13,X12,X3,X15)
| ~ c_Fun_Oinj__on(X13,c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_745_746,plain,
! [X2,X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X2),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_746_747,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_747_748,plain,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Lattices_Olower__semilattice__class_Oinf(X12,c_Collect(X21,X3),tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_748_749,axiom,
! [X50,X27,X16,X17,X3] :
( c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X27,c_Set_Oinsert(X50,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X17 = X50
| X17 = X27 ),
c_0_208 ).
fof(c_0_749_750,axiom,
! [X50,X27,X16,X17,X3] :
( c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X27,c_Set_Oinsert(X50,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X27
| X17 = X27 ),
c_0_209 ).
fof(c_0_750_751,axiom,
! [X50,X27,X16,X17,X3] :
( c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X27,c_Set_Oinsert(X50,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X17 = X50
| X16 = X50 ),
c_0_210 ).
fof(c_0_751_752,axiom,
! [X50,X27,X16,X17,X3] :
( c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X27,c_Set_Oinsert(X50,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X27
| X16 = X50 ),
c_0_211 ).
fof(c_0_752_753,plain,
! [X6,X11,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)),X12,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X12,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X6),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_753_754,plain,
! [X16,X17,X3] :
( X16 = X17
| ~ hBOOL(hAPP(hAPP(c_in(X3),X16),c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3))) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_754_755,plain,
! [X27,X14,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_755_756,plain,
! [X17,X14,X12,X15,X3] :
( c_lessequals(hAPP(X14,X17),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X3,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_756_757,plain,
! [X13,X17,X12,X15,X3] :
( c_Fun_Oinj__on(X13,X12,X3,X15)
| ~ c_Fun_Oinj__on(X13,c_Set_Oinsert(X17,X12,X3),X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_757_758,axiom,
! [X11,X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Oupper__semilattice__class_Osup(X14,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X11,X12,tc_fun(X3,tc_bool)) ),
c_0_217 ).
fof(c_0_758_759,plain,
! [X17,X12,X3] :
( c_Set_Oinsert(X17,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_759_760,plain,
! [X13,X14,X12,X15,X3] :
( c_Fun_Oinj__on(X13,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3,X15)
| ~ c_Fun_Oinj__on(X13,X12,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_760_761,axiom,
! [X48,X16,X49,X17,X15,X3] :
( c_Pair(X17,X16,X3,X15) != c_Pair(X49,X48,X3,X15)
| X17 = X49 ),
c_0_220 ).
fof(c_0_761_762,axiom,
! [X48,X16,X49,X17,X15,X3] :
( c_Pair(X17,X16,X3,X15) != c_Pair(X49,X48,X3,X15)
| X16 = X48 ),
c_0_221 ).
fof(c_0_762_763,plain,
! [X9,X6,X13,X12,X15,X3] :
( hAPP(X13,X6) != hAPP(X13,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| X6 = X9
| ~ c_Fun_Oinj__on(X13,X12,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_763_764,plain,
! [X9,X6,X13,X12,X15,X3] :
( hAPP(X13,X6) != hAPP(X13,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Fun_Oinj__on(X13,X12,X3,X15)
| X6 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_764_765,plain,
! [X30,X6,X13,X12,X15,X3] :
( hAPP(X13,X6) != hAPP(X13,X30)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X30),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_Fun_Oinj__on(X13,X12,X3,X15)
| X6 = X30 ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_765_766,plain,
! [X9,X6,X13,X12,X15,X3] :
( hAPP(X13,X6) != hAPP(X13,X9)
| ~ c_Fun_Oinj__on(X13,X12,X3,X15)
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_in(X3),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_766_767,plain,
! [X13,X14,X12,X15,X3] :
( c_Fun_Oinj__on(X13,X12,X3,X15)
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X13,X14,X3,X15) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_767_768,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_768_769,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_769_770,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_770_771,plain,
! [X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OInf__class_OInf(X11,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X12,X11,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_771_772,plain,
! [X17,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ hBOOL(hAPP(X21,X17)) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_772_773,plain,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexI__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(X21,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_773_774,plain,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexE__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_774_775,plain,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X12,X21,X3)),X12))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_775_776,plain,
! [X26,X52,X12,X15,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X15)
| c_lessequals(hAPP(X52,X26),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X52,X3,X15),X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_776_777,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_777_778,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_778_779,plain,
! [X27,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12))) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_779_780,plain,
! [X6,X21,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(X21,X6))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XballE__1__1(X12,X21,X3)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_780_781,plain,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),c_Lattices_Olower__semilattice__class_Oinf(X12,c_Collect(X21,X3),tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_781_782,plain,
! [X11,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X12,X11,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_782_783,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_783_784,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_784_785,plain,
! [X6,X14,X12,X15,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X15,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hAPP(X14,X6) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_785_786,plain,
! [X6,X14,X12,X15,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X14,X15,tc_fun(X3,tc_bool))
| hAPP(X14,X6) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_786_787,plain,
! [X6,X27,X12,X15,X3] :
( c_Set_Oimage(c_COMBK(X27,X15,X3),X12,X3,X15) = c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_787_788,plain,
! [X6,X17,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_788_789,plain,
! [X55,X11,X14,X12,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X11,X55,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X55,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_789_790,plain,
! [X55,X11,X14,X12,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X11,X55,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X55,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_790_791,plain,
! [X55,X11,X14,X12,X3] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X11,X55,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X55,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_791_792,plain,
! [X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X12),c_Set_OPow(X14,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_792_793,plain,
! [X16,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| X17 = X16
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Oinsert(X16,X12,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_793_794,plain,
! [X14,X12,X3] :
( c_lessequals(X14,X12,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_794_795,plain,
! [X14,X12,X3] :
( c_lessequals(X14,c_Complete__Lattice_OSup__class_OSup(X12,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_795,plain,
! [X14,X12,X3] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X12,tc_fun(X3,tc_bool)),X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_796,plain,
! [X16,X17,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_797,plain,
! [X16,X17,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X17,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_798,plain,
! [X11,X14,X12,X3] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X14,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_799,plain,
! [X11,X14,X12,X3] :
( c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X14,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_800,plain,
! [X6,X12,X3] :
( X12 = c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_801,plain,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(X14,X6))
| hBOOL(hAPP(X12,X6))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_802,plain,
! [X23,X29,X26,X3] :
( hBOOL(hAPP(hAPP(X23,X26),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatMost(X23,X29,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_803,plain,
! [X24,X29,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X29),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThan(X24,X29,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_804,plain,
! [X24,X29,X26,X3] :
( hBOOL(hAPP(hAPP(X24,X26),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OlessThan(X24,X29,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_805,plain,
! [X11,X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Oupper__semilattice__class_Osup(X14,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X12,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_806,plain,
! [X6,X21,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XballE__1__1(X12,X21,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_807,plain,
! [X6,X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_808,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_809,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_810,plain,
! [X17,X11,X14,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X17,X14,X3),X11,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X17,c_Lattices_Olower__semilattice__class_Oinf(X14,X11,tc_fun(X3,tc_bool)),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_811,plain,
! [X17,X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,c_Set_Oinsert(X17,X14,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X17,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_812,plain,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(X14,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_813,plain,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(X12,X6))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_814,plain,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_815,plain,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_816,plain,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_817,axiom,
! [X11,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X12,X11,X3),X12,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X11,tc_fun(X3,tc_bool)),X12,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_277 ).
fof(c_0_818,axiom,
! [X6,X12,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X12,X3),c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X12
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
c_0_278 ).
fof(c_0_819,plain,
! [X6,X14,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_820,axiom,
! [X6,X14,X12,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X6,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)),X3)
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
c_0_280 ).
fof(c_0_821,axiom,
! [X27,X12,X15,X3] :
( c_Set_Oimage(c_COMBK(X27,X3,X15),X12,X15,X3) = c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
c_0_281 ).
fof(c_0_822,plain,
! [X16,X17,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Oinsert(X16,X12,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_823,plain,
! [X16,X17,X14,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Set_Oinsert(X16,X14,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_824,axiom,
! [X27,X12,X15,X3] :
( c_Set_Ovimage(c_COMBK(X27,X15,X3),X12,X3,X15) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X15),X27),X12)) ),
c_0_284 ).
fof(c_0_825,plain,
! [X11,X14,X12,X3] :
( c_HOL_Ominus__class_Ominus(X14,c_HOL_Ominus__class_Ominus(X11,X12,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X12
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_826,plain,
! [X11,X14,X12,X3] :
( c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X12,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_827,plain,
! [X11,X14,X12,X3] :
( c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X12,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_828,plain,
! [X11,X14,X12,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_829,plain,
! [X11,X14,X12,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_830,plain,
! [X6,X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_831,plain,
! [X6,X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_832,plain,
! [X6,X14,X12,X3] :
( c_lessequals(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_833,plain,
! [X6,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_834,axiom,
! [X27,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12)))
| hBOOL(hAPP(hAPP(c_in(X3),X27),X12)) ),
c_0_294 ).
fof(c_0_835,plain,
! [X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X12),c_Set_OPow(X14,X3)))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_836,plain,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XbexI__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ hBOOL(hAPP(X21,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_837,plain,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XbexE__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_838,plain,
! [X17,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12))
| ~ hBOOL(hAPP(X21,X17)) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_839,plain,
! [X6,X21,X12,X3] :
( hBOOL(hAPP(X21,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X12,X21,X3)))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_840,axiom,
! [X13,X12,X15,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X13,X12,X15,X3)
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
c_0_300 ).
fof(c_0_841,axiom,
! [X13,X12,X15,X3] :
( c_Set_Oimage(X13,X12,X15,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
c_0_301 ).
fof(c_0_842,plain,
! [X14,X12,X3] :
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_843,plain,
! [X14,X12,X3] :
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_844,axiom,
! [X27,X12,X15,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,c_COMBK(X27,tc_fun(X3,tc_bool),X15),X15,tc_fun(X3,tc_bool)) = X27
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
c_0_304 ).
fof(c_0_845,plain,
! [X23,X29,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OatMost(X23,X29,X3)))
| ~ hBOOL(hAPP(hAPP(X23,X26),X29)) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_846,plain,
! [X24,X29,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OgreaterThan(X24,X29,X3)))
| ~ hBOOL(hAPP(hAPP(X24,X29),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_847,plain,
! [X24,X29,X26,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X26),c_SetInterval_Oord_OlessThan(X24,X29,X3)))
| ~ hBOOL(hAPP(hAPP(X24,X26),X29)) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_848,plain,
! [X11,X14,X12,X3] :
( c_lessequals(X12,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_849,plain,
! [X11,X14,X12,X3] :
( c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_850,plain,
! [X11,X14,X12,X3] :
( c_lessequals(X11,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_851,plain,
! [X11,X14,X12,X3] :
( c_lessequals(X11,X12,tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_852,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),c_Lattices_Oupper__semilattice__class_Osup(X6,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_853,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X6,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X9,X6,X3),c_Lattices_Oupper__semilattice__class_Osup(X45,X6,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_854,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_855,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X6,X3),c_Lattices_Olower__semilattice__class_Oinf(X45,X6,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_856,plain,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)),X6))
| ~ hBOOL(hAPP(X14,X6))
| ~ hBOOL(hAPP(X12,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_857,plain,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_858,plain,
! [X6,X14,X12,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_859,plain,
! [X9,X6,X12,X3] :
( hBOOL(hAPP(X12,X6))
| X9 = X6
| ~ hBOOL(hAPP(c_Set_Oinsert(X9,X12,X3),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_860,plain,
! [X17,X55,X11,X3] :
( c_lessequals(c_Set_Oinsert(X17,X11,X3),c_Set_Oinsert(X17,X55,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X11,X55,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_861,plain,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_862,plain,
! [X6,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X6,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_863,plain,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_lessequals(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_864,plain,
! [X53,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X53),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X53),X12))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_865,plain,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_866,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_867,plain,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_868,plain,
! [X27,X14,X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X27),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X27),X12))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_869,plain,
! [X52,X12,X15,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X15)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,c_COMBK(X52,X15,X3),X3,X15) = X52
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_870,axiom,
! [X6,X14,X12,X3] :
( c_Set_Oinsert(X6,X12,X3) != c_Set_Oinsert(X6,X14,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X6),X14))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X12))
| X12 = X14 ),
c_0_330 ).
fof(c_0_871,plain,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X6))
| ~ hBOOL(hAPP(X12,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_872,plain,
! [X6,X14,X12,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)),X6))
| ~ hBOOL(hAPP(X14,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_873,plain,
! [X6,X21,X3] :
( ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_874,axiom,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14),tc_fun(X3,tc_bool)) ),
c_0_334 ).
fof(c_0_875,axiom,
! [X17,X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,c_Set_Oinsert(X17,X14,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
c_0_335 ).
fof(c_0_876,axiom,
! [X17,X11,X14,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X17,X14,X3),X11,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X14,X11,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X17),X11)) ),
c_0_336 ).
fof(c_0_877,plain,
! [X6,X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X6,X12,X3),X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_878,plain,
! [X6,X21,X3] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_879,plain,
! [X12,X3] :
( X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_880,plain,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,c_HOL_Ominus__class_Ominus(X14,X12,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X14
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_881,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X3)
| ~ c_lessequals(X6,X16,X3)
| ~ c_lessequals(X6,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_882,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3)
| ~ c_lessequals(X6,X45,X3)
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_883,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3)
| ~ c_lessequals(X6,X45,X3)
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_884,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X6,X3)
| ~ c_lessequals(X16,X6,X3)
| ~ c_lessequals(X17,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_885,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X6,X3)
| ~ c_lessequals(X45,X6,X3)
| ~ c_lessequals(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_886,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3)
| ~ c_lessequals(X9,X45,X3)
| ~ c_lessequals(X6,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_887,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_888,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_889,axiom,
! [X16,X17,X3] :
( c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X17 = X16 ),
c_0_349 ).
fof(c_0_890,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_891,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X6,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_892,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X6,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_893,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X9,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_894,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X45,X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_895,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X6,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_896,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X6,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_897,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X45,X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_898,plain,
! [X11,X14,X12,X3] :
( c_lessequals(X12,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_899,plain,
! [X11,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X14,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_900,plain,
! [X11,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X14,X11,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_901,plain,
! [X11,X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X14,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_902,plain,
! [X46,X9,X47,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| c_lessequals(X46,X47,X3)
| ~ c_lessequals(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_903,plain,
! [X46,X9,X47,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| c_lessequals(X9,X6,X3)
| ~ c_lessequals(X46,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_904,plain,
! [X46,X9,X47,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| c_HOL_Oord__class_Oless(X47,X46,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_905,plain,
! [X46,X9,X47,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X47,X46,X3) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_906,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X16,X6,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_907,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,X45,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_908,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,X45,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_909,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X17,X6,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_910,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,X17,X3)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_911,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,X16,X3)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_912,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,X9,X3)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_913,plain,
! [X45,X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X6,X45,X3)
| ~ c_lessequals(X6,c_Lattices_Olower__semilattice__class_Oinf(X9,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_914,plain,
! [X16,X14,X12,X3] :
( c_lessequals(X12,c_Set_Oinsert(X16,X14,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_915,plain,
! [X19,X13,X15,X3] :
( ~ class_HOL_Oord(X15)
| c_HOL_Oord__class_Oless(X13,X19,tc_fun(X3,X15))
| c_lessequals(X19,X13,tc_fun(X3,X15))
| ~ c_lessequals(X13,X19,tc_fun(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_916,plain,
! [X9,X6,X12,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X9,X12,X3),X6))
| ~ hBOOL(hAPP(X12,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_917,plain,
! [X17,X21,X3] :
( hBOOL(hAPP(X21,X17))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),c_Collect(X21,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_918,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X17,X16,X3)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_919,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X17,X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_920,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_921,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X9),X3) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_922,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_923,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X9),X3) ),
inference(fof_simplification,[status(thm)],[c_0_383]) ).
fof(c_0_924,plain,
! [X19,X13,X15,X3] :
( ~ class_HOL_Oord(X15)
| ~ c_lessequals(X19,X13,tc_fun(X3,X15))
| ~ c_HOL_Oord__class_Oless(X13,X19,tc_fun(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_925,plain,
! [X6,X12,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(X6,c_Complete__Lattice_OSup__class_OSup(X12,X3),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_926,plain,
! [X6,X12,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X12,X3),X6,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_386]) ).
fof(c_0_927,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X3)
| ~ c_lessequals(X6,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_928,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X3)
| ~ c_lessequals(X6,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_929,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X6,X3)
| ~ c_lessequals(X17,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_930,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X6,X3)
| ~ c_lessequals(X16,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_931,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_HOL_Oord__class_Oless(X6,c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_932,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_HOL_Oord__class_Oless(X6,c_Lattices_Oupper__semilattice__class_Osup(X17,X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_933,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(X16,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_934,plain,
! [X6,X16,X17,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(X17,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_935,plain,
! [X14,X12,X3] :
( X12 = X14
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_936,plain,
! [X14,X12,X3] :
( X12 = X14
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_937,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X16,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3)
| ~ c_lessequals(X17,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_938,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X17,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3)
| ~ c_lessequals(X16,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_939,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X17,X3)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_940,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X16,X3)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_941,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X16,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3)
| ~ c_HOL_Oord__class_Oless(X17,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_401]) ).
fof(c_0_942,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X17,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X3)
| ~ c_HOL_Oord__class_Oless(X16,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3) ),
inference(fof_simplification,[status(thm)],[c_0_402]) ).
fof(c_0_943,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X17,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_403]) ).
fof(c_0_944,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_945,axiom,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X3,tc_bool)) = X12 ),
c_0_405 ).
fof(c_0_946,plain,
! [X6,X19,X13,X15,X3] :
( ~ class_HOL_Oord(X15)
| c_lessequals(hAPP(X13,X6),hAPP(X19,X6),X15)
| ~ c_lessequals(X13,X19,tc_fun(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_947,axiom,
! [X30,X6,X3] :
( c_Set_Oinsert(X6,X30,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X6),X30)) ),
c_0_407 ).
fof(c_0_948,plain,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X45,X6,X3)
| ~ c_lessequals(X45,X9,X3)
| ~ c_lessequals(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_949,plain,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X45,X6,X3)
| ~ c_lessequals(X45,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_950,plain,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X45,X6,X3)
| ~ c_HOL_Oord__class_Oless(X45,X9,X3)
| ~ c_lessequals(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_951,plain,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X6,X45,X3)
| ~ c_lessequals(X9,X45,X3)
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_952,plain,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X6,X45,X3)
| ~ c_HOL_Oord__class_Oless(X9,X45,X3)
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_953,plain,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X6,X45,X3)
| ~ c_lessequals(X9,X45,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_954,plain,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X45,X6,X3)
| ~ c_HOL_Oord__class_Oless(X45,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_955,plain,
! [X45,X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X6,X45,X3)
| ~ c_HOL_Oord__class_Oless(X9,X45,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_415]) ).
fof(c_0_956,plain,
! [X17,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X17 ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_957,plain,
! [X17,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X17 ),
inference(fof_simplification,[status(thm)],[c_0_417]) ).
fof(c_0_958,plain,
! [X12,X3] :
( X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_959,plain,
! [X18,X12,X3] :
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X12,X18,X3),tc_fun(X3,tc_bool)) = X12
| ~ c_Equiv__Relations_Oequiv(X12,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_960,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3)
| ~ c_lessequals(X17,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_961,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17),X3)
| ~ c_HOL_Oord__class_Oless(X17,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_962,plain,
! [X17,X12,X3] :
( c_Set_Oinsert(X17,X12,X3) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_422]) ).
fof(c_0_963,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_423]) ).
fof(c_0_964,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_965,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_425]) ).
fof(c_0_966,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_967,plain,
! [X19,X13,X15,X3] :
( ~ class_HOL_Oord(X15)
| c_lessequals(X13,X19,tc_fun(X3,X15))
| ~ c_HOL_Oord__class_Oless(X13,X19,tc_fun(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_968,axiom,
! [X14,X12,X3] :
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X12) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X14)
| X12 = X14 ),
c_0_428 ).
fof(c_0_969,plain,
! [X17,X12,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X17,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X17,c_Complete__Lattice_OSup__class_OSup(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_429]) ).
fof(c_0_970,plain,
! [X17,X12,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X17,X12,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X17,c_Complete__Lattice_OInf__class_OInf(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_971,plain,
! [X17,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X17),c_Collect(X21,X3)))
| ~ hBOOL(hAPP(X21,X17)) ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_972,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| c_lessequals(X9,X6,X3)
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_973,plain,
! [X14,X12,X3] :
( c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool))
| X12 = X14
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_974,plain,
! [X14,X12,X3] :
( X12 = X14
| c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool))
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_434]) ).
fof(c_0_975,axiom,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) != X14
| c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
c_0_435 ).
fof(c_0_976,plain,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) = X12
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_977,plain,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) = X14
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_978,plain,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) = X12
| ~ c_lessequals(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_979,plain,
! [X14,X12,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X12,X14,tc_fun(X3,tc_bool)) = X14
| ~ c_lessequals(X14,X12,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_980,plain,
! [X6,X38,X21,X3] :
( hBOOL(hAPP(X38,X6))
| ~ hBOOL(hAPP(X21,X6))
| ~ c_lessequals(X21,X38,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_981,plain,
! [X6,X38,X21,X3] :
( hBOOL(hAPP(X38,X6))
| ~ c_lessequals(X21,X38,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X21,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_982,plain,
! [X14,X12,X3] :
( c_lessequals(X12,X14,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_442]) ).
fof(c_0_983,plain,
! [X6,X7,X3] :
( hBOOL(hAPP(X7,X6))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_443]) ).
fof(c_0_984,axiom,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_444 ).
fof(c_0_985,axiom,
! [X14,X12,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X12,X14,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_445 ).
fof(c_0_986,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_HOL_Ominus__class_Ominus(X17,X16,X3)) = c_HOL_Ominus__class_Ominus(X16,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_987,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| X6 = X9
| ~ c_lessequals(X6,X9,X3)
| ~ c_lessequals(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_988,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| X6 = X9
| ~ c_lessequals(X9,X6,X3)
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_989,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| X6 = X9
| ~ c_lessequals(X9,X6,X3)
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_990,plain,
! [X46,X47,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X6,X3) != c_HOL_Ominus__class_Ominus(X47,X46,X3)
| X47 = X46 ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_991,plain,
! [X9,X30,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X30,X9,X3) != c_HOL_Ominus__class_Ominus(X6,X6,X3)
| X30 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_992,plain,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X6,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_993,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_lessequals(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_453]) ).
fof(c_0_994,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_454]) ).
fof(c_0_995,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_455]) ).
fof(c_0_996,plain,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X17,X16,X3)
| ~ c_HOL_Oord__class_Oless(X16,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_456]) ).
fof(c_0_997,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_457]) ).
fof(c_0_998,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_458]) ).
fof(c_0_999,plain,
! [X16,X17,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_459]) ).
fof(c_0_1000,plain,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_460]) ).
fof(c_0_1001,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_461]) ).
fof(c_0_1002,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_462]) ).
fof(c_0_1003,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_463]) ).
fof(c_0_1004,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_464]) ).
fof(c_0_1005,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_465]) ).
fof(c_0_1006,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3),X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_466]) ).
fof(c_0_1007,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_467]) ).
fof(c_0_1008,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_468]) ).
fof(c_0_1009,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1010,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1011,plain,
! [X6,X7,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X7))
| ~ hBOOL(hAPP(X7,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_471]) ).
fof(c_0_1012,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ominus__class_Ominus(X6,X9,X3) = c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X9),X3) ),
inference(fof_simplification,[status(thm)],[c_0_472]) ).
fof(c_0_1013,plain,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X17,X3)
| X17 = X16
| ~ c_lessequals(X16,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_473]) ).
fof(c_0_1014,plain,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X17,X3)
| ~ c_lessequals(X16,X17,X3)
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_474]) ).
fof(c_0_1015,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_475]) ).
fof(c_0_1016,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| X6 = X9
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_476]) ).
fof(c_0_1017,plain,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X17,X16,X3)
| X17 = X16
| ~ c_lessequals(X17,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_477]) ).
fof(c_0_1018,plain,
! [X16,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X17,X16,X3)
| ~ c_lessequals(X17,X16,X3)
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_478]) ).
fof(c_0_1019,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| X6 = X9
| ~ c_lessequals(X6,X9,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_479]) ).
fof(c_0_1020,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X6,X9,X3)
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_480]) ).
fof(c_0_1021,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) != X9
| c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_481]) ).
fof(c_0_1022,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) != X6
| c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1023,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) = X9
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_483]) ).
fof(c_0_1024,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) = X6
| ~ c_lessequals(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_484]) ).
fof(c_0_1025,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) = X6
| ~ c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_485]) ).
fof(c_0_1026,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) = X9
| ~ c_lessequals(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_486]) ).
fof(c_0_1027,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_487]) ).
fof(c_0_1028,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X6,X9,X3)
| ~ c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_488]) ).
fof(c_0_1029,plain,
! [X9,X6,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X9,X6,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| X6 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_489]) ).
fof(c_0_1030,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X9,X6,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_490]) ).
fof(c_0_1031,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X6,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| X6 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_491]) ).
fof(c_0_1032,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X6,X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_492]) ).
fof(c_0_1033,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| X6 = X9
| c_HOL_Oord__class_Oless(X6,X9,X3)
| c_HOL_Oord__class_Oless(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_493]) ).
fof(c_0_1034,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X6,X9,X3)
| c_lessequals(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_494]) ).
fof(c_0_1035,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X6,X3)
| c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_495]) ).
fof(c_0_1036,plain,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X6,X6,X3)
| c_lessequals(X6,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_496]) ).
fof(c_0_1037,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X6,X3)
| c_HOL_Oord__class_Oless(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_497]) ).
fof(c_0_1038,plain,
! [X9,X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X6,X3)
| c_lessequals(X6,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_498]) ).
fof(c_0_1039,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_499]) ).
fof(c_0_1040,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X9,X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_500]) ).
fof(c_0_1041,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) = c_Lattices_Olower__semilattice__class_Oinf(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_501]) ).
fof(c_0_1042,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X9,X3) = c_Lattices_Olower__semilattice__class_Oinf(X9,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_502]) ).
fof(c_0_1043,plain,
! [X6,X21,X3] :
( c_Collect(X21,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X21,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_503]) ).
fof(c_0_1044,plain,
! [X6,X21,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X21,X3)
| ~ hBOOL(hAPP(X21,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_504]) ).
fof(c_0_1045,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X12,X14,X3) != c_Orderings_Obot__class_Obot(X3)
| X12 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_505]) ).
fof(c_0_1046,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X12,X14,X3) != c_Orderings_Obot__class_Obot(X3)
| X14 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_506]) ).
fof(c_0_1047,plain,
! [X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6),X3) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_507]) ).
fof(c_0_1048,plain,
! [X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6),X6,X3) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_508]) ).
fof(c_0_1049,plain,
! [X6,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_509]) ).
fof(c_0_1050,plain,
! [X6,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_510]) ).
fof(c_0_1051,plain,
! [X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_511]) ).
fof(c_0_1052,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_512]) ).
fof(c_0_1053,plain,
! [X9,X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X9)
| X6 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_513]) ).
fof(c_0_1054,plain,
! [X16,X17,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16)
| X17 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_514]) ).
fof(c_0_1055,plain,
! [X6,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X3),X3) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_515]) ).
fof(c_0_1056,plain,
! [X6,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X3),X6,X3) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_516]) ).
fof(c_0_1057,plain,
! [X6,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X6,X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_517]) ).
fof(c_0_1058,plain,
! [X6,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X3),X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_518]) ).
fof(c_0_1059,plain,
! [X6,X3] :
( ~ class_Orderings_Obot(X3)
| c_lessequals(c_Orderings_Obot__class_Obot(X3),X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_519]) ).
fof(c_0_1060,plain,
! [X17,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17)) = X17 ),
inference(fof_simplification,[status(thm)],[c_0_520]) ).
fof(c_0_1061,plain,
! [X6,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X6)) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_521]) ).
fof(c_0_1062,plain,
! [X16,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X16 = hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_522]) ).
fof(c_0_1063,plain,
! [X17,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X17 = hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X17)) ),
inference(fof_simplification,[status(thm)],[c_0_523]) ).
fof(c_0_1064,plain,
! [X16,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X16)) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_524]) ).
fof(c_0_1065,plain,
! [X6,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_525]) ).
fof(c_0_1066,plain,
! [X6,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_526]) ).
fof(c_0_1067,plain,
! [X6,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X6,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_527]) ).
fof(c_0_1068,plain,
! [X6,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X6,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_528]) ).
fof(c_0_1069,plain,
! [X4,X5] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X4,X5))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_529]) ).
fof(c_0_1070,plain,
! [X4,X5] :
( class_Lattices_Oupper__semilattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_530]) ).
fof(c_0_1071,plain,
! [X4,X5] :
( class_Lattices_Olower__semilattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_531]) ).
fof(c_0_1072,plain,
! [X4,X5] :
( class_Lattices_Odistrib__lattice(tc_fun(X4,X5))
| ~ class_Lattices_Odistrib__lattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_532]) ).
fof(c_0_1073,plain,
! [X4,X5] :
( class_Lattices_Obounded__lattice(tc_fun(X4,X5))
| ~ class_Lattices_Obounded__lattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_533]) ).
fof(c_0_1074,plain,
! [X4,X5] :
( class_Lattices_Oboolean__algebra(tc_fun(X4,X5))
| ~ class_Lattices_Oboolean__algebra(X5) ),
inference(fof_simplification,[status(thm)],[c_0_534]) ).
fof(c_0_1075,plain,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_535]) ).
fof(c_0_1076,plain,
! [X4,X5] :
( class_Lattices_Olattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_536]) ).
fof(c_0_1077,plain,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_537]) ).
fof(c_0_1078,plain,
! [X4,X5] :
( class_Orderings_Obot(tc_fun(X4,X5))
| ~ class_Orderings_Obot(X5) ),
inference(fof_simplification,[status(thm)],[c_0_538]) ).
fof(c_0_1079,plain,
! [X4,X5] :
( class_HOL_Oord(tc_fun(X4,X5))
| ~ class_HOL_Oord(X5) ),
inference(fof_simplification,[status(thm)],[c_0_539]) ).
fof(c_0_1080,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45] :
( c_Complete__Lattice_Ocomplete__lattice(X43,X44,c_COMBC(X39,X45,X45,tc_bool),c_COMBC(X40,X45,X45,tc_bool),X38,X41,X37,X42,X45)
| ~ c_Complete__Lattice_Ocomplete__lattice(X44,X43,X39,X40,X41,X38,X42,X37,X45) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_1081,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45,X46,X47] :
( hAPP(X45,c_Set_Oinsert(X44,c_Set_Oinsert(X43,c_Orderings_Obot__class_Obot(tc_fun(X47,tc_bool)),X47),X47)) = hAPP(hAPP(X38,X44),X43)
| ~ c_Complete__Lattice_Ocomplete__lattice(X46,X45,X39,X40,X41,X38,X42,X37,X47) ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_1082,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45,X46,X47] :
( hAPP(X46,c_Set_Oinsert(X44,c_Set_Oinsert(X43,c_Orderings_Obot__class_Obot(tc_fun(X47,tc_bool)),X47),X47)) = hAPP(hAPP(X41,X44),X43)
| ~ c_Complete__Lattice_Ocomplete__lattice(X46,X45,X39,X40,X41,X38,X42,X37,X47) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_1083,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45,X46,X47] :
( hBOOL(hAPP(hAPP(X40,hAPP(X45,X46)),X37))
| ~ hBOOL(hAPP(hAPP(c_in(X47),X37),X46))
| ~ c_Complete__Lattice_Ocomplete__lattice(X45,X44,X40,X41,X42,X39,X43,X38,X47) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_543])])]) ).
fof(c_0_1084,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45,X46,X47] :
( hBOOL(hAPP(hAPP(X40,X37),hAPP(X44,X46)))
| ~ hBOOL(hAPP(hAPP(c_in(X47),X37),X46))
| ~ c_Complete__Lattice_Ocomplete__lattice(X45,X44,X40,X41,X42,X39,X43,X38,X47) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_544])])]) ).
fof(c_0_1085,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45,X46] :
( hAPP(X44,c_Set_Oinsert(X43,c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool)),X46)) = X43
| ~ c_Complete__Lattice_Ocomplete__lattice(X45,X44,X39,X40,X41,X38,X42,X37,X46) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_1086,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45,X46] :
( hAPP(X45,c_Set_Oinsert(X43,c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool)),X46)) = X43
| ~ c_Complete__Lattice_Ocomplete__lattice(X45,X44,X39,X40,X41,X38,X42,X37,X46) ),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_1087,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45,X46,X47] :
( hAPP(X44,c_Set_Oinsert(X43,X46,X47)) = hAPP(hAPP(X38,X43),hAPP(X44,X46))
| ~ c_Complete__Lattice_Ocomplete__lattice(X45,X44,X39,X40,X41,X38,X42,X37,X47) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_1088,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45,X46,X47] :
( hAPP(X45,c_Set_Oinsert(X43,X46,X47)) = hAPP(hAPP(X41,X43),hAPP(X45,X46))
| ~ c_Complete__Lattice_Ocomplete__lattice(X45,X44,X39,X40,X41,X38,X42,X37,X47) ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_1089,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45] :
( hAPP(X43,c_Orderings_Obot__class_Obot(tc_fun(X45,tc_bool))) = X42
| ~ c_Complete__Lattice_Ocomplete__lattice(X44,X43,X39,X40,X41,X38,X42,X37,X45) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_1090,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45] :
( hAPP(X44,c_Orderings_Obot__class_Obot(tc_fun(X45,tc_bool))) = X37
| ~ c_Complete__Lattice_Ocomplete__lattice(X44,X43,X39,X40,X41,X38,X42,X37,X45) ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_1091,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X20,X19)),X16),c_FuncSet_OPi(X18,X17,X20,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(X19),hAPP(X16,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X18,X17,X16,X20,X19))),hAPP(X17,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X18,X17,X16,X20,X19)))) ),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_1092,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X20,X19)),X16),c_FuncSet_OPi(X18,X17,X20,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(X19),hAPP(X16,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X18,X17,X16,X20,X19))),hAPP(X17,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X18,X17,X16,X20,X19)))) ),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_1093,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X20,X19)),X16),c_FuncSet_OPi(X18,c_COMBK(X17,tc_fun(X19,tc_bool),X20),X20,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(X19),hAPP(X16,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X18,X17,X16,X20,X19))),X17)) ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_1094,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( c_Nitpick_Ofold__graph_H(X49,X46,X50,hAPP(hAPP(X49,X48),X47),X52,X51)
| ~ c_Nitpick_Ofold__graph_H(X49,X46,c_HOL_Ominus__class_Ominus(X50,c_Set_Oinsert(X48,c_Orderings_Obot__class_Obot(tc_fun(X52,tc_bool)),X52),tc_fun(X52,tc_bool)),X47,X52,X51)
| ~ hBOOL(hAPP(hAPP(c_in(X52),X48),X50)) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_1095,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( c_Finite__Set_Ofold__graph(X49,X46,X50,hAPP(hAPP(X49,X48),X47),X52,X51)
| ~ hBOOL(hAPP(hAPP(c_in(X52),X48),X50))
| ~ c_Finite__Set_Ofold__graph(X49,X46,c_HOL_Ominus__class_Ominus(X50,c_Set_Oinsert(X48,c_Orderings_Obot__class_Obot(tc_fun(X52,tc_bool)),X52),tc_fun(X52,tc_bool)),X47,X52,X51) ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_1096,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( c_Finite__Set_Ofold__graph(X49,X46,c_Set_Oinsert(X48,X50,X52),hAPP(hAPP(X49,X48),X47),X52,X51)
| ~ c_Finite__Set_Ofold__graph(X49,X46,X50,X47,X52,X51)
| hBOOL(hAPP(hAPP(c_in(X52),X48),X50)) ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_1097,plain,
! [X19,X20,X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X24,X24)),c_Pair(X22,X21,X24,X24)),X20))
| ~ hBOOL(hAPP(hAPP(c_in(X24),X19),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X20,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24),c_Relation_OImage(X20,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24),tc_fun(X24,tc_bool))))
| ~ c_Equiv__Relations_Oequiv(X23,X20,X24) ),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_1098,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X21,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_1099,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X20,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_1100,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X20,X19)),X16),c_FuncSet_OPi(X18,c_COMBK(X17,tc_fun(X19,tc_bool),X20),X20,X19)))
| hBOOL(hAPP(hAPP(c_in(X20),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X18,X17,X16,X20,X19)),X18)) ),
inference(variable_rename,[status(thm)],[c_0_560]) ).
fof(c_0_1101,plain,
! [X20,X21,X22,X23,X24] :
( X21 = X20
| hBOOL(hAPP(hAPP(c_in(X24),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X22,X21,X20,X24,X23)),X22))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X24,X23)),X20),c_FuncSet_Oextensional(X22,X24,X23)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X24,X23)),X21),c_FuncSet_Oextensional(X22,X24,X23))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_561])])]) ).
fof(c_0_1102,plain,
! [X31,X32,X33,X34,X35,X36,X37] :
( hBOOL(hAPP(hAPP(c_in(X37),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X35,X34,X33,X36,X37)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X35,X34,X36,tc_fun(X37,tc_bool))))
| ~ hBOOL(hAPP(X33,X31))
| ~ hBOOL(hAPP(hAPP(c_in(X37),X31),hAPP(X34,X32)))
| ~ hBOOL(hAPP(hAPP(c_in(X36),X32),X35)) ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_1103,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X20,X19)),X16),c_FuncSet_OPi(X18,X17,X20,X19)))
| hBOOL(hAPP(hAPP(c_in(X20),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X18,X17,X16,X20,X19)),X18)) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_1104,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X20,X19)),X16),c_FuncSet_OPi(X18,X17,X20,X19)))
| hBOOL(hAPP(hAPP(c_in(X20),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X18,X17,X16,X20,X19)),X18)) ),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_1105,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X19 = X21
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_1106,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X20,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X18 = X21
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_1107,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X18 = X20
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X21,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_1108,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X19 = X20
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_1109,plain,
! [X17,X18,X19,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X20))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X20))
| X18 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X20),c_Arrow__Order__Mirabelle_OLin))
| X18 = X19
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X20,X18,X19))) ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_1110,plain,
! [X31,X32,X33,X34] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X34))
| X31 = X32
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X34),c_Arrow__Order__Mirabelle_OLin))
| X33 = X32
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X34,X33,X32)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X34)) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_1111,plain,
! [X31,X32,X33,X34] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X33,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X34))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X33,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X34))
| X31 = X32
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X34),c_Arrow__Order__Mirabelle_OLin))
| X33 = X32
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X34,X33,X32))) ),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_1112,plain,
! [X17,X18,X19,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X20))
| X18 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X20),c_Arrow__Order__Mirabelle_OLin))
| X18 = X19
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X20,X18,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X20)) ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_1113,plain,
! [X46,X47,X48,X49,X50] :
( X47 = X46
| ~ c_Finite__Set_Ofold__graph(X48,X46,c_Orderings_Obot__class_Obot(tc_fun(X50,tc_bool)),X47,X50,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_573])])]) ).
fof(c_0_1114,plain,
! [X20,X21,X22,X23,X24] :
( hAPP(X21,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X22,X21,X20,X24,X23)) != hAPP(X20,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X22,X21,X20,X24,X23))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X24,X23)),X20),c_FuncSet_Oextensional(X22,X24,X23)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X24,X23)),X21),c_FuncSet_Oextensional(X22,X24,X23)))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_1115,plain,
! [X11,X12,X13] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X12,X11,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X13))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X11,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X13))
| X12 = X11
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X13),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_1116,plain,
! [X18,X19,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X20))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X20))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X20),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_1117,plain,
! [X27,X28,X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(X29,X30),X31))
| ~ hBOOL(hAPP(hAPP(c_in(X32),X31),c_SetInterval_Oord_OgreaterThanAtMost(X28,X29,X30,X27,X32))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_577])])]) ).
fof(c_0_1118,plain,
! [X27,X28,X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(X28,X31),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X32),X31),c_SetInterval_Oord_OgreaterThanAtMost(X28,X29,X30,X27,X32))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_578])])]) ).
fof(c_0_1119,plain,
! [X27,X28,X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(X29,X31),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X32),X31),c_SetInterval_Oord_OatLeastLessThan(X28,X29,X30,X27,X32))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_579])])]) ).
fof(c_0_1120,plain,
! [X27,X28,X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(X28,X30),X31))
| ~ hBOOL(hAPP(hAPP(c_in(X32),X31),c_SetInterval_Oord_OatLeastLessThan(X28,X29,X30,X27,X32))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_580])])]) ).
fof(c_0_1121,plain,
! [X57,X58,X59,X60,X61,X62,X63] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X57,X61,X60,X63,X62),X59,X58,X63,X62) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X57,X59,X58,X63,X62),X61,X60,X63,X62)
| X61 = X59 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_581])])]) ).
fof(c_0_1122,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X18 = X20
| X19 = X20
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_1123,plain,
! [X31,X32,X33,X34] :
( X31 = X32
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X34,X33,X32)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X34),c_Arrow__Order__Mirabelle_OLin))
| X33 = X32
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X33,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X34))
| X31 = X33 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_583])])]) ).
fof(c_0_1124,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X19 = X21
| X18 = X21
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_1125,plain,
! [X17,X18,X19,X20] :
( X17 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X20,X18,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X20),c_Arrow__Order__Mirabelle_OLin))
| X18 = X19
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X20))
| X17 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_585])])]) ).
fof(c_0_1126,plain,
! [X18,X19,X20,X21] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X21,X20,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X21),c_Arrow__Order__Mirabelle_OLin))
| X20 = X19
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X20,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_1127,plain,
! [X31,X32,X33,X34] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X34,X32,X33)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X34),c_Arrow__Order__Mirabelle_OLin))
| X32 = X33
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X33,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X34)) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_1128,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X18 = X20
| X19 = X20
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_1129,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X22,X21,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X22))
| X19 = X21
| X18 = X21
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X22),c_Arrow__Order__Mirabelle_OLin))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_1130,plain,
! [X31,X32,X33,X34] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X33,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X34))
| X31 = X32
| X31 = X32
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X34),c_Arrow__Order__Mirabelle_OLin))
| X33 = X32
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X34,X33,X32))) ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_1131,plain,
! [X17,X18,X19,X20] :
( X18 = X19
| X18 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X20),c_Arrow__Order__Mirabelle_OLin))
| X18 = X19
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X20,X18,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_591])])]) ).
fof(c_0_1132,plain,
! [X17,X18,X19,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X20))
| X17 = X18
| X18 = X17
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X20),c_Arrow__Order__Mirabelle_OLin))
| X18 = X19
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X20,X18,X19))) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_1133,plain,
! [X31,X32,X33,X34] :
( X32 = X33
| X31 = X32
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X34),c_Arrow__Order__Mirabelle_OLin))
| X33 = X32
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X34,X33,X32)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_593])])]) ).
fof(c_0_1134,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X33))
| X31 = X32
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X33),c_Arrow__Order__Mirabelle_OLin))
| X31 = X32
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X33,X31,X32))) ),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_1135,plain,
! [X18,X19,X20,X21] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X20,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X21))
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X21),c_Arrow__Order__Mirabelle_OLin))
| X20 = X19
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X21,X20,X19))) ),
inference(variable_rename,[status(thm)],[c_0_595]) ).
fof(c_0_1136,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X32,X31,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X33))
| X32 = X31
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X33),c_Arrow__Order__Mirabelle_OLin))
| X32 = X31
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X32,X31,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X33,X32,X31))) ),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_1137,plain,
! [X31,X32,X33,X34] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X33,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X34))
| X31 = X32
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X34),c_Arrow__Order__Mirabelle_OLin))
| X32 = X33
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X34,X32,X33))) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_1138,plain,
! [X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X22,X23)),c_Pair(X20,X21,X22,X23)),X19))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X22)),c_Pair(X21,X20,X23,X22)),c_Relation_Oconverse(X19,X22,X23))) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_1139,plain,
! [X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X22,X23)),c_Pair(X20,X21,X22,X23)),c_Relation_Oconverse(X19,X23,X22)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X22)),c_Pair(X21,X20,X23,X22)),X19)) ),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_1140,plain,
! [X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X22)),c_Pair(X21,X20,X23,X22)),c_Relation_Oconverse(X19,X22,X23)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X22,X23)),c_Pair(X20,X21,X22,X23)),X19)) ),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_1141,plain,
! [X18,X19,X20,X21,X22] :
( ~ hBOOL(hAPP(hAPP(c_in(X21),hAPP(X18,X19)),c_Set_Oimage(X18,c_HOL_Ominus__class_Ominus(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),tc_fun(X22,tc_bool)),X22,X21)))
| ~ c_Fun_Oinj__on(X18,c_Set_Oinsert(X19,X20,X22),X22,X21) ),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_1142,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X49))
| X48 = X46
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X49,X46))) ),
inference(variable_rename,[status(thm)],[c_0_602]) ).
fof(c_0_1143,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X49))
| X47 = X46
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X49,X46))) ),
inference(variable_rename,[status(thm)],[c_0_603]) ).
fof(c_0_1144,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X49,X46)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X49))
| X48 = X46
| X47 = X46 ),
inference(variable_rename,[status(thm)],[c_0_604]) ).
fof(c_0_1145,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X49,X46)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X49))
| X48 = X47
| X47 = X46 ),
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_1146,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X49,X46)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X49))
| X47 = X46
| X48 = X46 ),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_1147,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X49,X46)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X48,X47,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X49))
| X48 = X47
| X48 = X46 ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_1148,plain,
! [X19,X20,X21,X22,X23,X24,X25] :
( X23 = X22
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X25,X25)),c_Pair(X20,X19,X25,X25)),X21))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X19),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X20),X23))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X25,tc_bool)),X22),c_Equiv__Relations_Oquotient(X24,X21,X25)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X25,tc_bool)),X23),c_Equiv__Relations_Oquotient(X24,X21,X25)))
| ~ c_Equiv__Relations_Oequiv(X24,X21,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_608])])]) ).
fof(c_0_1149,plain,
! [X19,X20,X21,X22,X23] :
( c_lessequals(c_Relation_OImage(X19,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23),c_Relation_OImage(X19,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23),tc_fun(X23,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X21,X20,X23,X23)),X19))
| ~ c_Equiv__Relations_Oequiv(X22,X19,X23) ),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_1150,plain,
! [X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X21,X20,X23,X23)),X19))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X20),X22))
| ~ c_lessequals(c_Relation_OImage(X19,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23),c_Relation_OImage(X19,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23),tc_fun(X23,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X22,X19,X23) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_1151,plain,
! [X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(X23),X20),c_Relation_OImage(X19,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22,X23)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X22,X23)),c_Pair(X21,X20,X22,X23)),X19)) ),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_1152,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X11,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X13))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X12,X11,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X13))
| X12 = X11
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X13),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_1153,plain,
! [X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X22,X23)),c_Pair(X21,X20,X22,X23)),X19))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X20),c_Relation_OImage(X19,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22,X23))) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1154,plain,
! [X31,X32,X33,X34,X35,X36,X37] :
( hBOOL(hAPP(X33,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X35,X34,X33,X36,X37)))
| ~ hBOOL(hAPP(X33,X31))
| ~ hBOOL(hAPP(hAPP(c_in(X37),X31),hAPP(X34,X32)))
| ~ hBOOL(hAPP(hAPP(c_in(X36),X32),X35)) ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1155,plain,
! [X27,X28,X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_in(X32),X31),c_SetInterval_Oord_OatLeastLessThan(X28,X29,X30,X27,X32)))
| ~ hBOOL(hAPP(hAPP(X29,X31),X27))
| ~ hBOOL(hAPP(hAPP(X28,X30),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_615])])]) ).
fof(c_0_1156,plain,
! [X27,X28,X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_in(X32),X31),c_SetInterval_Oord_OgreaterThanAtMost(X28,X29,X30,X27,X32)))
| ~ hBOOL(hAPP(hAPP(X28,X31),X27))
| ~ hBOOL(hAPP(hAPP(X29,X30),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_616])])]) ).
fof(c_0_1157,plain,
! [X19,X20,X21,X22,X23] :
( c_Relation_OImage(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23) = c_Relation_OImage(X21,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X20,X19,X23,X23)),X21))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X19),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X20),X22))
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_617]) ).
fof(c_0_1158,plain,
! [X19,X20,X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_in(X23),X20),c_Relation_OImage(X19,X22,X24,X23)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X24,X23)),c_Pair(X21,X20,X24,X23)),X19))
| ~ hBOOL(hAPP(hAPP(c_in(X24),X21),X22)) ),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_1159,plain,
! [X19,X20,X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_in(X24),X21),c_Relation_OImage(X20,X22,X23,X24)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X24)),c_Pair(X19,X21,X23,X24)),X20))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X19),X22)) ),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_1160,plain,
! [X18,X19,X20,X21] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X21,X20,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X21),c_Arrow__Order__Mirabelle_OLin))
| X20 = X19 ),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1161,plain,
! [X18,X19,X20,X21] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X18,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X21,X20,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X21),c_Arrow__Order__Mirabelle_OLin))
| X20 = X19 ),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1162,plain,
! [X19,X20,X21,X22,X23] :
( c_Relation_OImage(X19,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23) = c_Relation_OImage(X19,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X21,X20,X23,X23)),X19))
| ~ c_Equiv__Relations_Oequiv(X22,X19,X23) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1163,plain,
! [X19,X20,X21,X22,X23] :
( c_Relation_OImage(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23) = c_Relation_OImage(X21,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X20,X19,X23,X23)),X21))
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1164,plain,
! [X19,X20,X21,X22,X23] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X21,X23) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X21,X23)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X20,X19,X23,X23)),X21))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X19),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X20),X22))
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1165,plain,
! [X16,X17,X18,X19,X20,X21] :
( c_Set_Oimage(c_Fun_Ofun__upd(X18,X17,X16,X20,X21),X19,X20,X21) = c_Set_Oinsert(X16,c_Set_Oimage(X18,c_HOL_Ominus__class_Ominus(X19,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),tc_fun(X20,tc_bool)),X20,X21),X21)
| ~ hBOOL(hAPP(hAPP(c_in(X20),X17),X19)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_625])])]) ).
fof(c_0_1166,plain,
! [X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X22,tc_bool)),c_Relation_OImage(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22,X22)),c_Equiv__Relations_Oquotient(X21,X20,X22)))
| ~ hBOOL(hAPP(hAPP(c_in(X22),X19),X21)) ),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1167,plain,
! [X31,X32,X33,X34,X35,X36] :
( ~ hBOOL(hAPP(hAPP(c_in(X36),X31),X33))
| ~ hBOOL(hAPP(hAPP(c_in(X36),X32),X33))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X36,tc_bool)),X33),c_Equiv__Relations_Oquotient(X35,X34,X36)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X36,tc_bool)),X33),c_Equiv__Relations_Oquotient(X35,X34,X36)))
| ~ c_Equiv__Relations_Oequiv(X35,X34,X36)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X36,X36)),c_Pair(X32,X31,X36,X36)),X34)) ),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1168,plain,
! [X18,X19,X20,X21,X22] :
( c_Fun_Oinj__on(X18,c_Set_Oinsert(X19,X20,X22),X22,X21)
| hBOOL(hAPP(hAPP(c_in(X21),hAPP(X18,X19)),c_Set_Oimage(X18,c_HOL_Ominus__class_Ominus(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),tc_fun(X22,tc_bool)),X22,X21)))
| ~ c_Fun_Oinj__on(X18,X20,X22,X21) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1169,plain,
! [X19,X20,X21,X22,X23] :
( c_Relation_OImage(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23) != c_Relation_OImage(X21,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23)
| ~ hBOOL(hAPP(hAPP(c_in(X23),X19),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X20),X22))
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X20,X19,X23,X23)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1170,plain,
! [X19,X20,X21,X22,X23] :
( c_Relation_OImage(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23) != c_Relation_OImage(X21,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23)
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X20,X19,X23,X23)),X21))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X19),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1171,plain,
! [X16,X17,X18,X19,X20,X21] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X18,X17,X16,X21,X20),X19,X21,X20)
| hBOOL(hAPP(hAPP(c_in(X20),X16),c_Set_Oimage(X18,X19,X21,X20)))
| ~ c_Fun_Oinj__on(X18,X19,X21,X20) ),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1172,plain,
! [X19,X20,X21,X22,X23] :
( c_Relation_OImage(X19,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23) != c_Relation_OImage(X19,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23,X23)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X21,X20,X23,X23)),X19))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X20),X22))
| ~ c_Equiv__Relations_Oequiv(X22,X19,X23) ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1173,plain,
! [X19,X20,X21,X22,X23] :
( c_lessequals(c_Relation_OImage(X19,X21,X22,X23),X20,tc_fun(X23,tc_bool))
| ~ c_lessequals(X21,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X22,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X19,X22,X23),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X23,tc_bool)),X20),X23,X22)),tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1174,plain,
! [X16,X17,X18,X19,X20] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X16,c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X20,tc_bool)),X20,X19),c_Set_Oimage(X16,c_HOL_Ominus__class_Ominus(X17,X18,tc_fun(X20,tc_bool)),X20,X19),tc_fun(X19,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| ~ c_Fun_Oinj__on(X16,X17,X20,X19)
| ~ c_Fun_Oinj__on(X16,X18,X20,X19)
| c_Fun_Oinj__on(X16,c_Lattices_Oupper__semilattice__class_Osup(X18,X17,tc_fun(X20,tc_bool)),X20,X19) ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1175,plain,
! [X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(X23),X19),X22))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X20,X19,X23,X23)),X21))
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1176,plain,
! [X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(X23),X20),X22))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X20,X19,X23,X23)),X21))
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1177,plain,
! [X9,X10,X11] :
( c_lessequals(X10,X9,tc_fun(X11,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X11),X11,tc_fun(X11,tc_bool),tc_bool),X10),hAPP(c_COMBC(c_in(X11),X11,tc_fun(X11,tc_bool),tc_bool),X9),tc_fun(X11,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1178,plain,
! [X16,X17,X18,X19,X20] :
( c_lessequals(c_Set_Oimage(X16,X18,X20,X19),X17,tc_fun(X19,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X20,X19)),X16),c_FuncSet_OPi(X18,c_COMBK(X17,tc_fun(X19,tc_bool),X20),X20,X19))) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1179,plain,
! [X19,X20,X21,X22,X23] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X21,X23) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X21,X23)
| ~ hBOOL(hAPP(hAPP(c_in(X23),X19),X22))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X20),X22))
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X23,X23)),c_Pair(X20,X19,X23,X23)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1180,plain,
! [X42,X43,X44,X45,X46] :
( hBOOL(hAPP(X43,X42))
| ~ hBOOL(hAPP(hAPP(c_in(X46),X42),X45))
| ~ hBOOL(hAPP(X43,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X45,X44,X43,X46)))
| ~ hBOOL(hAPP(X44,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X45,X44,X43,X46))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_640])])]) ).
fof(c_0_1181,plain,
! [X41,X42,X43,X44,X45] :
( hBOOL(hAPP(X43,X41))
| ~ hBOOL(hAPP(hAPP(c_in(X45),X41),X44))
| ~ hBOOL(hAPP(X42,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X44,X43,X42,X45)))
| ~ hBOOL(hAPP(X43,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X44,X43,X42,X45))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_641])])]) ).
fof(c_0_1182,plain,
! [X31,X32,X33] :
( X31 = X32
| X32 = X31
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X33),c_Arrow__Order__Mirabelle_OLin))
| X32 = X31
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X32,X31,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X33,X32,X31))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_642])])]) ).
fof(c_0_1183,plain,
! [X31,X32,X33] :
( X31 = X32
| X31 = X32
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X33),c_Arrow__Order__Mirabelle_OLin))
| X31 = X32
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X33,X31,X32))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_643])])]) ).
fof(c_0_1184,plain,
! [X16,X17,X18,X19,X20,X21] :
( hBOOL(hAPP(hAPP(c_in(X20),hAPP(X17,X16)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X16),X19))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X21,X20)),X17),c_FuncSet_OPi(X19,c_COMBK(X18,tc_fun(X20,tc_bool),X21),X21,X20))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_644])])]) ).
fof(c_0_1185,plain,
! [X16,X17,X18,X19] :
( ~ class_OrderedGroup_Oab__group__add(X19)
| c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X19),X16,X19,X19,X18),X17,X18,X19) = hAPP(c_HOL_Ouminus__class_Ouminus(X19),c_Finite__Set_Osetsum(X16,X17,X18,X19)) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1186,plain,
! [X29,X30,X31,X32,X33,X34,X35,X36] :
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33,X32,X36,tc_fun(X35,tc_fun(X34,tc_bool))),X31),X30))
| ~ hBOOL(hAPP(hAPP(hAPP(X32,X29),X31),X30))
| ~ hBOOL(hAPP(hAPP(c_in(X36),X29),X33)) ),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_1187,plain,
! [X29,X30,X31,X32,X33,X34,X35,X36] :
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33,X32,X36,tc_fun(X35,tc_fun(X34,tc_bool))),X30),X29))
| ~ hBOOL(hAPP(hAPP(hAPP(X32,X31),X30),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X36),X31),X33)) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1188,plain,
! [X18,X19,X20,X21,X22] :
( hAPP(X18,X20) = X19
| ~ hBOOL(hAPP(hAPP(c_in(X22),X20),c_Set_Ovimage(X18,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21),X22,X21))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_648])])]) ).
fof(c_0_1189,plain,
! [X19,X20,X21,X22,X23] :
( c_lessequals(X21,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X22,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X19,X22,X23),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X23,tc_bool)),X20),X23,X22)),tc_fun(X22,tc_bool))
| ~ c_lessequals(c_Relation_OImage(X19,X21,X22,X23),X20,tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1190,plain,
! [X16,X17,X18,X19,X20,X21] :
( c_Set_Oimage(c_Fun_Ofun__upd(X18,X17,X16,X20,X21),X19,X20,X21) = c_Set_Oimage(X18,X19,X20,X21)
| hBOOL(hAPP(hAPP(c_in(X20),X17),X19)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_650])])]) ).
fof(c_0_1191,plain,
! [X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(X22),c_List_Osko__Equiv__Relations__XquotientE__1__1(X21,X20,X19,X22)),X21))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X22,tc_bool)),X20),c_Equiv__Relations_Oquotient(X21,X19,X22))) ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1192,plain,
! [X20,X21,X22,X23,X24,X25] :
( hAPP(c_Fun_Ooverride__on(X21,X20,X23,X25,X24),X22) = hAPP(X20,X22)
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X23)) ),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1193,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(hAPP(c_in(X26),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X25,X24,X23,X26)),c_Lattices_Oupper__semilattice__class_Osup(X25,X24,tc_fun(X26,tc_bool))))
| ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X26),X22),X24)) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1194,plain,
! [X31,X32,X33,X34,X35] :
( hBOOL(hAPP(hAPP(c_in(X35),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X34,X33,X32,X35)),c_Lattices_Oupper__semilattice__class_Osup(X34,X33,tc_fun(X35,tc_bool))))
| ~ hBOOL(hAPP(X32,X31))
| ~ hBOOL(hAPP(hAPP(c_in(X35),X31),X34)) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1195,plain,
! [X20,X21,X22,X23,X24,X25] :
( hAPP(c_Fun_Ooverride__on(X21,X20,X23,X25,X24),X22) = hAPP(X21,X22)
| hBOOL(hAPP(hAPP(c_in(X25),X22),X23)) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1196,plain,
! [X16,X17,X18,X19,X20,X21] :
( hBOOL(hAPP(hAPP(c_in(X20),hAPP(X17,X16)),hAPP(X18,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X16),X19))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X21,X20)),X17),c_FuncSet_OPi(X19,X18,X21,X20))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_656])])]) ).
fof(c_0_1197,plain,
! [X16,X17,X18,X19,X20,X21] :
( ~ hBOOL(hAPP(hAPP(c_in(X21),X16),X19))
| hBOOL(hAPP(hAPP(c_in(X20),hAPP(X17,X16)),hAPP(X18,X16)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X21,X20)),X17),c_FuncSet_OPi(X19,X18,X21,X20))) ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1198,plain,
! [X9,X10,X11] :
( c_lessequals(hAPP(c_COMBC(c_in(X11),X11,tc_fun(X11,tc_bool),tc_bool),X10),hAPP(c_COMBC(c_in(X11),X11,tc_fun(X11,tc_bool),tc_bool),X9),tc_fun(X11,tc_bool))
| ~ c_lessequals(X10,X9,tc_fun(X11,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1199,plain,
! [X46,X47,X48,X49,X50,X51] :
( hAPP(c_Fun_Ofun__upd(X49,X48,X47,X50,X51),X46) = hAPP(X49,X46)
| X46 = X48 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_659])])]) ).
fof(c_0_1200,plain,
! [X46,X47,X48,X49,X50,X51] :
( hAPP(c_Fun_Ofun__upd(X49,X48,X47,X51,X50),X46) = hAPP(X49,X46)
| X46 = X48 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_660])])]) ).
fof(c_0_1201,plain,
! [X16,X17,X18,X19,X20] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X16,c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X20,tc_bool)),X20,X19),c_Set_Oimage(X16,c_HOL_Ominus__class_Ominus(X17,X18,tc_fun(X20,tc_bool)),X20,X19),tc_fun(X19,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| ~ c_Fun_Oinj__on(X16,c_Lattices_Oupper__semilattice__class_Osup(X18,X17,tc_fun(X20,tc_bool)),X20,X19) ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1202,plain,
! [X40,X41,X42,X43,X44] :
( hBOOL(hAPP(X41,X40))
| ~ hBOOL(hAPP(hAPP(c_in(X44),X40),X43))
| hBOOL(hAPP(hAPP(c_in(X44),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X43,X42,X41,X44)),X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_662])])]) ).
fof(c_0_1203,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(X41,X39))
| ~ hBOOL(hAPP(hAPP(c_in(X43),X39),X42))
| hBOOL(hAPP(hAPP(c_in(X43),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X42,X41,X40,X43)),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_663])])]) ).
fof(c_0_1204,plain,
! [X45,X46,X47,X48,X49,X50,X51] :
( hAPP(X48,X46) != hAPP(X48,X45)
| ~ hBOOL(hAPP(hAPP(c_in(X50),X45),X49))
| ~ hBOOL(hAPP(hAPP(c_in(X50),X46),X49))
| ~ c_Typedef_Otype__definition(X47,X48,X49,X51,X50)
| X46 = X45 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_664])])]) ).
fof(c_0_1205,plain,
! [X31,X32,X33] :
( X31 = X32
| X31 = X32
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X31,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X33,X32))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_665])])]) ).
fof(c_0_1206,plain,
! [X11,X12,X13] :
( X12 = X11
| X11 = X12
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X12,X11,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X13,X12))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_666])])]) ).
fof(c_0_1207,plain,
! [X19,X20,X21,X22] :
( X20 = c_Relation_OImage(X19,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(X21,X20,X19,X22),c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22,X22)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X22,tc_bool)),X20),c_Equiv__Relations_Oquotient(X21,X19,X22))) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1208,plain,
! [X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(X22),X20),c_Relation_OImage(X19,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22,X22)))
| ~ hBOOL(hAPP(hAPP(c_in(X22),X20),X21))
| ~ c_Equiv__Relations_Oequiv(X21,X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1209,plain,
! [X11] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X11),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X11,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1210,plain,
! [X45,X46,X47,X48,X49,X50] :
( hBOOL(hAPP(hAPP(c_in(X49),hAPP(X46,X45)),X48))
| ~ c_Typedef_Otype__definition(X46,X47,X48,X50,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_670])])]) ).
fof(c_0_1211,plain,
! [X45,X46,X47,X48,X49,X50] :
( hAPP(X46,hAPP(X47,X45)) = X45
| ~ hBOOL(hAPP(hAPP(c_in(X49),X45),X48))
| ~ c_Typedef_Otype__definition(X46,X47,X48,X50,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_671])])]) ).
fof(c_0_1212,plain,
! [X16,X17,X18,X19,X20,X21] :
( c_Set_Oimage(X16,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X21,tc_bool)),X21,X20) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X16,X19,X21,X20),c_Set_Oimage(X16,X18,X21,X20),tc_fun(X20,tc_bool))
| ~ c_lessequals(X18,X17,tc_fun(X21,tc_bool))
| ~ c_lessequals(X19,X17,tc_fun(X21,tc_bool))
| ~ c_Fun_Oinj__on(X16,X17,X21,X20) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1213,plain,
! [X16,X17,X18,X19,X20,X21] :
( c_Set_Oimage(X16,c_HOL_Ominus__class_Ominus(X19,X18,tc_fun(X21,tc_bool)),X21,X20) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X16,X19,X21,X20),c_Set_Oimage(X16,X18,X21,X20),tc_fun(X20,tc_bool))
| ~ c_lessequals(X18,X17,tc_fun(X21,tc_bool))
| ~ c_lessequals(X19,X17,tc_fun(X21,tc_bool))
| ~ c_Fun_Oinj__on(X16,X17,X21,X20) ),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1214,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X13,X12,X11)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X13),c_Arrow__Order__Mirabelle_OLin))
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1215,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X13,X12,X11)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X13),c_Arrow__Order__Mirabelle_OLin))
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1216,plain,
! [X11] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X11,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X11),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1217,plain,
! [X45,X46,X47,X48,X49,X50,X51] :
( hAPP(X47,X46) != hAPP(X47,X45)
| ~ c_Typedef_Otype__definition(X47,X48,X49,X51,X50)
| X46 = X45 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_677])])]) ).
fof(c_0_1218,plain,
! [X45,X46,X47,X48,X49,X50] :
( hAPP(X47,hAPP(X46,X45)) = X45
| ~ c_Typedef_Otype__definition(X46,X47,X48,X50,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_678])])]) ).
fof(c_0_1219,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(X21),hAPP(X18,X19)),X20))
| ~ hBOOL(hAPP(hAPP(c_in(X22),X19),c_Set_Ovimage(X18,X20,X22,X21))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_679])])]) ).
fof(c_0_1220,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(X21),hAPP(X18,X19)),X20))
| ~ hBOOL(hAPP(hAPP(c_in(X22),X19),c_Set_Ovimage(X18,X20,X22,X21))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_680])])]) ).
fof(c_0_1221,plain,
! [X16,X17,X18,X19,X20] :
( c_Fun_Ofun__upd(X18,X17,X16,X20,X19) != X18
| hAPP(X18,X17) = X16 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_681])])]) ).
fof(c_0_1222,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(X28,X29),X30))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X30),c_SetInterval_Oord_OgreaterThanLessThan(X28,X29,X27,X31))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_682])])]) ).
fof(c_0_1223,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(X28,X30),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X30),c_SetInterval_Oord_OgreaterThanLessThan(X28,X29,X27,X31))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_683])])]) ).
fof(c_0_1224,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(X28,X30),X27))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X30),c_SetInterval_Oord_OatLeastAtMost(X28,X29,X27,X31))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_684])])]) ).
fof(c_0_1225,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(X28,X29),X30))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X30),c_SetInterval_Oord_OatLeastAtMost(X28,X29,X27,X31))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_685])])]) ).
fof(c_0_1226,plain,
! [X19,X20,X21,X22,X23] :
( c_Lattices_Olower__semilattice__class_Oinf(X21,X20,tc_fun(X23,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool))
| X21 = X20
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X23,tc_bool)),X20),c_Equiv__Relations_Oquotient(X22,X19,X23)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X23,tc_bool)),X21),c_Equiv__Relations_Oquotient(X22,X19,X23)))
| ~ c_Equiv__Relations_Oequiv(X22,X19,X23) ),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1227,plain,
! [X9,X10,X11] :
( hAPP(c_COMBC(c_in(X11),X11,tc_fun(X11,tc_bool),tc_bool),X10) != hAPP(c_COMBC(c_in(X11),X11,tc_fun(X11,tc_bool),tc_bool),X9)
| X10 = X9 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_687])])]) ).
fof(c_0_1228,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(X18,hAPP(X17,X16)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X17,X18,X20,X19),X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_688])])]) ).
fof(c_0_1229,plain,
! [X11,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X12,X11)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X12),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1230,plain,
! [X11,X12] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X12,X11)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X12),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1231,plain,
! [X17,X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(X22),X18),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X19,X21,tc_fun(X22,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X22),X18),hAPP(X19,X17)))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X17),X20)) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1232,plain,
! [X18,X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(X22),X18),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21,X20,X23,tc_fun(X22,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X22),X18),hAPP(X20,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X19),X21)) ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1233,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18),tc_fun(X18,tc_bool)),X16,tc_fun(X18,tc_bool))
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1234,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18),tc_fun(X18,tc_bool)),X16,tc_fun(X18,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1235,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18),tc_fun(X18,tc_bool)),X16,tc_fun(X18,tc_bool))
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1236,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18),tc_fun(X18,tc_bool)),X16,tc_fun(X18,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1237,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(X22),X19),c_Set_Ovimage(X18,X20,X22,X21)))
| ~ hBOOL(hAPP(hAPP(c_in(X21),hAPP(X18,X19)),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_697])])]) ).
fof(c_0_1238,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(X21),X19),c_Set_Ovimage(X18,X20,X21,X22)))
| ~ hBOOL(hAPP(hAPP(c_in(X22),hAPP(X18,X19)),X20)) ),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1239,plain,
! [X18,X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_in(X21),X19),c_Set_Ovimage(X18,X20,X21,X22)))
| ~ hBOOL(hAPP(hAPP(c_in(X22),hAPP(X18,X19)),X20)) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1240,plain,
! [X16,X17,X18,X19,X20] :
( c_Set_Oimage(X16,X18,X20,X19) != c_Set_Oimage(X16,X17,X20,X19)
| ~ c_Fun_Oinj__on(X16,c_Lattices_Oupper__semilattice__class_Osup(X18,X17,tc_fun(X20,tc_bool)),X20,X19)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1241,plain,
! [X17,X18,X19,X20,X21,X22] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X19,X22,tc_fun(X21,tc_bool)),X18))
| ~ hBOOL(hAPP(hAPP(X19,X17),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X22),X17),X20)) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1242,plain,
! [X18,X19,X20,X21,X22,X23] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21,X20,X23,tc_fun(X22,tc_bool)),X18))
| ~ hBOOL(hAPP(hAPP(X20,X19),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X19),X21)) ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1243,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X17,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18),tc_fun(X18,tc_bool)),X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1244,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X17,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18),tc_fun(X18,tc_bool)),X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1245,plain,
! [X21,X22,X23,X24,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(X24),X21),X23))
| hBOOL(hAPP(hAPP(c_in(X25),hAPP(X22,X21)),c_Set_Oimage(X22,X23,X24,X25))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_705])])]) ).
fof(c_0_1246,plain,
! [X16,X17,X18,X19,X20] :
( ~ hBOOL(hAPP(hAPP(c_in(X19),X16),X18))
| hBOOL(hAPP(hAPP(c_in(X20),hAPP(X17,X16)),c_Set_Oimage(X17,X18,X19,X20))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_706])])]) ).
fof(c_0_1247,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(c_in(X20),hAPP(X17,X16)),c_Set_Oimage(X17,X18,X19,X20)))
| ~ hBOOL(hAPP(hAPP(c_in(X19),X16),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_707])])]) ).
fof(c_0_1248,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(c_in(X19),hAPP(X17,X16)),c_Set_Oimage(X17,X18,X20,X19)))
| ~ hBOOL(hAPP(hAPP(c_in(X20),X16),X18)) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1249,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X30),c_SetInterval_Oord_OatLeastAtMost(X28,X29,X27,X31)))
| ~ hBOOL(hAPP(hAPP(X28,X30),X27))
| ~ hBOOL(hAPP(hAPP(X28,X29),X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_709])])]) ).
fof(c_0_1250,plain,
! [X27,X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X30),c_SetInterval_Oord_OgreaterThanLessThan(X28,X29,X27,X31)))
| ~ hBOOL(hAPP(hAPP(X28,X30),X27))
| ~ hBOOL(hAPP(hAPP(X28,X29),X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_710])])]) ).
fof(c_0_1251,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X17,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18),tc_fun(X18,tc_bool)),X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1252,plain,
! [X16,X17,X18,X19,X20,X21] :
( hBOOL(hAPP(hAPP(c_in(X21),hAPP(X17,X16)),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X20),X16),X19))
| ~ c_lessequals(c_Set_Oimage(X17,X19,X20,X21),X18,tc_fun(X21,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1253,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(X40,X39))
| ~ hBOOL(hAPP(hAPP(c_in(X43),X39),X42))
| hBOOL(hAPP(hAPP(c_in(X43),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X42,X40,X43)),X42))
| hBOOL(hAPP(hAPP(c_in(X43),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X42,X41,X43)),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_713])])]) ).
fof(c_0_1254,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(X41,X39))
| ~ hBOOL(hAPP(hAPP(c_in(X43),X39),X42))
| hBOOL(hAPP(hAPP(c_in(X43),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X42,X40,X43)),X42))
| hBOOL(hAPP(hAPP(c_in(X43),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X42,X41,X43)),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_714])])]) ).
fof(c_0_1255,plain,
! [X55,X56,X57,X58,X59,X60] :
( c_lessequals(hAPP(X58,X55),X57,tc_fun(X60,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X59),X55),X56))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X56,X58,X59,tc_fun(X60,tc_bool)),X57,tc_fun(X60,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1256,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X23,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X25,X24,X23,X26)))
| ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X26),X22),X24)) ),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1257,plain,
! [X31,X32,X33,X34,X35] :
( hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X34,X33,X32,X35)))
| ~ hBOOL(hAPP(X32,X31))
| ~ hBOOL(hAPP(hAPP(c_in(X35),X31),X34)) ),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1258,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18),tc_fun(X18,tc_bool)),X16,tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X16))
| ~ c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1259,plain,
! [X16,X17,X18,X19,X20] :
( c_lessequals(c_Set_Oimage(X16,X18,X20,X19),c_Set_Oimage(X16,X17,X20,X19),tc_fun(X19,tc_bool))
| ~ c_lessequals(X18,X17,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1260,plain,
! [X16,X17,X18,X19,X20] :
( ~ c_lessequals(X16,X18,tc_fun(X19,tc_bool))
| c_lessequals(c_Set_Oimage(X17,X16,X19,X20),c_Set_Oimage(X17,X18,X19,X20),tc_fun(X20,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_720])])]) ).
fof(c_0_1261,plain,
! [X16,X17,X18,X19,X20] :
( c_lessequals(c_Set_Ovimage(X16,X18,X19,X20),c_Set_Ovimage(X16,X17,X19,X20),tc_fun(X19,tc_bool))
| ~ c_lessequals(X18,X17,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1262,plain,
! [X18,X19,X20,X21] :
( c_Finite__Set_Osetsum(X18,c_HOL_Ominus__class_Ominus(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21),tc_fun(X21,tc_bool)),X21,tc_nat) = c_Finite__Set_Osetsum(X18,X20,X21,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X21),X19),X20)) ),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1263,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(c_Set_Ovimage(X17,X18,X20,X19),X16))
| ~ hBOOL(hAPP(X18,hAPP(X17,X16))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_723])])]) ).
fof(c_0_1264,plain,
! [X52,X53,X54,X55,X56] :
( hBOOL(hAPP(X53,X52))
| ~ hBOOL(hAPP(hAPP(c_in(X56),X52),X55))
| hBOOL(hAPP(hAPP(c_in(X56),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X55,X53,X56)),X55))
| ~ hBOOL(hAPP(X54,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X55,X54,X56))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_724])])]) ).
fof(c_0_1265,plain,
! [X52,X53,X54,X55,X56] :
( hBOOL(hAPP(X54,X52))
| ~ hBOOL(hAPP(hAPP(c_in(X56),X52),X55))
| hBOOL(hAPP(hAPP(c_in(X56),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X55,X53,X56)),X55))
| ~ hBOOL(hAPP(X54,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X55,X54,X56))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_725])])]) ).
fof(c_0_1266,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(X40,X39))
| ~ hBOOL(hAPP(hAPP(c_in(X43),X39),X42))
| ~ hBOOL(hAPP(X40,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X42,X40,X43)))
| hBOOL(hAPP(hAPP(c_in(X43),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X42,X41,X43)),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_726])])]) ).
fof(c_0_1267,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(X41,X39))
| ~ hBOOL(hAPP(hAPP(c_in(X43),X39),X42))
| ~ hBOOL(hAPP(X40,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X42,X40,X43)))
| hBOOL(hAPP(hAPP(c_in(X43),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X42,X41,X43)),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_727])])]) ).
fof(c_0_1268,plain,
! [X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X15,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X14,X13,X15)),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X14),c_Complete__Lattice_OSup__class_OSup(X13,tc_fun(X15,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1269,plain,
! [X15,X16,X17,X18] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X17,c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18),tc_fun(X18,tc_bool)),X16,tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| ~ c_lessequals(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1270,plain,
! [X55,X56,X57,X58,X59] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X57,X55),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X56,X57,X59,tc_fun(X58,tc_bool)),tc_fun(X58,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X56,X57,X59,tc_fun(X58,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X59),X55),X56)) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1271,plain,
! [X16,X17,X18,X19,X20] :
( c_Set_Oinsert(hAPP(X17,X16),c_Set_Oimage(X17,X18,X20,X19),X19) = c_Set_Oimage(X17,X18,X20,X19)
| ~ hBOOL(hAPP(hAPP(c_in(X20),X16),X18)) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1272,plain,
! [X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_in(X15),X14),c_Complete__Lattice_OInf__class_OInf(X13,tc_fun(X15,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X15,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X14,X13,X15)),X13)) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1273,plain,
! [X43,X44,X45,X46,X47] :
( hBOOL(hAPP(X44,X43))
| ~ hBOOL(hAPP(hAPP(c_in(X47),X43),X46))
| ~ hBOOL(hAPP(X44,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X46,X44,X47)))
| ~ hBOOL(hAPP(X45,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X46,X45,X47))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_733])])]) ).
fof(c_0_1274,plain,
! [X43,X44,X45,X46,X47] :
( hBOOL(hAPP(X45,X43))
| ~ hBOOL(hAPP(hAPP(c_in(X47),X43),X46))
| ~ hBOOL(hAPP(X44,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X46,X44,X47)))
| ~ hBOOL(hAPP(X45,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X46,X45,X47))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_734])])]) ).
fof(c_0_1275,plain,
! [X13,X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_in(X16),X15),X13))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X16,tc_bool)),X13),X14))
| ~ hBOOL(hAPP(hAPP(c_in(X16),X15),c_Complete__Lattice_OInf__class_OInf(X14,tc_fun(X16,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1276,plain,
! [X16,X17,X18,X19,X20] :
( hAPP(X17,X16) = c_HOL_Oundefined(X19)
| hBOOL(hAPP(hAPP(c_in(X20),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X20,X19)),X17),c_FuncSet_Oextensional(X18,X20,X19))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_736])])]) ).
fof(c_0_1277,plain,
! [X9] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X9),c_Arrow__Order__Mirabelle_OLin)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_737])])]) ).
fof(c_0_1278,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(hAPP(c_in(X26),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X25,X24,X26)),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X26),X23),X25))
| ~ hBOOL(hAPP(X24,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X26),X22),X25)) ),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1279,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_in(X25),X22),X24))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),c_Lattices_Olower__semilattice__class_Oinf(X24,c_Collect(X23,X25),tc_fun(X25,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1280,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olattice(X49)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X48,X47,X49),c_Lattices_Oupper__semilattice__class_Osup(X48,X46,X49),X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1281,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olattice(X49)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X48,X47,X49),c_Lattices_Olower__semilattice__class_Oinf(X48,X46,X49),X49),c_Lattices_Olower__semilattice__class_Oinf(X48,c_Lattices_Oupper__semilattice__class_Osup(X47,X46,X49),X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1282,plain,
! [X13,X14,X15] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X13,tc_fun(X15,tc_bool)),X14,tc_fun(X15,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X15,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X14,X13,X15)),X13)) ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1283,plain,
! [X16,X17,X18,X19,X20] :
( c_Fun_Oinj__on(X16,X17,X20,X19)
| ~ c_Fun_Oinj__on(X16,c_Lattices_Oupper__semilattice__class_Osup(X18,X17,tc_fun(X20,tc_bool)),X20,X19) ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1284,plain,
! [X16,X17,X18,X19,X20] :
( c_Fun_Oinj__on(X16,X18,X20,X19)
| ~ c_Fun_Oinj__on(X16,c_Lattices_Oupper__semilattice__class_Osup(X18,X17,tc_fun(X20,tc_bool)),X20,X19) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1285,plain,
! [X13,X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_in(X16),X15),c_Complete__Lattice_OSup__class_OSup(X14,tc_fun(X16,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X16),X15),X13))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X16,tc_bool)),X13),X14)) ),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1286,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),X29))
| hBOOL(hAPP(hAPP(c_in(X31),X28),X30))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),c_Lattices_Oupper__semilattice__class_Osup(X30,X29,tc_fun(X31,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1287,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),c_Lattices_Olower__semilattice__class_Oinf(X24,c_Collect(X23,X25),tc_fun(X25,tc_bool)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_747])])]) ).
fof(c_0_1288,plain,
! [X51,X52,X53,X54,X55] :
( c_Set_Oinsert(X54,c_Set_Oinsert(X53,c_Orderings_Obot__class_Obot(tc_fun(X55,tc_bool)),X55),X55) != c_Set_Oinsert(X52,c_Set_Oinsert(X51,c_Orderings_Obot__class_Obot(tc_fun(X55,tc_bool)),X55),X55)
| X54 = X51
| X54 = X52 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_748])])]) ).
fof(c_0_1289,plain,
! [X51,X52,X53,X54,X55] :
( c_Set_Oinsert(X54,c_Set_Oinsert(X53,c_Orderings_Obot__class_Obot(tc_fun(X55,tc_bool)),X55),X55) != c_Set_Oinsert(X52,c_Set_Oinsert(X51,c_Orderings_Obot__class_Obot(tc_fun(X55,tc_bool)),X55),X55)
| X53 = X52
| X54 = X52 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_749])])]) ).
fof(c_0_1290,plain,
! [X51,X52,X53,X54,X55] :
( c_Set_Oinsert(X54,c_Set_Oinsert(X53,c_Orderings_Obot__class_Obot(tc_fun(X55,tc_bool)),X55),X55) != c_Set_Oinsert(X52,c_Set_Oinsert(X51,c_Orderings_Obot__class_Obot(tc_fun(X55,tc_bool)),X55),X55)
| X54 = X51
| X53 = X51 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_750])])]) ).
fof(c_0_1291,plain,
! [X51,X52,X53,X54,X55] :
( c_Set_Oinsert(X54,c_Set_Oinsert(X53,c_Orderings_Obot__class_Obot(tc_fun(X55,tc_bool)),X55),X55) != c_Set_Oinsert(X52,c_Set_Oinsert(X51,c_Orderings_Obot__class_Obot(tc_fun(X55,tc_bool)),X55),X55)
| X53 = X52
| X53 = X51 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_751])])]) ).
fof(c_0_1292,plain,
! [X13,X14,X15,X16] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X14,tc_fun(X16,tc_bool)),X15,tc_fun(X16,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X13,X15,tc_fun(X16,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X16,tc_bool)),X13),X14)) ),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1293,plain,
! [X18,X19,X20] :
( X18 = X19
| ~ hBOOL(hAPP(hAPP(c_in(X20),X18),c_Set_Oinsert(X19,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_753])])]) ).
fof(c_0_1294,plain,
! [X28,X29,X30,X31] :
( ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),c_HOL_Ominus__class_Ominus(X30,X29,tc_fun(X31,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1295,plain,
! [X18,X19,X20,X21,X22] :
( c_lessequals(hAPP(X19,X18),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X19,X22,tc_fun(X21,tc_bool)),tc_fun(X21,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X22),X18),X20)) ),
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1296,plain,
! [X18,X19,X20,X21,X22] :
( c_Fun_Oinj__on(X18,X20,X22,X21)
| ~ c_Fun_Oinj__on(X18,c_Set_Oinsert(X19,X20,X22),X22,X21) ),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1297,plain,
! [X15,X16,X17,X18] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)),X15,tc_fun(X18,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X17,c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(X18,tc_bool)),tc_fun(X18,tc_bool))
| c_lessequals(X15,X17,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1298,plain,
! [X18,X19,X20] :
( c_Set_Oinsert(X18,c_HOL_Ominus__class_Ominus(X19,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),tc_fun(X20,tc_bool)),X20) = X19
| ~ hBOOL(hAPP(hAPP(c_in(X20),X18),X19)) ),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1299,plain,
! [X16,X17,X18,X19,X20] :
( c_Fun_Oinj__on(X16,c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X20,tc_bool)),X20,X19)
| ~ c_Fun_Oinj__on(X16,X18,X20,X19) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1300,plain,
! [X50,X51,X52,X53,X54,X55] :
( c_Pair(X53,X51,X55,X54) != c_Pair(X52,X50,X55,X54)
| X53 = X52 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_760])])]) ).
fof(c_0_1301,plain,
! [X50,X51,X52,X53,X54,X55] :
( c_Pair(X53,X51,X55,X54) != c_Pair(X52,X50,X55,X54)
| X51 = X50 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_761])])]) ).
fof(c_0_1302,plain,
! [X16,X17,X18,X19,X20,X21] :
( hAPP(X18,X17) != hAPP(X18,X16)
| ~ hBOOL(hAPP(hAPP(c_in(X21),X16),X19))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X17),X19))
| X17 = X16
| ~ c_Fun_Oinj__on(X18,X19,X21,X20) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_762])])]) ).
fof(c_0_1303,plain,
! [X16,X17,X18,X19,X20,X21] :
( hAPP(X18,X17) != hAPP(X18,X16)
| ~ hBOOL(hAPP(hAPP(c_in(X21),X16),X19))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X17),X19))
| ~ c_Fun_Oinj__on(X18,X19,X21,X20)
| X17 = X16 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_763])])]) ).
fof(c_0_1304,plain,
! [X31,X32,X33,X34,X35,X36] :
( hAPP(X33,X32) != hAPP(X33,X31)
| ~ hBOOL(hAPP(hAPP(c_in(X36),X31),X34))
| ~ hBOOL(hAPP(hAPP(c_in(X36),X32),X34))
| ~ c_Fun_Oinj__on(X33,X34,X36,X35)
| X32 = X31 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_764])])]) ).
fof(c_0_1305,plain,
! [X16,X17,X18,X19,X20,X21] :
( hAPP(X18,X17) != hAPP(X18,X16)
| ~ c_Fun_Oinj__on(X18,X19,X21,X20)
| X17 = X16
| ~ hBOOL(hAPP(hAPP(c_in(X21),X16),X19))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X17),X19)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_765])])]) ).
fof(c_0_1306,plain,
! [X16,X17,X18,X19,X20] :
( c_Fun_Oinj__on(X16,X18,X20,X19)
| ~ c_lessequals(X18,X17,tc_fun(X20,tc_bool))
| ~ c_Fun_Oinj__on(X16,X17,X20,X19) ),
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1307,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),X30))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),c_HOL_Ominus__class_Ominus(X30,X29,tc_fun(X31,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1308,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),c_Lattices_Olower__semilattice__class_Oinf(X30,X29,tc_fun(X31,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1309,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),X30))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),c_Lattices_Olower__semilattice__class_Oinf(X30,X29,tc_fun(X31,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_769]) ).
fof(c_0_1310,plain,
! [X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_in(X15),X14),c_Complete__Lattice_OInf__class_OInf(X13,tc_fun(X15,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X14),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X14,X13,X15))) ),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1311,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_in(X25),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X24,X23,X25)),X24))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24))
| ~ hBOOL(hAPP(X23,X22)) ),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1312,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_in(X25),c_ATP__Linkup_Osko__Set__XbexI__1__1(X24,X23,X25)),X24))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24))
| ~ hBOOL(hAPP(X23,X22)) ),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1313,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_in(X25),c_ATP__Linkup_Osko__Set__XbexE__1__1(X24,X23,X25)),X24))
| ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24)) ),
inference(variable_rename,[status(thm)],[c_0_773]) ).
fof(c_0_1314,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_in(X25),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X24,X23,X25)),X24))
| ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24)) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1315,plain,
! [X53,X54,X55,X56,X57] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X56)
| c_lessequals(hAPP(X54,X53),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X55,X54,X57,X56),X56)
| ~ hBOOL(hAPP(hAPP(c_in(X57),X53),X55)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_775])])]) ).
fof(c_0_1316,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),c_Lattices_Olower__semilattice__class_Oinf(X30,X29,tc_fun(X31,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X30)) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1317,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),c_Lattices_Olower__semilattice__class_Oinf(X30,X29,tc_fun(X31,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X30)) ),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1318,plain,
! [X28,X29,X30] :
( ~ hBOOL(hAPP(hAPP(c_in(X30),X28),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X30),X28),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X30,tc_bool)),X29))) ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1319,plain,
! [X22,X23,X24,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24))
| hBOOL(hAPP(X23,X22))
| hBOOL(hAPP(hAPP(c_in(X25),c_ATP__Linkup_Osko__Set__XballE__1__1(X24,X23,X25)),X24)) ),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1320,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_in(X25),X22),c_Lattices_Olower__semilattice__class_Oinf(X24,c_Collect(X23,X25),tc_fun(X25,tc_bool))))
| ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24)) ),
inference(variable_rename,[status(thm)],[c_0_780]) ).
fof(c_0_1321,plain,
! [X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_in(X15),X14),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X14,X13,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X14),c_Complete__Lattice_OSup__class_OSup(X13,tc_fun(X15,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1322,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),c_HOL_Ominus__class_Ominus(X30,X29,tc_fun(X31,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X31),X28),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X30)) ),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1323,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),c_HOL_Ominus__class_Ominus(X30,X29,tc_fun(X31,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X31),X28),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X30)) ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1324,plain,
! [X16,X17,X18,X19,X20] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X17,X19,tc_fun(X20,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))
| hAPP(X17,X16) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X19),X16),X18)) ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1325,plain,
! [X16,X17,X18,X19,X20] :
( c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X17,X19,tc_fun(X20,tc_bool))
| hAPP(X17,X16) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X19),X16),X18)) ),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1326,plain,
! [X28,X29,X30,X31,X32] :
( c_Set_Oimage(c_COMBK(X29,X31,X32),X30,X32,X31) = c_Set_Oinsert(X29,c_Orderings_Obot__class_Obot(tc_fun(X31,tc_bool)),X31)
| ~ hBOOL(hAPP(hAPP(c_in(X32),X28),X30)) ),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1327,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X24,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X25,X24,X26)))
| ~ hBOOL(hAPP(hAPP(c_in(X26),X23),X25))
| ~ hBOOL(hAPP(X24,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X26),X22),X25)) ),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1328,plain,
! [X56,X57,X58,X59,X60] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X59,X58,tc_fun(X60,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X57,X56,tc_fun(X60,tc_bool)),tc_fun(X60,tc_bool))
| ~ c_lessequals(X58,X56,tc_fun(X60,tc_bool))
| ~ c_lessequals(X59,X57,tc_fun(X60,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1329,plain,
! [X56,X57,X58,X59,X60] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X59,X58,tc_fun(X60,tc_bool)),c_HOL_Ominus__class_Ominus(X57,X56,tc_fun(X60,tc_bool)),tc_fun(X60,tc_bool))
| ~ c_lessequals(X56,X58,tc_fun(X60,tc_bool))
| ~ c_lessequals(X59,X57,tc_fun(X60,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1330,plain,
! [X56,X57,X58,X59,X60] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X59,X58,tc_fun(X60,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X57,X56,tc_fun(X60,tc_bool)),tc_fun(X60,tc_bool))
| ~ c_lessequals(X58,X56,tc_fun(X60,tc_bool))
| ~ c_lessequals(X59,X57,tc_fun(X60,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_790]) ).
fof(c_0_1331,plain,
! [X15,X16,X17] :
( c_lessequals(X16,X15,tc_fun(X17,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X17,tc_bool)),X16),c_Set_OPow(X15,X17))) ),
inference(variable_rename,[status(thm)],[c_0_791]) ).
fof(c_0_1332,plain,
! [X18,X19,X20,X21] :
( hBOOL(hAPP(hAPP(c_in(X21),X19),X20))
| X19 = X18
| ~ hBOOL(hAPP(hAPP(c_in(X21),X19),c_Set_Oinsert(X18,X20,X21))) ),
inference(variable_rename,[status(thm)],[c_0_792]) ).
fof(c_0_1333,plain,
! [X15,X16,X17] :
( c_lessequals(X15,X16,tc_fun(X17,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X16),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X15),tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1334,plain,
! [X15,X16,X17] :
( c_lessequals(X15,c_Complete__Lattice_OSup__class_OSup(X16,tc_fun(X17,tc_bool)),tc_fun(X17,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X17,tc_bool)),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_794]) ).
fof(c_0_1335,plain,
! [X15,X16,X17] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X16,tc_fun(X17,tc_bool)),X15,tc_fun(X17,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X17,tc_bool)),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_795]) ).
fof(c_0_1336,plain,
! [X18,X19,X20] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X19,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X20),X20) = c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_796]) ).
fof(c_0_1337,plain,
! [X18,X19,X20] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X19,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X20),X20) = c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1338,plain,
! [X15,X16,X17,X18] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,tc_fun(X18,tc_bool)),X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(X18,tc_bool)),tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_798]) ).
fof(c_0_1339,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(X18,tc_bool)),tc_fun(X18,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,tc_fun(X18,tc_bool)),X15,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_799]) ).
fof(c_0_1340,plain,
! [X13,X14,X15] :
( X14 = c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15)
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_800]) ).
fof(c_0_1341,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(X16,X15))
| hBOOL(hAPP(X17,X15))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(X18,tc_bool)),X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_801])])]) ).
fof(c_0_1342,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(X30,X32),X31))
| ~ hBOOL(hAPP(hAPP(c_in(X33),X32),c_SetInterval_Oord_OatMost(X30,X31,X33))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_802])])]) ).
fof(c_0_1343,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(X30,X31),X32))
| ~ hBOOL(hAPP(hAPP(c_in(X33),X32),c_SetInterval_Oord_OgreaterThan(X30,X31,X33))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_803])])]) ).
fof(c_0_1344,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(X30,X32),X31))
| ~ hBOOL(hAPP(hAPP(c_in(X33),X32),c_SetInterval_Oord_OlessThan(X30,X31,X33))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_804])])]) ).
fof(c_0_1345,plain,
! [X15,X16,X17,X18] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)),X15,tc_fun(X18,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X17,c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(X18,tc_bool)),tc_fun(X18,tc_bool))
| ~ c_lessequals(X15,X17,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_805]) ).
fof(c_0_1346,plain,
! [X22,X23,X24,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24))
| hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(X23,c_ATP__Linkup_Osko__Set__XballE__1__1(X24,X23,X25))) ),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1347,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X16))
| ~ c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_807]) ).
fof(c_0_1348,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),c_Lattices_Oupper__semilattice__class_Osup(X30,X29,tc_fun(X31,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X30)) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1349,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),c_Lattices_Oupper__semilattice__class_Osup(X30,X29,tc_fun(X31,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X29)) ),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1350,plain,
! [X18,X19,X20,X21] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X18,X20,X21),X19,tc_fun(X21,tc_bool)) = c_Set_Oinsert(X18,c_Lattices_Olower__semilattice__class_Oinf(X20,X19,tc_fun(X21,tc_bool)),X21)
| ~ hBOOL(hAPP(hAPP(c_in(X21),X18),X19)) ),
inference(variable_rename,[status(thm)],[c_0_810]) ).
fof(c_0_1351,plain,
! [X18,X19,X20,X21] :
( c_Lattices_Olower__semilattice__class_Oinf(X20,c_Set_Oinsert(X18,X19,X21),tc_fun(X21,tc_bool)) = c_Set_Oinsert(X18,c_Lattices_Olower__semilattice__class_Oinf(X20,X19,tc_fun(X21,tc_bool)),X21)
| ~ hBOOL(hAPP(hAPP(c_in(X21),X18),X20)) ),
inference(variable_rename,[status(thm)],[c_0_811]) ).
fof(c_0_1352,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(X16,X15))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)),X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_812])])]) ).
fof(c_0_1353,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(X17,X15))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)),X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_813])])]) ).
fof(c_0_1354,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_814]) ).
fof(c_0_1355,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,X16,tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X16))
| ~ c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_815]) ).
fof(c_0_1356,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_816]) ).
fof(c_0_1357,plain,
! [X13,X14,X15] :
( c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X14,X13,X15),X14,tc_fun(X15,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X13,tc_fun(X15,tc_bool)),X14,tc_fun(X15,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_817]) ).
fof(c_0_1358,plain,
! [X13,X14,X15] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X13,X14,X15),c_Set_Oinsert(X13,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),tc_fun(X15,tc_bool)) = X14
| hBOOL(hAPP(hAPP(c_in(X15),X13),X14)) ),
inference(variable_rename,[status(thm)],[c_0_818]) ).
fof(c_0_1359,plain,
! [X15,X16,X17,X18] :
( ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X16))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_819]) ).
fof(c_0_1360,plain,
! [X15,X16,X17,X18] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X15,X17,X18),X16,tc_fun(X18,tc_bool)) = c_Set_Oinsert(X15,c_HOL_Ominus__class_Ominus(X17,X16,tc_fun(X18,tc_bool)),X18)
| hBOOL(hAPP(hAPP(c_in(X18),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1361,plain,
! [X28,X29,X30,X31] :
( c_Set_Oimage(c_COMBK(X28,X31,X30),X29,X30,X31) = c_Set_Oinsert(X28,c_Orderings_Obot__class_Obot(tc_fun(X31,tc_bool)),X31)
| X29 = c_Orderings_Obot__class_Obot(tc_fun(X30,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_821])])]) ).
fof(c_0_1362,plain,
! [X18,X19,X20,X21] :
( hBOOL(hAPP(hAPP(c_in(X21),X19),c_Set_Oinsert(X18,X20,X21)))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X19),X20)) ),
inference(variable_rename,[status(thm)],[c_0_822]) ).
fof(c_0_1363,plain,
! [X18,X19,X20,X21] :
( hBOOL(hAPP(hAPP(c_in(X21),X19),c_Set_Oinsert(X18,X20,X21)))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X19),X20)) ),
inference(variable_rename,[status(thm)],[c_0_823]) ).
fof(c_0_1364,plain,
! [X28,X29,X30,X31] :
( c_Set_Ovimage(c_COMBK(X28,X30,X31),X29,X31,X30) = c_Orderings_Obot__class_Obot(tc_fun(X31,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X30),X28),X29)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_824])])]) ).
fof(c_0_1365,plain,
! [X15,X16,X17,X18] :
( c_HOL_Ominus__class_Ominus(X16,c_HOL_Ominus__class_Ominus(X15,X17,tc_fun(X18,tc_bool)),tc_fun(X18,tc_bool)) = X17
| ~ c_lessequals(X16,X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_825]) ).
fof(c_0_1366,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)),tc_fun(X18,tc_bool))
| ~ c_lessequals(X15,X16,tc_fun(X18,tc_bool))
| ~ c_lessequals(X15,X17,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_826]) ).
fof(c_0_1367,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)),tc_fun(X18,tc_bool))
| ~ c_lessequals(X15,X16,tc_fun(X18,tc_bool))
| ~ c_lessequals(X15,X17,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_827]) ).
fof(c_0_1368,plain,
! [X15,X16,X17,X18] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(X18,tc_bool)),X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X16,X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X15,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1369,plain,
! [X15,X16,X17,X18] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(X18,tc_bool)),X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X16,X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X15,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_829]) ).
fof(c_0_1370,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X17)) ),
inference(variable_rename,[status(thm)],[c_0_830]) ).
fof(c_0_1371,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| ~ c_lessequals(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1372,plain,
! [X15,X16,X17,X18] :
( c_lessequals(c_Set_Oinsert(X15,X17,X18),X16,tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_832]) ).
fof(c_0_1373,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X16))
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1374,plain,
! [X28,X29,X30] :
( hBOOL(hAPP(hAPP(c_in(X30),X28),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X30,tc_bool)),X29)))
| hBOOL(hAPP(hAPP(c_in(X30),X28),X29)) ),
inference(variable_rename,[status(thm)],[c_0_834]) ).
fof(c_0_1375,plain,
! [X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(X17,tc_bool)),X16),c_Set_OPow(X15,X17)))
| ~ c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1376,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X23,c_ATP__Linkup_Osko__Set__XbexI__1__1(X24,X23,X25)))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24))
| ~ hBOOL(hAPP(X23,X22)) ),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1377,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X23,c_ATP__Linkup_Osko__Set__XbexE__1__1(X24,X23,X25)))
| ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24)) ),
inference(variable_rename,[status(thm)],[c_0_837]) ).
fof(c_0_1378,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X23,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X24,X23,X25)))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24))
| ~ hBOOL(hAPP(X23,X22)) ),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1379,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X23,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X24,X23,X25)))
| ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X25),X22),X24)) ),
inference(variable_rename,[status(thm)],[c_0_839]) ).
fof(c_0_1380,plain,
! [X16,X17,X18,X19] :
( c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) != c_Set_Oimage(X16,X17,X18,X19)
| X17 = c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_840])])]) ).
fof(c_0_1381,plain,
! [X16,X17,X18,X19] :
( c_Set_Oimage(X16,X17,X18,X19) != c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| X17 = c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_841])])]) ).
fof(c_0_1382,plain,
! [X15,X16,X17] :
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X16),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X15),tc_fun(X17,tc_bool))
| ~ c_lessequals(X15,X16,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1383,plain,
! [X15,X16,X17] :
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X15),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X16),tc_fun(X17,tc_bool))
| ~ c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_843]) ).
fof(c_0_1384,plain,
! [X28,X29,X30,X31] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,c_COMBK(X28,tc_fun(X31,tc_bool),X30),X30,tc_fun(X31,tc_bool)) = X28
| X29 = c_Orderings_Obot__class_Obot(tc_fun(X30,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_844])])]) ).
fof(c_0_1385,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(c_in(X33),X32),c_SetInterval_Oord_OatMost(X30,X31,X33)))
| ~ hBOOL(hAPP(hAPP(X30,X32),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_845])])]) ).
fof(c_0_1386,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(c_in(X33),X32),c_SetInterval_Oord_OgreaterThan(X30,X31,X33)))
| ~ hBOOL(hAPP(hAPP(X30,X31),X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_846])])]) ).
fof(c_0_1387,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(c_in(X33),X32),c_SetInterval_Oord_OlessThan(X30,X31,X33)))
| ~ hBOOL(hAPP(hAPP(X30,X32),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_847])])]) ).
fof(c_0_1388,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(X18,tc_bool)),X15,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_848]) ).
fof(c_0_1389,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X16,X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(X18,tc_bool)),X15,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_849]) ).
fof(c_0_1390,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X15,X16,tc_fun(X18,tc_bool))
| ~ c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)),tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_850]) ).
fof(c_0_1391,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X15,X17,tc_fun(X18,tc_bool))
| ~ c_lessequals(X15,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)),tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_851]) ).
fof(c_0_1392,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Odistrib__lattice(X49)
| c_Lattices_Oupper__semilattice__class_Osup(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X48,X47,X49),c_Lattices_Oupper__semilattice__class_Osup(X48,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_852]) ).
fof(c_0_1393,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Odistrib__lattice(X49)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X48,X49) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X47,X48,X49),c_Lattices_Oupper__semilattice__class_Osup(X46,X48,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_853]) ).
fof(c_0_1394,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Odistrib__lattice(X49)
| c_Lattices_Olower__semilattice__class_Oinf(X48,c_Lattices_Oupper__semilattice__class_Osup(X47,X46,X49),X49) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X48,X47,X49),c_Lattices_Olower__semilattice__class_Oinf(X48,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_854]) ).
fof(c_0_1395,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Odistrib__lattice(X49)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X47,X46,X49),X48,X49) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X47,X48,X49),c_Lattices_Olower__semilattice__class_Oinf(X46,X48,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_855]) ).
fof(c_0_1396,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(X18,tc_bool)),X15))
| ~ hBOOL(hAPP(X16,X15))
| ~ hBOOL(hAPP(X17,X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_856])])]) ).
fof(c_0_1397,plain,
! [X15,X16,X17] :
( c_Lattices_Olower__semilattice__class_Oinf(X16,X15,tc_fun(X17,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))
| ~ c_lessequals(X16,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X15),tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_857]) ).
fof(c_0_1398,plain,
! [X15,X16,X17,X18] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X15,X17,X18),X16,tc_fun(X18,tc_bool)) = c_HOL_Ominus__class_Ominus(X17,X16,tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_858]) ).
fof(c_0_1399,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_859])])]) ).
fof(c_0_1400,plain,
! [X56,X57,X58,X59] :
( c_lessequals(c_Set_Oinsert(X56,X58,X59),c_Set_Oinsert(X56,X57,X59),tc_fun(X59,tc_bool))
| ~ c_lessequals(X58,X57,tc_fun(X59,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_860]) ).
fof(c_0_1401,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X17)) ),
inference(variable_rename,[status(thm)],[c_0_861]) ).
fof(c_0_1402,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,c_Set_Oinsert(X15,X16,X18),tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X17)) ),
inference(variable_rename,[status(thm)],[c_0_862]) ).
fof(c_0_1403,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(hAPP(c_in(X18),X15),X16))
| ~ c_lessequals(c_Set_Oinsert(X15,X17,X18),X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_863]) ).
fof(c_0_1404,plain,
! [X54,X55,X56,X57] :
( hBOOL(hAPP(hAPP(c_in(X57),X54),X55))
| ~ hBOOL(hAPP(hAPP(c_in(X57),X54),X56))
| ~ c_lessequals(X56,X55,tc_fun(X57,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_864]) ).
fof(c_0_1405,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(hAPP(c_in(X18),X15),X16))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17)) ),
inference(variable_rename,[status(thm)],[c_0_865]) ).
fof(c_0_1406,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X30))
| ~ c_lessequals(X30,X29,tc_fun(X31,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_866]) ).
fof(c_0_1407,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(hAPP(c_in(X18),X15),X16))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_867]) ).
fof(c_0_1408,plain,
! [X28,X29,X30,X31] :
( hBOOL(hAPP(hAPP(c_in(X31),X28),X29))
| ~ hBOOL(hAPP(hAPP(c_in(X31),X28),X30))
| ~ c_HOL_Oord__class_Oless(X30,X29,tc_fun(X31,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_868]) ).
fof(c_0_1409,plain,
! [X53,X54,X55,X56] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X55)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,c_COMBK(X53,X55,X56),X56,X55) = X53
| X54 = c_Orderings_Obot__class_Obot(tc_fun(X56,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_869])])]) ).
fof(c_0_1410,plain,
! [X15,X16,X17,X18] :
( c_Set_Oinsert(X15,X17,X18) != c_Set_Oinsert(X15,X16,X18)
| hBOOL(hAPP(hAPP(c_in(X18),X15),X16))
| hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| X17 = X16 ),
inference(variable_rename,[status(thm)],[c_0_870]) ).
fof(c_0_1411,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(X18,tc_bool)),X15))
| ~ hBOOL(hAPP(X17,X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_871])])]) ).
fof(c_0_1412,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(X18,tc_bool)),X15))
| ~ hBOOL(hAPP(X16,X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_872])])]) ).
fof(c_0_1413,plain,
! [X22,X23,X24] :
( ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X24),X22),c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_873])])]) ).
fof(c_0_1414,plain,
! [X15,X16,X17] :
( c_Lattices_Olower__semilattice__class_Oinf(X16,X15,tc_fun(X17,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))
| c_lessequals(X16,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X15),tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_874]) ).
fof(c_0_1415,plain,
! [X18,X19,X20,X21] :
( c_Lattices_Olower__semilattice__class_Oinf(X20,c_Set_Oinsert(X18,X19,X21),tc_fun(X21,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X20,X19,tc_fun(X21,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X21),X18),X20)) ),
inference(variable_rename,[status(thm)],[c_0_875]) ).
fof(c_0_1416,plain,
! [X18,X19,X20,X21] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X18,X20,X21),X19,tc_fun(X21,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X20,X19,tc_fun(X21,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X21),X18),X19)) ),
inference(variable_rename,[status(thm)],[c_0_876]) ).
fof(c_0_1417,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,X16,tc_fun(X18,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X15,X17,X18),X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_877]) ).
fof(c_0_1418,plain,
! [X22,X23,X24] :
( hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X24),X22),c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_878])])]) ).
fof(c_0_1419,plain,
! [X13,X14] :
( X13 = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X14,tc_bool)),X13),tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_879]) ).
fof(c_0_1420,plain,
! [X15,X16,X17] :
( c_Lattices_Oupper__semilattice__class_Osup(X16,c_HOL_Ominus__class_Ominus(X15,X16,tc_fun(X17,tc_bool)),tc_fun(X17,tc_bool)) = X15
| ~ c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_880]) ).
fof(c_0_1421,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Olower__semilattice(X21)
| c_lessequals(X18,c_Lattices_Olower__semilattice__class_Oinf(X20,X19,X21),X21)
| ~ c_lessequals(X18,X19,X21)
| ~ c_lessequals(X18,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_881]) ).
fof(c_0_1422,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_lessequals(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49)
| ~ c_lessequals(X48,X46,X49)
| ~ c_lessequals(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_882]) ).
fof(c_0_1423,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_lessequals(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49)
| ~ c_lessequals(X48,X46,X49)
| ~ c_lessequals(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_883]) ).
fof(c_0_1424,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Oupper__semilattice(X21)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X20,X19,X21),X18,X21)
| ~ c_lessequals(X19,X18,X21)
| ~ c_lessequals(X20,X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_884]) ).
fof(c_0_1425,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Oupper__semilattice(X49)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X47,X46,X49),X48,X49)
| ~ c_lessequals(X46,X48,X49)
| ~ c_lessequals(X47,X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_885]) ).
fof(c_0_1426,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Oupper__semilattice(X49)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X48,X47,X49),X46,X49)
| ~ c_lessequals(X47,X46,X49)
| ~ c_lessequals(X48,X46,X49) ),
inference(variable_rename,[status(thm)],[c_0_886]) ).
fof(c_0_1427,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
| c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X20) = hAPP(c_HOL_Ouminus__class_Ouminus(X20),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X20)) ),
inference(variable_rename,[status(thm)],[c_0_887]) ).
fof(c_0_1428,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
| c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20) = hAPP(c_HOL_Ouminus__class_Ouminus(X20),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X20)) ),
inference(variable_rename,[status(thm)],[c_0_888]) ).
fof(c_0_1429,plain,
! [X18,X19,X20] :
( c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20) != c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20)
| X19 = X18 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_889])])]) ).
fof(c_0_1430,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Oupper__semilattice(X49)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X48,X47,X49),X46,X49) = c_Lattices_Oupper__semilattice__class_Osup(X48,c_Lattices_Oupper__semilattice__class_Osup(X47,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_890]) ).
fof(c_0_1431,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Oupper__semilattice(X49)
| c_Lattices_Oupper__semilattice__class_Osup(X48,c_Lattices_Oupper__semilattice__class_Osup(X47,X46,X49),X49) = c_Lattices_Oupper__semilattice__class_Osup(X47,c_Lattices_Oupper__semilattice__class_Osup(X48,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_891]) ).
fof(c_0_1432,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olattice(X49)
| c_Lattices_Oupper__semilattice__class_Osup(X48,c_Lattices_Oupper__semilattice__class_Osup(X47,X46,X49),X49) = c_Lattices_Oupper__semilattice__class_Osup(X47,c_Lattices_Oupper__semilattice__class_Osup(X48,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_892]) ).
fof(c_0_1433,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olattice(X49)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X48,X47,X49),X46,X49) = c_Lattices_Oupper__semilattice__class_Osup(X48,c_Lattices_Oupper__semilattice__class_Osup(X47,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_893]) ).
fof(c_0_1434,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olattice(X49)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X48,X47,X49),X46,X49) = c_Lattices_Olower__semilattice__class_Oinf(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_894]) ).
fof(c_0_1435,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olattice(X49)
| c_Lattices_Olower__semilattice__class_Oinf(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49) = c_Lattices_Olower__semilattice__class_Oinf(X47,c_Lattices_Olower__semilattice__class_Oinf(X48,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_895]) ).
fof(c_0_1436,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_Lattices_Olower__semilattice__class_Oinf(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49) = c_Lattices_Olower__semilattice__class_Oinf(X47,c_Lattices_Olower__semilattice__class_Oinf(X48,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_896]) ).
fof(c_0_1437,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X48,X47,X49),X46,X49) = c_Lattices_Olower__semilattice__class_Oinf(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_897]) ).
fof(c_0_1438,plain,
! [X15,X16,X17,X18] :
( c_lessequals(X17,X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X16,X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_898]) ).
fof(c_0_1439,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X16,X15,tc_fun(X18,tc_bool))
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_899]) ).
fof(c_0_1440,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,X15,tc_fun(X18,tc_bool))
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_900]) ).
fof(c_0_1441,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,X15,tc_fun(X18,tc_bool))
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_fun(X18,tc_bool))
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_901]) ).
fof(c_0_1442,plain,
! [X48,X49,X50,X51,X52] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X52)
| c_HOL_Ominus__class_Ominus(X51,X49,X52) != c_HOL_Ominus__class_Ominus(X50,X48,X52)
| c_lessequals(X48,X50,X52)
| ~ c_lessequals(X49,X51,X52) ),
inference(variable_rename,[status(thm)],[c_0_902]) ).
fof(c_0_1443,plain,
! [X48,X49,X50,X51,X52] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X52)
| c_HOL_Ominus__class_Ominus(X51,X49,X52) != c_HOL_Ominus__class_Ominus(X50,X48,X52)
| c_lessequals(X49,X51,X52)
| ~ c_lessequals(X48,X50,X52) ),
inference(variable_rename,[status(thm)],[c_0_903]) ).
fof(c_0_1444,plain,
! [X48,X49,X50,X51,X52] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X52)
| c_HOL_Ominus__class_Ominus(X51,X49,X52) != c_HOL_Ominus__class_Ominus(X50,X48,X52)
| c_HOL_Oord__class_Oless(X50,X48,X52)
| ~ c_HOL_Oord__class_Oless(X51,X49,X52) ),
inference(variable_rename,[status(thm)],[c_0_904]) ).
fof(c_0_1445,plain,
! [X48,X49,X50,X51,X52] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X52)
| c_HOL_Ominus__class_Ominus(X51,X49,X52) != c_HOL_Ominus__class_Ominus(X50,X48,X52)
| c_HOL_Oord__class_Oless(X51,X49,X52)
| ~ c_HOL_Oord__class_Oless(X50,X48,X52) ),
inference(variable_rename,[status(thm)],[c_0_905]) ).
fof(c_0_1446,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Oupper__semilattice(X21)
| c_lessequals(X19,X18,X21)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X20,X19,X21),X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_906]) ).
fof(c_0_1447,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Oupper__semilattice(X49)
| c_lessequals(X48,X46,X49)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X48,X47,X49),X46,X49) ),
inference(variable_rename,[status(thm)],[c_0_907]) ).
fof(c_0_1448,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Oupper__semilattice(X49)
| c_lessequals(X47,X46,X49)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X48,X47,X49),X46,X49) ),
inference(variable_rename,[status(thm)],[c_0_908]) ).
fof(c_0_1449,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Oupper__semilattice(X21)
| c_lessequals(X20,X18,X21)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X20,X19,X21),X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_909]) ).
fof(c_0_1450,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Olower__semilattice(X21)
| c_lessequals(X18,X20,X21)
| ~ c_lessequals(X18,c_Lattices_Olower__semilattice__class_Oinf(X20,X19,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_910]) ).
fof(c_0_1451,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Olower__semilattice(X21)
| c_lessequals(X18,X19,X21)
| ~ c_lessequals(X18,c_Lattices_Olower__semilattice__class_Oinf(X20,X19,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_911]) ).
fof(c_0_1452,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_lessequals(X48,X47,X49)
| ~ c_lessequals(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_912]) ).
fof(c_0_1453,plain,
! [X46,X47,X48,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_lessequals(X48,X46,X49)
| ~ c_lessequals(X48,c_Lattices_Olower__semilattice__class_Oinf(X47,X46,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_913]) ).
fof(c_0_1454,plain,
! [X17,X18,X19,X20] :
( c_lessequals(X19,c_Set_Oinsert(X17,X18,X20),tc_fun(X20,tc_bool))
| ~ c_lessequals(X19,X18,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_914]) ).
fof(c_0_1455,plain,
! [X20,X21,X22,X23] :
( ~ class_HOL_Oord(X22)
| c_HOL_Oord__class_Oless(X21,X20,tc_fun(X23,X22))
| c_lessequals(X20,X21,tc_fun(X23,X22))
| ~ c_lessequals(X21,X20,tc_fun(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_915])])]) ).
fof(c_0_1456,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_916])])]) ).
fof(c_0_1457,plain,
! [X22,X23,X24] :
( hBOOL(hAPP(X23,X22))
| ~ hBOOL(hAPP(hAPP(c_in(X24),X22),c_Collect(X23,X24))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_917])])]) ).
fof(c_0_1458,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_lessequals(X19,X18,X20)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X20) ),
inference(variable_rename,[status(thm)],[c_0_918]) ).
fof(c_0_1459,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X20) ),
inference(variable_rename,[status(thm)],[c_0_919]) ).
fof(c_0_1460,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
| hAPP(c_HOL_Ouminus__class_Ouminus(X20),c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_920]) ).
fof(c_0_1461,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oboolean__algebra(X12)
| hAPP(c_HOL_Ouminus__class_Ouminus(X12),c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X12),X11),hAPP(c_HOL_Ouminus__class_Ouminus(X12),X10),X12) ),
inference(variable_rename,[status(thm)],[c_0_921]) ).
fof(c_0_1462,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
| hAPP(c_HOL_Ouminus__class_Ouminus(X20),c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X20)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_922]) ).
fof(c_0_1463,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oboolean__algebra(X12)
| hAPP(c_HOL_Ouminus__class_Ouminus(X12),c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X12),X11),hAPP(c_HOL_Ouminus__class_Ouminus(X12),X10),X12) ),
inference(variable_rename,[status(thm)],[c_0_923]) ).
fof(c_0_1464,plain,
! [X20,X21,X22,X23] :
( ~ class_HOL_Oord(X22)
| ~ c_lessequals(X20,X21,tc_fun(X23,X22))
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_fun(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_924])])]) ).
fof(c_0_1465,plain,
! [X13,X14,X15] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X15)
| c_lessequals(X13,c_Complete__Lattice_OSup__class_OSup(X14,X15),X15)
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14)) ),
inference(variable_rename,[status(thm)],[c_0_925]) ).
fof(c_0_1466,plain,
! [X13,X14,X15] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X15)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X14,X15),X13,X15)
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14)) ),
inference(variable_rename,[status(thm)],[c_0_926]) ).
fof(c_0_1467,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Oupper__semilattice(X21)
| c_lessequals(X18,c_Lattices_Oupper__semilattice__class_Osup(X20,X19,X21),X21)
| ~ c_lessequals(X18,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_927]) ).
fof(c_0_1468,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Oupper__semilattice(X21)
| c_lessequals(X18,c_Lattices_Oupper__semilattice__class_Osup(X20,X19,X21),X21)
| ~ c_lessequals(X18,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_928]) ).
fof(c_0_1469,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Olower__semilattice(X21)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X20,X19,X21),X18,X21)
| ~ c_lessequals(X20,X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_929]) ).
fof(c_0_1470,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Olower__semilattice(X21)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X20,X19,X21),X18,X21)
| ~ c_lessequals(X19,X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_930]) ).
fof(c_0_1471,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Oupper__semilattice(X21)
| c_HOL_Oord__class_Oless(X18,c_Lattices_Oupper__semilattice__class_Osup(X20,X19,X21),X21)
| ~ c_HOL_Oord__class_Oless(X18,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_931]) ).
fof(c_0_1472,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Oupper__semilattice(X21)
| c_HOL_Oord__class_Oless(X18,c_Lattices_Oupper__semilattice__class_Osup(X20,X19,X21),X21)
| ~ c_HOL_Oord__class_Oless(X18,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_932]) ).
fof(c_0_1473,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Olower__semilattice(X21)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X20,X19,X21),X18,X21)
| ~ c_HOL_Oord__class_Oless(X19,X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_933]) ).
fof(c_0_1474,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Olower__semilattice(X21)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X20,X19,X21),X18,X21)
| ~ c_HOL_Oord__class_Oless(X20,X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_934]) ).
fof(c_0_1475,plain,
! [X15,X16,X17] :
( X16 = X15
| ~ c_lessequals(X15,X16,tc_fun(X17,tc_bool))
| ~ c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_935])])]) ).
fof(c_0_1476,plain,
! [X15,X16,X17] :
( X16 = X15
| ~ c_lessequals(X15,X16,tc_fun(X17,tc_bool))
| ~ c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_936])])]) ).
fof(c_0_1477,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_lessequals(X18,hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X20)
| ~ c_lessequals(X19,hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_937]) ).
fof(c_0_1478,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_lessequals(X19,hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X20)
| ~ c_lessequals(X18,hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X20) ),
inference(variable_rename,[status(thm)],[c_0_938]) ).
fof(c_0_1479,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X19,X20)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_939]) ).
fof(c_0_1480,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X18,X20)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_940]) ).
fof(c_0_1481,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_HOL_Oord__class_Oless(X18,hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X20)
| ~ c_HOL_Oord__class_Oless(X19,hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_941]) ).
fof(c_0_1482,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_HOL_Oord__class_Oless(X19,hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X20)
| ~ c_HOL_Oord__class_Oless(X18,hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X20) ),
inference(variable_rename,[status(thm)],[c_0_942]) ).
fof(c_0_1483,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X19,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_943]) ).
fof(c_0_1484,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X18,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_944]) ).
fof(c_0_1485,plain,
! [X15,X16,X17] :
( c_Lattices_Olower__semilattice__class_Oinf(X16,X15,tc_fun(X17,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))
| c_HOL_Ominus__class_Ominus(X16,X15,tc_fun(X17,tc_bool)) = X16 ),
inference(variable_rename,[status(thm)],[c_0_945]) ).
fof(c_0_1486,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_HOL_Oord(X23)
| c_lessequals(hAPP(X22,X20),hAPP(X21,X20),X23)
| ~ c_lessequals(X22,X21,tc_fun(X24,X23)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_946])])]) ).
fof(c_0_1487,plain,
! [X31,X32,X33] :
( c_Set_Oinsert(X32,X31,X33) != c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X33),X32),X31)) ),
inference(variable_rename,[status(thm)],[c_0_947]) ).
fof(c_0_1488,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Oorder(X49)
| c_lessequals(X46,X48,X49)
| ~ c_lessequals(X46,X47,X49)
| ~ c_lessequals(X47,X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_948]) ).
fof(c_0_1489,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Oorder(X49)
| c_HOL_Oord__class_Oless(X46,X48,X49)
| ~ c_lessequals(X46,X47,X49)
| ~ c_HOL_Oord__class_Oless(X47,X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_949]) ).
fof(c_0_1490,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Oorder(X49)
| c_HOL_Oord__class_Oless(X46,X48,X49)
| ~ c_HOL_Oord__class_Oless(X46,X47,X49)
| ~ c_lessequals(X47,X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_950]) ).
fof(c_0_1491,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Opreorder(X49)
| c_lessequals(X48,X46,X49)
| ~ c_lessequals(X47,X46,X49)
| ~ c_lessequals(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_951]) ).
fof(c_0_1492,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Opreorder(X49)
| c_HOL_Oord__class_Oless(X48,X46,X49)
| ~ c_HOL_Oord__class_Oless(X47,X46,X49)
| ~ c_lessequals(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_952]) ).
fof(c_0_1493,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Opreorder(X49)
| c_HOL_Oord__class_Oless(X48,X46,X49)
| ~ c_lessequals(X47,X46,X49)
| ~ c_HOL_Oord__class_Oless(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_953]) ).
fof(c_0_1494,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Oorder(X49)
| c_HOL_Oord__class_Oless(X46,X48,X49)
| ~ c_HOL_Oord__class_Oless(X46,X47,X49)
| ~ c_HOL_Oord__class_Oless(X47,X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_954]) ).
fof(c_0_1495,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Opreorder(X49)
| c_HOL_Oord__class_Oless(X48,X46,X49)
| ~ c_HOL_Oord__class_Oless(X47,X46,X49)
| ~ c_HOL_Oord__class_Oless(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_955]) ).
fof(c_0_1496,plain,
! [X18,X19] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X19)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19),X19) = X18 ),
inference(variable_rename,[status(thm)],[c_0_956]) ).
fof(c_0_1497,plain,
! [X18,X19] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X19)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19),X19) = X18 ),
inference(variable_rename,[status(thm)],[c_0_957]) ).
fof(c_0_1498,plain,
! [X13,X14] :
( X13 = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_958]) ).
fof(c_0_1499,plain,
! [X19,X20,X21] :
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X20,X19,X21),tc_fun(X21,tc_bool)) = X20
| ~ c_Equiv__Relations_Oequiv(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_959]) ).
fof(c_0_1500,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X20)
| ~ c_lessequals(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_960]) ).
fof(c_0_1501,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18),hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19),X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_961]) ).
fof(c_0_1502,plain,
! [X18,X19,X20] :
( c_Set_Oinsert(X18,X19,X20) = X19
| ~ hBOOL(hAPP(hAPP(c_in(X20),X18),X19)) ),
inference(variable_rename,[status(thm)],[c_0_962]) ).
fof(c_0_1503,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oupper__semilattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12),X12) = c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_963]) ).
fof(c_0_1504,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12),X12) = c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_964]) ).
fof(c_0_1505,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X12) = c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_965]) ).
fof(c_0_1506,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X12) = c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_966]) ).
fof(c_0_1507,plain,
! [X20,X21,X22,X23] :
( ~ class_HOL_Oord(X22)
| c_lessequals(X21,X20,tc_fun(X23,X22))
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_fun(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_967])])]) ).
fof(c_0_1508,plain,
! [X15,X16,X17] :
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X16) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X17,tc_bool)),X15)
| X16 = X15 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_968])])]) ).
fof(c_0_1509,plain,
! [X18,X19,X20] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X18,X19,X20),X20) = c_Lattices_Oupper__semilattice__class_Osup(X18,c_Complete__Lattice_OSup__class_OSup(X19,X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_969]) ).
fof(c_0_1510,plain,
! [X18,X19,X20] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X18,X19,X20),X20) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Complete__Lattice_OInf__class_OInf(X19,X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_970]) ).
fof(c_0_1511,plain,
! [X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_in(X24),X22),c_Collect(X23,X24)))
| ~ hBOOL(hAPP(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_971])])]) ).
fof(c_0_1512,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_972]) ).
fof(c_0_1513,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X16,X15,tc_fun(X17,tc_bool))
| X16 = X15
| ~ c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_973]) ).
fof(c_0_1514,plain,
! [X15,X16,X17] :
( X16 = X15
| c_HOL_Oord__class_Oless(X16,X15,tc_fun(X17,tc_bool))
| ~ c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_974])])]) ).
fof(c_0_1515,plain,
! [X15,X16,X17] :
( c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(X17,tc_bool)) != X15
| c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_975]) ).
fof(c_0_1516,plain,
! [X15,X16,X17] :
( c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(X17,tc_bool)) = X16
| ~ c_lessequals(X15,X16,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_976]) ).
fof(c_0_1517,plain,
! [X15,X16,X17] :
( c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(X17,tc_bool)) = X15
| ~ c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_977]) ).
fof(c_0_1518,plain,
! [X15,X16,X17] :
( c_Lattices_Olower__semilattice__class_Oinf(X16,X15,tc_fun(X17,tc_bool)) = X16
| ~ c_lessequals(X16,X15,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_978]) ).
fof(c_0_1519,plain,
! [X15,X16,X17] :
( c_Lattices_Olower__semilattice__class_Oinf(X16,X15,tc_fun(X17,tc_bool)) = X15
| ~ c_lessequals(X15,X16,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_979]) ).
fof(c_0_1520,plain,
! [X39,X40,X41,X42] :
( hBOOL(hAPP(X40,X39))
| ~ hBOOL(hAPP(X41,X39))
| ~ c_lessequals(X41,X40,tc_fun(X42,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_980])])]) ).
fof(c_0_1521,plain,
! [X39,X40,X41,X42] :
( hBOOL(hAPP(X40,X39))
| ~ c_lessequals(X41,X40,tc_fun(X42,tc_bool))
| ~ hBOOL(hAPP(X41,X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_981])])]) ).
fof(c_0_1522,plain,
! [X15,X16,X17] :
( c_lessequals(X16,X15,tc_fun(X17,tc_bool))
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_982]) ).
fof(c_0_1523,plain,
! [X8,X9,X10] :
( hBOOL(hAPP(X9,X8))
| ~ hBOOL(hAPP(hAPP(c_in(X10),X8),X9)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_983])])]) ).
fof(c_0_1524,plain,
! [X15,X16,X17] :
( c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(X17,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_984]) ).
fof(c_0_1525,plain,
! [X15,X16,X17] :
( c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(X17,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))
| X16 = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_985]) ).
fof(c_0_1526,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Oab__group__add(X20)
| hAPP(c_HOL_Ouminus__class_Ouminus(X20),c_HOL_Ominus__class_Ominus(X19,X18,X20)) = c_HOL_Ominus__class_Ominus(X18,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_986]) ).
fof(c_0_1527,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_987]) ).
fof(c_0_1528,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_988]) ).
fof(c_0_1529,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_989]) ).
fof(c_0_1530,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Oab__group__add(X51)
| c_HOL_Ominus__class_Ominus(X50,X50,X51) != c_HOL_Ominus__class_Ominus(X49,X48,X51)
| X49 = X48 ),
inference(variable_rename,[status(thm)],[c_0_990]) ).
fof(c_0_1531,plain,
! [X31,X32,X33,X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| c_HOL_Ominus__class_Ominus(X32,X31,X34) != c_HOL_Ominus__class_Ominus(X33,X33,X34)
| X32 = X31 ),
inference(variable_rename,[status(thm)],[c_0_991]) ).
fof(c_0_1532,plain,
! [X7,X8] :
( ~ class_Orderings_Olinorder(X8)
| ~ c_lessequals(X7,X7,X8)
| ~ c_HOL_Oord__class_Oless(X7,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_992]) ).
fof(c_0_1533,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_993]) ).
fof(c_0_1534,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_994]) ).
fof(c_0_1535,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_lessequals(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_995]) ).
fof(c_0_1536,plain,
! [X18,X19,X20] :
( ~ class_Orderings_Oorder(X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(X18,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_996]) ).
fof(c_0_1537,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_997]) ).
fof(c_0_1538,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_998]) ).
fof(c_0_1539,plain,
! [X18,X19,X20] :
( ~ class_Orderings_Opreorder(X20)
| ~ c_HOL_Oord__class_Oless(X18,X19,X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_999]) ).
fof(c_0_1540,plain,
! [X4,X5,X6] :
( X5 = X4
| ~ hBOOL(hAPP(hAPP(c_fequal(X6),X5),X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1000])])]) ).
fof(c_0_1541,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12),X12) = X11 ),
inference(variable_rename,[status(thm)],[c_0_1001]) ).
fof(c_0_1542,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X12) = X11 ),
inference(variable_rename,[status(thm)],[c_0_1002]) ).
fof(c_0_1543,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1003]) ).
fof(c_0_1544,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1004]) ).
fof(c_0_1545,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1005]) ).
fof(c_0_1546,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1006]) ).
fof(c_0_1547,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oupper__semilattice(X12)
| c_lessequals(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1007]) ).
fof(c_0_1548,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oupper__semilattice(X12)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1008]) ).
fof(c_0_1549,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1009]) ).
fof(c_0_1550,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_lessequals(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1010]) ).
fof(c_0_1551,plain,
! [X8,X9,X10] :
( hBOOL(hAPP(hAPP(c_in(X10),X8),X9))
| ~ hBOOL(hAPP(X9,X8)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1011])])]) ).
fof(c_0_1552,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oboolean__algebra(X12)
| c_HOL_Ominus__class_Ominus(X11,X10,X12) = c_Lattices_Olower__semilattice__class_Oinf(X11,hAPP(c_HOL_Ouminus__class_Ouminus(X12),X10),X12) ),
inference(variable_rename,[status(thm)],[c_0_1012]) ).
fof(c_0_1553,plain,
! [X18,X19,X20] :
( ~ class_Orderings_Oorder(X20)
| c_HOL_Oord__class_Oless(X18,X19,X20)
| X19 = X18
| ~ c_lessequals(X18,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_1013]) ).
fof(c_0_1554,plain,
! [X18,X19,X20] :
( ~ class_Orderings_Oorder(X20)
| c_HOL_Oord__class_Oless(X18,X19,X20)
| ~ c_lessequals(X18,X19,X20)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[c_0_1014]) ).
fof(c_0_1555,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1015]) ).
fof(c_0_1556,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1016]) ).
fof(c_0_1557,plain,
! [X18,X19,X20] :
( ~ class_Orderings_Oorder(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| X19 = X18
| ~ c_lessequals(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_1017]) ).
fof(c_0_1558,plain,
! [X18,X19,X20] :
( ~ class_Orderings_Oorder(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_lessequals(X19,X18,X20)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[c_0_1018]) ).
fof(c_0_1559,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1019]) ).
fof(c_0_1560,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1020]) ).
fof(c_0_1561,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oupper__semilattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12) != X10
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1021]) ).
fof(c_0_1562,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) != X11
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1022]) ).
fof(c_0_1563,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oupper__semilattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12) = X10
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1023]) ).
fof(c_0_1564,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oupper__semilattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12) = X11
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1024]) ).
fof(c_0_1565,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) = X11
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1025]) ).
fof(c_0_1566,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) = X10
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1026]) ).
fof(c_0_1567,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1027]) ).
fof(c_0_1568,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1028]) ).
fof(c_0_1569,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1029]) ).
fof(c_0_1570,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1030]) ).
fof(c_0_1571,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1031]) ).
fof(c_0_1572,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1032]) ).
fof(c_0_1573,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1033]) ).
fof(c_0_1574,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1034]) ).
fof(c_0_1575,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(X10,X11,X12)
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1035]) ).
fof(c_0_1576,plain,
! [X7,X8] :
( ~ class_Orderings_Olinorder(X8)
| c_HOL_Oord__class_Oless(X7,X7,X8)
| c_lessequals(X7,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1036]) ).
fof(c_0_1577,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1037]) ).
fof(c_0_1578,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1038]) ).
fof(c_0_1579,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oupper__semilattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12) = c_Lattices_Oupper__semilattice__class_Osup(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1039]) ).
fof(c_0_1580,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12) = c_Lattices_Oupper__semilattice__class_Osup(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1040]) ).
fof(c_0_1581,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) = c_Lattices_Olower__semilattice__class_Oinf(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1041]) ).
fof(c_0_1582,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) = c_Lattices_Olower__semilattice__class_Oinf(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1042]) ).
fof(c_0_1583,plain,
! [X22,X23,X24] :
( c_Collect(X23,X24) != c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool))
| ~ hBOOL(hAPP(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1043])])]) ).
fof(c_0_1584,plain,
! [X22,X23,X24] :
( c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) != c_Collect(X23,X24)
| ~ hBOOL(hAPP(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1044])])]) ).
fof(c_0_1585,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Obounded__lattice(X17)
| c_Lattices_Oupper__semilattice__class_Osup(X16,X15,X17) != c_Orderings_Obot__class_Obot(X17)
| X16 = c_Orderings_Obot__class_Obot(X17) ),
inference(variable_rename,[status(thm)],[c_0_1045]) ).
fof(c_0_1586,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Obounded__lattice(X17)
| c_Lattices_Oupper__semilattice__class_Osup(X16,X15,X17) != c_Orderings_Obot__class_Obot(X17)
| X15 = c_Orderings_Obot__class_Obot(X17) ),
inference(variable_rename,[status(thm)],[c_0_1046]) ).
fof(c_0_1587,plain,
! [X7,X8] :
( ~ class_Lattices_Oboolean__algebra(X8)
| c_Lattices_Olower__semilattice__class_Oinf(X7,hAPP(c_HOL_Ouminus__class_Ouminus(X8),X7),X8) = c_Orderings_Obot__class_Obot(X8) ),
inference(variable_rename,[status(thm)],[c_0_1047]) ).
fof(c_0_1588,plain,
! [X7,X8] :
( ~ class_Lattices_Oboolean__algebra(X8)
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X8),X7),X7,X8) = c_Orderings_Obot__class_Obot(X8) ),
inference(variable_rename,[status(thm)],[c_0_1048]) ).
fof(c_0_1589,plain,
! [X7,X8] :
( ~ class_Orderings_Oorder(X8)
| ~ c_HOL_Oord__class_Oless(X7,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1049]) ).
fof(c_0_1590,plain,
! [X7,X8] :
( ~ class_Orderings_Olinorder(X8)
| ~ c_HOL_Oord__class_Oless(X7,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1050]) ).
fof(c_0_1591,plain,
! [X7,X8] :
( ~ class_Orderings_Opreorder(X8)
| ~ c_HOL_Oord__class_Oless(X7,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1051]) ).
fof(c_0_1592,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_1052]) ).
fof(c_0_1593,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oboolean__algebra(X12)
| hAPP(c_HOL_Ouminus__class_Ouminus(X12),X11) != hAPP(c_HOL_Ouminus__class_Ouminus(X12),X10)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1053]) ).
fof(c_0_1594,plain,
! [X18,X19,X20] :
( ~ class_OrderedGroup_Ogroup__add(X20)
| hAPP(c_HOL_Ouminus__class_Ouminus(X20),X19) != hAPP(c_HOL_Ouminus__class_Ouminus(X20),X18)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[c_0_1054]) ).
fof(c_0_1595,plain,
! [X7,X8] :
( ~ class_Lattices_Obounded__lattice(X8)
| c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Obot__class_Obot(X8),X8) = c_Orderings_Obot__class_Obot(X8) ),
inference(variable_rename,[status(thm)],[c_0_1055]) ).
fof(c_0_1596,plain,
! [X7,X8] :
( ~ class_Lattices_Obounded__lattice(X8)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X8),X7,X8) = c_Orderings_Obot__class_Obot(X8) ),
inference(variable_rename,[status(thm)],[c_0_1056]) ).
fof(c_0_1597,plain,
! [X7,X8] :
( ~ class_Lattices_Obounded__lattice(X8)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X8),X7,X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_1057]) ).
fof(c_0_1598,plain,
! [X7,X8] :
( ~ class_Lattices_Obounded__lattice(X8)
| c_Lattices_Oupper__semilattice__class_Osup(X7,c_Orderings_Obot__class_Obot(X8),X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_1058]) ).
fof(c_0_1599,plain,
! [X7,X8] :
( ~ class_Orderings_Obot(X8)
| c_lessequals(c_Orderings_Obot__class_Obot(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1059]) ).
fof(c_0_1600,plain,
! [X18,X19] :
( ~ class_OrderedGroup_Ogroup__add(X19)
| hAPP(c_HOL_Ouminus__class_Ouminus(X19),hAPP(c_HOL_Ouminus__class_Ouminus(X19),X18)) = X18 ),
inference(variable_rename,[status(thm)],[c_0_1060]) ).
fof(c_0_1601,plain,
! [X7,X8] :
( ~ class_Lattices_Oboolean__algebra(X8)
| hAPP(c_HOL_Ouminus__class_Ouminus(X8),hAPP(c_HOL_Ouminus__class_Ouminus(X8),X7)) = X7 ),
inference(variable_rename,[status(thm)],[c_0_1061]) ).
fof(c_0_1602,plain,
! [X17,X18] :
( ~ class_OrderedGroup_Ogroup__add(X18)
| X17 = hAPP(c_HOL_Ouminus__class_Ouminus(X18),hAPP(c_HOL_Ouminus__class_Ouminus(X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_1062]) ).
fof(c_0_1603,plain,
! [X18,X19] :
( ~ class_OrderedGroup_Ogroup__add(X19)
| X18 = hAPP(c_HOL_Ouminus__class_Ouminus(X19),hAPP(c_HOL_Ouminus__class_Ouminus(X19),X18)) ),
inference(variable_rename,[status(thm)],[c_0_1063]) ).
fof(c_0_1604,plain,
! [X17,X18] :
( ~ class_OrderedGroup_Ogroup__add(X18)
| hAPP(c_HOL_Ouminus__class_Ouminus(X18),hAPP(c_HOL_Ouminus__class_Ouminus(X18),X17)) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1064]) ).
fof(c_0_1605,plain,
! [X7,X8] :
( ~ class_Lattices_Oupper__semilattice(X8)
| c_Lattices_Oupper__semilattice__class_Osup(X7,X7,X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_1065]) ).
fof(c_0_1606,plain,
! [X7,X8] :
( ~ class_Lattices_Olower__semilattice(X8)
| c_Lattices_Olower__semilattice__class_Oinf(X7,X7,X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_1066]) ).
fof(c_0_1607,plain,
! [X7,X8] :
( ~ class_Orderings_Oorder(X8)
| c_lessequals(X7,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1067]) ).
fof(c_0_1608,plain,
! [X7,X8] :
( ~ class_Orderings_Opreorder(X8)
| c_lessequals(X7,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1068]) ).
fof(c_0_1609,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_1069]) ).
fof(c_0_1610,plain,
! [X6,X7] :
( class_Lattices_Oupper__semilattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1070]) ).
fof(c_0_1611,plain,
! [X6,X7] :
( class_Lattices_Olower__semilattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1071]) ).
fof(c_0_1612,plain,
! [X6,X7] :
( class_Lattices_Odistrib__lattice(tc_fun(X6,X7))
| ~ class_Lattices_Odistrib__lattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1072]) ).
fof(c_0_1613,plain,
! [X6,X7] :
( class_Lattices_Obounded__lattice(tc_fun(X6,X7))
| ~ class_Lattices_Obounded__lattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1073]) ).
fof(c_0_1614,plain,
! [X6,X7] :
( class_Lattices_Oboolean__algebra(tc_fun(X6,X7))
| ~ class_Lattices_Oboolean__algebra(X7) ),
inference(variable_rename,[status(thm)],[c_0_1074]) ).
fof(c_0_1615,plain,
! [X6,X7] :
( class_Orderings_Opreorder(tc_fun(X6,X7))
| ~ class_Orderings_Opreorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_1075]) ).
fof(c_0_1616,plain,
! [X6,X7] :
( class_Lattices_Olattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1076]) ).
fof(c_0_1617,plain,
! [X6,X7] :
( class_Orderings_Oorder(tc_fun(X6,X7))
| ~ class_Orderings_Oorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_1077]) ).
fof(c_0_1618,plain,
! [X6,X7] :
( class_Orderings_Obot(tc_fun(X6,X7))
| ~ class_Orderings_Obot(X7) ),
inference(variable_rename,[status(thm)],[c_0_1078]) ).
fof(c_0_1619,plain,
! [X6,X7] :
( class_HOL_Oord(tc_fun(X6,X7))
| ~ class_HOL_Oord(X7) ),
inference(variable_rename,[status(thm)],[c_0_1079]) ).
cnf(c_0_1620,plain,
( c_Complete__Lattice_Ocomplete__lattice(X2,X1,c_COMBC(X3,X9,X9,tc_bool),c_COMBC(X4,X9,X9,tc_bool),X6,X5,X8,X7,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1080]) ).
cnf(c_0_1621,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_1081]) ).
cnf(c_0_1622,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_1082]) ).
cnf(c_0_1623,plain,
( hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X9),X10),X11)) ),
inference(split_conjunct,[status(thm)],[c_0_1083]) ).
cnf(c_0_1624,plain,
( hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X9),X10),X11)) ),
inference(split_conjunct,[status(thm)],[c_0_1084]) ).
cnf(c_0_1625,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_1085]) ).
cnf(c_0_1626,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_1086]) ).
cnf(c_0_1627,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_1087]) ).
cnf(c_0_1628,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_1088]) ).
cnf(c_0_1629,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_1089]) ).
cnf(c_0_1630,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_1090]) ).
cnf(c_0_1631,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X5,X1))),hAPP(X4,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X5,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1091]) ).
cnf(c_0_1632,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X5,X1))),hAPP(X4,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X5,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1092]) ).
cnf(c_0_1633,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,c_COMBK(X4,tc_fun(X1,tc_bool),X5),X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X3,X4,X2,X5,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1093]) ).
cnf(c_0_1634,plain,
( c_Nitpick_Ofold__graph_H(X4,X5,X3,hAPP(hAPP(X4,X2),X6),X1,X7)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X6,X1,X7) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1635,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(hAPP(hAPP(c_in(X5),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1095]) ).
cnf(c_0_1636,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X2,X3,X1),hAPP(hAPP(X4,X2),X6),X1,X7)
| ~ c_Finite__Set_Ofold__graph(X4,X5,X3,X6,X1,X7) ),
inference(split_conjunct,[status(thm)],[c_0_1096]) ).
cnf(c_0_1637,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X6,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1097]) ).
cnf(c_0_1638,plain,
( X1 = X2
| X4 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1098]) ).
cnf(c_0_1639,plain,
( X1 = X2
| X4 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1640,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X2,X3,X4,X1,X5)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X5,tc_bool),X1),X1,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1641,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X4,X3,X5,X1,X2)),X4))
| X3 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X5),c_FuncSet_Oextensional(X4,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1642,plain,
( hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(X7,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1643,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X4,X1,X5)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,X3,X1,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1644,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X4,X1,X5)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,X3,X1,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1645,plain,
( X1 = X2
| X4 = X5
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1646,plain,
( X1 = X2
| X4 = X5
| X5 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1647,plain,
( X1 = X2
| X4 = X5
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1648,plain,
( X1 = X2
| X4 = X5
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1649,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| X1 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1650,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| X4 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1651,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| X4 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1652,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| X1 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1653,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_1113]) ).
cnf(c_0_1654,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_Oextensional(X5,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X2),c_FuncSet_Oextensional(X5,X3,X4)))
| hAPP(X1,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) != hAPP(X2,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1655,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1656,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1657,plain,
( hBOOL(hAPP(hAPP(X4,X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1117]) ).
cnf(c_0_1658,plain,
( hBOOL(hAPP(hAPP(X3,X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1118]) ).
cnf(c_0_1659,plain,
( hBOOL(hAPP(hAPP(X4,X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1660,plain,
( hBOOL(hAPP(hAPP(X3,X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1661,plain,
( X1 = X2
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1662,plain,
( X1 = X2
| X4 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1663,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X2 = X4
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1664,plain,
( X1 = X2
| X5 = X1
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1665,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X4 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1666,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1667,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X4 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1668,plain,
( X1 = X2
| X4 = X5
| X4 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1669,plain,
( X1 = X2
| X4 = X5
| X5 = X1
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1670,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| X4 = X2
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1671,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| X1 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1672,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| X1 = X4
| X1 = X2
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1673,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| X4 = X2
| X1 = X2
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1674,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1675,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1)))
| X4 = X1
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1676,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1677,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4)))
| X2 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1137]) ).
cnf(c_0_1678,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Oconverse(X5,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1138]) ).
cnf(c_0_1679,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1680,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1140]) ).
cnf(c_0_1681,plain,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X1,X2)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_1141]) ).
cnf(c_0_1682,plain,
( X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1683,plain,
( X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1684,plain,
( X1 = X2
| X3 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1685,plain,
( X1 = X2
| X3 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1145]) ).
cnf(c_0_1686,plain,
( X1 = X2
| X3 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1146]) ).
cnf(c_0_1687,plain,
( X1 = X2
| X1 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1147]) ).
cnf(c_0_1688,plain,
( X4 = X5
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X7,X3,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1148]) ).
cnf(c_0_1689,plain,
( c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1149]) ).
cnf(c_0_1690,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1150]) ).
cnf(c_0_1691,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1151]) ).
cnf(c_0_1692,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1693,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X4,X2,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1153]) ).
cnf(c_0_1694,plain,
( hBOOL(hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(X7,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1695,plain,
( hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X1,X4,X2,X5,X6)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1696,plain,
( hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X2,X5,X6)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1697,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1157]) ).
cnf(c_0_1698,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1699,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1700,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1701,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1161]) ).
cnf(c_0_1702,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1162]) ).
cnf(c_0_1703,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1704,plain,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1164]) ).
cnf(c_0_1705,plain,
( c_Set_Oimage(c_Fun_Ofun__upd(X4,X2,X5,X1,X6),X3,X1,X6) = c_Set_Oinsert(X5,c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1,X6),X6)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1165]) ).
cnf(c_0_1706,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)),c_Equiv__Relations_Oquotient(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1707,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1167]) ).
cnf(c_0_1708,plain,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X5)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4)))
| c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1709,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1169]) ).
cnf(c_0_1710,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1)
| c_Relation_OImage(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1170]) ).
cnf(c_0_1711,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Set_Oimage(X1,X2,X3,X4)))
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1712,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1172]) ).
cnf(c_0_1713,plain,
( c_lessequals(c_Relation_OImage(X3,X1,X2,X4),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X3,X2,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X2)),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1173]) ).
cnf(c_0_1714,plain,
( c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| ~ c_Fun_Oinj__on(X1,X2,X4,X5)
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1174]) ).
cnf(c_0_1715,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1175]) ).
cnf(c_0_1716,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1176]) ).
cnf(c_0_1717,plain,
( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X3),tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1177]) ).
cnf(c_0_1718,plain,
( c_lessequals(c_Set_Oimage(X3,X4,X1,X2),X5,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,c_COMBK(X5,tc_fun(X2,tc_bool),X1),X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1719,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1179]) ).
cnf(c_0_1720,plain,
( hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1180]) ).
cnf(c_0_1721,plain,
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1181]) ).
cnf(c_0_1722,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X1 = X2
| X1 = X2
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1723,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X1 = X2
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1183]) ).
cnf(c_0_1724,plain,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,c_COMBK(X5,tc_fun(X2,tc_bool),X1),X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1184]) ).
cnf(c_0_1725,plain,
( c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1185]) ).
cnf(c_0_1726,plain,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1186]) ).
cnf(c_0_1727,plain,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1187]) ).
cnf(c_0_1728,plain,
( hAPP(X3,X2) = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X1,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_1188]) ).
cnf(c_0_1729,plain,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X1,X3,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X3)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1189]) ).
cnf(c_0_1730,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oimage(c_Fun_Ofun__upd(X4,X2,X5,X1,X6),X3,X1,X6) = c_Set_Oimage(X4,X3,X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1190]) ).
cnf(c_0_1731,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_List_Osko__Equiv__Relations__XquotientE__1__1(X3,X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Equiv__Relations_Oquotient(X3,X4,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1732,plain,
( hAPP(c_Fun_Ooverride__on(X4,X5,X3,X1,X6),X2) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1192]) ).
cnf(c_0_1733,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X5,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1193]) ).
cnf(c_0_1734,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1194]) ).
cnf(c_0_1735,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(c_Fun_Ooverride__on(X4,X5,X3,X1,X6),X2) = hAPP(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1195]) ).
cnf(c_0_1736,plain,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1196]) ).
cnf(c_0_1737,plain,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1197]) ).
cnf(c_0_1738,plain,
( c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1198]) ).
cnf(c_0_1739,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1740,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1741,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1201]) ).
cnf(c_0_1742,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1202]) ).
cnf(c_0_1743,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1744,plain,
( X1 = X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| ~ hBOOL(hAPP(hAPP(c_in(X7),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X7),X2),X5))
| hAPP(X4,X1) != hAPP(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1204]) ).
cnf(c_0_1745,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X2)))
| X1 = X2
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_1205]) ).
cnf(c_0_1746,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X1)))
| X2 = X1
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_1206]) ).
cnf(c_0_1747,plain,
( X2 = c_Relation_OImage(X4,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(X3,X2,X4,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Equiv__Relations_Oquotient(X3,X4,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1748,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1749,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1209]) ).
cnf(c_0_1750,plain,
( hBOOL(hAPP(hAPP(c_in(X5),hAPP(X1,X6)),X3))
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1210]) ).
cnf(c_0_1751,plain,
( hAPP(X1,hAPP(X2,X6)) = X6
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X6),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1752,plain,
( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1753,plain,
( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1754,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1755,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1215]) ).
cnf(c_0_1756,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1216]) ).
cnf(c_0_1757,plain,
( X1 = X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1758,plain,
( hAPP(X2,hAPP(X1,X6)) = X6
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1759,plain,
( hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_1219]) ).
cnf(c_0_1760,plain,
( hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_1220]) ).
cnf(c_0_1761,plain,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1221]) ).
cnf(c_0_1762,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1222]) ).
cnf(c_0_1763,plain,
( hBOOL(hAPP(hAPP(X3,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1223]) ).
cnf(c_0_1764,plain,
( hBOOL(hAPP(hAPP(X3,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1224]) ).
cnf(c_0_1765,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1225]) ).
cnf(c_0_1766,plain,
( X4 = X5
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1226]) ).
cnf(c_0_1767,plain,
( X1 = X2
| hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1) != hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1227]) ).
cnf(c_0_1768,plain,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1228]) ).
cnf(c_0_1769,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1229]) ).
cnf(c_0_1770,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1230]) ).
cnf(c_0_1771,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1231]) ).
cnf(c_0_1772,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1232]) ).
cnf(c_0_1773,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1233]) ).
cnf(c_0_1774,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1234]) ).
cnf(c_0_1775,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1235]) ).
cnf(c_0_1776,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1236]) ).
cnf(c_0_1777,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1237]) ).
cnf(c_0_1778,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1238]) ).
cnf(c_0_1779,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1239]) ).
cnf(c_0_1780,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1240]) ).
cnf(c_0_1781,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1241]) ).
cnf(c_0_1782,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1242]) ).
cnf(c_0_1783,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(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1243]) ).
cnf(c_0_1784,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(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1244]) ).
cnf(c_0_1785,plain,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),c_Set_Oimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1245]) ).
cnf(c_0_1786,plain,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),c_Set_Oimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1246]) ).
cnf(c_0_1787,plain,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X5,X2)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1247]) ).
cnf(c_0_1788,plain,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X5,X2)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1248]) ).
cnf(c_0_1789,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OatLeastAtMost(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1249]) ).
cnf(c_0_1790,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1250]) ).
cnf(c_0_1791,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_1251]) ).
cnf(c_0_1792,plain,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X6)),X5))
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1252]) ).
cnf(c_0_1793,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1253]) ).
cnf(c_0_1794,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1254]) ).
cnf(c_0_1795,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(hAPP(hAPP(c_in(X3),X6),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1255]) ).
cnf(c_0_1796,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1256]) ).
cnf(c_0_1797,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1257]) ).
cnf(c_0_1798,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1258]) ).
cnf(c_0_1799,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_1259]) ).
cnf(c_0_1800,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_1260]) ).
cnf(c_0_1801,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_1261]) ).
cnf(c_0_1802,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1,tc_nat) = c_Finite__Set_Osetsum(X4,X3,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1262]) ).
cnf(c_0_1803,plain,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1263]) ).
cnf(c_0_1804,plain,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1264]) ).
cnf(c_0_1805,plain,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1265]) ).
cnf(c_0_1806,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1266]) ).
cnf(c_0_1807,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1267]) ).
cnf(c_0_1808,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1268]) ).
cnf(c_0_1809,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(hAPP(hAPP(c_in(X4),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1269]) ).
cnf(c_0_1810,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1270]) ).
cnf(c_0_1811,plain,
( c_Set_Oinsert(hAPP(X4,X2),c_Set_Oimage(X4,X3,X1,X5),X5) = c_Set_Oimage(X4,X3,X1,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1271]) ).
cnf(c_0_1812,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1272]) ).
cnf(c_0_1813,plain,
( hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1273]) ).
cnf(c_0_1814,plain,
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1274]) ).
cnf(c_0_1815,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1275]) ).
cnf(c_0_1816,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X5),X4))
| hAPP(X3,X5) = c_HOL_Oundefined(X2)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1276]) ).
cnf(c_0_1817,plain,
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_1277]) ).
cnf(c_0_1818,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1278]) ).
cnf(c_0_1819,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1279]) ).
cnf(c_0_1820,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1280]) ).
cnf(c_0_1821,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1281]) ).
cnf(c_0_1822,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X2,X3,X1)),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1282]) ).
cnf(c_0_1823,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1283]) ).
cnf(c_0_1824,plain,
( c_Fun_Oinj__on(X1,X2,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1284]) ).
cnf(c_0_1825,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1285]) ).
cnf(c_0_1826,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1286]) ).
cnf(c_0_1827,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1287]) ).
cnf(c_0_1828,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_1288]) ).
cnf(c_0_1829,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_1289]) ).
cnf(c_0_1830,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_1290]) ).
cnf(c_0_1831,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_1291]) ).
cnf(c_0_1832,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),X4,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1292]) ).
cnf(c_0_1833,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1293]) ).
cnf(c_0_1834,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1294]) ).
cnf(c_0_1835,plain,
( c_lessequals(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1295]) ).
cnf(c_0_1836,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1296]) ).
cnf(c_0_1837,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1297]) ).
cnf(c_0_1838,plain,
( c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1298]) ).
cnf(c_0_1839,plain,
( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1299]) ).
cnf(c_0_1840,plain,
( X1 = X2
| c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1300]) ).
cnf(c_0_1841,plain,
( X1 = X2
| c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1301]) ).
cnf(c_0_1842,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1302]) ).
cnf(c_0_1843,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1303]) ).
cnf(c_0_1844,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1304]) ).
cnf(c_0_1845,plain,
( X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ c_Fun_Oinj__on(X5,X3,X1,X6)
| hAPP(X5,X2) != hAPP(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1305]) ).
cnf(c_0_1846,plain,
( c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1306]) ).
cnf(c_0_1847,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1307]) ).
cnf(c_0_1848,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1308]) ).
cnf(c_0_1849,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1309]) ).
cnf(c_0_1850,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1310]) ).
cnf(c_0_1851,plain,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1311]) ).
cnf(c_0_1852,plain,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1312]) ).
cnf(c_0_1853,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1313]) ).
cnf(c_0_1854,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1314]) ).
cnf(c_0_1855,plain,
( c_lessequals(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,X5),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1315]) ).
cnf(c_0_1856,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1316]) ).
cnf(c_0_1857,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1317]) ).
cnf(c_0_1858,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1318]) ).
cnf(c_0_1859,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X3,X1)),X2))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1319]) ).
cnf(c_0_1860,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1320]) ).
cnf(c_0_1861,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1321]) ).
cnf(c_0_1862,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1322]) ).
cnf(c_0_1863,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1323]) ).
cnf(c_0_1864,plain,
( hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1324]) ).
cnf(c_0_1865,plain,
( hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1325]) ).
cnf(c_0_1866,plain,
( c_Set_Oimage(c_COMBK(X4,X5,X1),X3,X1,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1326]) ).
cnf(c_0_1867,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1327]) ).
cnf(c_0_1868,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_1328]) ).
cnf(c_0_1869,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_1329]) ).
cnf(c_0_1870,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(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_1330]) ).
cnf(c_0_1871,plain,
( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1331]) ).
cnf(c_0_1872,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,X4,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1332]) ).
cnf(c_0_1873,plain,
( c_lessequals(X3,X2,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1333]) ).
cnf(c_0_1874,plain,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1334]) ).
cnf(c_0_1875,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1335]) ).
cnf(c_0_1876,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_1336]) ).
cnf(c_0_1877,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) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1337]) ).
cnf(c_0_1878,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_1338]) ).
cnf(c_0_1879,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_1339]) ).
cnf(c_0_1880,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_1340]) ).
cnf(c_0_1881,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_1341]) ).
cnf(c_0_1882,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatMost(X3,X4,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1342]) ).
cnf(c_0_1883,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThan(X3,X4,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1343]) ).
cnf(c_0_1884,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1344]) ).
cnf(c_0_1885,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1345]) ).
cnf(c_0_1886,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1346]) ).
cnf(c_0_1887,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1347]) ).
cnf(c_0_1888,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1348]) ).
cnf(c_0_1889,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1349]) ).
cnf(c_0_1890,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)),X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1350]) ).
cnf(c_0_1891,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)),X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1351]) ).
cnf(c_0_1892,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1352]) ).
cnf(c_0_1893,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1353]) ).
cnf(c_0_1894,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1354]) ).
cnf(c_0_1895,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1355]) ).
cnf(c_0_1896,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1356]) ).
cnf(c_0_1897,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X3,X1,X2),X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1357]) ).
cnf(c_0_1898,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X3,X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_1358]) ).
cnf(c_0_1899,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1359]) ).
cnf(c_0_1900,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1360]) ).
cnf(c_0_1901,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1361]) ).
cnf(c_0_1902,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1362]) ).
cnf(c_0_1903,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1363]) ).
cnf(c_0_1904,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Ovimage(c_COMBK(X2,X1,X4),X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1364]) ).
cnf(c_0_1905,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_1365]) ).
cnf(c_0_1906,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),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_1366]) ).
cnf(c_0_1907,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),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_1367]) ).
cnf(c_0_1908,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_1368]) ).
cnf(c_0_1909,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_1369]) ).
cnf(c_0_1910,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1370]) ).
cnf(c_0_1911,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| 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_1371]) ).
cnf(c_0_1912,plain,
( c_lessequals(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1372]) ).
cnf(c_0_1913,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1373]) ).
cnf(c_0_1914,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1374]) ).
cnf(c_0_1915,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),c_Set_OPow(X2,X3)))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1375]) ).
cnf(c_0_1916,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1376]) ).
cnf(c_0_1917,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1377]) ).
cnf(c_0_1918,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1378]) ).
cnf(c_0_1919,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1379]) ).
cnf(c_0_1920,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_1380]) ).
cnf(c_0_1921,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_1381]) ).
cnf(c_0_1922,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_1923,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1383]) ).
cnf(c_0_1924,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,tc_fun(X4,tc_bool)) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_1384]) ).
cnf(c_0_1925,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1385]) ).
cnf(c_0_1926,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X3),c_SetInterval_Oord_OgreaterThan(X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1386]) ).
cnf(c_0_1927,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1387]) ).
cnf(c_0_1928,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_1388]) ).
cnf(c_0_1929,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_1389]) ).
cnf(c_0_1930,plain,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1390]) ).
cnf(c_0_1931,plain,
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1391]) ).
cnf(c_0_1932,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1392]) ).
cnf(c_0_1933,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1393]) ).
cnf(c_0_1934,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1394]) ).
cnf(c_0_1935,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1395]) ).
cnf(c_0_1936,plain,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1396]) ).
cnf(c_0_1937,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1397]) ).
cnf(c_0_1938,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1398]) ).
cnf(c_0_1939,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_1940,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_1400]) ).
cnf(c_0_1941,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1401]) ).
cnf(c_0_1942,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1402]) ).
cnf(c_0_1943,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X1),X4))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1403]) ).
cnf(c_0_1944,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1404]) ).
cnf(c_0_1945,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1405]) ).
cnf(c_0_1946,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1406]) ).
cnf(c_0_1947,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1407]) ).
cnf(c_0_1948,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1408]) ).
cnf(c_0_1949,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1409]) ).
cnf(c_0_1950,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| c_Set_Oinsert(X4,X1,X3) != c_Set_Oinsert(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1410]) ).
cnf(c_0_1951,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_1411]) ).
cnf(c_0_1952,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_1412]) ).
cnf(c_0_1953,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1413]) ).
cnf(c_0_1954,plain,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_1955,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_1956,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_1957,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_1417]) ).
cnf(c_0_1958,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_1959,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_1960,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_1420]) ).
cnf(c_0_1961,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_1962,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_1963,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1423]) ).
cnf(c_0_1964,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_1424]) ).
cnf(c_0_1965,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_1425]) ).
cnf(c_0_1966,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_1426]) ).
cnf(c_0_1967,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3))
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1427]) ).
cnf(c_0_1968,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3))
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1428]) ).
cnf(c_0_1969,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_1429]) ).
cnf(c_0_1970,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_1430]) ).
cnf(c_0_1971,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_1431]) ).
cnf(c_0_1972,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_1432]) ).
cnf(c_0_1973,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_1433]) ).
cnf(c_0_1974,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1434]) ).
cnf(c_0_1975,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1435]) ).
cnf(c_0_1976,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1436]) ).
cnf(c_0_1977,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1437]) ).
cnf(c_0_1978,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_1438]) ).
cnf(c_0_1979,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1439]) ).
cnf(c_0_1980,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1440]) ).
cnf(c_0_1981,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1441]) ).
cnf(c_0_1982,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_1442]) ).
cnf(c_0_1983,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_1443]) ).
cnf(c_0_1984,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1444]) ).
cnf(c_0_1985,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1445]) ).
cnf(c_0_1986,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_1446]) ).
cnf(c_0_1987,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_1447]) ).
cnf(c_0_1988,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_1448]) ).
cnf(c_0_1989,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_1449]) ).
cnf(c_0_1990,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1450]) ).
cnf(c_0_1991,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1451]) ).
cnf(c_0_1992,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1452]) ).
cnf(c_0_1993,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1453]) ).
cnf(c_0_1994,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_1454]) ).
cnf(c_0_1995,plain,
( c_lessequals(X2,X1,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1455]) ).
cnf(c_0_1996,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1456]) ).
cnf(c_0_1997,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1457]) ).
cnf(c_0_1998,plain,
( c_lessequals(X3,X2,X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1458]) ).
cnf(c_0_1999,plain,
( c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1459]) ).
cnf(c_0_2000,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1460]) ).
cnf(c_0_2001,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1461]) ).
cnf(c_0_2002,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1462]) ).
cnf(c_0_2003,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1463]) ).
cnf(c_0_2004,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1464]) ).
cnf(c_0_2005,plain,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1465]) ).
cnf(c_0_2006,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X3,X1),X2,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1466]) ).
cnf(c_0_2007,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_1467]) ).
cnf(c_0_2008,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_1468]) ).
cnf(c_0_2009,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1469]) ).
cnf(c_0_2010,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1470]) ).
cnf(c_0_2011,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1471]) ).
cnf(c_0_2012,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1472]) ).
cnf(c_0_2013,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1473]) ).
cnf(c_0_2014,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1474]) ).
cnf(c_0_2015,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_1475]) ).
cnf(c_0_2016,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_1476]) ).
cnf(c_0_2017,plain,
( c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2018,plain,
( c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1478]) ).
cnf(c_0_2019,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1479]) ).
cnf(c_0_2020,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1480]) ).
cnf(c_0_2021,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1481]) ).
cnf(c_0_2022,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1482]) ).
cnf(c_0_2023,plain,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1483]) ).
cnf(c_0_2024,plain,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1484]) ).
cnf(c_0_2025,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1485]) ).
cnf(c_0_2026,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_1486]) ).
cnf(c_0_2027,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oinsert(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1487]) ).
cnf(c_0_2028,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_1488]) ).
cnf(c_0_2029,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1489]) ).
cnf(c_0_2030,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1490]) ).
cnf(c_0_2031,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_1491]) ).
cnf(c_0_2032,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1492]) ).
cnf(c_0_2033,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1493]) ).
cnf(c_0_2034,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1494]) ).
cnf(c_0_2035,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1495]) ).
cnf(c_0_2036,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_1496]) ).
cnf(c_0_2037,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_1497]) ).
cnf(c_0_2038,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_1498]) ).
cnf(c_0_2039,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool)) = X1
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1499]) ).
cnf(c_0_2040,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1500]) ).
cnf(c_0_2041,plain,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1501]) ).
cnf(c_0_2042,plain,
( c_Set_Oinsert(X2,X3,X1) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1502]) ).
cnf(c_0_2043,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_1503]) ).
cnf(c_0_2044,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_1504]) ).
cnf(c_0_2045,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1505]) ).
cnf(c_0_2046,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1506]) ).
cnf(c_0_2047,plain,
( c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1507]) ).
cnf(c_0_2048,plain,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1508]) ).
cnf(c_0_2049,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_1509]) ).
cnf(c_0_2050,plain,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2051,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1511]) ).
cnf(c_0_2052,plain,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1512]) ).
cnf(c_0_2053,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1513]) ).
cnf(c_0_2054,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1514]) ).
cnf(c_0_2055,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_1515]) ).
cnf(c_0_2056,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_1516]) ).
cnf(c_0_2057,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_1517]) ).
cnf(c_0_2058,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1518]) ).
cnf(c_0_2059,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1519]) ).
cnf(c_0_2060,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_1520]) ).
cnf(c_0_2061,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_1521]) ).
cnf(c_0_2062,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1522]) ).
cnf(c_0_2063,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1523]) ).
cnf(c_0_2064,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_1524]) ).
cnf(c_0_2065,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_1525]) ).
cnf(c_0_2066,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1526]) ).
cnf(c_0_2067,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1527]) ).
cnf(c_0_2068,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1528]) ).
cnf(c_0_2069,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1529]) ).
cnf(c_0_2070,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_1530]) ).
cnf(c_0_2071,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_1531]) ).
cnf(c_0_2072,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1532]) ).
cnf(c_0_2073,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1533]) ).
cnf(c_0_2074,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1534]) ).
cnf(c_0_2075,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1535]) ).
cnf(c_0_2076,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1536]) ).
cnf(c_0_2077,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1537]) ).
cnf(c_0_2078,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1538]) ).
cnf(c_0_2079,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1539]) ).
cnf(c_0_2080,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1540]) ).
cnf(c_0_2081,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1541]) ).
cnf(c_0_2082,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1542]) ).
cnf(c_0_2083,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1543]) ).
cnf(c_0_2084,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1544]) ).
cnf(c_0_2085,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1545]) ).
cnf(c_0_2086,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1546]) ).
cnf(c_0_2087,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_1547]) ).
cnf(c_0_2088,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_1548]) ).
cnf(c_0_2089,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_1549]) ).
cnf(c_0_2090,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_1550]) ).
cnf(c_0_2091,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1551]) ).
cnf(c_0_2092,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1552]) ).
cnf(c_0_2093,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1553]) ).
cnf(c_0_2094,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1554]) ).
cnf(c_0_2095,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1555]) ).
cnf(c_0_2096,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1556]) ).
cnf(c_0_2097,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1557]) ).
cnf(c_0_2098,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1558]) ).
cnf(c_0_2099,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1559]) ).
cnf(c_0_2100,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1560]) ).
cnf(c_0_2101,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_1561]) ).
cnf(c_0_2102,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1562]) ).
cnf(c_0_2103,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_1563]) ).
cnf(c_0_2104,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_1564]) ).
cnf(c_0_2105,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1565]) ).
cnf(c_0_2106,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1566]) ).
cnf(c_0_2107,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1567]) ).
cnf(c_0_2108,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1568]) ).
cnf(c_0_2109,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1569]) ).
cnf(c_0_2110,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1570]) ).
cnf(c_0_2111,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1571]) ).
cnf(c_0_2112,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1572]) ).
cnf(c_0_2113,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1573]) ).
cnf(c_0_2114,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1574]) ).
cnf(c_0_2115,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1575]) ).
cnf(c_0_2116,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1576]) ).
cnf(c_0_2117,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1577]) ).
cnf(c_0_2118,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1578]) ).
cnf(c_0_2119,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_1579]) ).
cnf(c_0_2120,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_1580]) ).
cnf(c_0_2121,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1581]) ).
cnf(c_0_2122,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1582]) ).
cnf(c_0_2123,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_1583]) ).
cnf(c_0_2124,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_1584]) ).
cnf(c_0_2125,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_1585]) ).
cnf(c_0_2126,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_1586]) ).
cnf(c_0_2127,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1587]) ).
cnf(c_0_2128,plain,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1588]) ).
cnf(c_0_2129,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1589]) ).
cnf(c_0_2130,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1590]) ).
cnf(c_0_2131,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1591]) ).
cnf(c_0_2132,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_1592]) ).
cnf(c_0_2133,plain,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1593]) ).
cnf(c_0_2134,plain,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1594]) ).
cnf(c_0_2135,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1595]) ).
cnf(c_0_2136,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1596]) ).
cnf(c_0_2137,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_1597]) ).
cnf(c_0_2138,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_1598]) ).
cnf(c_0_2139,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1599]) ).
cnf(c_0_2140,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1600]) ).
cnf(c_0_2141,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1601]) ).
cnf(c_0_2142,plain,
( X1 = hAPP(c_HOL_Ouminus__class_Ouminus(X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1))
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1602]) ).
cnf(c_0_2143,plain,
( X1 = hAPP(c_HOL_Ouminus__class_Ouminus(X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1))
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1603]) ).
cnf(c_0_2144,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1604]) ).
cnf(c_0_2145,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1605]) ).
cnf(c_0_2146,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1606]) ).
cnf(c_0_2147,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1607]) ).
cnf(c_0_2148,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1608]) ).
cnf(c_0_2149,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1609]) ).
cnf(c_0_2150,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1610]) ).
cnf(c_0_2151,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1611]) ).
cnf(c_0_2152,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1612]) ).
cnf(c_0_2153,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1613]) ).
cnf(c_0_2154,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1614]) ).
cnf(c_0_2155,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1615]) ).
cnf(c_0_2156,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1616]) ).
cnf(c_0_2157,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1617]) ).
cnf(c_0_2158,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1618]) ).
cnf(c_0_2159,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1619]) ).
cnf(c_0_2160,plain,
( c_Complete__Lattice_Ocomplete__lattice(X2,X1,c_COMBC(X3,X9,X9,tc_bool),c_COMBC(X4,X9,X9,tc_bool),X6,X5,X8,X7,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1620,
[final] ).
cnf(c_0_2161,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_1621,
[final] ).
cnf(c_0_2162,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_1622,
[final] ).
cnf(c_0_2163,plain,
( hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X9),X10),X11)) ),
c_0_1623,
[final] ).
cnf(c_0_2164,plain,
( hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(hAPP(hAPP(c_in(X9),X10),X11)) ),
c_0_1624,
[final] ).
cnf(c_0_2165,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_1625,
[final] ).
cnf(c_0_2166,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_1626,
[final] ).
cnf(c_0_2167,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_1627,
[final] ).
cnf(c_0_2168,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_1628,
[final] ).
cnf(c_0_2169,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_1629,
[final] ).
cnf(c_0_2170,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_1630,
[final] ).
cnf(c_0_2171,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X5,X1))),hAPP(X4,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X5,X1)))) ),
c_0_1631,
[final] ).
cnf(c_0_2172,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X5,X1))),hAPP(X4,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X5,X1)))) ),
c_0_1632,
[final] ).
cnf(c_0_2173,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,c_COMBK(X4,tc_fun(X1,tc_bool),X5),X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X3,X4,X2,X5,X1))),X4)) ),
c_0_1633,
[final] ).
cnf(c_0_2174,plain,
( c_Nitpick_Ofold__graph_H(X4,X5,X3,hAPP(hAPP(X4,X2),X6),X1,X7)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X6,X1,X7) ),
c_0_1634,
[final] ).
cnf(c_0_2175,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(hAPP(hAPP(c_in(X5),X4),X3)) ),
c_0_1635,
[final] ).
cnf(c_0_2176,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X2,X3,X1),hAPP(hAPP(X4,X2),X6),X1,X7)
| ~ c_Finite__Set_Ofold__graph(X4,X5,X3,X6,X1,X7) ),
c_0_1636,
[final] ).
cnf(c_0_2177,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X6,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)))) ),
c_0_1637,
[final] ).
cnf(c_0_2178,plain,
( X1 = X2
| X4 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1638,
[final] ).
cnf(c_0_2179,plain,
( X1 = X2
| X4 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1639,
[final] ).
cnf(c_0_2180,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X2,X3,X4,X1,X5)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X5,tc_bool),X1),X1,X5))) ),
c_0_1640,
[final] ).
cnf(c_0_2181,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X4,X3,X5,X1,X2)),X4))
| X3 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X5),c_FuncSet_Oextensional(X4,X1,X2))) ),
c_0_1641,
[final] ).
cnf(c_0_2182,plain,
( hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(X7,X5)) ),
c_0_1642,
[final] ).
cnf(c_0_2183,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X4,X1,X5)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,X3,X1,X5))) ),
c_0_1643,
[final] ).
cnf(c_0_2184,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X4,X1,X5)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,X3,X1,X5))) ),
c_0_1644,
[final] ).
cnf(c_0_2185,plain,
( X1 = X2
| X4 = X5
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1645,
[final] ).
cnf(c_0_2186,plain,
( X1 = X2
| X4 = X5
| X5 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1646,
[final] ).
cnf(c_0_2187,plain,
( X1 = X2
| X4 = X5
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1647,
[final] ).
cnf(c_0_2188,plain,
( X1 = X2
| X4 = X5
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1648,
[final] ).
cnf(c_0_2189,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| X1 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1649,
[final] ).
cnf(c_0_2190,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| X4 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1650,
[final] ).
cnf(c_0_2191,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| X4 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1651,
[final] ).
cnf(c_0_2192,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| X1 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1652,
[final] ).
cnf(c_0_2193,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_1653,
[final] ).
cnf(c_0_2194,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_Oextensional(X5,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X2),c_FuncSet_Oextensional(X5,X3,X4)))
| hAPP(X1,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) != hAPP(X2,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) ),
c_0_1654,
[final] ).
cnf(c_0_2195,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1)) ),
c_0_1655,
[final] ).
cnf(c_0_2196,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1)) ),
c_0_1656,
[final] ).
cnf(c_0_2197,plain,
( hBOOL(hAPP(hAPP(X4,X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1))) ),
c_0_1657,
[final] ).
cnf(c_0_2198,plain,
( hBOOL(hAPP(hAPP(X3,X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1))) ),
c_0_1658,
[final] ).
cnf(c_0_2199,plain,
( hBOOL(hAPP(hAPP(X4,X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1))) ),
c_0_1659,
[final] ).
cnf(c_0_2200,plain,
( hBOOL(hAPP(hAPP(X3,X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1))) ),
c_0_1660,
[final] ).
cnf(c_0_2201,plain,
( X1 = X2
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6) ),
c_0_1661,
[final] ).
cnf(c_0_2202,plain,
( X1 = X2
| X4 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
c_0_1662,
[final] ).
cnf(c_0_2203,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X2 = X4
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4))) ),
c_0_1663,
[final] ).
cnf(c_0_2204,plain,
( X1 = X2
| X5 = X1
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
c_0_1664,
[final] ).
cnf(c_0_2205,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X4 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
c_0_1665,
[final] ).
cnf(c_0_2206,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4))) ),
c_0_1666,
[final] ).
cnf(c_0_2207,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X4 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
c_0_1667,
[final] ).
cnf(c_0_2208,plain,
( X1 = X2
| X4 = X5
| X4 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1668,
[final] ).
cnf(c_0_2209,plain,
( X1 = X2
| X4 = X5
| X5 = X1
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1669,
[final] ).
cnf(c_0_2210,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| X4 = X2
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1670,
[final] ).
cnf(c_0_2211,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| X1 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1671,
[final] ).
cnf(c_0_2212,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| X1 = X4
| X1 = X2
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1672,
[final] ).
cnf(c_0_2213,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| X4 = X2
| X1 = X2
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1673,
[final] ).
cnf(c_0_2214,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1674,
[final] ).
cnf(c_0_2215,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1)))
| X4 = X1
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1675,
[final] ).
cnf(c_0_2216,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1676,
[final] ).
cnf(c_0_2217,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4)))
| X2 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_1677,
[final] ).
cnf(c_0_2218,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Oconverse(X5,X2,X1))) ),
c_0_1678,
[final] ).
cnf(c_0_2219,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5)) ),
c_0_1679,
[final] ).
cnf(c_0_2220,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5)) ),
c_0_1680,
[final] ).
cnf(c_0_2221,plain,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X1,X2)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5))) ),
c_0_1681,
[final] ).
cnf(c_0_2222,plain,
( X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4))) ),
c_0_1682,
[final] ).
cnf(c_0_2223,plain,
( X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X4))) ),
c_0_1683,
[final] ).
cnf(c_0_2224,plain,
( X1 = X2
| X3 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
c_0_1684,
[final] ).
cnf(c_0_2225,plain,
( X1 = X2
| X3 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
c_0_1685,
[final] ).
cnf(c_0_2226,plain,
( X1 = X2
| X3 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
c_0_1686,
[final] ).
cnf(c_0_2227,plain,
( X1 = X2
| X1 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
c_0_1687,
[final] ).
cnf(c_0_2228,plain,
( X4 = X5
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X7,X3,X3)),X2)) ),
c_0_1688,
[final] ).
cnf(c_0_2229,plain,
( c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
c_0_1689,
[final] ).
cnf(c_0_2230,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
c_0_1690,
[final] ).
cnf(c_0_2231,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5)) ),
c_0_1691,
[final] ).
cnf(c_0_2232,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1692,
[final] ).
cnf(c_0_2233,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X4,X2,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5,X1))) ),
c_0_1693,
[final] ).
cnf(c_0_2234,plain,
( hBOOL(hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(X7,X5)) ),
c_0_1694,
[final] ).
cnf(c_0_2235,plain,
( hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X1,X4,X2,X5,X6)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
c_0_1695,
[final] ).
cnf(c_0_2236,plain,
( hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X2,X5,X6)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
c_0_1696,
[final] ).
cnf(c_0_2237,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
c_0_1697,
[final] ).
cnf(c_0_2238,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6)) ),
c_0_1698,
[final] ).
cnf(c_0_2239,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6)) ),
c_0_1699,
[final] ).
cnf(c_0_2240,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
c_0_1700,
[final] ).
cnf(c_0_2241,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
c_0_1701,
[final] ).
cnf(c_0_2242,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
c_0_1702,
[final] ).
cnf(c_0_2243,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
c_0_1703,
[final] ).
cnf(c_0_2244,plain,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
c_0_1704,
[final] ).
cnf(c_0_2245,plain,
( c_Set_Oinsert(X5,c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1,X6),X6) = c_Set_Oimage(c_Fun_Ofun__upd(X4,X2,X5,X1,X6),X3,X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1705,
[final] ).
cnf(c_0_2246,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)),c_Equiv__Relations_Oquotient(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1706,
[final] ).
cnf(c_0_2247,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X6)) ),
c_0_1707,
[final] ).
cnf(c_0_2248,plain,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X5)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4)))
| c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_1708,
[final] ).
cnf(c_0_2249,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
c_0_1709,
[final] ).
cnf(c_0_2250,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1)
| c_Relation_OImage(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
c_0_1710,
[final] ).
cnf(c_0_2251,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Set_Oimage(X1,X2,X3,X4)))
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_1711,
[final] ).
cnf(c_0_2252,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
c_0_1712,
[final] ).
cnf(c_0_2253,plain,
( c_lessequals(c_Relation_OImage(X3,X1,X2,X4),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X3,X2,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X2)),tc_fun(X2,tc_bool)) ),
c_0_1713,
[final] ).
cnf(c_0_2254,plain,
( c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| ~ c_Fun_Oinj__on(X1,X2,X4,X5)
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1714,
[final] ).
cnf(c_0_2255,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
c_0_1715,
[final] ).
cnf(c_0_2256,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
c_0_1716,
[final] ).
cnf(c_0_2257,plain,
( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X3),tc_fun(X1,tc_bool)) ),
c_0_1717,
[final] ).
cnf(c_0_2258,plain,
( c_lessequals(c_Set_Oimage(X3,X4,X1,X2),X5,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,c_COMBK(X5,tc_fun(X2,tc_bool),X1),X1,X2))) ),
c_0_1718,
[final] ).
cnf(c_0_2259,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) ),
c_0_1719,
[final] ).
cnf(c_0_2260,plain,
( hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
c_0_1720,
[final] ).
cnf(c_0_2261,plain,
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
c_0_1721,
[final] ).
cnf(c_0_2262,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X1 = X2
| X1 = X2
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1722,
[final] ).
cnf(c_0_2263,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X1 = X2
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1723,
[final] ).
cnf(c_0_2264,plain,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,c_COMBK(X5,tc_fun(X2,tc_bool),X1),X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
c_0_1724,
[final] ).
cnf(c_0_2265,plain,
( c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1725,
[final] ).
cnf(c_0_2266,plain,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
c_0_1726,
[final] ).
cnf(c_0_2267,plain,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
c_0_1727,
[final] ).
cnf(c_0_2268,plain,
( hAPP(X3,X2) = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X1,X5))) ),
c_0_1728,
[final] ).
cnf(c_0_2269,plain,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X1,X3,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X3)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
c_0_1729,
[final] ).
cnf(c_0_2270,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oimage(c_Fun_Ofun__upd(X4,X2,X5,X1,X6),X3,X1,X6) = c_Set_Oimage(X4,X3,X1,X6) ),
c_0_1730,
[final] ).
cnf(c_0_2271,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_List_Osko__Equiv__Relations__XquotientE__1__1(X3,X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Equiv__Relations_Oquotient(X3,X4,X1))) ),
c_0_1731,
[final] ).
cnf(c_0_2272,plain,
( hAPP(c_Fun_Ooverride__on(X4,X5,X3,X1,X6),X2) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1732,
[final] ).
cnf(c_0_2273,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X5,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
c_0_1733,
[final] ).
cnf(c_0_2274,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
c_0_1734,
[final] ).
cnf(c_0_2275,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(c_Fun_Ooverride__on(X4,X5,X3,X1,X6),X2) = hAPP(X4,X2) ),
c_0_1735,
[final] ).
cnf(c_0_2276,plain,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
c_0_1736,
[final] ).
cnf(c_0_2277,plain,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
c_0_1737,
[final] ).
cnf(c_0_2278,plain,
( c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1738,
[final] ).
cnf(c_0_2279,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
c_0_1739,
[final] ).
cnf(c_0_2280,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
c_0_1740,
[final] ).
cnf(c_0_2281,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
c_0_1741,
[final] ).
cnf(c_0_2282,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
c_0_1742,
[final] ).
cnf(c_0_2283,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
c_0_1743,
[final] ).
cnf(c_0_2284,plain,
( X1 = X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| ~ hBOOL(hAPP(hAPP(c_in(X7),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X7),X2),X5))
| hAPP(X4,X1) != hAPP(X4,X2) ),
c_0_1744,
[final] ).
cnf(c_0_2285,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X2)))
| X1 = X2
| X1 = X2 ),
c_0_1745,
[final] ).
cnf(c_0_2286,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X1)))
| X2 = X1
| X1 = X2 ),
c_0_1746,
[final] ).
cnf(c_0_2287,plain,
( c_Relation_OImage(X4,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(X3,X2,X4,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Equiv__Relations_Oquotient(X3,X4,X1))) ),
c_0_1747,
[final] ).
cnf(c_0_2288,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
c_0_1748,
[final] ).
cnf(c_0_2289,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1749,
[final] ).
cnf(c_0_2290,plain,
( hBOOL(hAPP(hAPP(c_in(X5),hAPP(X1,X6)),X3))
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
c_0_1750,
[final] ).
cnf(c_0_2291,plain,
( hAPP(X1,hAPP(X2,X6)) = X6
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X6),X3)) ),
c_0_1751,
[final] ).
cnf(c_0_2292,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
c_0_1752,
[final] ).
cnf(c_0_2293,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
c_0_1753,
[final] ).
cnf(c_0_2294,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1754,
[final] ).
cnf(c_0_2295,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1755,
[final] ).
cnf(c_0_2296,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1756,
[final] ).
cnf(c_0_2297,plain,
( X1 = X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_1757,
[final] ).
cnf(c_0_2298,plain,
( hAPP(X2,hAPP(X1,X6)) = X6
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
c_0_1758,
[final] ).
cnf(c_0_2299,plain,
( hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5))) ),
c_0_1759,
[final] ).
cnf(c_0_2300,plain,
( hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5))) ),
c_0_1760,
[final] ).
cnf(c_0_2301,plain,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
c_0_1761,
[final] ).
cnf(c_0_2302,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1))) ),
c_0_1762,
[final] ).
cnf(c_0_2303,plain,
( hBOOL(hAPP(hAPP(X3,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1))) ),
c_0_1763,
[final] ).
cnf(c_0_2304,plain,
( hBOOL(hAPP(hAPP(X3,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1))) ),
c_0_1764,
[final] ).
cnf(c_0_2305,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1))) ),
c_0_1765,
[final] ).
cnf(c_0_2306,plain,
( X4 = X5
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3))) ),
c_0_1766,
[final] ).
cnf(c_0_2307,plain,
( X1 = X2
| hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1) != hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2) ),
c_0_1767,
[final] ).
cnf(c_0_2308,plain,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
c_0_1768,
[final] ).
cnf(c_0_2309,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1769,
[final] ).
cnf(c_0_2310,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1770,
[final] ).
cnf(c_0_2311,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2))) ),
c_0_1771,
[final] ).
cnf(c_0_2312,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2))) ),
c_0_1772,
[final] ).
cnf(c_0_2313,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
c_0_1773,
[final] ).
cnf(c_0_2314,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
c_0_1774,
[final] ).
cnf(c_0_2315,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1775,
[final] ).
cnf(c_0_2316,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
c_0_1776,
[final] ).
cnf(c_0_2317,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4)) ),
c_0_1777,
[final] ).
cnf(c_0_2318,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4)) ),
c_0_1778,
[final] ).
cnf(c_0_2319,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4)) ),
c_0_1779,
[final] ).
cnf(c_0_2320,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
c_0_1780,
[final] ).
cnf(c_0_2321,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
c_0_1781,
[final] ).
cnf(c_0_2322,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
c_0_1782,
[final] ).
cnf(c_0_2323,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(hAPP(hAPP(c_in(X3),X2),X1)) ),
c_0_1783,
[final] ).
cnf(c_0_2324,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(hAPP(hAPP(c_in(X3),X2),X1)) ),
c_0_1784,
[final] ).
cnf(c_0_2325,plain,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),c_Set_Oimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4)) ),
c_0_1785,
[final] ).
cnf(c_0_2326,plain,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),c_Set_Oimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4)) ),
c_0_1786,
[final] ).
cnf(c_0_2327,plain,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X5,X2)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1787,
[final] ).
cnf(c_0_2328,plain,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X5,X2)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1788,
[final] ).
cnf(c_0_2329,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OatLeastAtMost(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
c_0_1789,
[final] ).
cnf(c_0_2330,plain,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
c_0_1790,
[final] ).
cnf(c_0_2331,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_1791,
[final] ).
cnf(c_0_2332,plain,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X6)),X5))
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2)) ),
c_0_1792,
[final] ).
cnf(c_0_2333,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
c_0_1793,
[final] ).
cnf(c_0_2334,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
c_0_1794,
[final] ).
cnf(c_0_2335,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(hAPP(hAPP(c_in(X3),X6),X1)) ),
c_0_1795,
[final] ).
cnf(c_0_2336,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
c_0_1796,
[final] ).
cnf(c_0_2337,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
c_0_1797,
[final] ).
cnf(c_0_2338,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X1)) ),
c_0_1798,
[final] ).
cnf(c_0_2339,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_1799,
[final] ).
cnf(c_0_2340,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_1800,
[final] ).
cnf(c_0_2341,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_1801,
[final] ).
cnf(c_0_2342,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1,tc_nat) = c_Finite__Set_Osetsum(X4,X3,X1,tc_nat) ),
c_0_1802,
[final] ).
cnf(c_0_2343,plain,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
c_0_1803,
[final] ).
cnf(c_0_2344,plain,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
c_0_1804,
[final] ).
cnf(c_0_2345,plain,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
c_0_1805,
[final] ).
cnf(c_0_2346,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
c_0_1806,
[final] ).
cnf(c_0_2347,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
c_0_1807,
[final] ).
cnf(c_0_2348,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)))) ),
c_0_1808,
[final] ).
cnf(c_0_2349,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(hAPP(hAPP(c_in(X4),X2),X1)) ),
c_0_1809,
[final] ).
cnf(c_0_2350,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1810,
[final] ).
cnf(c_0_2351,plain,
( c_Set_Oinsert(hAPP(X4,X2),c_Set_Oimage(X4,X3,X1,X5),X5) = c_Set_Oimage(X4,X3,X1,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1811,
[final] ).
cnf(c_0_2352,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool)))) ),
c_0_1812,
[final] ).
cnf(c_0_2353,plain,
( hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
c_0_1813,
[final] ).
cnf(c_0_2354,plain,
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
c_0_1814,
[final] ).
cnf(c_0_2355,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X4),X3)) ),
c_0_1815,
[final] ).
cnf(c_0_2356,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X5),X4))
| hAPP(X3,X5) = c_HOL_Oundefined(X2)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2))) ),
c_0_1816,
[final] ).
cnf(c_0_2357,plain,
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_1817,
[final] ).
cnf(c_0_2358,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
c_0_1818,
[final] ).
cnf(c_0_2359,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool)))) ),
c_0_1819,
[final] ).
cnf(c_0_2360,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4),X4)
| ~ class_Lattices_Olattice(X4) ),
c_0_1820,
[final] ).
cnf(c_0_2361,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1821,
[final] ).
cnf(c_0_2362,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X2,X3,X1)),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
c_0_1822,
[final] ).
cnf(c_0_2363,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
c_0_1823,
[final] ).
cnf(c_0_2364,plain,
( c_Fun_Oinj__on(X1,X2,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
c_0_1824,
[final] ).
cnf(c_0_2365,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
c_0_1825,
[final] ).
cnf(c_0_2366,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))) ),
c_0_1826,
[final] ).
cnf(c_0_2367,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool)))) ),
c_0_1827,
[final] ).
cnf(c_0_2368,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_1828,
[final] ).
cnf(c_0_2369,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_1829,
[final] ).
cnf(c_0_2370,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_1830,
[final] ).
cnf(c_0_2371,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_1831,
[final] ).
cnf(c_0_2372,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),X4,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
c_0_1832,
[final] ).
cnf(c_0_2373,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))) ),
c_0_1833,
[final] ).
cnf(c_0_2374,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
c_0_1834,
[final] ).
cnf(c_0_2375,plain,
( c_lessequals(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1835,
[final] ).
cnf(c_0_2376,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
c_0_1836,
[final] ).
cnf(c_0_2377,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
c_0_1837,
[final] ).
cnf(c_0_2378,plain,
( c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1838,
[final] ).
cnf(c_0_2379,plain,
( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_1839,
[final] ).
cnf(c_0_2380,plain,
( X1 = X2
| c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
c_0_1840,
[final] ).
cnf(c_0_2381,plain,
( X1 = X2
| c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
c_0_1841,
[final] ).
cnf(c_0_2382,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| hAPP(X1,X5) != hAPP(X1,X6) ),
c_0_1842,
[final] ).
cnf(c_0_2383,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_1843,
[final] ).
cnf(c_0_2384,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_1844,
[final] ).
cnf(c_0_2385,plain,
( X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ c_Fun_Oinj__on(X5,X3,X1,X6)
| hAPP(X5,X2) != hAPP(X5,X4) ),
c_0_1845,
[final] ).
cnf(c_0_2386,plain,
( c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
c_0_1846,
[final] ).
cnf(c_0_2387,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool)))) ),
c_0_1847,
[final] ).
cnf(c_0_2388,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
c_0_1848,
[final] ).
cnf(c_0_2389,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
c_0_1849,
[final] ).
cnf(c_0_2390,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1))) ),
c_0_1850,
[final] ).
cnf(c_0_2391,plain,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
c_0_1851,
[final] ).
cnf(c_0_2392,plain,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
c_0_1852,
[final] ).
cnf(c_0_2393,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
c_0_1853,
[final] ).
cnf(c_0_2394,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
c_0_1854,
[final] ).
cnf(c_0_2395,plain,
( c_lessequals(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,X5),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
c_0_1855,
[final] ).
cnf(c_0_2396,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
c_0_1856,
[final] ).
cnf(c_0_2397,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
c_0_1857,
[final] ).
cnf(c_0_2398,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1858,
[final] ).
cnf(c_0_2399,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X3,X1)),X2))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
c_0_1859,
[final] ).
cnf(c_0_2400,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
c_0_1860,
[final] ).
cnf(c_0_2401,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)))) ),
c_0_1861,
[final] ).
cnf(c_0_2402,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1862,
[final] ).
cnf(c_0_2403,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1863,
[final] ).
cnf(c_0_2404,plain,
( hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1864,
[final] ).
cnf(c_0_2405,plain,
( hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1865,
[final] ).
cnf(c_0_2406,plain,
( c_Set_Oimage(c_COMBK(X4,X5,X1),X3,X1,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1866,
[final] ).
cnf(c_0_2407,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
c_0_1867,
[final] ).
cnf(c_0_2408,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_1868,
[final] ).
cnf(c_0_2409,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_1869,
[final] ).
cnf(c_0_2410,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(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_1870,
[final] ).
cnf(c_0_2411,plain,
( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X3,X1))) ),
c_0_1871,
[final] ).
cnf(c_0_2412,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,X4,X1))) ),
c_0_1872,
[final] ).
cnf(c_0_2413,plain,
( c_lessequals(X3,X2,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool)) ),
c_0_1873,
[final] ).
cnf(c_0_2414,plain,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1874,
[final] ).
cnf(c_0_2415,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1875,
[final] ).
cnf(c_0_2416,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_1876,
[final] ).
cnf(c_0_2417,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) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1877,
[final] ).
cnf(c_0_2418,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_1878,
[final] ).
cnf(c_0_2419,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_1879,
[final] ).
cnf(c_0_2420,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_1880,
[final] ).
cnf(c_0_2421,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_1881,
[final] ).
cnf(c_0_2422,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatMost(X3,X4,X1))) ),
c_0_1882,
[final] ).
cnf(c_0_2423,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThan(X3,X4,X1))) ),
c_0_1883,
[final] ).
cnf(c_0_2424,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1))) ),
c_0_1884,
[final] ).
cnf(c_0_2425,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1885,
[final] ).
cnf(c_0_2426,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
c_0_1886,
[final] ).
cnf(c_0_2427,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
c_0_1887,
[final] ).
cnf(c_0_2428,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1888,
[final] ).
cnf(c_0_2429,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1889,
[final] ).
cnf(c_0_2430,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)),X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1890,
[final] ).
cnf(c_0_2431,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)),X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1891,
[final] ).
cnf(c_0_2432,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_1892,
[final] ).
cnf(c_0_2433,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_1893,
[final] ).
cnf(c_0_2434,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1894,
[final] ).
cnf(c_0_2435,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X3)) ),
c_0_1895,
[final] ).
cnf(c_0_2436,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
c_0_1896,
[final] ).
cnf(c_0_2437,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X3,X1,X2),X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1897,
[final] ).
cnf(c_0_2438,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X3,X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = X3 ),
c_0_1898,
[final] ).
cnf(c_0_2439,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
c_0_1899,
[final] ).
cnf(c_0_2440,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool)),X1) ),
c_0_1900,
[final] ).
cnf(c_0_2441,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
c_0_1901,
[final] ).
cnf(c_0_2442,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1902,
[final] ).
cnf(c_0_2443,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1903,
[final] ).
cnf(c_0_2444,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Ovimage(c_COMBK(X2,X1,X4),X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_1904,
[final] ).
cnf(c_0_2445,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_1905,
[final] ).
cnf(c_0_2446,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),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_1906,
[final] ).
cnf(c_0_2447,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),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_1907,
[final] ).
cnf(c_0_2448,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_1908,
[final] ).
cnf(c_0_2449,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_1909,
[final] ).
cnf(c_0_2450,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) ),
c_0_1910,
[final] ).
cnf(c_0_2451,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| 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_1911,
[final] ).
cnf(c_0_2452,plain,
( c_lessequals(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
c_0_1912,
[final] ).
cnf(c_0_2453,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
c_0_1913,
[final] ).
cnf(c_0_2454,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
c_0_1914,
[final] ).
cnf(c_0_2455,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),c_Set_OPow(X2,X3)))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1915,
[final] ).
cnf(c_0_2456,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
c_0_1916,
[final] ).
cnf(c_0_2457,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
c_0_1917,
[final] ).
cnf(c_0_2458,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
c_0_1918,
[final] ).
cnf(c_0_2459,plain,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
c_0_1919,
[final] ).
cnf(c_0_2460,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_1920,
[final] ).
cnf(c_0_2461,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_1921,
[final] ).
cnf(c_0_2462,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1922,
[final] ).
cnf(c_0_2463,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1923,
[final] ).
cnf(c_0_2464,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,tc_fun(X4,tc_bool)) = X3 ),
c_0_1924,
[final] ).
cnf(c_0_2465,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1925,
[final] ).
cnf(c_0_2466,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X3),c_SetInterval_Oord_OgreaterThan(X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1926,
[final] ).
cnf(c_0_2467,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1927,
[final] ).
cnf(c_0_2468,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_1928,
[final] ).
cnf(c_0_2469,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_1929,
[final] ).
cnf(c_0_2470,plain,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
c_0_1930,
[final] ).
cnf(c_0_2471,plain,
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
c_0_1931,
[final] ).
cnf(c_0_2472,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
c_0_1932,
[final] ).
cnf(c_0_2473,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
c_0_1933,
[final] ).
cnf(c_0_2474,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
c_0_1934,
[final] ).
cnf(c_0_2475,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
c_0_1935,
[final] ).
cnf(c_0_2476,plain,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_1936,
[final] ).
cnf(c_0_2477,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool)) ),
c_0_1937,
[final] ).
cnf(c_0_2478,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_1938,
[final] ).
cnf(c_0_2479,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
c_0_1939,
[final] ).
cnf(c_0_2480,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_1940,
[final] ).
cnf(c_0_2481,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
c_0_1941,
[final] ).
cnf(c_0_2482,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
c_0_1942,
[final] ).
cnf(c_0_2483,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X1),X4))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_1943,
[final] ).
cnf(c_0_2484,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
c_0_1944,
[final] ).
cnf(c_0_2485,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
c_0_1945,
[final] ).
cnf(c_0_2486,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
c_0_1946,
[final] ).
cnf(c_0_2487,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
c_0_1947,
[final] ).
cnf(c_0_2488,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
c_0_1948,
[final] ).
cnf(c_0_2489,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
c_0_1949,
[final] ).
cnf(c_0_2490,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| c_Set_Oinsert(X4,X1,X3) != c_Set_Oinsert(X4,X2,X3) ),
c_0_1950,
[final] ).
cnf(c_0_2491,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1951,
[final] ).
cnf(c_0_2492,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1952,
[final] ).
cnf(c_0_2493,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_1953,
[final] ).
cnf(c_0_2494,plain,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1954,
[final] ).
cnf(c_0_2495,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)) ),
c_0_1955,
[final] ).
cnf(c_0_2496,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) ),
c_0_1956,
[final] ).
cnf(c_0_2497,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_1957,
[final] ).
cnf(c_0_2498,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
c_0_1958,
[final] ).
cnf(c_0_2499,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) ),
c_0_1959,
[final] ).
cnf(c_0_2500,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_1960,
[final] ).
cnf(c_0_2501,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1961,
[final] ).
cnf(c_0_2502,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1962,
[final] ).
cnf(c_0_2503,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1963,
[final] ).
cnf(c_0_2504,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_1964,
[final] ).
cnf(c_0_2505,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_1965,
[final] ).
cnf(c_0_2506,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_1966,
[final] ).
cnf(c_0_2507,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
c_0_1967,
[final] ).
cnf(c_0_2508,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
c_0_1968,
[final] ).
cnf(c_0_2509,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_1969,
[final] ).
cnf(c_0_2510,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_1970,
[final] ).
cnf(c_0_2511,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_1971,
[final] ).
cnf(c_0_2512,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_1972,
[final] ).
cnf(c_0_2513,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_1973,
[final] ).
cnf(c_0_2514,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1974,
[final] ).
cnf(c_0_2515,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
c_0_1975,
[final] ).
cnf(c_0_2516,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1976,
[final] ).
cnf(c_0_2517,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1977,
[final] ).
cnf(c_0_2518,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_1978,
[final] ).
cnf(c_0_2519,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1979,
[final] ).
cnf(c_0_2520,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1980,
[final] ).
cnf(c_0_2521,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1981,
[final] ).
cnf(c_0_2522,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_1982,
[final] ).
cnf(c_0_2523,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_1983,
[final] ).
cnf(c_0_2524,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1984,
[final] ).
cnf(c_0_2525,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1985,
[final] ).
cnf(c_0_2526,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_1986,
[final] ).
cnf(c_0_2527,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_1987,
[final] ).
cnf(c_0_2528,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_1988,
[final] ).
cnf(c_0_2529,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_1989,
[final] ).
cnf(c_0_2530,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1990,
[final] ).
cnf(c_0_2531,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1991,
[final] ).
cnf(c_0_2532,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1992,
[final] ).
cnf(c_0_2533,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1993,
[final] ).
cnf(c_0_2534,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_1994,
[final] ).
cnf(c_0_2535,plain,
( c_lessequals(X2,X1,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_1995,
[final] ).
cnf(c_0_2536,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1996,
[final] ).
cnf(c_0_2537,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1))) ),
c_0_1997,
[final] ).
cnf(c_0_2538,plain,
( c_lessequals(X3,X2,X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1998,
[final] ).
cnf(c_0_2539,plain,
( c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1999,
[final] ).
cnf(c_0_2540,plain,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_2000,
[final] ).
cnf(c_0_2541,plain,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
c_0_2001,
[final] ).
cnf(c_0_2542,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_2002,
[final] ).
cnf(c_0_2543,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
c_0_2003,
[final] ).
cnf(c_0_2544,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_2004,
[final] ).
cnf(c_0_2545,plain,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_2005,
[final] ).
cnf(c_0_2546,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X3,X1),X2,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_2006,
[final] ).
cnf(c_0_2547,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_2007,
[final] ).
cnf(c_0_2548,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_2008,
[final] ).
cnf(c_0_2549,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2009,
[final] ).
cnf(c_0_2550,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2010,
[final] ).
cnf(c_0_2551,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2011,
[final] ).
cnf(c_0_2552,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2012,
[final] ).
cnf(c_0_2553,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2013,
[final] ).
cnf(c_0_2554,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2014,
[final] ).
cnf(c_0_2555,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_2015,
[final] ).
cnf(c_0_2556,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_2016,
[final] ).
cnf(c_0_2557,plain,
( c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_2017,
[final] ).
cnf(c_0_2558,plain,
( c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_2018,
[final] ).
cnf(c_0_2559,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_2019,
[final] ).
cnf(c_0_2560,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_2020,
[final] ).
cnf(c_0_2561,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_2021,
[final] ).
cnf(c_0_2562,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_2022,
[final] ).
cnf(c_0_2563,plain,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_2023,
[final] ).
cnf(c_0_2564,plain,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_2024,
[final] ).
cnf(c_0_2565,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_2025,
[final] ).
cnf(c_0_2566,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_2026,
[final] ).
cnf(c_0_2567,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oinsert(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
c_0_2027,
[final] ).
cnf(c_0_2568,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2028,
[final] ).
cnf(c_0_2569,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2029,
[final] ).
cnf(c_0_2570,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2030,
[final] ).
cnf(c_0_2571,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2031,
[final] ).
cnf(c_0_2572,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2032,
[final] ).
cnf(c_0_2573,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2033,
[final] ).
cnf(c_0_2574,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2034,
[final] ).
cnf(c_0_2575,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2035,
[final] ).
cnf(c_0_2576,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_2036,
[final] ).
cnf(c_0_2577,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_2037,
[final] ).
cnf(c_0_2578,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_2038,
[final] ).
cnf(c_0_2579,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool)) = X1
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_2039,
[final] ).
cnf(c_0_2580,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_2040,
[final] ).
cnf(c_0_2581,plain,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_2041,
[final] ).
cnf(c_0_2582,plain,
( c_Set_Oinsert(X2,X3,X1) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_2042,
[final] ).
cnf(c_0_2583,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_2043,
[final] ).
cnf(c_0_2584,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_2044,
[final] ).
cnf(c_0_2585,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2045,
[final] ).
cnf(c_0_2586,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2046,
[final] ).
cnf(c_0_2587,plain,
( c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_2047,
[final] ).
cnf(c_0_2588,plain,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2) ),
c_0_2048,
[final] ).
cnf(c_0_2589,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_2049,
[final] ).
cnf(c_0_2590,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,X3),X3) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_2050,
[final] ).
cnf(c_0_2591,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_2051,
[final] ).
cnf(c_0_2592,plain,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2052,
[final] ).
cnf(c_0_2593,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_2053,
[final] ).
cnf(c_0_2594,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_2054,
[final] ).
cnf(c_0_2595,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_2055,
[final] ).
cnf(c_0_2596,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_2056,
[final] ).
cnf(c_0_2597,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_2057,
[final] ).
cnf(c_0_2598,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_2058,
[final] ).
cnf(c_0_2599,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_2059,
[final] ).
cnf(c_0_2600,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
c_0_2060,
[final] ).
cnf(c_0_2601,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
c_0_2061,
[final] ).
cnf(c_0_2602,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_2062,
[final] ).
cnf(c_0_2603,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_2063,
[final] ).
cnf(c_0_2604,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_2064,
[final] ).
cnf(c_0_2605,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_2065,
[final] ).
cnf(c_0_2606,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_2066,
[final] ).
cnf(c_0_2607,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2067,
[final] ).
cnf(c_0_2608,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2068,
[final] ).
cnf(c_0_2609,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2069,
[final] ).
cnf(c_0_2610,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_2070,
[final] ).
cnf(c_0_2611,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_2071,
[final] ).
cnf(c_0_2612,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_2072,
[final] ).
cnf(c_0_2613,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2073,
[final] ).
cnf(c_0_2614,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2074,
[final] ).
cnf(c_0_2615,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2075,
[final] ).
cnf(c_0_2616,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2076,
[final] ).
cnf(c_0_2617,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2077,
[final] ).
cnf(c_0_2618,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2078,
[final] ).
cnf(c_0_2619,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2079,
[final] ).
cnf(c_0_2620,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
c_0_2080,
[final] ).
cnf(c_0_2621,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
c_0_2081,
[final] ).
cnf(c_0_2622,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
c_0_2082,
[final] ).
cnf(c_0_2623,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2083,
[final] ).
cnf(c_0_2624,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2084,
[final] ).
cnf(c_0_2625,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2085,
[final] ).
cnf(c_0_2626,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2086,
[final] ).
cnf(c_0_2627,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2087,
[final] ).
cnf(c_0_2628,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2088,
[final] ).
cnf(c_0_2629,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2089,
[final] ).
cnf(c_0_2630,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2090,
[final] ).
cnf(c_0_2631,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_2091,
[final] ).
cnf(c_0_2632,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
c_0_2092,
[final] ).
cnf(c_0_2633,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2093,
[final] ).
cnf(c_0_2634,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2094,
[final] ).
cnf(c_0_2635,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2095,
[final] ).
cnf(c_0_2636,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2096,
[final] ).
cnf(c_0_2637,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2097,
[final] ).
cnf(c_0_2638,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2098,
[final] ).
cnf(c_0_2639,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2099,
[final] ).
cnf(c_0_2640,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2100,
[final] ).
cnf(c_0_2641,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2101,
[final] ).
cnf(c_0_2642,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2102,
[final] ).
cnf(c_0_2643,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2103,
[final] ).
cnf(c_0_2644,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2104,
[final] ).
cnf(c_0_2645,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2105,
[final] ).
cnf(c_0_2646,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2106,
[final] ).
cnf(c_0_2647,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2107,
[final] ).
cnf(c_0_2648,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2108,
[final] ).
cnf(c_0_2649,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_2109,
[final] ).
cnf(c_0_2650,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
c_0_2110,
[final] ).
cnf(c_0_2651,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2111,
[final] ).
cnf(c_0_2652,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2112,
[final] ).
cnf(c_0_2653,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
c_0_2113,
[final] ).
cnf(c_0_2654,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2114,
[final] ).
cnf(c_0_2655,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2115,
[final] ).
cnf(c_0_2656,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_2116,
[final] ).
cnf(c_0_2657,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2117,
[final] ).
cnf(c_0_2658,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2118,
[final] ).
cnf(c_0_2659,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_2119,
[final] ).
cnf(c_0_2660,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_2120,
[final] ).
cnf(c_0_2661,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2121,
[final] ).
cnf(c_0_2662,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2122,
[final] ).
cnf(c_0_2663,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_2123,
[final] ).
cnf(c_0_2664,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3) ),
c_0_2124,
[final] ).
cnf(c_0_2665,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_2125,
[final] ).
cnf(c_0_2666,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_2126,
[final] ).
cnf(c_0_2667,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Oboolean__algebra(X2) ),
c_0_2127,
[final] ).
cnf(c_0_2668,plain,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
c_0_2128,
[final] ).
cnf(c_0_2669,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_2129,
[final] ).
cnf(c_0_2670,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_2130,
[final] ).
cnf(c_0_2671,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_2131,
[final] ).
cnf(c_0_2672,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_2132,
[final] ).
cnf(c_0_2673,plain,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| ~ class_Lattices_Oboolean__algebra(X3) ),
c_0_2133,
[final] ).
cnf(c_0_2674,plain,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_2134,
[final] ).
cnf(c_0_2675,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_2135,
[final] ).
cnf(c_0_2676,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2136,
[final] ).
cnf(c_0_2677,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2137,
[final] ).
cnf(c_0_2678,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_2138,
[final] ).
cnf(c_0_2679,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
c_0_2139,
[final] ).
cnf(c_0_2680,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_2140,
[final] ).
cnf(c_0_2681,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
c_0_2141,
[final] ).
cnf(c_0_2682,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1)) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_2142,
[final] ).
cnf(c_0_2683,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1)) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_2143,
[final] ).
cnf(c_0_2684,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_2144,
[final] ).
cnf(c_0_2685,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_2145,
[final] ).
cnf(c_0_2686,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_2146,
[final] ).
cnf(c_0_2687,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_2147,
[final] ).
cnf(c_0_2688,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_2148,
[final] ).
cnf(c_0_2689,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_2149,
[final] ).
cnf(c_0_2690,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_2150,
[final] ).
cnf(c_0_2691,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_2151,
[final] ).
cnf(c_0_2692,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_2152,
[final] ).
cnf(c_0_2693,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2153,
[final] ).
cnf(c_0_2694,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
c_0_2154,
[final] ).
cnf(c_0_2695,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_2155,
[final] ).
cnf(c_0_2696,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_2156,
[final] ).
cnf(c_0_2697,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_2157,
[final] ).
cnf(c_0_2698,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
c_0_2158,
[final] ).
cnf(c_0_2699,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
c_0_2159,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_2160_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice(X2,X1,c_COMBC(X3,X9,X9,tc_bool),c_COMBC(X4,X9,X9,tc_bool),X6,X5,X8,X7,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| c_Complete__Lattice_Ocomplete__lattice(X2,X1,c_COMBC(X3,X9,X9,tc_bool),c_COMBC(X4,X9,X9,tc_bool),X6,X5,X8,X7,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2161_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_2161]) ).
cnf(c_0_2161_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_2161]) ).
cnf(c_0_2162_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_2162]) ).
cnf(c_0_2162_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_2162]) ).
cnf(c_0_2163_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(hAPP(hAPP(c_in(X9),X10),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_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(hAPP(hAPP(c_in(X9),X10),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X9),X10),X11))
| ~ 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_2163]) ).
cnf(c_0_2164_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(hAPP(hAPP(c_in(X9),X10),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_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(hAPP(hAPP(c_in(X9),X10),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X9),X10),X11))
| ~ 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_2164]) ).
cnf(c_0_2165_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_2165]) ).
cnf(c_0_2165_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_2165]) ).
cnf(c_0_2166_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_2166]) ).
cnf(c_0_2166_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_2166]) ).
cnf(c_0_2167_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_2167]) ).
cnf(c_0_2167_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_2167]) ).
cnf(c_0_2168_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_2168]) ).
cnf(c_0_2168_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_2168]) ).
cnf(c_0_2169_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_2169]) ).
cnf(c_0_2169_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_2169]) ).
cnf(c_0_2170_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_2170]) ).
cnf(c_0_2170_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_2170]) ).
cnf(c_0_2171_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X5,X1))),hAPP(X4,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X5,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2171_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X5,X1))),hAPP(X4,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X4,X2,X5,X1))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2172_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X5,X1))),hAPP(X4,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X5,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X5,X1))),hAPP(X4,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X4,X2,X5,X1))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2173_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,c_COMBK(X4,tc_fun(X1,tc_bool),X5),X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X3,X4,X2,X5,X1))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X3,X4,X2,X5,X1))),X4))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X3,c_COMBK(X4,tc_fun(X1,tc_bool),X5),X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2174_0,axiom,
( c_Nitpick_Ofold__graph_H(X4,X5,X3,hAPP(hAPP(X4,X2),X6),X1,X7)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X6,X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Nitpick_Ofold__graph_H(X4,X5,X3,hAPP(hAPP(X4,X2),X6),X1,X7)
| ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X6,X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_2,axiom,
( ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X6,X1,X7)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Nitpick_Ofold__graph_H(X4,X5,X3,hAPP(hAPP(X4,X2),X6),X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2175_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(hAPP(hAPP(c_in(X5),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2175_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(hAPP(hAPP(c_in(X5),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2175_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X5),X4),X3))
| ~ 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_2175]) ).
cnf(c_0_2176_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X2,X3,X1),hAPP(hAPP(X4,X2),X6),X1,X7)
| ~ c_Finite__Set_Ofold__graph(X4,X5,X3,X6,X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_1,axiom,
( c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X2,X3,X1),hAPP(hAPP(X4,X2),X6),X1,X7)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_Finite__Set_Ofold__graph(X4,X5,X3,X6,X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_2,axiom,
( ~ c_Finite__Set_Ofold__graph(X4,X5,X3,X6,X1,X7)
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X2,X3,X1),hAPP(hAPP(X4,X2),X6),X1,X7)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2177_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X6,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X6,X3,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X6,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2178_0,axiom,
( X1 = X2
| X4 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_1,axiom,
( X4 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2179_0,axiom,
( X1 = X2
| X4 = X5
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_1,axiom,
( X4 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2180_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X2,X3,X4,X1,X5)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X5,tc_bool),X1),X1,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X5,tc_bool),X1),X1,X5)))
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X2,X3,X4,X1,X5)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2181_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X4,X3,X5,X1,X2)),X4))
| X3 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X5),c_FuncSet_Oextensional(X4,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2181_1,axiom,
( X3 = X5
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X4,X3,X5,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X5),c_FuncSet_Oextensional(X4,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2181_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2)))
| X3 = X5
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X4,X3,X5,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X5),c_FuncSet_Oextensional(X4,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2181_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X5),c_FuncSet_Oextensional(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2)))
| X3 = X5
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X4,X3,X5,X1,X2)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2182_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(X7,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2182_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(X7,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2182_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(X7,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2182_3,axiom,
( ~ hBOOL(hAPP(X7,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2183_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X4,X1,X5)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,X3,X1,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2183_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,X3,X1,X5)))
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X4,X1,X5)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2184_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X4,X1,X5)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,X3,X1,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2184_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X5)),X4),c_FuncSet_OPi(X2,X3,X1,X5)))
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X4,X1,X5)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2185_0,axiom,
( X1 = X2
| X4 = X5
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_1,axiom,
( X4 = X5
| X1 = X2
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_2,axiom,
( X4 = X1
| X4 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_3,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X1
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X1
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X1
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X1
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2186_0,axiom,
( X1 = X2
| X4 = X5
| X5 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_1,axiom,
( X4 = X5
| X1 = X2
| X5 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_2,axiom,
( X5 = X1
| X4 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_3,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X5 = X1
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X5 = X1
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X5 = X1
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X5 = X1
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2187_0,axiom,
( X1 = X2
| X4 = X5
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_1,axiom,
( X4 = X5
| X1 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_2,axiom,
( X5 = X2
| X4 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_3,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X5 = X2
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X5 = X2
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X5 = X2
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X5 = X2
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2188_0,axiom,
( X1 = X2
| X4 = X5
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_1,axiom,
( X4 = X5
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_2,axiom,
( X4 = X2
| X4 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_3,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X4 = X2
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X4 = X2
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X4 = X2
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X4 = X2
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2189_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| X1 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_1,axiom,
( X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_2,axiom,
( X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2190_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| X4 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_1,axiom,
( X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_2,axiom,
( X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2191_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| X4 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_1,axiom,
( X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_2,axiom,
( X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2192_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| X1 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_1,axiom,
( X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_2,axiom,
( X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2193_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_2193]) ).
cnf(c_0_2193_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_2193]) ).
cnf(c_0_2194_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_Oextensional(X5,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X2),c_FuncSet_Oextensional(X5,X3,X4)))
| hAPP(X1,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) != hAPP(X2,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_Oextensional(X5,X3,X4)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X2),c_FuncSet_Oextensional(X5,X3,X4)))
| hAPP(X1,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) != hAPP(X2,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X2),c_FuncSet_Oextensional(X5,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_Oextensional(X5,X3,X4)))
| X1 = X2
| hAPP(X1,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) != hAPP(X2,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_3,axiom,
( hAPP(X1,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4)) != hAPP(X2,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(X5,X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X2),c_FuncSet_Oextensional(X5,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_Oextensional(X5,X3,X4)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2195_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2195_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2195_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2195_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2196_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2196_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2196_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2197_0,axiom,
( hBOOL(hAPP(hAPP(X4,X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1)))
| hBOOL(hAPP(hAPP(X4,X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2198_0,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1)))
| hBOOL(hAPP(hAPP(X3,X2),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2199_0,axiom,
( hBOOL(hAPP(hAPP(X4,X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1)))
| hBOOL(hAPP(hAPP(X4,X2),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2200_0,axiom,
( hBOOL(hAPP(hAPP(X3,X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2200_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1)))
| hBOOL(hAPP(hAPP(X3,X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2201_0,axiom,
( X1 = X2
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2201_1,axiom,
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2202_0,axiom,
( X1 = X2
| X4 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2202_1,axiom,
( X4 = X2
| X1 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2202_2,axiom,
( X5 = X2
| X4 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2202_3,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X5 = X2
| X4 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2202_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X5 = X2
| X4 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2202_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X5 = X2
| X4 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2203_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X2 = X4
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X2 = X4
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_2,axiom,
( X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_3,axiom,
( X1 = X4
| X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X4
| X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X4
| X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2204_0,axiom,
( X1 = X2
| X5 = X1
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_1,axiom,
( X5 = X1
| X1 = X2
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_2,axiom,
( X4 = X1
| X5 = X1
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_3,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X4 = X1
| X5 = X1
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X4 = X1
| X5 = X1
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X4 = X1
| X5 = X1
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2205_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X4 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X4 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_2,axiom,
( X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_3,axiom,
( X1 = X4
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X4
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X4
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2206_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_1,axiom,
( X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2207_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X4 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2207_1,axiom,
( X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2207_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2207_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2208_0,axiom,
( X1 = X2
| X4 = X5
| X4 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_1,axiom,
( X4 = X5
| X1 = X2
| X4 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_2,axiom,
( X4 = X2
| X4 = X5
| X1 = X2
| X5 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_3,axiom,
( X5 = X2
| X4 = X2
| X4 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_4,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X5 = X2
| X4 = X2
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X5 = X2
| X4 = X2
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X5 = X2
| X4 = X2
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2209_0,axiom,
( X1 = X2
| X4 = X5
| X5 = X1
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_1,axiom,
( X4 = X5
| X1 = X2
| X5 = X1
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_2,axiom,
( X5 = X1
| X4 = X5
| X1 = X2
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_3,axiom,
( X4 = X1
| X5 = X1
| X4 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_4,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X1
| X5 = X1
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X1
| X5 = X1
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X4 = X1
| X5 = X1
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2210_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| X4 = X2
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_1,axiom,
( X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_2,axiom,
( X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_3,axiom,
( X1 = X2
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2211_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| X1 = X4
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_1,axiom,
( X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_2,axiom,
( X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_3,axiom,
( X1 = X4
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X4
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X4
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2212_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| X1 = X4
| X1 = X2
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_1,axiom,
( X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| X1 = X2
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_2,axiom,
( X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_3,axiom,
( X2 = X1
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X2 = X1
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X2 = X1
| X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2213_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| X4 = X2
| X1 = X2
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_1,axiom,
( X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| X1 = X2
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_2,axiom,
( X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_3,axiom,
( X2 = X4
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X2 = X4
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X2 = X4
| X1 = X2
| X4 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2214_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_1,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_2,axiom,
( X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2215_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1)))
| X4 = X1
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_1,axiom,
( X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_2,axiom,
( X1 = X2
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X4 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2216_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_1,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_2,axiom,
( X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2217_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4)))
| X2 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_1,axiom,
( X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_2,axiom,
( X1 = X2
| X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2218_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Oconverse(X5,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Oconverse(X5,X2,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2219_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2220_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2221_0,axiom,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X1,X2)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2221_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X1,X2)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5)))
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2222_0,axiom,
( X1 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2223_0,axiom,
( X2 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X4)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X2 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2224_0,axiom,
( X1 = X2
| X3 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_1,axiom,
( X3 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| X3 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2225_0,axiom,
( X1 = X2
| X3 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_1,axiom,
( X3 = X1
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| X3 = X1
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| X3 = X1
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2226_0,axiom,
( X1 = X2
| X3 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_1,axiom,
( X3 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| X3 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2227_0,axiom,
( X1 = X2
| X1 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_1,axiom,
( X1 = X3
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| X1 = X3
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2228_0,axiom,
( X4 = X5
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X7,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X7,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X7,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X7,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_in(X3),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X7,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X7,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X6,X7,X3,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2229_0,axiom,
( c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2230_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_2,axiom,
( ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2231_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2232_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| X2 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2233_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X4,X2,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X4,X2,X5,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2234_0,axiom,
( hBOOL(hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(X7,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(X7,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4)))
| ~ hBOOL(hAPP(X7,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_3,axiom,
( ~ hBOOL(hAPP(X7,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(X3,X6,X7,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2235_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X1,X4,X2,X5,X6)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X1,X4,X2,X5,X6)))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_2,axiom,
( ~ hBOOL(hAPP(hAPP(X4,X3),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X1,X4,X2,X5,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2236_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X2,X5,X6)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X2,X5,X6)))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_2,axiom,
( ~ hBOOL(hAPP(hAPP(X4,X3),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X2,X5,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2237_0,axiom,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2238_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2239_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2240_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2240_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2240_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2241_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2241_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2241_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2242_0,axiom,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2243_0,axiom,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2244_0,axiom,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2245_0,axiom,
( c_Set_Oinsert(X5,c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1,X6),X6) = c_Set_Oimage(c_Fun_Ofun__upd(X4,X2,X5,X1,X6),X3,X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oinsert(X5,c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1,X6),X6) = c_Set_Oimage(c_Fun_Ofun__upd(X4,X2,X5,X1,X6),X3,X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2246_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)),c_Equiv__Relations_Oquotient(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)),c_Equiv__Relations_Oquotient(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2247_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X6),c_Equiv__Relations_Oquotient(X5,X4,X1)))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2248_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X5)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4)))
| c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_1,axiom,
( c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X5)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_2,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X5)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2249_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_4,axiom,
( c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2250_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1)
| c_Relation_OImage(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1)
| c_Relation_OImage(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1)
| c_Relation_OImage(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_3,axiom,
( ~ c_Equiv__Relations_Oequiv(X3,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| c_Relation_OImage(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_4,axiom,
( c_Relation_OImage(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2251_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Set_Oimage(X1,X2,X3,X4)))
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_1,axiom,
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Set_Oimage(X1,X2,X3,X4)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_2,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Set_Oimage(X1,X2,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2252_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2))
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_3,axiom,
( c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X5,X4,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2253_0,axiom,
( c_lessequals(c_Relation_OImage(X3,X1,X2,X4),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X3,X2,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X2)),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_1,axiom,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X3,X2,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X2)),tc_fun(X2,tc_bool))
| c_lessequals(c_Relation_OImage(X3,X1,X2,X4),X5,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2254_0,axiom,
( c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| ~ c_Fun_Oinj__on(X1,X2,X4,X5)
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X4,X5)
| c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_2,axiom,
( ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,X2,X4,X5)
| c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_3,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,X2,X4,X5)
| c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2255_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X5),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2256_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X5,X3,X3)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2257_0,axiom,
( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X3),tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_1,axiom,
( ~ c_lessequals(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X3),tc_fun(X1,tc_bool))
| c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2258_0,axiom,
( c_lessequals(c_Set_Oimage(X3,X4,X1,X2),X5,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,c_COMBK(X5,tc_fun(X2,tc_bool),X1),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,c_COMBK(X5,tc_fun(X2,tc_bool),X1),X1,X2)))
| c_lessequals(c_Set_Oimage(X3,X4,X1,X2),X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2259_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_4,axiom,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X4,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2260_0,axiom,
( hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_1,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_2,axiom,
( ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| hBOOL(hAPP(X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2261_0,axiom,
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_1,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_2,axiom,
( ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X2))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X1,X3,X4)))
| hBOOL(hAPP(X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2262_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X1 = X2
| X1 = X2
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_1,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X1 = X2
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_2,axiom,
( X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_3,axiom,
( X2 = X1
| X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X2 = X1
| X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2263_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X1 = X2
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_1,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X1 = X2
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_2,axiom,
( X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_3,axiom,
( X1 = X2
| X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2264_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,c_COMBK(X5,tc_fun(X2,tc_bool),X1),X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,c_COMBK(X5,tc_fun(X2,tc_bool),X1),X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,c_COMBK(X5,tc_fun(X2,tc_bool),X1),X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2265_0,axiom,
( c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2265_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2266_0,axiom,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2267_0,axiom,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X7,tc_fun(X8,tc_bool))),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2268_0,axiom,
( hAPP(X3,X2) = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X1,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X1,X5)))
| hAPP(X3,X2) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2269_0,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X1,X3,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X3)),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_1,axiom,
( ~ c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X1,X3,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X3)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2270_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oimage(c_Fun_Ofun__upd(X4,X2,X5,X1,X6),X3,X1,X6) = c_Set_Oimage(X4,X3,X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_1,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(X4,X2,X5,X1,X6),X3,X1,X6) = c_Set_Oimage(X4,X3,X1,X6)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2271_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_List_Osko__Equiv__Relations__XquotientE__1__1(X3,X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Equiv__Relations_Oquotient(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Equiv__Relations_Oquotient(X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_in(X1),c_List_Osko__Equiv__Relations__XquotientE__1__1(X3,X2,X4,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2272_0,axiom,
( hAPP(c_Fun_Ooverride__on(X4,X5,X3,X1,X6),X2) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(c_Fun_Ooverride__on(X4,X5,X3,X1,X6),X2) = hAPP(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2273_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X5,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X5,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X5,X3,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2274_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2275_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(c_Fun_Ooverride__on(X4,X5,X3,X1,X6),X2) = hAPP(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_1,axiom,
( hAPP(c_Fun_Ooverride__on(X4,X5,X3,X1,X6),X2) = hAPP(X4,X2)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2276_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2276_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2276_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2277_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2277_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2277_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(X3,X6)),hAPP(X5,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2278_0,axiom,
( c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2279_0,axiom,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_1,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2280_0,axiom,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_1,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2281_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2282_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2282_1,axiom,
( hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2282_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2))
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2283_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_1,axiom,
( hBOOL(hAPP(X3,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2))
| hBOOL(hAPP(X3,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X2,X3,X4,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2284_0,axiom,
( X1 = X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| ~ hBOOL(hAPP(hAPP(c_in(X7),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X7),X2),X5))
| hAPP(X4,X1) != hAPP(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_1,axiom,
( ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X7),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X7),X2),X5))
| hAPP(X4,X1) != hAPP(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X7),X1),X5))
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X7),X2),X5))
| hAPP(X4,X1) != hAPP(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X7),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X7),X1),X5))
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| X1 = X2
| hAPP(X4,X1) != hAPP(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_4,axiom,
( hAPP(X4,X1) != hAPP(X4,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X7),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X7),X1),X5))
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2285_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X2)))
| X1 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_1,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X2)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_2,axiom,
( X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2286_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X1)))
| X2 = X1
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_1,axiom,
( X2 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X1)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_2,axiom,
( X1 = X2
| X2 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2287_0,axiom,
( c_Relation_OImage(X4,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(X3,X2,X4,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Equiv__Relations_Oquotient(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Equiv__Relations_Oquotient(X3,X4,X1)))
| c_Relation_OImage(X4,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(X3,X2,X4,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2288_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X4),c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X4),c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2289_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2290_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X5),hAPP(X1,X6)),X3))
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2290_1,axiom,
( ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5)
| hBOOL(hAPP(hAPP(c_in(X5),hAPP(X1,X6)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2291_0,axiom,
( hAPP(X1,hAPP(X2,X6)) = X6
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X6),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_1,axiom,
( ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5)
| hAPP(X1,hAPP(X2,X6)) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X5),X6),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X5),X6),X3))
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5)
| hAPP(X1,hAPP(X2,X6)) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2292_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_3,axiom,
( ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2293_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_3,axiom,
( ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2294_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2295_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2296_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2297_0,axiom,
( X1 = X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_1,axiom,
( ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| X1 = X2
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_2,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X7)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2298_0,axiom,
( hAPP(X2,hAPP(X1,X6)) = X6
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_1,axiom,
( ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5)
| hAPP(X2,hAPP(X1,X6)) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2299_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5)))
| hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2300_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2300_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5)))
| hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2301_0,axiom,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2301_1,axiom,
( c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2302_0,axiom,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2302_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1)))
| hBOOL(hAPP(hAPP(X3,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2303_0,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1)))
| hBOOL(hAPP(hAPP(X3,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2304_0,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1)))
| hBOOL(hAPP(hAPP(X3,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2305_0,axiom,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1)))
| hBOOL(hAPP(hAPP(X3,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2306_0,axiom,
( X4 = X5
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X4 = X5
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_2,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X5),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X4),c_Equiv__Relations_Oquotient(X1,X2,X3)))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2307_0,axiom,
( X1 = X2
| hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1) != hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2307_1,axiom,
( hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1) != hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2309_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(X1,X2)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2310_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(X1,X2)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2311_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2312_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2312_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2312_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X5),hAPP(X6,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X6,X1,tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2313_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2314_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2315_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2315_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2315_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(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_2315]) ).
cnf(c_0_2315_3,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2316_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2316_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2316_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2316_3,axiom,
( ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2317_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2317_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2318_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2318_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2319_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2319_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2320_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2320_1,axiom,
( ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2320_2,axiom,
( c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5)
| ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2321_0,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2321_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2321_2,axiom,
( ~ hBOOL(hAPP(hAPP(X4,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2322_0,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_2,axiom,
( ~ hBOOL(hAPP(hAPP(X4,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X6,tc_bool)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2323_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(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2323_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(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2323_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| ~ 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_2323]) ).
cnf(c_0_2324_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(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2324_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(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2324_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| ~ 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_2324]) ).
cnf(c_0_2325_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),c_Set_Oimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2325_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4))
| hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),c_Set_Oimage(X2,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2326_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),c_Set_Oimage(X2,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4))
| hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),c_Set_Oimage(X2,X4,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2327_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X5,X2)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),hAPP(X5,X2)),c_Set_Oimage(X5,X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2328_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X5,X2)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),hAPP(X5,X2)),c_Set_Oimage(X5,X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2329_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OatLeastAtMost(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2329_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OatLeastAtMost(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2329_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OatLeastAtMost(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2330_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2331_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_2331]) ).
cnf(c_0_2331_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_2331]) ).
cnf(c_0_2331_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_2331]) ).
cnf(c_0_2332_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X6)),X5))
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_1,axiom,
( ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),hAPP(X1,X6)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2333_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2333_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2333_2,axiom,
( hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2333_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2))
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2334_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_2,axiom,
( hBOOL(hAPP(X3,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2))
| hBOOL(hAPP(X3,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2335_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(hAPP(hAPP(c_in(X3),X6),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_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(hAPP(hAPP(c_in(X3),X6),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X1))
| ~ 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_2335]) ).
cnf(c_0_2336_0,axiom,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1)))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X5,X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2337_0,axiom,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1)))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(X3,X5,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2338_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_1,axiom,
( c_HOL_Oord__class_Oless(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(hAPP(hAPP(c_in(X4),X2),X3))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(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(hAPP(hAPP(c_in(X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(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(hAPP(hAPP(c_in(X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2339_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_2339]) ).
cnf(c_0_2339_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_2339]) ).
cnf(c_0_2340_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_2340]) ).
cnf(c_0_2340_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_2340]) ).
cnf(c_0_2341_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_2341]) ).
cnf(c_0_2341_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_2341]) ).
cnf(c_0_2342_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1,tc_nat) = c_Finite__Set_Osetsum(X4,X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_1,axiom,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1,tc_nat) = c_Finite__Set_Osetsum(X4,X3,X1,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2343_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_2343]) ).
cnf(c_0_2343_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_2343]) ).
cnf(c_0_2344_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2344_1,axiom,
( hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2344_2,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2344_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2345_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_1,axiom,
( hBOOL(hAPP(X1,X5))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_2,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X1,X5))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X1,X5))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2346_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_1,axiom,
( hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_2,axiom,
( ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2347_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_1,axiom,
( hBOOL(hAPP(X3,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_2,axiom,
( ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| hBOOL(hAPP(X3,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X2))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X1)))
| hBOOL(hAPP(X3,X5))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X3,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2348_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2349_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(hAPP(hAPP(c_in(X4),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_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(hAPP(hAPP(c_in(X4),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| ~ 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_2349]) ).
cnf(c_0_2350_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2350_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2351_0,axiom,
( c_Set_Oinsert(hAPP(X4,X2),c_Set_Oimage(X4,X3,X1,X5),X5) = c_Set_Oimage(X4,X3,X1,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2351_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oinsert(hAPP(X4,X2),c_Set_Oimage(X4,X3,X1,X5),X5) = c_Set_Oimage(X4,X3,X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2352_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2353_0,axiom,
( hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_1,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_2,axiom,
( ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X4,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2354_0,axiom,
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_1,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_2,axiom,
( ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X4,X3)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X2,X1,X3)))
| hBOOL(hAPP(X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2355_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2356_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X5),X4))
| hAPP(X3,X5) = c_HOL_Oundefined(X2)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_1,axiom,
( hAPP(X3,X5) = c_HOL_Oundefined(X2)
| hBOOL(hAPP(hAPP(c_in(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X4,X1,X2)))
| hAPP(X3,X5) = c_HOL_Oundefined(X2)
| hBOOL(hAPP(hAPP(c_in(X1),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2357_0,axiom,
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin))
| v_thesis____ ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2358_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2359_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2359_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2360_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2360_1,axiom,
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2361_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2361_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2362_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X2,X3,X1)),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2362_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X2,X3,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2363_0,axiom,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2363_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| c_Fun_Oinj__on(X1,X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2364_0,axiom,
( c_Fun_Oinj__on(X1,X2,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2364_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| c_Fun_Oinj__on(X1,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2365_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X4),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2366_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2367_0,axiom,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool))))
| hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2368_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_2368]) ).
cnf(c_0_2368_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_2368]) ).
cnf(c_0_2368_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_2368]) ).
cnf(c_0_2369_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_2369]) ).
cnf(c_0_2369_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_2369]) ).
cnf(c_0_2369_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_2369]) ).
cnf(c_0_2370_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_2370]) ).
cnf(c_0_2370_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_2370]) ).
cnf(c_0_2370_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_2370]) ).
cnf(c_0_2371_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_2371]) ).
cnf(c_0_2371_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_2371]) ).
cnf(c_0_2371_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_2371]) ).
cnf(c_0_2372_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),X4,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),X4,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_2,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),X4,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2373_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2373_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2374_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2374_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2375_0,axiom,
( c_lessequals(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2375_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2376_0,axiom,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2376_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| c_Fun_Oinj__on(X1,X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2377_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2377]) ).
cnf(c_0_2377_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2377]) ).
cnf(c_0_2378_0,axiom,
( c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2378_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)),X1) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2379_0,axiom,
( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2379]) ).
cnf(c_0_2379_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2379]) ).
cnf(c_0_2380_0,axiom,
( X1 = X2
| c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2380_1,axiom,
( c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2381_0,axiom,
( X1 = X2
| c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2381_1,axiom,
( c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2382_0,axiom,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2382_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2382_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2382_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2382_4,axiom,
( hAPP(X1,X5) != hAPP(X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2383_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_1,axiom,
( ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_4,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2384_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_1,axiom,
( ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_4,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X1),X4))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2385_0,axiom,
( X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ c_Fun_Oinj__on(X5,X3,X1,X6)
| hAPP(X5,X2) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2385_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ c_Fun_Oinj__on(X5,X3,X1,X6)
| hAPP(X5,X2) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2385_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| X2 = X4
| ~ c_Fun_Oinj__on(X5,X3,X1,X6)
| hAPP(X5,X2) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2385_3,axiom,
( ~ c_Fun_Oinj__on(X5,X3,X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| X2 = X4
| hAPP(X5,X2) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2385_4,axiom,
( hAPP(X5,X2) != hAPP(X5,X4)
| ~ c_Fun_Oinj__on(X5,X3,X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| X2 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2386_0,axiom,
( c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2386_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2386_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2387_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2387_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2388_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2388_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2389_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2389_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2390_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2390_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2391_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2391_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2391_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2392_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2392_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2392_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2393_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2393_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2393_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2394_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1)),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2395_0,axiom,
( c_lessequals(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,X5),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2395_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,X5),X5)
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2395_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(hAPP(X4,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2396_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2397_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2397_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2397_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2398_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2398_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2399_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X3,X1)),X2))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2399_1,axiom,
( hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2399_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X3,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2400_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2400_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2400_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X4,X1),tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2401_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2401_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2402_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2402_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2402_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2403_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2403_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2403_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2404_0,axiom,
( hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2404_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2404_2,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2405_0,axiom,
( hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2405_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2405_2,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(X4,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2406_0,axiom,
( c_Set_Oimage(c_COMBK(X4,X5,X1),X3,X1,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2406_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oimage(c_COMBK(X4,X5,X1),X3,X1,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2407_0,axiom,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2408_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_2408]) ).
cnf(c_0_2408_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_2408]) ).
cnf(c_0_2408_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_2408]) ).
cnf(c_0_2409_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_2409]) ).
cnf(c_0_2409_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_2409]) ).
cnf(c_0_2409_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_2409]) ).
cnf(c_0_2410_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(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_2410]) ).
cnf(c_0_2410_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(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_2410]) ).
cnf(c_0_2410_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2411_0,axiom,
( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2411_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X3,X1)))
| c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2412_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2412_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2412_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2413_0,axiom,
( c_lessequals(X3,X2,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2413_1,axiom,
( ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool))
| c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2414_0,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2414_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2415_0,axiom,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2415_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),X3))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2416_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_2416]) ).
cnf(c_0_2416_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_2416]) ).
cnf(c_0_2417_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) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2417_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) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2418_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_2418]) ).
cnf(c_0_2418_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_2418]) ).
cnf(c_0_2419_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_2419]) ).
cnf(c_0_2419_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_2419]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2421_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_2421]) ).
cnf(c_0_2421_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_2421]) ).
cnf(c_0_2421_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_2421]) ).
cnf(c_0_2422_0,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatMost(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2422_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatMost(X3,X4,X1)))
| hBOOL(hAPP(hAPP(X3,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2423_0,axiom,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThan(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2423_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThan(X3,X4,X1)))
| hBOOL(hAPP(hAPP(X3,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2424_0,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2424_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1)))
| hBOOL(hAPP(hAPP(X3,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2425_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2425_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2426_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_1,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X1,X3)))
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XballE__1__1(X2,X1,X3)))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2427_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_2,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_3,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2428_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2428_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2429_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2430_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)),X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2431_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)),X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2431_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2432_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2432_1,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2433_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2433_1,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2434_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_3,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2435_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2435_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2435_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2436_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2436_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2436_2,axiom,
( c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2436_3,axiom,
( ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2437_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X3,X1,X2),X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2437_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(X3,X1,X2),X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2438_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X3,X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2438]) ).
cnf(c_0_2438_1,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X3,X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2438]) ).
cnf(c_0_2439_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2439_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2439_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2440_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2440_1,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool)),X1)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2441_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2441_1,axiom,
( c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2442_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2443_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2444_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Ovimage(c_COMBK(X2,X1,X4),X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_1,axiom,
( c_Set_Ovimage(c_COMBK(X2,X1,X4),X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2445_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_2445]) ).
cnf(c_0_2445_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_2445]) ).
cnf(c_0_2445_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_2445]) ).
cnf(c_0_2446_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),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_2446]) ).
cnf(c_0_2446_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2447_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),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_2447]) ).
cnf(c_0_2447_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2448_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_2448]) ).
cnf(c_0_2448_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_2448]) ).
cnf(c_0_2448_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_2448]) ).
cnf(c_0_2449_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_2449]) ).
cnf(c_0_2449_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_2449]) ).
cnf(c_0_2449_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_2449]) ).
cnf(c_0_2450_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_1,axiom,
( c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_2,axiom,
( ~ c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2451_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| 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_2451]) ).
cnf(c_0_2451_1,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_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(hAPP(hAPP(c_in(X4),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2452_0,axiom,
( c_lessequals(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2452_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2452_2,axiom,
( ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2453_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2454_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2454_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2455_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),c_Set_OPow(X2,X3)))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2455_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),c_Set_OPow(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2456_0,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
cnf(c_0_2456_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
cnf(c_0_2456_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X4,X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
cnf(c_0_2457_0,axiom,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2457_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2457_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XbexE__1__1(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2458_0,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X4,X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2459_0,axiom,
( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1)))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_2,axiom,
( ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2460_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_2460]) ).
cnf(c_0_2460_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_2460]) ).
cnf(c_0_2461_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_2461]) ).
cnf(c_0_2461_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_2461]) ).
cnf(c_0_2462_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2463_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2463_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2464_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,tc_fun(X4,tc_bool)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2464_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,tc_fun(X4,tc_bool)) = X3
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2465_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2465_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OatMost(X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2466_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X3),c_SetInterval_Oord_OgreaterThan(X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2466_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X3),c_SetInterval_Oord_OgreaterThan(X1,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2467_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2467_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2468_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_2468]) ).
cnf(c_0_2468_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_2468]) ).
cnf(c_0_2469_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_2469]) ).
cnf(c_0_2469_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_2469]) ).
cnf(c_0_2470_0,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2470_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2471_0,axiom,
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2471_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2472_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2472_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2473_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2473_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2474_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2475_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2476_0,axiom,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_2,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2477_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_1,axiom,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2478_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2478_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2479_0,axiom,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2479_1,axiom,
( hBOOL(hAPP(X2,X4))
| X1 = X4
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2479_2,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| hBOOL(hAPP(X2,X4))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2481_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2481_1,axiom,
( c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2481_2,axiom,
( ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2482_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_1,axiom,
( c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_2,axiom,
( ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| c_lessequals(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2483_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X1),X4))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X1),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2484_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2485_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_2,axiom,
( ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2486_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2487_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2488_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2489_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2490_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| c_Set_Oinsert(X4,X1,X3) != c_Set_Oinsert(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| c_Set_Oinsert(X4,X1,X3) != c_Set_Oinsert(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_2,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| X1 = X2
| c_Set_Oinsert(X4,X1,X3) != c_Set_Oinsert(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_3,axiom,
( c_Set_Oinsert(X4,X1,X3) != c_Set_Oinsert(X4,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2491_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_2491]) ).
cnf(c_0_2491_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_2491]) ).
cnf(c_0_2492_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_2492]) ).
cnf(c_0_2492_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_2492]) ).
cnf(c_0_2493_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_1,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2494_0,axiom,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2494_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2495_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2495]) ).
cnf(c_0_2495_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2495]) ).
cnf(c_0_2496_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2496]) ).
cnf(c_0_2496_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2496]) ).
cnf(c_0_2497_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_2497]) ).
cnf(c_0_2497_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_2497]) ).
cnf(c_0_2498_0,axiom,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2498]) ).
cnf(c_0_2498_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2498]) ).
cnf(c_0_2499_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2499_1,axiom,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2500_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_2500]) ).
cnf(c_0_2500_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_2500]) ).
cnf(c_0_2501_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2501_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2501_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2501_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2502_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2502_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2502_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2502_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2503_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2503]) ).
cnf(c_0_2503_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2503]) ).
cnf(c_0_2503_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2503]) ).
cnf(c_0_2503_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2503]) ).
cnf(c_0_2504_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_2504]) ).
cnf(c_0_2504_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_2504]) ).
cnf(c_0_2504_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_2504]) ).
cnf(c_0_2504_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_2504]) ).
cnf(c_0_2505_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_2505]) ).
cnf(c_0_2505_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_2505]) ).
cnf(c_0_2505_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_2505]) ).
cnf(c_0_2505_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_2505]) ).
cnf(c_0_2506_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_2506]) ).
cnf(c_0_2506_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_2506]) ).
cnf(c_0_2506_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_2506]) ).
cnf(c_0_2506_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_2506]) ).
cnf(c_0_2507_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2507]) ).
cnf(c_0_2507_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2507]) ).
cnf(c_0_2508_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2509_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_2509]) ).
cnf(c_0_2509_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_2509]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2511_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_2511]) ).
cnf(c_0_2511_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_2511]) ).
cnf(c_0_2512_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_2512]) ).
cnf(c_0_2512_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_2512]) ).
cnf(c_0_2513_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_2513]) ).
cnf(c_0_2513_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_2513]) ).
cnf(c_0_2514_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2515_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_1,axiom,
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2516_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2516_1,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2517_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2517]) ).
cnf(c_0_2517_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2517]) ).
cnf(c_0_2518_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_2518]) ).
cnf(c_0_2518_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_2518]) ).
cnf(c_0_2518_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_2518]) ).
cnf(c_0_2519_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2519]) ).
cnf(c_0_2519_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2519]) ).
cnf(c_0_2519_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2519]) ).
cnf(c_0_2520_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2520]) ).
cnf(c_0_2520_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2520]) ).
cnf(c_0_2520_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2520]) ).
cnf(c_0_2521_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2521_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2521_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2522_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_2522]) ).
cnf(c_0_2522_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_2522]) ).
cnf(c_0_2522_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_2522]) ).
cnf(c_0_2522_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_2522]) ).
cnf(c_0_2523_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_2523]) ).
cnf(c_0_2523_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_2523]) ).
cnf(c_0_2523_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_2523]) ).
cnf(c_0_2523_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_2523]) ).
cnf(c_0_2524_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2524_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2524_2,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2524_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2525_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2525]) ).
cnf(c_0_2525_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2525]) ).
cnf(c_0_2525_2,axiom,
( c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2525]) ).
cnf(c_0_2525_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2525]) ).
cnf(c_0_2526_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_2526]) ).
cnf(c_0_2526_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_2526]) ).
cnf(c_0_2526_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_2526]) ).
cnf(c_0_2527_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_2527]) ).
cnf(c_0_2527_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_2527]) ).
cnf(c_0_2527_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_2527]) ).
cnf(c_0_2528_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_2528]) ).
cnf(c_0_2528_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_2528]) ).
cnf(c_0_2528_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_2528]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2530_0,axiom,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2530]) ).
cnf(c_0_2530_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2530]) ).
cnf(c_0_2530_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2530]) ).
cnf(c_0_2531_0,axiom,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2531]) ).
cnf(c_0_2531_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2531]) ).
cnf(c_0_2531_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2531]) ).
cnf(c_0_2532_0,axiom,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2532_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2532_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2533_0,axiom,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2533_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2533_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2534_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_2534]) ).
cnf(c_0_2534_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_2534]) ).
cnf(c_0_2535_0,axiom,
( c_lessequals(X2,X1,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2535_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2535_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2535_3,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X2,X1,tc_fun(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2536_0,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2536]) ).
cnf(c_0_2536_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2536]) ).
cnf(c_0_2537_0,axiom,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2537_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1)))
| hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2538_0,axiom,
( c_lessequals(X3,X2,X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2538]) ).
cnf(c_0_2538_1,axiom,
( ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2538]) ).
cnf(c_0_2538_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| c_lessequals(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2538]) ).
cnf(c_0_2539_0,axiom,
( c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2539]) ).
cnf(c_0_2539_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2539]) ).
cnf(c_0_2539_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2539]) ).
cnf(c_0_2540_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2540]) ).
cnf(c_0_2540_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2540]) ).
cnf(c_0_2541_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2541_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2542_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2542_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2543_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2544_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2544_1,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2544_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2545_0,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2546_0,axiom,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X3,X1),X2,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X3,X1),X2,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X3,X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2547_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_2547]) ).
cnf(c_0_2547_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_2547]) ).
cnf(c_0_2547_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_2547]) ).
cnf(c_0_2548_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_2548]) ).
cnf(c_0_2548_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_2548]) ).
cnf(c_0_2548_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_2548]) ).
cnf(c_0_2549_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2549]) ).
cnf(c_0_2549_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2549]) ).
cnf(c_0_2549_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2549]) ).
cnf(c_0_2550_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2550]) ).
cnf(c_0_2550_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2550]) ).
cnf(c_0_2550_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2550]) ).
cnf(c_0_2551_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2551_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2551_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2552_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2552_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2552_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2553_0,axiom,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2553_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2553_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2554_0,axiom,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2554_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2554_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2557_0,axiom,
( c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2557_1,axiom,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2557_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2558_0,axiom,
( c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2558]) ).
cnf(c_0_2558_1,axiom,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2558]) ).
cnf(c_0_2558_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2558]) ).
cnf(c_0_2559_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2559_1,axiom,
( ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2559_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2560_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2560_1,axiom,
( ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2560_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2561_0,axiom,
( c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2561_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2561_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2562_0,axiom,
( c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3),X2)
| c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2563_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2563_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2563_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2564_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2564_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2564_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2565_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2565_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != 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_2565]) ).
cnf(c_0_2566_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_2566]) ).
cnf(c_0_2566_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_2566]) ).
cnf(c_0_2566_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_2566]) ).
cnf(c_0_2567_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oinsert(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2567_1,axiom,
( c_Set_Oinsert(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2568_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_2568]) ).
cnf(c_0_2568_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_2568]) ).
cnf(c_0_2568_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_2568]) ).
cnf(c_0_2568_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_2568]) ).
cnf(c_0_2569_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2569_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2569_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2569_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2570_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2571_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_2571]) ).
cnf(c_0_2571_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_2571]) ).
cnf(c_0_2571_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_2571]) ).
cnf(c_0_2571_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_2571]) ).
cnf(c_0_2572_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2572_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2572_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2572_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2573_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2573_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2573_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2573_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2574_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2574_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2574_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2574_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2575_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2575_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2575_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2575_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2576_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_2576]) ).
cnf(c_0_2576_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_2576]) ).
cnf(c_0_2577_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_2577]) ).
cnf(c_0_2577_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_2577]) ).
cnf(c_0_2578_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_2578]) ).
cnf(c_0_2578_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_2578]) ).
cnf(c_0_2579_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool)) = X1
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2579_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2580_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2581_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2582_0,axiom,
( c_Set_Oinsert(X2,X3,X1) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2582_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oinsert(X2,X3,X1) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2583_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_2583]) ).
cnf(c_0_2583_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_2583]) ).
cnf(c_0_2584_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_2584]) ).
cnf(c_0_2584_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_2584]) ).
cnf(c_0_2585_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2585_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2586_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2587_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2587_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2587_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X1,X2,tc_fun(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2588_0,axiom,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2588_1,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2589_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_2589]) ).
cnf(c_0_2589_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_2589]) ).
cnf(c_0_2590_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,X3),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_2590]) ).
cnf(c_0_2590_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,X3),X3) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2591_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2591_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2592_0,axiom,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2592_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2592_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2592_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2593_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2593_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2593_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2594_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2594_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2594_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2595_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_2595]) ).
cnf(c_0_2595_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_2595]) ).
cnf(c_0_2596_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_2596]) ).
cnf(c_0_2596_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_2596]) ).
cnf(c_0_2597_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_2597]) ).
cnf(c_0_2597_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_2597]) ).
cnf(c_0_2598_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2598_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2599_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2599]) ).
cnf(c_0_2599_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2599]) ).
cnf(c_0_2600_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_2600]) ).
cnf(c_0_2600_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_2600]) ).
cnf(c_0_2600_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_2600]) ).
cnf(c_0_2601_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_2601]) ).
cnf(c_0_2601_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_2601]) ).
cnf(c_0_2601_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_2601]) ).
cnf(c_0_2602_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2603_0,axiom,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2603_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2604_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_2604]) ).
cnf(c_0_2604_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_2604]) ).
cnf(c_0_2605_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_2605]) ).
cnf(c_0_2605_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_2605]) ).
cnf(c_0_2606_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2606_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)) = c_HOL_Ominus__class_Ominus(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2607_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_2607]) ).
cnf(c_0_2607_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_2607]) ).
cnf(c_0_2607_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_2607]) ).
cnf(c_0_2607_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_2607]) ).
cnf(c_0_2608_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_2608]) ).
cnf(c_0_2608_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_2608]) ).
cnf(c_0_2608_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_2608]) ).
cnf(c_0_2608_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_2608]) ).
cnf(c_0_2609_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_2609]) ).
cnf(c_0_2609_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_2609]) ).
cnf(c_0_2609_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_2609]) ).
cnf(c_0_2609_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_2609]) ).
cnf(c_0_2610_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_2610]) ).
cnf(c_0_2610_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_2610]) ).
cnf(c_0_2610_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_2610]) ).
cnf(c_0_2611_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_2611]) ).
cnf(c_0_2611_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_2611]) ).
cnf(c_0_2611_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_2611]) ).
cnf(c_0_2612_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2612_1,axiom,
( ~ c_lessequals(X1,X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2612_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2613_0,axiom,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2613_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2613_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2614_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2614_1,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2614_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2615_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2615_1,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2615_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2616_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2616_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2616_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2617_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2617_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2617_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2618_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2619_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2619_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2619_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2620_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2620_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2621_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2621_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2622_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2622]) ).
cnf(c_0_2622_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2622]) ).
cnf(c_0_2623_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2623]) ).
cnf(c_0_2623_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2623]) ).
cnf(c_0_2624_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2625_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2625_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2626_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2626_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2627_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_2627]) ).
cnf(c_0_2627_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_2627]) ).
cnf(c_0_2628_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_2628]) ).
cnf(c_0_2628_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_2628]) ).
cnf(c_0_2629_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_2629]) ).
cnf(c_0_2629_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_2629]) ).
cnf(c_0_2630_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_2630]) ).
cnf(c_0_2630_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_2630]) ).
cnf(c_0_2631_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2631_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2632_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2632_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2633_0,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2633_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2633_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2633_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2634_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2634_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2634_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2634_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2635_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2635_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2635_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2635_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2636_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2636_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2636_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2636_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2637_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2637_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2637_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2637_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2638_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2639_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2640_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2641_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_2641]) ).
cnf(c_0_2641_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_2641]) ).
cnf(c_0_2641_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_2641]) ).
cnf(c_0_2642_0,axiom,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2642_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2642_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2643_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_2643]) ).
cnf(c_0_2643_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_2643]) ).
cnf(c_0_2643_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_2643]) ).
cnf(c_0_2644_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_2644]) ).
cnf(c_0_2644_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_2644]) ).
cnf(c_0_2644_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_2644]) ).
cnf(c_0_2645_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2645_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2645_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2646_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2646]) ).
cnf(c_0_2646_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2646]) ).
cnf(c_0_2646_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2646]) ).
cnf(c_0_2647_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2647_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2647_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2648_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2648_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2648_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2649_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2650_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2650_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2650_2,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2650_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2651_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2651_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2651_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2651_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2652_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2652_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2652_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2652_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2653_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2653_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2653_2,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2653_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2654_0,axiom,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2654_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2654_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2655_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2656_0,axiom,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,X2)
| c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2657_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2657_1,axiom,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2657_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2658_0,axiom,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2658_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2658_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2659_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_2659]) ).
cnf(c_0_2659_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_2659]) ).
cnf(c_0_2660_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_2660]) ).
cnf(c_0_2660_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_2660]) ).
cnf(c_0_2661_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2661]) ).
cnf(c_0_2661_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2661]) ).
cnf(c_0_2662_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2662_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2663_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_2663]) ).
cnf(c_0_2663_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_2663]) ).
cnf(c_0_2664_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_2664]) ).
cnf(c_0_2664_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_2664]) ).
cnf(c_0_2665_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_2665]) ).
cnf(c_0_2665_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_2665]) ).
cnf(c_0_2665_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_2665]) ).
cnf(c_0_2666_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_2666]) ).
cnf(c_0_2666_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_2666]) ).
cnf(c_0_2666_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_2666]) ).
cnf(c_0_2667_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2667_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1),X2) = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2668_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2668_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2669_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2669_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2670_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2670_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2671_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2671]) ).
cnf(c_0_2671_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2671]) ).
cnf(c_0_2672_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_2672]) ).
cnf(c_0_2672_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_2672]) ).
cnf(c_0_2673_0,axiom,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2673_1,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| X1 = X2
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2673_2,axiom,
( ~ class_Lattices_Oboolean__algebra(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2674_0,axiom,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2674_1,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2674_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(c_HOL_Ouminus__class_Ouminus(X3),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2675_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2675_1,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2676_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2676_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2677_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_2677]) ).
cnf(c_0_2677_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_2677]) ).
cnf(c_0_2678_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_2678]) ).
cnf(c_0_2678_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_2678]) ).
cnf(c_0_2679_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2679_1,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2680_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2680]) ).
cnf(c_0_2680_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2680]) ).
cnf(c_0_2681_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2681]) ).
cnf(c_0_2681_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2681]) ).
cnf(c_0_2682_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1)) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2682]) ).
cnf(c_0_2682_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| hAPP(c_HOL_Ouminus__class_Ouminus(X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2682]) ).
cnf(c_0_2683_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1)) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2683_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| hAPP(c_HOL_Ouminus__class_Ouminus(X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2684_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2684_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2685_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2685_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2686_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2686]) ).
cnf(c_0_2686_1,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2686]) ).
cnf(c_0_2687_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2687]) ).
cnf(c_0_2687_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2687]) ).
cnf(c_0_2688_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2688_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2689_0,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2690_0,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2690_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Oupper__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2691_0,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2691_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olower__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2692_0,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2692_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2693_0,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2693_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2694_0,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2694_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2695_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2695_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2696_0,axiom,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2696]) ).
cnf(c_0_2696_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2696]) ).
cnf(c_0_2697_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2697]) ).
cnf(c_0_2697_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2697]) ).
cnf(c_0_2698_0,axiom,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2698]) ).
cnf(c_0_2698_1,axiom,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2698]) ).
cnf(c_0_2699_0,axiom,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2699]) ).
cnf(c_0_2699_1,axiom,
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2699]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_796,negated_conjecture,
! [X1] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_1_797,negated_conjecture,
~ v_thesis____,
file('<stdin>',cls_conjecture_0) ).
fof(c_0_2_798,negated_conjecture,
! [X1] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_3_799,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_4_800,negated_conjecture,
! [X2] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X2),c_Arrow__Order__Mirabelle_OLin)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2])])]) ).
fof(c_0_5_801,negated_conjecture,
~ v_thesis____,
c_0_3 ).
cnf(c_0_6_802,negated_conjecture,
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7_803,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8_804,negated_conjecture,
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
c_0_6,
[final] ).
cnf(c_0_9_805,negated_conjecture,
~ v_thesis____,
c_0_7,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_1714,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/tmp/iprover_modulo_7a0834.p',c_0_9) ).
cnf(c_2151,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_1714]) ).
cnf(c_2155,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_2151]) ).
cnf(c_2156,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_2155]) ).
cnf(c_2157,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_2156]) ).
cnf(c_7212,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_2157]) ).
cnf(c_649,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| v_thesis____ ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7a0834.p',c_0_2357_0) ).
cnf(c_5172,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| v_thesis____ ),
inference(copy,[status(esa)],[c_649]) ).
cnf(c_7216,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin)),
inference(backward_subsumption_resolution,[status(thm)],[c_7212,c_5172]) ).
cnf(c_7217,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin)),
inference(rewriting,[status(thm)],[c_7216]) ).
cnf(c_1554,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_7a0834.p',c_0_794_0) ).
cnf(c_6982,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
inference(copy,[status(esa)],[c_1554]) ).
cnf(c_7220,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_7217,c_6982]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SCT027-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n020.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 : Sat Jul 2 09:20:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.21/0.56 % Orienting using strategy Equiv(ClausalAll)
% 0.21/0.56 % Orientation found
% 0.21/0.56 % 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/sandbox2/tmp/iprover_proof_4c25bd.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_7a0834.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_995a01 | grep -v "SZS"
% 0.21/0.59
% 0.21/0.59 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.21/0.59
% 0.21/0.59 %
% 0.21/0.59 % ------ iProver source info
% 0.21/0.59
% 0.21/0.59 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.21/0.59 % git: non_committed_changes: true
% 0.21/0.59 % git: last_make_outside_of_git: true
% 0.21/0.59
% 0.21/0.59 %
% 0.21/0.59 % ------ Input Options
% 0.21/0.59
% 0.21/0.59 % --out_options all
% 0.21/0.59 % --tptp_safe_out true
% 0.21/0.59 % --problem_path ""
% 0.21/0.59 % --include_path ""
% 0.21/0.59 % --clausifier .//eprover
% 0.21/0.59 % --clausifier_options --tstp-format
% 0.21/0.59 % --stdin false
% 0.21/0.59 % --dbg_backtrace false
% 0.21/0.59 % --dbg_dump_prop_clauses false
% 0.21/0.59 % --dbg_dump_prop_clauses_file -
% 0.21/0.59 % --dbg_out_stat false
% 0.21/0.59
% 0.21/0.59 % ------ General Options
% 0.21/0.59
% 0.21/0.59 % --fof false
% 0.21/0.59 % --time_out_real 150.
% 0.21/0.59 % --time_out_prep_mult 0.2
% 0.21/0.59 % --time_out_virtual -1.
% 0.21/0.59 % --schedule none
% 0.21/0.59 % --ground_splitting input
% 0.21/0.59 % --splitting_nvd 16
% 0.21/0.59 % --non_eq_to_eq false
% 0.21/0.59 % --prep_gs_sim true
% 0.21/0.59 % --prep_unflatten false
% 0.21/0.59 % --prep_res_sim true
% 0.21/0.59 % --prep_upred true
% 0.21/0.59 % --res_sim_input true
% 0.21/0.59 % --clause_weak_htbl true
% 0.21/0.59 % --gc_record_bc_elim false
% 0.21/0.59 % --symbol_type_check false
% 0.21/0.59 % --clausify_out false
% 0.21/0.59 % --large_theory_mode false
% 0.21/0.59 % --prep_sem_filter none
% 0.21/0.59 % --prep_sem_filter_out false
% 0.21/0.59 % --preprocessed_out false
% 0.21/0.59 % --sub_typing false
% 0.21/0.59 % --brand_transform false
% 0.21/0.59 % --pure_diseq_elim true
% 0.21/0.59 % --min_unsat_core false
% 0.21/0.59 % --pred_elim true
% 0.21/0.59 % --add_important_lit false
% 0.21/0.59 % --soft_assumptions false
% 0.21/0.59 % --reset_solvers false
% 0.21/0.59 % --bc_imp_inh []
% 0.21/0.59 % --conj_cone_tolerance 1.5
% 0.21/0.59 % --prolific_symb_bound 500
% 0.21/0.59 % --lt_threshold 2000
% 0.21/0.59
% 0.21/0.59 % ------ SAT Options
% 0.21/0.59
% 0.21/0.59 % --sat_mode false
% 0.21/0.59 % --sat_fm_restart_options ""
% 0.21/0.59 % --sat_gr_def false
% 0.21/0.59 % --sat_epr_types true
% 0.21/0.59 % --sat_non_cyclic_types false
% 0.21/0.59 % --sat_finite_models false
% 0.21/0.59 % --sat_fm_lemmas false
% 0.21/0.59 % --sat_fm_prep false
% 0.21/0.59 % --sat_fm_uc_incr true
% 0.21/0.59 % --sat_out_model small
% 0.21/0.59 % --sat_out_clauses false
% 0.21/0.59
% 0.21/0.59 % ------ QBF Options
% 0.21/0.59
% 0.21/0.59 % --qbf_mode false
% 0.21/0.59 % --qbf_elim_univ true
% 0.21/0.59 % --qbf_sk_in true
% 0.21/0.59 % --qbf_pred_elim true
% 0.21/0.59 % --qbf_split 32
% 0.21/0.59
% 0.21/0.59 % ------ BMC1 Options
% 0.21/0.59
% 0.21/0.59 % --bmc1_incremental false
% 0.21/0.59 % --bmc1_axioms reachable_all
% 0.21/0.59 % --bmc1_min_bound 0
% 0.21/0.59 % --bmc1_max_bound -1
% 0.21/0.59 % --bmc1_max_bound_default -1
% 0.21/0.59 % --bmc1_symbol_reachability true
% 0.21/0.59 % --bmc1_property_lemmas false
% 0.21/0.59 % --bmc1_k_induction false
% 0.21/0.59 % --bmc1_non_equiv_states false
% 0.21/0.59 % --bmc1_deadlock false
% 0.21/0.59 % --bmc1_ucm false
% 0.21/0.59 % --bmc1_add_unsat_core none
% 0.21/0.59 % --bmc1_unsat_core_children false
% 0.21/0.59 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.59 % --bmc1_out_stat full
% 0.21/0.59 % --bmc1_ground_init false
% 0.21/0.59 % --bmc1_pre_inst_next_state false
% 0.21/0.59 % --bmc1_pre_inst_state false
% 0.21/0.59 % --bmc1_pre_inst_reach_state false
% 0.21/0.59 % --bmc1_out_unsat_core false
% 0.21/0.59 % --bmc1_aig_witness_out false
% 0.21/0.59 % --bmc1_verbose false
% 0.21/0.59 % --bmc1_dump_clauses_tptp false
% 0.65/0.90 % --bmc1_dump_unsat_core_tptp false
% 0.65/0.90 % --bmc1_dump_file -
% 0.65/0.90 % --bmc1_ucm_expand_uc_limit 128
% 0.65/0.90 % --bmc1_ucm_n_expand_iterations 6
% 0.65/0.90 % --bmc1_ucm_extend_mode 1
% 0.65/0.90 % --bmc1_ucm_init_mode 2
% 0.65/0.90 % --bmc1_ucm_cone_mode none
% 0.65/0.90 % --bmc1_ucm_reduced_relation_type 0
% 0.65/0.90 % --bmc1_ucm_relax_model 4
% 0.65/0.90 % --bmc1_ucm_full_tr_after_sat true
% 0.65/0.90 % --bmc1_ucm_expand_neg_assumptions false
% 0.65/0.90 % --bmc1_ucm_layered_model none
% 0.65/0.90 % --bmc1_ucm_max_lemma_size 10
% 0.65/0.90
% 0.65/0.90 % ------ AIG Options
% 0.65/0.90
% 0.65/0.90 % --aig_mode false
% 0.65/0.90
% 0.65/0.90 % ------ Instantiation Options
% 0.65/0.90
% 0.65/0.90 % --instantiation_flag true
% 0.65/0.90 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.65/0.90 % --inst_solver_per_active 750
% 0.65/0.90 % --inst_solver_calls_frac 0.5
% 0.65/0.90 % --inst_passive_queue_type priority_queues
% 0.65/0.90 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.65/0.90 % --inst_passive_queues_freq [25;2]
% 0.65/0.90 % --inst_dismatching true
% 0.65/0.90 % --inst_eager_unprocessed_to_passive true
% 0.65/0.90 % --inst_prop_sim_given true
% 0.65/0.90 % --inst_prop_sim_new false
% 0.65/0.90 % --inst_orphan_elimination true
% 0.65/0.90 % --inst_learning_loop_flag true
% 0.65/0.90 % --inst_learning_start 3000
% 0.65/0.90 % --inst_learning_factor 2
% 0.65/0.90 % --inst_start_prop_sim_after_learn 3
% 0.65/0.90 % --inst_sel_renew solver
% 0.65/0.90 % --inst_lit_activity_flag true
% 0.65/0.90 % --inst_out_proof true
% 0.65/0.90
% 0.65/0.90 % ------ Resolution Options
% 0.65/0.90
% 0.65/0.90 % --resolution_flag true
% 0.65/0.90 % --res_lit_sel kbo_max
% 0.65/0.90 % --res_to_prop_solver none
% 0.65/0.90 % --res_prop_simpl_new false
% 0.65/0.90 % --res_prop_simpl_given false
% 0.65/0.90 % --res_passive_queue_type priority_queues
% 0.65/0.90 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.65/0.90 % --res_passive_queues_freq [15;5]
% 0.65/0.90 % --res_forward_subs full
% 0.65/0.90 % --res_backward_subs full
% 0.65/0.90 % --res_forward_subs_resolution true
% 0.65/0.90 % --res_backward_subs_resolution true
% 0.65/0.90 % --res_orphan_elimination false
% 0.65/0.90 % --res_time_limit 1000.
% 0.65/0.90 % --res_out_proof true
% 0.65/0.90 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_4c25bd.s
% 0.65/0.90 % --modulo true
% 0.65/0.90
% 0.65/0.90 % ------ Combination Options
% 0.65/0.90
% 0.65/0.90 % --comb_res_mult 1000
% 0.65/0.90 % --comb_inst_mult 300
% 0.65/0.90 % ------
% 0.65/0.90
% 0.65/0.90 % ------ Parsing...% successful
% 0.65/0.90
% 0.65/0.90 % ------ 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 %
% 0.65/0.90
% 0.65/0.90 % ------ Proving...
% 0.65/0.90 % ------ Problem Properties
% 0.65/0.90
% 0.65/0.90 %
% 0.65/0.90 % EPR false
% 0.65/0.90 % Horn false
% 0.65/0.90 % Has equality true
% 0.65/0.90
% 0.65/0.90 % % ------ Input Options Time Limit: Unbounded
% 0.65/0.90
% 0.65/0.90
% 0.65/0.90 % warning: Clause {~(hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin)));v_thesis____} has no selected literals
% 0.65/0.90 cnf(c_1713,negated_conjecture,
% 0.65/0.90 ( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
% 0.65/0.90 | v_thesis____ ),
% 0.65/0.90 file('/export/starexec/sandbox2/tmp/iprover_modulo_7a0834.p', c_0_8) ).
% 0.65/0.90
% 0.65/0.90 % warning: Clause {~(hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin)));v_thesis____} has no selected literals
% 0.65/0.90 cnf(c_1713,negated_conjecture,
% 0.65/0.90 ( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
% 0.65/0.90 | v_thesis____ ),
% 0.65/0.90 file('/export/starexec/sandbox2/tmp/iprover_modulo_7a0834.p', c_0_8) ).
% 0.65/0.90
% 0.65/0.90 Compiling...
% 0.65/0.90 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 % warning: Clause {~(hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin)));v_thesis____} has no selected literals
% 6.56/7.37 cnf(c_1713,negated_conjecture,
% 6.56/7.37 ( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
% 6.56/7.37 | v_thesis____ ),
% 6.56/7.37 file('/export/starexec/sandbox2/tmp/iprover_modulo_7a0834.p', c_0_8) ).
% 6.56/7.37
% 6.56/7.37 Compiling...
% 6.56/7.37 Loading plugin: done.
% 6.56/7.37 % warning: Clause {~(hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin)));v_thesis____} has no selected literals
% 6.56/7.37 cnf(c_1713,negated_conjecture,
% 6.56/7.37 ( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
% 6.56/7.37 | v_thesis____ ),
% 6.56/7.37 file('/export/starexec/sandbox2/tmp/iprover_modulo_7a0834.p', c_0_8) ).
% 6.56/7.37
% 6.56/7.37 % % ------ Current options:
% 6.56/7.37
% 6.56/7.37 % ------ Input Options
% 6.56/7.37
% 6.56/7.37 % --out_options all
% 6.56/7.37 % --tptp_safe_out true
% 6.56/7.37 % --problem_path ""
% 6.56/7.37 % --include_path ""
% 6.56/7.37 % --clausifier .//eprover
% 6.56/7.37 % --clausifier_options --tstp-format
% 6.56/7.37 % --stdin false
% 6.56/7.37 % --dbg_backtrace false
% 6.56/7.37 % --dbg_dump_prop_clauses false
% 6.56/7.37 % --dbg_dump_prop_clauses_file -
% 6.56/7.37 % --dbg_out_stat false
% 6.56/7.37
% 6.56/7.37 % ------ General Options
% 6.56/7.37
% 6.56/7.37 % --fof false
% 6.56/7.37 % --time_out_real 150.
% 6.56/7.37 % --time_out_prep_mult 0.2
% 6.56/7.37 % --time_out_virtual -1.
% 6.56/7.37 % --schedule none
% 6.56/7.37 % --ground_splitting input
% 6.56/7.37 % --splitting_nvd 16
% 6.56/7.37 % --non_eq_to_eq false
% 6.56/7.37 % --prep_gs_sim true
% 6.56/7.37 % --prep_unflatten false
% 6.56/7.37 % --prep_res_sim true
% 6.56/7.37 % --prep_upred true
% 6.56/7.37 % --res_sim_input true
% 6.56/7.37 % --clause_weak_htbl true
% 6.56/7.37 % --gc_record_bc_elim false
% 6.56/7.37 % --symbol_type_check false
% 6.56/7.37 % --clausify_out false
% 6.56/7.37 % --large_theory_mode false
% 6.56/7.37 % --prep_sem_filter none
% 6.56/7.37 % --prep_sem_filter_out false
% 6.56/7.37 % --preprocessed_out false
% 6.56/7.37 % --sub_typing false
% 6.56/7.37 % --brand_transform false
% 6.56/7.37 % --pure_diseq_elim true
% 6.56/7.37 % --min_unsat_core false
% 6.56/7.37 % --pred_elim true
% 6.56/7.37 % --add_important_lit false
% 6.56/7.37 % --soft_assumptions false
% 6.56/7.37 % --reset_solvers false
% 6.56/7.37 % --bc_imp_inh []
% 6.56/7.37 % --conj_cone_tolerance 1.5
% 6.56/7.37 % --prolific_symb_bound 500
% 6.56/7.37 % --lt_threshold 2000
% 6.56/7.37
% 6.56/7.37 % ------ SAT Options
% 6.56/7.37
% 6.56/7.37 % --sat_mode false
% 6.56/7.37 % --sat_fm_restart_options ""
% 6.56/7.37 % --sat_gr_def false
% 6.56/7.37 % --sat_epr_types true
% 6.56/7.37 % --sat_non_cyclic_types false
% 6.56/7.37 % --sat_finite_models false
% 6.56/7.37 % --sat_fm_lemmas false
% 6.56/7.37 % --sat_fm_prep false
% 6.56/7.37 % --sat_fm_uc_incr true
% 6.56/7.37 % --sat_out_model small
% 6.56/7.37 % --sat_out_clauses false
% 6.56/7.37
% 6.56/7.37 % ------ QBF Options
% 6.56/7.37
% 6.56/7.37 % --qbf_mode false
% 6.56/7.37 % --qbf_elim_univ true
% 6.56/7.37 % --qbf_sk_in true
% 6.56/7.37 % --qbf_pred_elim true
% 6.56/7.37 % --qbf_split 32
% 6.56/7.37
% 6.56/7.37 % ------ BMC1 Options
% 6.56/7.37
% 6.56/7.37 % --bmc1_incremental false
% 6.56/7.37 % --bmc1_axioms reachable_all
% 6.56/7.37 % --bmc1_min_bound 0
% 6.56/7.37 % --bmc1_max_bound -1
% 6.56/7.37 % --bmc1_max_bound_default -1
% 6.56/7.37 % --bmc1_symbol_reachability true
% 6.56/7.37 % --bmc1_property_lemmas false
% 6.56/7.37 % --bmc1_k_induction false
% 6.56/7.37 % --bmc1_non_equiv_states false
% 6.56/7.37 % --bmc1_deadlock false
% 6.56/7.37 % --bmc1_ucm false
% 6.56/7.37 % --bmc1_add_unsat_core none
% 6.56/7.37 % --bmc1_unsat_core_children false
% 6.56/7.37 % --bmc1_unsat_core_extrapolate_axioms false
% 6.56/7.37 % --bmc1_out_stat full
% 6.56/7.37 % --bmc1_ground_init false
% 6.56/7.37 % --bmc1_pre_inst_next_state false
% 6.56/7.37 % --bmc1_pre_inst_state false
% 6.56/7.37 % --bmc1_pre_inst_reach_state false
% 6.56/7.37 % --bmc1_out_unsat_core false
% 6.56/7.37 % --bmc1_aig_witness_out false
% 6.56/7.37 % --bmc1_verbose false
% 6.56/7.37 % --bmc1_dump_clauses_tptp false
% 6.56/7.37 % --bmc1_dump_unsat_core_tptp false
% 6.56/7.37 % --bmc1_dump_file -
% 6.56/7.37 % --bmc1_ucm_expand_uc_limit 128
% 6.56/7.37 % --bmc1_ucm_n_expand_iterations 6
% 6.56/7.37 % --bmc1_ucm_extend_mode 1
% 6.56/7.37 % --bmc1_ucm_init_mode 2
% 6.56/7.37 % --bmc1_ucm_cone_mode none
% 6.56/7.37 % --bmc1_ucm_reduced_relation_type 0
% 6.56/7.37 % --bmc1_ucm_relax_model 4
% 6.56/7.37 % --bmc1_ucm_full_tr_after_sat true
% 6.56/7.37 % --bmc1_ucm_expand_neg_assumptions false
% 6.56/7.37 % --bmc1_ucm_layered_model none
% 6.56/7.37 % --bmc1_ucm_max_lemma_size 10
% 6.56/7.37
% 6.56/7.37 % ------ AIG Options
% 6.56/7.37
% 6.56/7.37 % --aig_mode false
% 6.56/7.37
% 6.56/7.37 % ------ Instantiation Options
% 6.56/7.37
% 6.56/7.37 % --instantiation_flag true
% 6.56/7.37 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 6.56/7.37 % --inst_solver_per_active 750
% 6.56/7.37 % --inst_solver_calls_frac 0.5
% 6.56/7.37 % --inst_passive_queue_type priority_queues
% 6.56/7.37 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 6.56/7.37 % --inst_passive_queues_freq [25;2]
% 6.56/7.37 % --inst_dismatching true
% 6.56/7.37 % --inst_eager_unprocessed_to_passive true
% 6.56/7.37 % --inst_prop_sim_given true
% 6.56/7.37 % --inst_prop_sim_new false
% 6.56/7.37 % --inst_orphan_elimination true
% 6.56/7.37 % --inst_learning_loop_flag true
% 6.56/7.37 % --inst_learning_start 3000
% 6.56/7.37 % --inst_learning_factor 2
% 6.56/7.37 % --inst_start_prop_sim_after_learn 3
% 6.56/7.37 % --inst_sel_renew solver
% 6.56/7.37 % --inst_lit_activity_flag true
% 6.56/7.37 % --inst_out_proof true
% 6.56/7.37
% 6.56/7.37 % ------ Resolution Options
% 6.56/7.37
% 6.56/7.37 % --resolution_flag true
% 6.56/7.37 % --res_lit_sel kbo_max
% 6.56/7.37 % --res_to_prop_solver none
% 6.56/7.37 % --res_prop_simpl_new false
% 6.56/7.37 % --res_prop_simpl_given false
% 6.56/7.37 % --res_passive_queue_type priority_queues
% 6.56/7.37 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 6.56/7.37 % --res_passive_queues_freq [15;5]
% 6.56/7.37 % --res_forward_subs full
% 6.56/7.37 % --res_backward_subs full
% 6.56/7.37 % --res_forward_subs_resolution true
% 6.56/7.37 % --res_backward_subs_resolution true
% 6.56/7.37 % --res_orphan_elimination false
% 6.56/7.37 % --res_time_limit 1000.
% 6.56/7.37 % --res_out_proof true
% 6.56/7.37 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_4c25bd.s
% 6.56/7.37 % --modulo true
% 6.56/7.37
% 6.56/7.37 % ------ Combination Options
% 6.56/7.37
% 6.56/7.37 % --comb_res_mult 1000
% 6.56/7.37 % --comb_inst_mult 300
% 6.56/7.37 % ------
% 6.56/7.37
% 6.56/7.37
% 6.56/7.37
% 6.56/7.37 % ------ Proving...
% 6.56/7.37 %
% 6.56/7.37
% 6.56/7.37
% 6.56/7.37 % Resolution empty clause
% 6.56/7.37
% 6.56/7.37 % ------ Statistics
% 6.56/7.37
% 6.56/7.37 % ------ General
% 6.56/7.37
% 6.56/7.37 % num_of_input_clauses: 1715
% 6.56/7.37 % num_of_input_neg_conjectures: 2
% 6.56/7.37 % num_of_splits: 0
% 6.56/7.37 % num_of_split_atoms: 0
% 6.56/7.37 % num_of_sem_filtered_clauses: 0
% 6.56/7.37 % num_of_subtypes: 0
% 6.56/7.37 % monotx_restored_types: 0
% 6.56/7.37 % sat_num_of_epr_types: 0
% 6.56/7.37 % sat_num_of_non_cyclic_types: 0
% 6.56/7.37 % sat_guarded_non_collapsed_types: 0
% 6.56/7.37 % is_epr: 0
% 6.56/7.37 % is_horn: 0
% 6.56/7.37 % has_eq: 1
% 6.56/7.37 % num_pure_diseq_elim: 0
% 6.56/7.37 % simp_replaced_by: 0
% 6.56/7.37 % res_preprocessed: 2
% 6.56/7.37 % prep_upred: 0
% 6.56/7.37 % prep_unflattend: 0
% 6.56/7.37 % pred_elim_cands: 0
% 6.56/7.37 % pred_elim: 0
% 6.56/7.37 % pred_elim_cl: 0
% 6.56/7.37 % pred_elim_cycles: 0
% 6.56/7.37 % forced_gc_time: 0
% 6.56/7.37 % gc_basic_clause_elim: 0
% 6.56/7.37 % parsing_time: 0.124
% 6.56/7.37 % sem_filter_time: 0.
% 6.56/7.37 % pred_elim_time: 0.
% 6.56/7.37 % out_proof_time: 0.
% 6.56/7.37 % monotx_time: 0.
% 6.56/7.37 % subtype_inf_time: 0.
% 6.56/7.37 % unif_index_cands_time: 0.
% 6.56/7.37 % unif_index_add_time: 0.001
% 6.56/7.37 % total_time: 6.801
% 6.56/7.37 % num_of_symbols: 118
% 6.56/7.37 % num_of_terms: 5823
% 6.56/7.37
% 6.56/7.37 % ------ Propositional Solver
% 6.56/7.37
% 6.56/7.37 % prop_solver_calls: 1
% 6.56/7.37 % prop_fast_solver_calls: 3
% 6.56/7.37 % prop_num_of_clauses: 1560
% 6.56/7.37 % prop_preprocess_simplified: 5266
% 6.56/7.37 % prop_fo_subsumed: 0
% 6.56/7.37 % prop_solver_time: 0.
% 6.56/7.37 % prop_fast_solver_time: 0.
% 6.56/7.37 % prop_unsat_core_time: 0.
% 6.56/7.37
% 6.56/7.37 % ------ QBF
% 6.56/7.37
% 6.56/7.37 % qbf_q_res: 0
% 6.56/7.37 % qbf_num_tautologies: 0
% 6.56/7.37 % qbf_prep_cycles: 0
% 6.56/7.37
% 6.56/7.37 % ------ BMC1
% 6.56/7.37
% 6.56/7.37 % bmc1_current_bound: -1
% 6.56/7.37 % bmc1_last_solved_bound: -1
% 6.56/7.37 % bmc1_unsat_core_size: -1
% 6.56/7.37 % bmc1_unsat_core_parents_size: -1
% 6.56/7.37 % bmc1_merge_next_fun: 0
% 6.56/7.37 % bmc1_unsat_core_clauses_time: 0.
% 6.56/7.37
% 6.56/7.37 % ------ Instantiation
% 6.56/7.37
% 6.56/7.37 % inst_num_of_clauses: 1513
% 6.56/7.37 % inst_num_in_passive: 0
% 6.56/7.37 % inst_num_in_active: 0
% 6.56/7.37 % inst_num_in_unprocessed: 1716
% 6.56/7.37 % inst_num_of_loops: 0
% 6.56/7.37 % inst_num_of_learning_restarts: 0
% 6.56/7.37 % inst_num_moves_active_passive: 0
% 6.56/7.37 % inst_lit_activity: 0
% 6.56/7.37 % inst_lit_activity_moves: 0
% 6.56/7.37 % inst_num_tautologies: 0
% 6.56/7.37 % inst_num_prop_implied: 0
% 6.56/7.37 % inst_num_existing_simplified: 0
% 6.56/7.37 % inst_num_eq_res_simplified: 0
% 6.56/7.37 % inst_num_child_elim: 0
% 6.56/7.37 % inst_num_of_dismatching_blockings: 0
% 6.56/7.37 % inst_num_of_non_proper_insts: 0
% 6.56/7.37 % inst_num_of_duplicates: 0
% 6.56/7.37 % inst_inst_num_from_inst_to_res: 0
% 6.56/7.37 % inst_dismatching_checking_time: 0.
% 6.56/7.37
% 6.56/7.37 % ------ Resolution
% 6.56/7.37
% 6.56/7.37 % res_num_of_clauses: 1666
% 6.56/7.37 % res_num_in_passive: 0
% 6.56/7.37 % res_num_in_active: 581
% 6.56/7.37 % res_num_of_loops: 2
% 6.56/7.37 % res_forward_subset_subsumed: 955
% 6.56/7.37 % res_backward_subset_subsumed: 81
% 6.56/7.37 % res_forward_subsumed: 0
% 6.56/7.37 % res_backward_subsumed: 6
% 6.56/7.37 % res_forward_subsumption_resolution: 0
% 6.56/7.37 % res_backward_subsumption_resolution: 2
% 6.56/7.37 % res_clause_to_clause_subsumption: 9
% 6.56/7.37 % res_orphan_elimination: 0
% 6.56/7.37 % res_tautology_del: 0
% 6.56/7.37 % res_num_eq_res_simplified: 0
% 6.56/7.37 % res_num_sel_changes: 0
% 6.56/7.37 % res_moves_from_active_to_pass: 0
% 6.56/7.37
% 6.56/7.37 % Status Unsatisfiable
% 6.56/7.37 % SZS status Unsatisfiable
% 6.56/7.37 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------